Sven Peter Näsholm

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• Vorobeva, Ekaterina; Eggen, Mari Dahl; Midtfjord, Alise Danielle; Benth, Fred Espen; Hupe, Patrick & Brissaud, Quentin [Show all 8 contributors for this article] (2024). Estimating stratospheric polar vortex strength using ambient ocean-generated infrasound and stochastics-based machine learning. Quarterly Journal of the Royal Meteorological Society. ISSN 0035-9009. doi: 10.1002/qj.4731. Full text in Research Archive Show summary

  There are sparse opportunities for direct measurement of upper stratospheric winds, yet improving their representation in subseasonal-to-seasonal prediction models can have significant benefits. There is solid evidence from previous research that global atmospheric infrasound waves are sensitive to stratospheric dynamics. However, there is a lack of results providing a direct mapping between infrasound recordings and polar-cap upper stratospheric winds. The global International Monitoring System (IMS), which monitors compliance with the Comprehensive Nuclear-Test-Ban Treaty, includes ground-based stations that can be used to characterize the infrasound soundscape continuously. In this study, multi-station IMS infrasound data were utilized along with a machine-learning supported stochastic model, Delay-SDE-net, to demonstrate how a near-real-time estimate of the polar-cap averaged zonal wind at 1-hPa pressure level can be found from infrasound data. The infrasound was filtered to a temporal low-frequency regime dominated by microbaroms, which are ambient-noise infrasonic waves continuously radiated into the atmosphere from nonlinear interaction between counter-propagating ocean surface waves. Delay-SDE-net was trained on 5 years (2014–2018) of infrasound data from three stations and the ERA5 reanalysis 1-hPa polar-cap averaged zonal wind. Using infrasound in 2019–2020 for validation, we demonstrate a prediction of the polar-cap averaged zonal wind, with an error standard deviation of around 12 m·s compared with ERA5. These findings highlight the potential of using infrasound data for near-real-time measurements of upper stratospheric dynamics. A long-term goal is to improve high-top atmospheric model accuracy, which can have significant implications for weather and climate prediction.

• Chandrasekaran, Sri Nivas; Holm, Sverre & Näsholm, Sven Peter (2023). Wave equations of the two common sediment acoustic theories. Proceedings of Meetings on Acoustics (POMA). ISSN 1939-800X. 51. doi: 10.1121/2.0001795. Full text in Research Archive Show summary

  Two popular theories for wave propagation in sediments, the Biot poroelastic theory and the Viscous Grain Shearing (VGS) theory, have been formulated in terms of dispersion relations. The lack of explicit wave equations for these models could be considered to be a weakness. Hence, providing wave equations that are fully consistent with these theories might confirm that they have a physical basis. In the Biot theory, it is the frequency-dependent viscodynamic operator that poses the problem as there is no equivalent time-domain operator. Previous work has shown that this factor can be approximated well with a simplified square root operator. Drawing on the parallel to the Cole-Davidson dielectric theory for complex media where the same factor appears, and using the equivalent time-domain operator, which is a fractional pseudo-differential operator, enables the formulation of wave equations for all three wave modes of the Biot theory. The same operator turns out to be central for transforming the dispersion relations of the VGS theory to time-space wave equations. In this case, the relation between the dispersion equations and the wave equations is exact. The wave equations of these two theories will enable a closer study of the properties of the medium models.

• Holm, Sverre; Chandrasekaran, Sri Nivas & Näsholm, Sven Peter (2023). Adding a low frequency limit to fractional wave propagation models. Frontiers in Physics. ISSN 2296-424X. 11, p. 1–8. doi: 10.3389/fphy.2023.1250742. Full text in Research Archive Show summary

  Power-law attenuation in elastic wave propagation of both compressional and shear waves can be described with multiple relaxation processes. It may be less physical to describe it with fractional calculus medium models, but this approach is useful for simulation and for parameterization where the underlying relaxation structure is very complex. It is easy to enforce a low-frequency limit on a relaxation distribution and this gives frequency squared characteristics for low frequencies which seems to fit some media in practice. Here the goal is to change the low-frequency behavior of fractional models also. This is done by tempering the relaxation moduli of the fractional Kelvin-Voigt and diffusion models with an exponential function and the effect is that the low-frequency attenuation will increase with frequency squared and the square root of frequency respectively. The time-space wave equations for the tempered models have also been found, and for this purpose the concept of the fractional pseudo-differential operator borrowed from the field of Cole-Davidson dielectrics is useful. The tempering does not remove the singularity in the relaxation moduli of the models, but this has only a minor effect on the solutions.

• Kværna, Tormod; Harris, David B; Näsholm, Sven Peter; Köhler, Andreas & Gibbons, Steven John (2023). Tracking aftershock sequences using empirical matched field processing. Geophysical Journal International. ISSN 0956-540X. 235(2), p. 1183–1200. doi: 10.1093/gji/ggad297. Full text in Research Archive Show summary

  Extensive aftershock sequences present a significant problem to seismological data centres attempting to produce near real-time comprehensive seismic event bulletins. An elevated number of events to process and poorer performance of automatic phase association algorithms can lead to large delays in processing and a greatly increased human workload. Global monitoring is often performed using seismic array stations at considerable distances from the events involved. Empirical matched field processing (EMFP) is a narrow-frequency band array signal processing technique that recognizes the inter-sensor phase and amplitude relations associated with wavefronts approaching a sensor array from a given direction. We demonstrate that EMFP, using a template obtained from the first P arrival from the main shock alone, can efficiently detect and identify P arrivals on that array from subsequent events in the aftershock zone with exceptionally few false alarms (signals from other sources). The empirical wavefield template encodes all the narrow-band phase and amplitude relations observed for the main shock signal. These relations are also often robust and repeatable characteristics of signals from nearby events. The EMFP detection statistic compares the phase and amplitude relations at a given time in the incoming data stream with those for the template and is sensitive to very short-duration signals with the required characteristics. Significant deviations from the plane-wavefront model that typically degrade the performance of standard beamforming techniques can enhance signal characterization using EMFP. Waveform correlation techniques typically perform poorly for aftershocks from large earthquakes due to the distances between hypocentres and the wide range of event magnitudes and source mechanisms. EMFP on remote seismic arrays mitigates these difficulties; the narrow-band nature of the procedure makes arrival identification less sensitive to the signals’ temporal form and spectral content. The empirical steering vectors derived for the main shock P arrival can reduce the frequency dependency of the slowness vector estimates. This property helps us to automatically screen out arrivals from outside of the aftershock zone. Standard array processing pipelines could be enhanced by including both plane-wave and empirical matched field steering vectors. This would maintain present capability for the plane-wave steering vectors and provide increased sensitivity and resolution for those sources for which we have empirical calibrations.

• Belova, Evgenia; Barabash, Victoria; Godin, Oleg A.; Kero, Johan; Näsholm, Sven Peter & Vorobeva, Ekaterina [Show all 7 contributors for this article] (2023). High-speed echoes in the polar winter mesosphere: Infrasound as a probable cause. Advances in Space Research. ISSN 0273-1177. doi: 10.1016/j.asr.2023.07.010. Full text in Research Archive Show summary

  We considered three events on 4 November 2015, 22 December 2016, and 12 November 2018, when the signals travelling in the polar winter mesosphere with high horizontal velocities above 300 m/s were measured by the atmospheric radar ESRAD (Chilson et al., 1999) located at Esrange, near Kiruna in northern Sweden. We proposed four mechanisms of generation of such special cases of polar mesosphere echoes, e.g. high-speed PMWE, that involve microbaroms, i.e. infrasound waves at 0.1 - 0.35 Hz frequencies created by ocean swell. These mechanisms are (i) generation of viscous waves, (ii) generation of thermal waves, (iii) direct contributions of infrasound, and (iv) generation of secondary waves at sound dissipation. These processes necessarily accompany sound propagation in inhomogeneous, thermally conducting and viscous fluid (air). The four models were theoretically analysed and their efficiency was estimated. The infrasound measurements at the IS37 station (Gibbons et al., 2019) located about 170 km north-west from the ESRAD radar, modelled maps of the microbarom sources, infrasound propagation conditions and ionospheric conditions for these three PMWE events support the proposed models. Infrasound-generated thermal waves are suggested to be the most probable specific cause of the observed high-speed, high-aspect-ratio PMWE events. However, absence of in-situ infrasound and plasma measurements did not allow us to quantify contributions of individual physical mechanisms to the fast-travelling echoes generation.

• Vorobeva, Ekaterina; Assink, Jelle; Espy, Patrick Joseph; Renkwitz, Toralf; Chunchuzov, Igor & Näsholm, Sven Peter (2023). Probing Gravity Waves in the Middle Atmosphere Using Infrasound From Explosions. Journal of Geophysical Research (JGR): Atmospheres. ISSN 2169-897X. 128(13), p. 1–21. doi: 10.1029/2023JD038725. Full text in Research Archive Show summary

  This study uses low-frequency, inaudible acoustic waves (infrasound) to probe wind and temperature fluctuations associated with breaking gravity waves (GWs) in the middle atmosphere. Building on an approach introduced by Chunchuzov et al., infrasound recordings are used to retrieve effective sound-speed fluctuations in an inhomogeneous atmospheric layer that causes infrasound backscattering. The infrasound was generated by controlled blasts at Hukkakero, Finland, and recorded at the IS37 infrasound station, Norway in the late summers 2014?2017. Our findings indicate that the analyzed infrasound scattering occurs at mesospheric altitudes of 50?75 km, a region where GWs interact under non-linearity, forming thin layers of strong wind shear. The retrieved fluctuations were analyzed in terms of vertical wave number spectra, resulting in an approximate power law that corresponds to the ?universal? saturated spectrum of atmospheric GWs. The power law wavenumber range corresponds to vertical atmospheric scales of 33?625 m. The fluctuation spectra were compared to theoretical GW saturation theories as well as to independent wind measurements by the Saura medium-frequency radar near And?ya Space Center around 100 km west of IS37, yielding a good agreement in terms of vertical wavenumber spectrum amplitudes and slopes. This suggests that the radar and infrasound-based effective sound-speed profiles represent low- and high-wavenumber regimes of the same ?universal? GW spectrum. The results illustrate that infrasound allows for probing fine-scale dynamics not well captured by other techniques, suggesting that infrasound can provide a complementary technique to probe atmospheric GWs.

• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2023). Worst-case analysis of array beampatterns using interval arithmetic. Journal of the Acoustical Society of America. ISSN 0001-4966. 153(6), p. 3312–3323. doi: 10.1121/10.0019715. Full text in Research Archive Show summary

  Over the past decade, interval arithmetic (IA) has been used to determine tolerance bounds of phased-array beampatterns. IA only requires that the errors of the array elements are bounded and can provide reliable beampattern bounds even when a statistical model is missing. However, previous research has not explored the use of IA to find the error realizations responsible for achieving specific bounds. In this study, the capabilities of IA are extended by introducing the concept of “backtracking,” which provides a direct way of addressing how specific bounds can be attained. Backtracking allows for the recovery of the specific error realization and corresponding beampattern, enabling the study and verification of which errors result in the worst-case array performance in terms of the peak sidelobe level (PSLL). Moreover, IA is made applicable to a wider range of arrays by adding support for arbitrary array geometries with directive elements and mutual coupling in addition to element amplitude, phase, and positioning errors. Last, a simple formula for approximate bounds of uniformly bounded errors is derived and numerically verified. This formula gives insights into how array size and apodization cannot reduce the worst-case PSLL beyond a certain limit.

• Arnestad, Håvard; Austeng, Andreas; Näsholm, Sven Peter & Rindal, Ole Marius Hoel (2022). The Effect of Retrospective Transmit Focusing on Minimum Variance Beamforming. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. doi: 10.1109/IUS54386.2022.9958050. Show summary

  Minimum variance (MV) beamforming is a well-known adaptive beamforming approach. Retrospective transmit beamforming (RTB), on the other hand, is a technique implemented in some modern ultrasound scanners that strives to obtain two-way focus everywhere in the imaged region. However, it is not immediately clear how these methods should be combined in the image reconstruction pipeline. In this work, we suggest a general and efficient implementation for combining MV with RTB, and we study a few effects and synergetic benefits in comparison to multiple line acquisition processing and conventional delay-and-sum beamforming. Our finding is that RTB improves the resolution and robustness of MV beamforming outside the focal zone.

• Vierinen, Juha; Aslaksen, Torsten; Chau, Jorge L.; Gritsevich, Maria; Gustavsson, Bjorn Johan & Kastinen, Daniel [Show all 14 contributors for this article] (2022). Multi-instrument observations of the Pajala fireball: Origin, characteristics, and atmospheric implications. Frontiers in Astronomy and Space Sciences. 9. doi: 10.3389/fspas.2022.1027750. Full text in Research Archive Show summary

  Meteor observations provide information about Solar System constituents and their influx onto Earth, their interaction processes in the atmosphere, as well as the neutral dynamics of the upper atmosphere. This study presents optical, radar, and infrasound measurements of a daytime fireball that occurred on 4 December 2020 at 13:30 UTC over Northeast Sweden. The fireball was recorded with two video cameras, allowing a trajectory determination to be made. The orbital parameters are compatible with the Northern Taurid meteor shower. The dynamic mass estimate based on the optical trajectory was found to be 0.6–1.7 kg, but this estimate can greatly vary from the true entry mass significantly due to the assumptions made. The meteor trail plasma was observed with an ionosonde as a sporadic E-like ionogram trace that lasted for 30 min. Infrasound emissions were detected at two sites, having propagation times consistent with a source location at an altitude of 80–90 km. Two VHF specular meteor radars observed a 6 minute long non-specular range spread trail echo as well as a faint head echo. Combined interferometric range-Doppler analysis of the meteor trail echoes at the two radars, allowed estimation of the mesospheric horizontal wind altitude profile, as well as tracking of the gradual deformation of the trail over time due to a prevailing neutral wind shear. This combined analysis indicates that the radar measurements of long-lived non-specular range-spread meteor trails produced by larger meteoroids can be used to measure the meteor radiant by observing the line traveled by the meteor. Furthermore, a multistatic meteor radar observation of these types of events can be used to estimate mesospheric neutral wind altitude profiles.

• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Sonar array beampattern bounds and an interval arithmetic toolbox. Proceedings of Meetings on Acoustics (POMA). ISSN 1939-800X. 47. doi: 10.1121/2.0001613. Show summary

  The framework of interval arithmetic (IA) and its extension to complex numbers has in the last decade been applied as a tool for finding robust tolerance bounds of antenna arrays. The IA framework complements statistical methods, as inclusive upper and lower bounds of the beampattern are obtained directly, only assuming error bounds on specifically chosen array parameters. Recently, beampattern synthesis for sonar arrays subject to amplitude excitation errors has been extended from linear arrays with omnidirectional elements to non-linear arrays with directive elements. In this work, we demonstrate that the analysis can be developed further to include both amplitude and phase errors. Moreover, we account for error bounds in element position and orientation, thus representing a more comprehensive method for evaluating the worst-case performance due to uncertainty bounds in a multitude of design parameters. For this purpose, we have created an open-source MATLAB toolbox to calculate beampattern bounds for an array with bounded error tolerances. The toolbox features an object oriented library of interval classes and an interactive graphical user interface with easily configurable settings, where results for different interval representations are shown along with their corresponding bounds. The beampattern bounds of a sonar array is illustrated through an example.

• Brissaud, Quentin; Näsholm, Sven Peter; Turquet, Antoine Leo & Le Pichon, Alexis (2022). Predicting infrasound transmission loss using deep learning. Geophysical Journal International. ISSN 0956-540X. 232(1), p. 274–286. doi: 10.1093/gji/ggac307. Full text in Research Archive Show summary

  Modelling the spatial distribution of infrasound attenuation (or transmission loss, TL) is key to understanding and interpreting microbarometer data and observations. Such predictions enable the reliable assessment of infrasound source characteristics such as ground pressure levels associated with earthquakes, man-made or volcanic explosion properties, and ocean-generated microbarom wavefields. However, the computational cost inherent in full-waveform modelling tools, such as parabolic equation (PE) codes, often prevents the exploration of a large parameter space, that is variations in wind models, source frequency and source location, when deriving reliable estimates of source or atmospheric properties—in particular for real-time and near-real-time applications. Therefore, many studies rely on analytical regression-based heuristic TL equations that neglect complex vertical wind variations and the range-dependent variation in the atmospheric properties. This introduces significant uncertainties in the predicted TL. In the current contribution, we propose a deep learning approach trained on a large set of simulated wavefields generated using PE simulations and realistic atmospheric winds to predict infrasound ground-level amplitudes up to 1000 km from a ground-based source. Realistic range dependent atmospheric winds are constructed by combining ERA5, NRLMSISE-00 and HWM-14 atmospheric models, and small-scale gravity-wave perturbations computed using the Gardner model. Given a set of wind profiles as input, our new modelling framework provides a fast (0.05 s runtime) and reliable (∼5 dB error on average, compared to PE simulations) estimate of the infrasound TL.

• Vergoz, Julien; Hupe, Patrick; Listowski, Constantino; Le Pichon, Alexis; Milton A., Garcés & Marchetti, Emanuele [Show all 16 contributors for this article] (2022). IMS observations of infrasound and acoustic-gravity waves produced by the January 2022 volcanic eruption of Hunga, Tonga: A global analysis. Earth and Planetary Science Letters. ISSN 0012-821X. 591, p. 1–13. doi: 10.1016/j.epsl.2022.117639. Full text in Research Archive Show summary

  The 15 January 2022 Hunga, Tonga, volcano's explosive eruption produced the most powerful blast recorded in the last century, with an estimated equivalent TNT yield of 100–200 megatons. The blast energy was propagated through the atmosphere as various wave types. The most prominent wave was a long-period (>2000 s) surface-guided Lamb wave with energy comparable to that of the 1883 Krakatoa Lamb wave; both were clearly observed by pressure sensors (barometers) worldwide. Internal gravity, acoustic-gravity, and infrasound waves were captured in great detail by the entire infrasound component of the International Monitoring System (IMS). For instance, infrasound ...

• Chandrasekaran, Sri Nivas; Näsholm, Sven Peter & Holm, Sverre (2022). Wave equations for porous media described by the Biot model. Journal of the Acoustical Society of America. ISSN 0001-4966. 151(4), p. 2576–2586. doi: 10.1121/10.0010164. Full text in Research Archive Show summary

  Single-mode equivalent space-time representations of the acoustic wave propagating in a Biot poroelastic medium have previously been found only for asymptotic cases: In the low frequency regime, where the viscous skin depth is greater than the characteristic pore size, the time domain equivalent is represented with integer order temporal and spatial loss terms, whereas in the high frequency regime, it is represented with fractional order temporal and spatial loss terms. In the current work, a time domain representation in terms of a partial differential equation is proposed for all three wave solutions of the Biot model across all frequencies, and it is derived from the material response function of the Biot poroelastic medium with suitable approximations for the compressional modes and the dynamic permeability. The dynamic permeability in the time domain is represented by a fractional pseudo-differential operator. Optimal correction factors are introduced into the wave equation to compensate for the discrepancies in the compressional wave dispersion and attenuation. Additionally, the method for incorporating the squirt flow mechanism into the wave equation via the Extended Biot poroviscoelastic model is described. The proposed wave equation has a physical basis and satisfies the passivity criterion.

• Näsholm, Sven Peter; Iranpour, Kamran; Wüstefeld, Andreas; Dando, Benjamin; Baird, Alan F. & Oye, Volker (2022). Array Signal Processing on Distributed Acoustic Sensing Data: Directivity Effects in Slowness Space. Journal of Geophysical Research (JGR): Solid Earth. ISSN 2169-9313. 127(2). doi: 10.1029/2021JB023587. Full text in Research Archive Show summary

  Distributed Acoustic Sensing (DAS) involves the transmission of laser pulses along a fiber-optic cable. These pulses are backscattered at fiber inhomogeneities and again detected by the same interrogator unit that emits the pulses. Elastic deformation along the fiber causes phase shifts in the backscattered laser pulses which are converted to spatially averaged strain measurements, typically at regular fiber intervals. DAS systems provide the potential to employ array processing algorithms. However, there are certain differences between DAS and conventional sensors. While seismic sensors typically record the directional particle displacement, velocity, or acceleration, the DAS axial strain is inherently proportional to the spatial gradient of the axial cable displacement. DAS is therefore insensitive to broadside displacement, for example, broadside P-waves. In classical delay-and-sum beamforming, the array response function is the far-field response on a horizontal slowness (or wavenumber) grid. However, for geometrically non-linear DAS layouts, the angle between wavefront and cable varies, requiring the analysis of a steered response that varies with the direction of arrival. This contrasts with the traditional array response function which is given in terms of slowness difference between arrival and steering. This paper provides a framework for DAS steered response estimation accounting also for cable directivity and gauge-length averaging – hereby demonstrating the applicability of DAS in array seismology and to assess DAS design aspects. It bridges a gap between DAS and array theory frameworks and communities, facilitating increased employment of DAS as a seismic array, while providing building blocks for the development of DAS array design tools.

• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2022). Stochastic Modeling of Stratospheric Temperature. Mathematical Geosciences. ISSN 1874-8961. 54, p. 651–678. doi: 10.1007/s11004-021-09990-6. Full text in Research Archive Show summary

  This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

• Kværna, Tormod; Gibbons, Steven John & Näsholm, Sven Peter (2021). CTBT seismic monitoring using coherent and incoherent array processing. Journal of Seismology. ISSN 1383-4649. doi: 10.1007/s10950-021-10026-z. Full text in Research Archive Show summary

  The detection and location capability of the International Monitoring System for small seismic events in the continental and oceanic regions surrounding the Sea of Japan is determined mainly by three primary seismic arrays: USRK, KSRS, and MJAR. Body wave arrivals are coherent on USRK and KSRS up to frequencies of around 4 Hz and classical array processing methods can detect and extract features for most regional signals on these stations. We demonstrate how empirical matched field processing (EMFP), a generalization of frequency-wavenumber or f-k analysis, can contribute to calibrated direction estimates which mitigate bias resulting from near-station geological structure. It does this by comparing the narrowband phase shifts between the signals on different sensors, observed at a given time, with corresponding measurements on signals from historical seismic events. The EMFP detection statistic is usually evaluated as a function of source location rather than slowness space and the size of the geographical footprint valid for EMFP templates is affected by array geometry, the available signal bandwidth, and Earth structure over the propagation path. The MJAR array has similar dimensions to KSRS but is sited in far more complex geology which results in poor parameter estimates with classical f-k analysis for all signals lacking energy at 1 Hz or below. EMFP mitigates the signal incoherence to some degree but the geographical footprint valid for a given matched field template on MJAR is very small. Spectrogram beamforming provides a robust detection algorithm for high-frequency signals at MJAR. The array aperture is large enough that f-k analysis performed on continuous AR-AIC functions, calculated from optimally bandpass-filtered signals at the different sites, can provide robust slowness estimates for regional P-waves. Given a significantly higher SNR for regional S-phases on the horizontal components of the 3-component site of MJAR, we would expect incoherent detection and estimation of S-phases to improve with 3-component sensors at all sites. Given the diversity of the IMS stations, and the diversity of the methods which provide optimal results for a given station, we advocate the development of seismic processing pipelines which can process highly heterogeneous inputs to help associate characteristics of the incoming signals with physical events.

• Vorobeva, Ekaterina; De Carlo, Marine; Le Pichon, Alexis; Espy, Patrick Joseph & Näsholm, Sven Peter (2021). Benchmarking microbarom radiation and propagation model against infrasound recordings: a vespagram-based approach. Annales Geophysicae. ISSN 0992-7689. 39(3), p. 515–531. doi: 10.5194/angeo-39-515-2021. Full text in Research Archive Show summary

  This study investigates the use of a vespagram-based approach as a tool for multi-directional comparison between simulated microbarom soundscapes and infrasound data recorded at ground-based array stations. Data recorded at the IS37 station in northern Norway during 2014–2019 have been processed to generate vespagrams (velocity spectral analysis) for five frequency bands between 0.1 and 0.6 Hz. The back azimuth resolution between the vespagram and the microbarom model is harmonized by smoothing the modeled soundscapes along the back azimuth axis with a kernel corresponding to the frequency-dependent array resolution. An estimate of similarity between the output of the microbarom radiation and propagation model and infrasound observations is then generated based on the image-processing approach of the mean square difference. The analysis reveals that vespagrams can monitor seasonal variations in the microbarom azimuthal distribution, amplitude, and frequency, as well as changes during sudden stratospheric warming events. The vespagram-based approach is computationally inexpensive, can uncover microbarom source variability, and has the potential for near-real-time stratospheric diagnostics and atmospheric model assessment.

• Fang, Jun; Näsholm, Sven Peter; Chen, Wen & Holm, Sverre (2020). The fractional constitutive models for nonlocal material based on scattering wave equations. Mechanics of Time-Dependent Materials. ISSN 1385-2000. doi: 10.1007/s11043-020-09482-w. Show summary

  This paper proposes some fractional nonlocal viscoelastic models which are under the framework of both Eringen’s nonlocal theory and gradient elasticity theory. Introducing different combinations of new mechanical elements derived from the spatial nonlocal theory, a set of time-space-fractional constitutive models for nonlocal material, such as the Kelvin–Voigt model and the Maxwell model, and their corresponding wave equations are presented. In addition, by applying the wave equations to describe the scattering attenuation from a general energy loss standpoint, the undetermined parameters of the presented constitutive models are obtained. As a discussion of the results, the scattering attenuation curve of the presented model is investigated and is found to be in good agreement with the Blair scattering model. Moreover, the nonlocal fractional Kelvin–Voigt model is applied to describe the creep of sand-bearing soft soil and then compared to existing models as well as experimental data.

• Vera Rodriguez, Ismael; Näsholm, S.P. & Le Pichon, Alexis (2020). Atmospheric wind and temperature profiles inversion using infrasound: An ensemble model context. Journal of the Acoustical Society of America. ISSN 0001-4966. 148(5), p. 2923–2934. doi: 10.1121/10.0002482. Show summary

  This paper presents an inversion methodology where acoustic observations of infrasound waves are used to update an atmospheric model. This paper sought a flexible parameterization that permits to incorporate physical and numerical constraints without the need to reformulate the inversion. On the other hand, the optimization conveys an explicit search over the solution space, making the solver computationally expensive. Nevertheless, through a parallel implementation and the use of tight constraints, this study demonstrates that the methodology is computationally tractable. Constraints to the solution space are derived from the spread (variance) of ERA5 ensemble reanalysis members, which summarize the best current knowledge of the atmosphere from assimilated measurements and physical models. Similarly, the initial model temperature and winds for the inversion are chosen to be the average of these parameters in the ensemble members. The performance of the inversion is demonstrated with the application to infrasound observations from an explosion generated by the destruction of ammunition at Hukkakero, Finland. The acoustic signals are recorded at an array station located at 178 km range, which is within the classical shadow zone distance. The observed returns are assumed to come from stratospheric reflections. Thus, the reflection altitude is also an inverted parameter.

• Amezcua, Javier; Näsholm, Sven Peter; Blixt, Erik Mårten & Charlton-Perez, Andrew J. (2020). Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds. Quarterly Journal of the Royal Meteorological Society. ISSN 0035-9009. 146(731), p. 2634–2653. doi: 10.1002/qj.3809. Show summary

  This data assimilation study exploits infrasound from explosions to probe an atmospheric wind component from the ground up to stratospheric altitudes. Planned explosions of old ammunition in Finland generate transient infrasound waves that travel through the atmosphere. These waves are partially reflected back towards the ground from stratospheric levels, and are detected at a receiver station located in northern Norway at 178 km almost due north from the explosion site. The difference between the true horizontal direction towards the source and the backazimuth direction (the horizontal direction of arrival) of the incoming infrasound wavefronts, in combination with the pulse propagation time, are exploited to provide an estimate of the average cross-wind component in the penetrated atmosphere. We perform offline assimilation experiments with an ensemble Kalman filter and these observations, using the ERA5 ensemble reanalysis atmospheric product as background (prior) for the wind at different vertical levels. We demonstrate that information from both sources can be combined to obtain analysis (posterior) estimates of cross-winds at different vertical levels of the atmospheric slice between the explosion site and the recording station. The assimilation makes greatest impact at the 12–60 km levels, with some changes with respect to the prior of the order of 0.1–1.0 m·s−1, which is a magnitude larger than the typical standard deviation of the ERA5 background. The reduction of background variance in the higher levels often reached 2–5%. This is the first published study demonstrating techniques to implement assimilation of infrasound data into atmospheric models. It paves the way for further exploration in the use of infrasound observations – especially natural and continuous sources – to probe the middle atmospheric dynamics and to assimilate these data into atmospheric model products.

• Blixt, Erik Mårten; Näsholm, Sven Peter; Gibbons, Steven John; Evers, Laslo; Charlton-Perez, Andrew & Orsolini, Yvan [Show all 7 contributors for this article] (2019). Estimating tropospheric and stratospheric winds using infrasound from explosions. Journal of the Acoustical Society of America. ISSN 0001-4966. 146(2), p. 973–982. doi: 10.1121/1.5120183. Show summary

  The receiver-to-source backazimuth of atmospheric infrasound signals is biased when cross-winds are present along the propagation path. Infrasound from 598 surface explosions from over 30 years in northern Finland is measured with high spatial resolution on an array 178 km almost due North. The array is situated in the classical shadow-zone distance from the explosions. However, strong infrasound is almost always observed, which is most plausibly due to partial reflections from stratospheric altitudes. The most probable propagation paths are subject to both tropospheric and stratospheric cross-winds, and the wave-propagation modelling in this study yields good correspondence between the observed backazimuth deviation and cross-winds from the European Centre for Medium-Range Weather Forecasts Reanalysis (ERA)-Interim reanalysis product. This study demonstrates that atmospheric cross-winds can be estimated directly from infrasound data using propagation time and backazimuth deviation observations. This study finds these cross-wind estimates to be in good agreement with the ERA-Interim reanalysis.

• Dando, Benjamin; Oye, Volker; Näsholm, Sven Peter; Zühlsdorff, Lars & Wüstefeld, Andreas (2019). Complexity in microseismic phase identification: full waveform modelling, traveltime computations and implications for eventlocations within the Groningen gas field. Geophysical Journal International. ISSN 0956-540X. 217(1), p. 620–649. doi: 10.1093/gji/ggz017. Show summary

  Determining accurate microseismic event locations at the Groningen gas field in the Netherlands has important implications for understanding the ongoing induced seismicity and its associated seismic hazard. To improve the depth constraint of the microseismicity, downhole monitoring arrays have been deployed in the central region of the Groningen field. The observed seismicity at these receivers is characterized by significant complexity in the waveforms, due to the high velocity contrasts that exist and the acquisition geometry. Reliably identifying and picking phases for use in earthquake location algorithms is therefore particularly challenging. Using a well constrained and highly detailed 3-D velocity model, we show how full waveform modelling can be used to understand the causes of the observed phase complexity. By identifying the different modelled phase arrivals in detail, we look to identify any systematic changes in waveform complexity with source location, to aid phase identification of the recorded downhole data. Theoretical traveltimes are often the foundation of earthquake location algorithms. We highlight the associated problems of their computation for the downhole monitoring setup for the Groningen model by complementing the full waveform simulations with traveltime computations and their associated ray paths from both an eikonal solver and using the wavefront construction method. We highlight large inconsistencies in the traveltimes, demonstrate the limitations and sensitivity of ray tracing in a layered velocity model, and show how the theoretical traveltimes do not equate with the dominant phase arrivals observed within the modelled waveforms. Finally, we propose an approach based on computing P- and S-wave traveltimes directly from the full waveform modelling, such that phase picking is based on an amplitude threshold rather than individual phase identification, which can also be adjusted for any given moment tensor.

• Gibbons, Steven John; Kværna, Tormod & Näsholm, Sven Peter (2019). Characterization of the Infrasonic Wavefield from Repeating Seismo-Acoustic Events. In Le Pichon, Alexis; Blanc, Elisabeth & Hauchecorne, Alain (Ed.), Infrasound Monitoring for Atmospheric Studies: Challenges in Middle Atmosphere Dynamics and Societal Benefits. Springer. ISSN 978-3-319-75138-2. p. 387–407. doi: 10.1007/978-3-319-75140-5_10. Show summary

  Infrasound can provide unique data on extreme atmospheric events such as meteor impacts, severe weather systems, man-made explosions, and volcanic eruptions. Use of infrasound for remote event detection and location requires high-quality temporal and spatial atmospheric models, and infrasound generated by so-called Ground Truth events (for which the time and location are known) are necessary to evaluate atmospheric models and assess network performance. Large industrial blasts and military explosions are tightly constrained in time and space using seismic data and can generate infrasound recorded both regionally and at great distances. The most useful seismo-acoustic sources are repeating sources at which explosions take place relatively frequently. Over time, these may provide records of up to many hundreds of events from the same location from which characteristics and variability of the infrasonic wavefield and atmospheric conditions can be assessed on a broad range of timescales. Over the past 20 years or so, numerous databases of repeating explosions have been compiled in various parts of the world. Events are associated confidently with known sources, with accurately determined origin times, usually by applying waveform correlation or similar techniques to the characteristic seismic signals generated by each explosive source. The sets of sources and stations ideally result in atmospheric propagation paths covering a wide range of distances and directions, and the databases ideally include events covering all seasons. For selected repeating sources and infrasound arrays, we have assessed the variability of infrasonic observation: including the documentation of lack of observed infrasound. These observations provide empirical celerity, back azimuth deviation, and apparent velocity probability distributions. Such empirical distributions have been demonstrated in numerous recent studies to provide infrasonic event location estimates with significantly improved uncertainty estimates. Tropospheric, stratospheric, and thermospheric returns have been observed, even at distances below 200 km. This information is now providing essential input data for studies of the middle and upper atmosphere.

• Dando, Benjamin; Oye, Volker; Näsholm, Sven Peter; Zühlsdorff, Lars; Kühn, Daniela & Wüstefeld, Andreas (2019). Complexity in microseismic phase identification: full waveform modelling, travel-time computations, and implications for event locations within the Groningen gas field. Geophysical Journal International. ISSN 0956-540X. 217, p. 620–649. doi: 10.1093/gji/ggz017.
• De Carlo, Marine; Pichon, Alexis Le; Ardhuin, Fabrice & Näsholm, Sven Peter (2018). Characterizing and modelling ocean ambient noise using infrasound network and middle atmospheric models. Research and Technology Review. ISSN 1729-7516. p. 144–151. Show summary

  Infrasound is one of the technologies of the International Monitoring System (IMS) supporting the verification regime of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). In the frequency band of interest to detect atmospheric explosions, ambient noise may affect detection and particularly ocean noise referred to as microbaroms. Ocean wave interactions generate acoustic noise almost continuously which can obscure signals of interest in their frequency range. The detectability of such noise strongly depends on atmospheric conditions along the propagation paths. Using ocean wave action model developed by IFREMER and considering the effects of general middle-atmospheric products delivered by ECMWF in long-range propagation, microbarom amplitudes and direction of arrivals derived from various propagation models are compared with the observations. With this study, it is expected to enhance the characterization of the ocean-atmosphere coupling. In return, a better knowledge of microbarom sources would allow to better characterize explosive atmospheric events hidden in the ambient noise.

• Gibbons, Steven John; Kværna, Tormod; Näsholm, Sven Peter & Mykkeltveit, Svein (2018). Probing the DPRK Nuclear Test Site down to Low‐Seismic Magnitude. Seismological Research Letters. ISSN 0895-0695. 89(6), p. 2034–2041. doi: 10.1785/0220180116. Show summary

  On 3 September 2017, the Democratic People’s Republic of Korea (DPRK) carried out its sixth declared underground nuclear test (NK6) at the Punggye‐ri test site. With body‐wave magnitude 6.1, this explosion was significantly larger than any of the previous five explosions, and it has been followed by numerous smaller seismic events. The explosion generated seismic waves dominated by significantly lower frequencies than the earlier tests, which makes accurate measurement of relative time delays using cross‐correlation challenging. Finding a frequency band at which one observes common features in the NK6 signals and the corresponding signals from an earlier event can result in reduced signal‐to‐noise ratio (SNR). Classical double‐difference location estimates for NK6 show a significant spread, depending on the set of measurements used. We treat the first five declared DPRK explosions as a source array and demonstrate, using a geometrical argument about the relative time shifts visible between the signals on pairs of stations, that NK6 was very close to the 9 September 2016 explosion (NK5), assumed to be close to the maximal overburden beneath the summit of Mount Mantap. In addition to the magnitude 4.1 presumed collapse event 8 min after NK6, numerous other small events have been observed at or close to the test site since September 2017. We demonstrate how the test site is monitored to magnitudes below two using multichannel correlation templates from all existing observations. Processing all available historical data from the KSRS and USRK arrays reveals a few small events in 2013, 2014, and 2016 that are similar in nature to those observed in late 2017. This suggests that the more recent low‐magnitude events are not simply a direct result of NK6. We urge caution in the interpretation of the correlation functions between the signals from different events at or close to the test site because the signals are a function of both the source term and of near‐source structure, with the effects of topography likely to be significant.

• Pilger, Christoph; Ceranna, Lars; Ross, J. Ole; Vergoz, Julien; Le Pichon, Alexis & Brachet, Nicolas [Show all 21 contributors for this article] (2018). The European Infrasound Bulletin. Pure and Applied Geophysics (PAGEOPH). ISSN 0033-4553. 175(10), p. 3619–3638. doi: 10.1007/s00024-018-1900-3. Show summary

  The European Infrasound Bulletin highlights infrasound activity produced mostly by anthropogenic sources, recorded all over Europe and collected in the course of the ARISE and ARISE2 projects (Atmospheric dynamics Research InfraStructure in Europe). Data includes high-frequency (> 0.7 Hz) infrasound detections at 24 European infrasound arrays from nine different national institutions complemented with infrasound stations of the International Monitoring System for the Comprehensive Nuclear-Test-Ban Treaty (CTBT). Data were acquired during 16 years of operation (from 2000 to 2015) and processed to identify and locate ∼ 48,000 infrasound events within Europe. The source locations of these events were derived by combining at least two corresponding station detections per event. Comparisons with ground-truth sources, e.g., Scandinavian mining activity, are provided as well as comparisons with the CTBT Late Event Bulletin (LEB). Relocation is performed using ray-tracing methods to estimate celerity and back-azimuth corrections for source location based on meteorological wind and temperature values for each event derived from European Centre for Medium-range Weather Forecast (ECMWF) data. This study focuses on the analysis of repeating, man-made infrasound events (e.g., mining blasts and supersonic flights) and on the seasonal, weekly and diurnal variation of the infrasonic activity of sources in Europe. Drawing comparisons to previous studies shows that improvements in terms of detection, association and location are made within this study due to increasing the station density and thus the number of events and determined source regions. This improves the capability of the infrasound station network in Europe to more comprehensively estimate the activity of anthropogenic infrasound sources in Europe.

• Wüstefeld, Andreas; Greve, Solveig; Näsholm, Sven Peter & Oye, Volker (2018). Benchmarking earthquake location algorithms: A synthetic comparison. Geophysics. ISSN 0016-8033. 83(4), p. KS35–KS47. doi: 10.1190/geo2017-0317.1. Show summary

  A priori assessment of the expected location accuracy of a sensor network is typically done through inversion of the traveltime spatial gradients. This approach assumes that the applied location algorithm successfully recovers the global minimum of the objective function. However, even for accurate and precise phase picks, complexity in the velocity model and limitations in the network layout may inhibit the finding of a global minimum. The location algorithms may end up in a local minimum instead. We compare the location performance of various objective functions and minimization approaches. Although most of the analyzed location approaches mostly lead to good location results, none of the analyzed approaches recovered the correct location for all event locations. This implies that (microseismic) event locations estimates include an additional inherent error, which is linked to the applied location approach. This aspect is often neglected when interpreting event locations. Our site comprises a sensor network of two vertical strings, in a 1D velocity model of the Groningen gas field (The Netherlands), complicated by two thin, very high-velocity layers. For a series of synthetic event locations, we calculate arrival times, add picking errors, and then feed these synthetic picks into a set of different location routines. We also determine a novel way to analyze this approach-dependent location error of the sensor network for the given velocity model and a set of event locations: We compare the distances between a set of assumed event locations to resulting locations in the target region of the subsurface. From the cumulative distribution function of that mislocation distance, we determine the 1𝜎 and 2𝜎 confidence distances for each method. This results in scalar values representing the location confidence distances for a given method. In turn, this can be used to easily compare the location capabilities of different sensor layouts.

• Gibbons, Steven John; Näsholm, Sven Peter; Ruigrok, Elmer & Kværna, Tormod (2018). Improving slowness estimate stability and visualization using limited sensor pair correlation on seismic arrays. Geophysical Journal International. ISSN 0956-540X. 213(1), p. 447–460. doi: 10.1093/GJI/GGX550. Show summary

  Seismic arrays enhance signal detection and parameter estimation by exploiting the time-delays between arriving signals on sensors at nearby locations. Parameter estimates can suffer due to both signal incoherence, with diminished waveform similarity between sensors, and aberration, with time-delays between coherent waveforms poorly represented by the wave-front model. Sensor-to-sensor correlation approaches to parameter estimation have an advantage over direct beamforming approaches in that individual sensor-pairs can be omitted without necessarily omitting entirely the data from each of the sensors involved. Specifically, we can omit correlations between sensors for which signal coherence in an optimal frequency band is anticipated to be poor or for which anomalous time-delays are anticipated. In practice, this usually means omitting correlations between more distant sensors. We present examples from International Monitoring System seismic arrays with poor parameter estimates resulting when classical f–k analysis is performed over the full array aperture. We demonstrate improved estimates and slowness grid displays using correlation beamforming restricted to correlations between sufficiently closely spaced sensors. This limited sensor-pair correlation (LSPC) approach has lower slowness resolution than would ideally be obtained by considering all sensor-pairs. However, this ideal estimate may be unattainable due to incoherence and/or aberration and the LSPC estimate can often exploit all channels, with the associated noise-suppression, while mitigating the complications arising from correlations between very distant sensors. The greatest need for the method is for short-period signals on large aperture arrays although we also demonstrate significant improvement for secondary regional phases on a small aperture array. LSPC can also provide a robust and flexible approach to parameter estimation on three-component seismic arrays.

• Gibbons, Steven John; Pabian, F; Näsholm, Sven Peter; Kværna, Tormod & Mykkeltveit, Svein (2017). Accurate relative location estimates for the North Korean nuclear tests using empirical slowness corrections. Geophysical Journal International. ISSN 0956-540X. 208(1), p. 101–117. doi: 10.1093/gji/ggw379. Show summary

  Declared North Korean nuclear tests in 2006, 2009, 2013 and 2016 were observed seismically at regional and teleseismic distances. Waveform similarity allows the events to be located relatively with far greater accuracy than the absolute locations can be determined from seismic data alone. There is now significant redundancy in the data given the large number of regional and teleseismic stations that have recorded multiple events, and relative location estimates can be confirmed independently by performing calculations on many mutually exclusive sets of measurements. Using a 1-D global velocity model, the distances between the events estimated using teleseismic P phases are found to be approximately 25 per cent shorter than the distances between events estimated using regional Pn phases. The 2009, 2013 and 2016 events all take place within 1 km of each other and the discrepancy between the regional and teleseismic relative location estimates is no more than about 150 m. The discrepancy is much more significant when estimating the location of the more distant 2006 event relative to the later explosions with regional and teleseismic estimates varying by many hundreds of metres. The relative location of the 2006 event is challenging given the smaller number of observing stations, the lower signal-to-noise ratio and significant waveform dissimilarity at some regional stations. The 2006 event is however highly significant in constraining the absolute locations in the terrain at the Punggye-ri test-site in relation to observed surface infrastructure. For each seismic arrival used to estimate the relative locations, we define a slowness scaling factor which multiplies the gradient of seismic traveltime versus distance, evaluated at the source, relative to the applied 1-D velocity model. A procedure for estimating correction terms which reduce the double-difference time residual vector norms is presented together with a discussion of the associated uncertainty. The modified velocity gradients reduce the residuals, the relative location uncertainties and the sensitivity to the combination of stations used. The traveltime gradients appear to be overestimated for the regional phases, and teleseismic relative location estimates are likely to be more accurate despite an apparent lower precision. Calibrations for regional phases are essential given that smaller magnitude events are likely not to be recorded teleseismically. We discuss the implications for the absolute event locations. Placing the 2006 event under a local maximum of overburden at 41.293°N, 129.105°E would imply a location of 41.299°N, 129.075°E for the January 2016 event, providing almost optimal overburden for the later four events.

• Blanc, Elisabeth; Ceranna, L; Hauchecorne, A.; Charlton-Perez, Andrew; Marchetti, E & Evers, LG [Show all 33 contributors for this article] (2017). Toward an improved representation of middle atmospheric dynamics thanks to the ARISE project. Surveys in geophysics. ISSN 0169-3298. 39(2), p. 171–225. doi: 10.1007/s10712-017-9444-0. Show summary

  This paper reviews recent progress toward understanding the dynamics of the middle atmosphere in the framework of the Atmospheric Dynamics Research InfraStructure in Europe (ARISE) initiative. The middle atmosphere, integrating the stratosphere and mesosphere, is a crucial region which influences tropospheric weather and climate. Enhancing the understanding of middle atmosphere dynamics requires improved measurement of the propagation and breaking of planetary and gravity waves originating in the lowest levels of the atmosphere. Inter-comparison studies have shown large discrepancies between observations and models, especially during unresolved disturbances such as sudden stratospheric warmings for which model accuracy is poorer due to a lack of observational constraints. Correctly predicting the variability of the middle atmosphere can lead to improvements in tropospheric weather forecasts on timescales of weeks to season. The ARISE project integrates different station networks providing observations from ground to the lower thermosphere, including the infrasound system developed for the Comprehensive Nuclear-Test-Ban Treaty verification, the Lidar Network for the Detection of Atmospheric Composition Change, complementary meteor radars, wind radiometers, ionospheric sounders and satellites. This paper presents several examples which show how multi-instrument observations can provide a better description of the vertical dynamics structure of the middle atmosphere, especially during large disturbances such as gravity waves activity and stratospheric warming events. The paper then demonstrates the interest of ARISE data in data assimilation for weather forecasting and re-analyzes the determination of dynamics evolution with climate change and the monitoring of atmospheric extreme events which have an atmospheric signature, such as thunderstorms or volcanic eruptions.

• Wuestefeld, A.; Lavadera, P.L.; Näsholm, Sven Peter; Lang, Dominik & Kaschwich, Tina (2016). Microseismic network design in 3D velocity models. EarthDoc. doi: 10.3997/2214-4609.201600002.
• Pandey, Vikash; Näsholm, Sven Peter & Holm, Sverre (2016). Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity. Fractional Calculus and Applied Analysis. ISSN 1311-0454. 19(2), p. 498–515. doi: 10.1515/fca-2016-0026.
• Gibbons, Steven John; Asming, Vladimir; Eliasson, Lars; Fedorov, Andrei; Fyen, Jan & Kero, Johan [Show all 14 contributors for this article] (2015). The European Arctic: A Laboratory for Seismoacoustic Studies. Seismological Research Letters. ISSN 0895-0695. 86(3), p. 917–928. doi: 10.1785/0220140230.
• Smets, PSM; Evers, LG; Näsholm, Sven Peter & Gibbons, Steven John (2015). Probabilistic infrasound propagation using realistic atmospheric perturbations. Geophysical Research Letters. ISSN 0094-8276. 42(15), p. 6510–6517. doi: 10.1002/2015GL064992. Show summary

  This study demonstrates probabilistic infrasound propagation modeling using realistic perturbations. The ensembles of perturbed analyses, provided by the European Centre for Medium-Range Weather Forecasts (ECMWF), include error variances of both model and assimilated observations. Ensemble spread profiles indicate a yearly mean effective sound speed variation of up to 8 ms−1 in the stratosphere, exceeding occasionally 25 ms−1 for a single ensemble set. It is shown that errors in point estimates of effective sound speed are dominated by variations in wind strength and direction. One year of large mining explosions in the Aitik mine, northern Sweden, observed at infrasound array IS37 in northern Norway are simulated using 3-D ray tracing. Probabilistic propagation modeling using the ensembles demonstrates that small-scale fluctuations are not always necessary to improve the match between predictions and observations.

• Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane & Serfaty, Jean-Michel [Show all 10 contributors for this article] (2015). Bridging three orders of magnitude: multiple scattered waves sense fractal microscopic structures via dispersion. Physical Review Letters. ISSN 0031-9007. 115:094301(9). doi: 10.1103/PhysRevLett.115.094301. Full text in Research Archive Show summary

  Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5  μm in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

• Gal, Martin; Reading, Anya M.; Ellingsen, Simon P.; Koper, Keith D.; Gibbons, Steven John & Näsholm, Sven Peter (2014). Improved implementation of the fk and Capon methods for array analysis of seismic noise. Geophysical Journal International. ISSN 0956-540X. 198(2), p. 1045–1054. doi: 10.1093/gji/ggu183. Show summary

  The frequency–wavenumber (fk) and Capon methods are widely used in seismic array studies of background or ambient noise to infer the backazimuth and slowness of microseismic sources. We present an implementation of these techniques for the analysis of microseisms (0.05–2 Hz) which draws on array signal processing literature from a range of disciplines. The presented techniques avoid frequency mixing in the cross-power spectral density and therefore yield an accurate slowness vector estimation of the incoming seismic waves. Using synthetic data, we show explicitly how the frequency averaged broad-band approach can result in a slowness-shifted spectrum. The presented implementation performs the slowness estimations individually for each frequency bin and sums the resulting slowness spectra over a specific frequency range. This may be termed an incoherently averaged signal, or IAS, approach. We further modify the method through diagonal loading to ensure a robust solution. The synthetic data show good agreement between the analytically derived and inferred error in slowness. Results for real (observed) data are compared between the approximate and IAS methods for two different seismic arrays. The IAS method results in the improved resolution of features, particularly for the Capon spectrum, and enables, for instance, Rg and Lg arrivals from similar backazimuths to be separated in the case of real data.

• Holm, Sverre & Näsholm, Sven Peter (2014). Comparison of fractional wave equations for power law attenuation in ultrasound and elastography. Ultrasound in Medicine and Biology. ISSN 0301-5629. 40(4), p. 695–703. doi: 10.1016/j.ultrasmedbio.2013.09.033. Show summary

  A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.

• Holm, Sverre; Näsholm, Sven Peter; Prieur, Fabrice Jean Gabriel & Sinkus, Ralph (2013). Deriving fractional acoustic wave equations from mechanical and thermal constitutive equations. Computers and Mathematics with Applications. ISSN 0898-1221. 66(5), p. 621–629. doi: 10.1016/j.camwa.2013.02.024. Show summary

  It is argued that fractional acoustic wave equations come in two kinds. The first kind is constructed ad hoc to have loss operators that fit power law measurements. The second kind is more fundamental as they in addition are based on underlying physical equations. Here that means constitutive equations. These equations are the fractional Kelvin–Voigt and the more general fractional Zener stress–strain relationships as well as a fractional version of the Fourier heat law. The properties of the wave equations are given in terms of attenuation, and phase/group velocities for low-, intermediate- and high-frequency regions. In the most general case, the attenuation exhibits power law behavior in all frequency ranges while the phase and group velocities increase sharply in the intermediate frequency range and converge to a constant, finite value for high frequencies. It is also shown that the fractional Zener wave equation is equivalent to the multiple relaxation model for attenuation.

• Näsholm, Sven Peter (2013). Model-based discrete relaxation process representation of band-limited power-law attenuation. Journal of the Acoustical Society of America. ISSN 0001-4966. 133(3), p. 1742–1750. doi: 10.1121/1.4789001. Full text in Research Archive Show summary

  Frequency-dependent acoustical loss due to a multitude of physical mechanisms is commonly modeled by multiple relaxations. For discrete relaxation distributions, such models correspond with causal wave equations of integer-order temporal derivatives. It has also been shown that certain continuous distributions may give causal wave equations with fractional-order temporal derivatives. This paper demonstrates analytically that if the wave-frequency ω satisfies ΩL≪ω ≪ΩH, a continuous relaxation distribution populating only Ω∈[ΩL,ΩH] gives the same effective wave equation as for a fully populated distribution. This insight sparks the main contribution: the elaboration of a method to determine discrete relaxation parameters intended for mimicking a desired attenuation behavior for band-limited waves. In particular, power-law attenuation is discussed as motivated by its prevalence in complex media, e.g., biological tissue. A Mittag-Leffler function related distribution of relaxation mechanisms has previously been shown to be related to the fractional Zener wave equation of three power-law attenuation regimes. Because these regimes correspond to power-law regimes in the relaxation distribution, the idea is to sample the distribution's compressibility contributions evenly in logarithmic frequency while appropriately taking the stepsize into account. This work thence claims to provide a model-based approach to determination of discrete relaxation parameters intended to adequately model attenuation power-laws.

• Näsholm, Sven Peter & Holm, Sverre (2013). On a fractional Zener elastic wave equation. Fractional Calculus and Applied Analysis. ISSN 1311-0454. 16(1), p. 26–50. doi: 10.2478/s13540-013-0003-1. Show summary

  This survey concerns a causal elastic wave equation which implies frequency power-law attenuation. The wave equation can be derived from a fractional Zener stress-strain relation plus linearized conservation of mass and momentum. A connection between this four-parameter fractional wave equation and a physically well established multiple relaxation acoustical wave equation is reviewed. The fractional Zener wave equation implies three distinct attenuation power-law regimes and a continuous distribution of compressibility contributions which also has power-law regimes. Furthermore it is underlined that these wave equation considerations are tightly connected to the representation of the fractional Zener stress-strain relation, which includes the spring-pot viscoelastic element, and by a Maxwell-Wiechert model of conventional springs and dashpots. A purpose of the paper is to make available recently published results on fractional calculus modeling in the field of acoustics and elastography, with special focus on medical applications.

• Jensen, Are Charles; Näsholm, Sven Peter; Nilsen, Carl-Inge Colombo; Austeng, Andreas & Holm, Sverre (2012). Applying Thomson's Multitaper Approach to Reduce Speckle in Medical Ultrasound Imaging. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 59(10), p. 2178–2185. doi: 10.1109/TUFFC.2012.2444. Show summary

  To reduce the variance of speckle in coherent imaging systems, one must average images with different speckle realizations. Traditionally, these images have been formed by observing the target region from slightly different angles (spatial compounding) or by varying the involved temporal frequencies (frequency compounding). In this paper, we investigate a third option based on Thomson's multitaper approach to power spectrum estimation. The tapers are applied spatially, as array weights. Our investigations, based on both recorded ultrasound data and simulations, verify that the multitaper approach can be used for speckle reduction at a rate comparable to that of the more traditional method of spatial compounding. Because of the spectral concentration of the tapers, an added benefit is reduced side lobe levels, which can result in steeper edges and better definition of cyst-like structures.

• Näsholm, Sven Peter & Angelsen, Bjørn Atle J. (2012). SURF Imaging Beams in an Aberrative Medium: Generation and Postprocessing Enhancement. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 59(11), p. 2588–2595. doi: 10.1109/TUFFC.2012.2494. Show summary

  This paper presents numerical simulations of dual-frequency second-order ultrasound field (SURF) reverberation suppression transmit-pulse complexes. Such propagation was previously studied in a homogeneous medium. In this work, the propagation path includes a strongly aberrating body wall modeled by a sequence of delay screens. Each of the applied SURF transmit pulse complexes consists of a high-frequency 3.5-MHz imaging pulse combined with a low-frequency 0.5-MHz sound speed manipulation pulse. Furthermore, the feasibility of two signal postprocessing methods are investigated using the aberrated transmit SURF beams. These methods have previously been shown to adjust the depth of maximum SURF reverberation suppression within a homogeneous medium. The need for this study arises because imaging situations in which reverberation suppression is useful are also likely to produce pulse wave front distortion (aberration). Such distortions could potentially produce time delays that cancel the accumulated propagation time delay needed for the SURF reverberation suppression technique. Results show that both the generation of synthetic SURF reverberation suppression imaging transmit beams and the following postprocessing adjustments are attainable even when a body wall introduces time delays which are larger than previously reported delays measured on human body wall specimens.

• Prieur, Fabrice Jean Gabriel; Näsholm, Sven Peter; Austeng, Andreas; Tichy, Frank & Holm, Sverre (2012). Feasibility of Second Harmonic Imaging in Active Sonar: Measurements and Simulations. IEEE Journal of Oceanic Engineering. ISSN 0364-9059. 37(3), p. 467–477. doi: 10.1109/JOE.2012.2198933. Show summary

  Abstract—Nonlinear acoustics allows for applications like tissue harmonic imaging in medicine and parametric arrays in underwater acoustics. Mainstream sonars transmit and receive signals at the same frequency and up to now energy transferred to higher harmonic frequencies has been mainly seen as a disturbance for target strength estimation, e.g., in fishery research. This paper investigates the feasibility of utilizing the part of the signal generated around the second harmonic frequency band by nonlinear propagation of sound in water. It presents the potential enhancements the second harmonic signal may provide for target imaging as well as multifrequency target recognition. It compares measurements of the pressure field radiated by commercial transducers in water at 121 and 200 kHz up to a range of 12 m with numerical simulations. The detected levels of higher harmonic signals agree with simulations of nonlinear wave propagation. This verifies the implementation of the simulator and allows a comparison of the beam characteristics at longer ranges when filtered around the fundamental or second harmonic frequencies. An example of pulse-echo imaging with spherical targets is also shown using signals at the fundamental and second harmonic frequencies where the second harmonic signal can detect one of the targets that the fundamental signal cannot. Using the active sonar equation to estimate the maximum range, simulations based on a simple model including ambient noise and volume reverberation confirm that with a source level of 228 dB and a detection threshold of 12 dB the fundamental signal at 200 kHz can detect a fish of target strength 36 dB to approximately 343 m while the detection range of the second harmonic signal is approximately 243 m. The combined use of the signal components in the second harmonic and fundamental frequency bands provides a high-resolution image at short range and a long-range imaging capability at a lower resolution as well as a multifrequency characterization of targets. Index Terms—Harmonic analysis, nonlinear

• Näsholm, Sven Peter; Austeng, Andreas; Jensen, Are Charles; Nilsen, Carl-Inge Colombo & Holm, Sverre (2012). Capon Beamforming Applied to Second-Harmonic Ultrasound Experimental Data. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. p. 2217–2220. doi: 10.1109/ULTSYM.2011.0550. Show summary

  This paper presents the novelty of adaptive Capon beamforming on received experimental second-harmonic pulse-echo ultrasound imaging channel-data. IQ channel datasets were collected when imaging a tissue-mimicking phantom: two with the transmit frequency 1.7 MHz and the receive band-pass filters centered around 1.7 and 3.4 MHz respectively, as well as one with both the transmit and receive center frequencies being 3.4 MHz. Images are displayed and analyzed for all datasets both using Capon and conventional delay-and-sum beamforming. This work proves the feasibility of Capon beamforming applied to tissue-harmonic imaging.

• Jensen, Are Charles; Nilsen, Carl-Inge Colombo; Austeng, Andreas; Näsholm, Sven Peter & Holm, Sverre (2012). A Multitaper Approach to Speckle Reduction for Medical Ultrasound Imaging. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. p. 397–400. doi: 10.1109/ULTSYM.2011.0095. Show summary

  A typical approach to reduce unwanted speckle patterns in coherent imaging systems is to average images with different speckle realizations. Traditionally, these images have been formed by observing the target region from slightly different angles (spatial compounding) or by varying the involved frequencies (frequency compounding). In this paper we investigate a third option based on Thomson's multitaper approach to power spectrum estimation applied in the spatial domain. Our investigations, based on both real, measured ultrasound data and data from simulated scenes of point scatterers, verify that the multitaper approach can be used for speckle reduction at a rate compared to that of the more traditional method of spatial compounding. Due to the spectral concentration of the tapers, an added benefit is reduced sidelobe levels, which can yield sharper edges and more defined cyst-like structures.

• Austeng, Andreas; Nilsen, Carl-Inge Colombo; Jensen, Are Charles; Näsholm, Sven Peter & Holm, Sverre (2012). Coherent Plane-Wave Compounding and Minimum Variance Beamforming. Proceedings - IEEE Ultrasonics Symposium. ISSN 1948-5719. p. 2448–2451. doi: 10.1109/ULTSYM.2011.0608. Show summary

  Achieving increased frame rate without compromising the image quality is desirable in medical ultrasound imaging. Coherent plane-wave compounding has recently been suggested as an approach to achieve this. This work proposes to generate coherent compound plane-wave images using a minimum variance adaptive beamformer. Through simulations of point scatterers and cyst phantoms, a threefold increase in frame rate is shown.

• Näsholm, Sven Peter & Holm, Sverre (2011). Linking multiple relaxation, power-law attenuation, and fractional wave equations. Journal of the Acoustical Society of America. ISSN 0001-4966. 130(5), p. 3038–3045. doi: 10.1121/1.3641457. Full text in Research Archive Show summary

  The acoustic wave attenuation is described by an experimentally established frequency power law in a variety of complex media, e.g., biological tissue, polymers, rocks, and rubber. Recent papers present a variety of acoustical fractional derivative wave equations that have the ability to model power-law attenuation. On the other hand, a multiple relaxation model is widely recognized as a physically based description of the acoustic loss mechanisms as developed by Nachman et al. [J. Acoust. Soc. Am. 88, 1584-1595 (1990)]. Through assumption of a continuum of relaxation mechanisms, each with an effective compressibility described by a distribution related to the Mittag-Leffler function, this paper shows that the wave equation corresponding to the multiple relaxation approach is identical to a given fractional derivative wave equation. This work therefore provides a physically based motivation for use of fractional wave equations in acoustic modeling.

• Holm, Sverre & Näsholm, Sven Peter (2011). A causal and fractional all-frequency wave equation for lossy media. Journal of the Acoustical Society of America. ISSN 0001-4966. 130(4), p. 2195–2202. doi: 10.1121/1.3631626. Full text in Research Archive Show summary

  This work presents a lossy partial differential acoustic wave equation including fractional derivative terms. It is derived from first principles of physics (mass and momentum conservation) and an equation of state given by the fractional Zener stress-strain constitutive relation. For a derivative order α in the fractional Zener relation, the resulting absorption αk obeys frequency power-laws as αk ∝ ω1+α in a low-frequency regime, αk ∝ ω1–α/2 in an intermediate-frequency regime, and αk ∝ ω1–α in a high-frequency regime. The value α = 1 corresponds to the case of a single relaxation process. The wave equation is causal for all frequencies. In addition the sound speed does not diverge as the frequency approaches infinity. This is an improvement over a previously published wave equation building on the fractional Kelvin–Voigt constitutive relation.

• Näsholm, Sven Peter; Hansen, Rune & Angelsen, Bjørn Atle J. (2011). Post-processing enhancement of reverberation-noise suppression in dual-frequency SURF imaging. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 58(2), p. 338–348. doi: 10.1109/TUFFC.2011.1811. Show summary

  A post-processing adjustment technique to enhance dual-frequency second-order ultrasound field (SURF) reverberation-noise suppression imaging in medical ultrasound is analyzed. Two variant methods are investigated through numerical simulations. They both solely involve post-processing of the propagated high-frequency (HF) imaging wave fields, which in real-time imaging corresponds to post-processing of the beamformed receive radio-frequency signals. Hence, the transmit pulse complexes are the same as for the previously published SURF reverberation-suppression imaging method. The adjustment technique is tested on simulated data from propagation of SURF pulse complexes consisting of a 3.5-MHz HF imaging pulse added to a 0.5-MHz low-frequency soundspeed manipulation pulse. Imaging transmit beams are constructed with and without adjustment. The post-processing involves filtering, e.g., by a time-shift, to equalize the two SURF HF pulses at a chosen depth. This depth is typically chosen to coincide with the depth where the first scattering or reflection occurs for the reverberation noise one intends to suppress. The beams realized with post-processing show energy decrease at the chosen depth, especially for shallow depths where, in a medical imaging situation, a body-wall is often located. This indicates that the post-processing may further enhance the reverberation- suppression abilities of SURF imaging. Moreover, it is shown that the methods might be utilized to reduce the accumulated near-field energy of the SURF transmit-beam relative to its imaging region energy. The adjustments presented may therefore potentially be utilized to attain a slightly better general suppression of multiple scattering and multiple reflection noise compared with non-adjusted SURF reverberation-suppression imaging.

• Måsøy, Svein-Erik; Standal, Øyvind; Deibele, Jochen; Näsholm, Sven Peter; Angelsen, Bjørn Atle J. & Johansen, Tonni Franke [Show all 8 contributors for this article] (2010). Nonlinear propagation acoustics of dual-frequency wide-band excitation pulses in a focused ultrasound system. Journal of the Acoustical Society of America. ISSN 0001-4966. 128(5), p. 2695–2703. doi: 10.1121/1.3488308. Show summary

  In this article, acoustic propagation effects of dual-frequency wide-band excitation pulses in a focused ultrasound system are demonstrated in vitro. A designed and manufactured dual-frequency band annular array capable of transmitting 0.9/7.5 MHz center frequency wide-band pulses was used for this purpose. The dual-frequency band annular array, has been designed using a bi-layer piezo-electric stack. Water tank measurements demonstrate the function of the array by activating the low- and high-frequency layers individually and simultaneously. The results show that the array works as intended. Activating the low- and high-frequency layers individually, results in less than -50 dB signal level from the high- and low-frequency layers respectively. Activating both layers simultaneously, produce a well defined dual-frequency pulse. The presence of the low-frequency pulse leads to compression, expansion, and a time delay of the high-frequency pulse. There is a phase shift between the low- and high-frequency pulse as it propagates from the array to the focus. This makes the latter described effects also dependent on the array configuration. By varying the low-frequency pressure, a shift of up to 0.5 MHz in center frequency of a 8.0 MHz transmitted high-frequency pulse is observed at the array focus. The results demonstrate the high propagation complexity of dual-frequency pulses.

• Näsholm, Sven Peter; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2009). An Annular Array Design Proposal with Multiple Geometric Pre-foci. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 56(1), p. 146–155. doi: 10.1109/TUFFC.2009.1014. Show summary

  An annular array design method is described and used for definition of an array proposal. The geometric pre-focus, realized by curving or use of an acoustic lens, varies among the annuli. Element sizes and geometric pre-focus depths are determined by a maximum allowed phase-shift within the active depth region of each element on receive, resulting in fewer elements or larger apertures compared with the standard equal area design. The method allows combination of large aperture and high frequency with a large receive depth of field. The developed design rules are used to define an array for imaging within the frequency interval [7.5, 15] MHz. Its total aperture diameter is 22 mm and the thinnest element is 0.23 mm wide. Receive beams resulting from this array are simulated. The beams and their sidelobe-to-mainlobe energy ratios are compared with an ideally focused reference where there are no phase shifts over the elements. Within nearly the entire depth of field, the sidelobe-to-mainlobe energy ratio is less than 5 dB higher than for the ideal reference.

• Näsholm, Sven Peter; Hansen, Rune; Måsøy, Svein-Erik; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2009). Transmit Beams Adapted to Reverberation Noise Suppression Using Dual-Frequency SURF Imaging. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 56(10), p. 2124–2133. doi: 10.1109/TUFFC.2009.1295. Show summary

  A method that uses dual-frequency pulse complexes of widely separated frequency bands to suppress noise caused by multiple scattering or multiple reflections in medical ultrasound imaging is presented. The excitation pulse complexes are transmitted to generate a second order ultrasound field (SURF) imaging synthetic transmit beam. This beam has reduced amplitude near the transducer, which illustrates the multiple scattering suppression ability of the imaging method. Field simulations solving a nonlinear wave equation are used to calculate SURF imaging beams, which are compared with beams for pulse inversion (PI) and fundamental imaging. In addition, a combined SURF and PI beam generation is described and compared with the beams mentioned above. A quality ratio, relating the energy within the near-field to that within the imaging region, is defined and used to score the multiple scattering and multiple reflection suppression abilities when imaging with the different beams. The realized combined SURF-PI beam scores highest, followed by SURF, PI (that score equally well), and the fundamental. The amplitude in the imaging region and therefore also the SNR is highest for the fundamental followed by SURF, PI, and SURF-PI. The work hence indicates that when substituting PI for SURF, one may trade increased SNR into use of increased imaging frequencies without loss of multiple scattering and multiple reflection noise suppression.

• Måsøy, Svein-Erik; Standal, Øyvind; Näsholm, Sven Peter; Johansen, Tonni Franke; Angelsen, Bjørn Atle J. & Hansen, Rune (2008). SURF Imaging: In vivo Demonstration of an Ultrasound Contrast Agent Detection Technique. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. ISSN 0885-3010. 55(5), p. 1112–1121. doi: 10.1109/TUFFC.2008.763. Show summary

  A dual-band method for ultrasound contrast agent detection is demonstrated in vivo in an animal experiment using pigs. The method is named Second-order UltRasound Field Imaging, abbreviated SURF Imaging. It relies on simultaneously transmitting two ultrasound pulses with a large separation in frequency. Here, a low-frequency pulse of 0.9 MHz is combined with a high-frequency pulse of 7.5 MHz. The low-frequency pulse is used to manipulate the properties of the contrast agent, and the high-frequency pulse is used for high-resolution contrast detection and imaging. An annular array capable of transmitting the low- and high-frequency pulses simultaneously was constructed and fitted to a mechanically scanned probe used in a GE Vingmed System 5 ultrasound scanner. The scanner was modified and adapted for the dual-band transmit technique. In-house software was written for post-processing of recorded IQ-data. Contrast-processed B-mode images of pig kidneys after bolus injections of 1 mL of Sonovue are presented. The images display contrast detection with contrast-to-tissue ratios ranging from 15-40 dB. The results demonstrate the potential of SURF Imaging as an ultrasound contrast detection technique for clinically high ultrasound frequencies. This may allow ultrasound contrast imaging to be available for a wide range of applications.

• Näsholm, Sven Peter; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2004). Effect of a Curved Dome on the Effective Foci of an Annular Array - Numerical Simulations and Experimental Measurements. IEEE International Ultrasonics Symposium Proceedings. ISSN 1051-0117. 3, p. 1647–1650. doi: 10.1109/ULTSYM.2004.1418138. Show summary

  A numerical method to estimate the {effective focus} and {effective aperture} changes when a geometrically pre-focused ultrasound annular array is placed inside a curved fluid filled dome is developed. The method is based on ray tracing. The {effective element} hypothesis and our numerical method to calculate it are verified by comparing simulated ultrasound fields for the following two cases: 1) The {real elements} in the inhomogeneous dome fluid/dome plastic/tissue medium. 2) The {effective elements} in a homogeneous medium. The ultrasonic fields both along the x- and z axes are found to be very similar within each array element's active region. The focus moving effect prediction from the effective element model is verified by water tank ultrasound field hydrophone measurements of the on-axis z fields from elements of an array disposed in a fluid filled dome.

• Näsholm, Sven Peter; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2004). Effect of a Curved Dome on the Effective Foci of an Annular Array - Numerical Simulations and Experimental Measurements. IEEE International Ultrasonics Symposium Proceedings. ISSN 1051-0117. 3, p. 1647–1650. doi: 10.1109/ULTSYM.2004.1418138. Show summary

  A numerical method to estimate the effective focus and effective aperture changes when a geometrically pre-focused ultrasound annular array is placed inside a curved fluid filled dome is developed. The method is based on ray tracing. The effective element hypothesis and our numerical method to calculate it are verified by comparing simulated ultrasound fields for the following two cases: (1) the real elements in the inhomogeneous dome fluid/dome plastic/tissue medium; (2) the effective elements in a homogeneous medium. The ultrasonic fields both along the x- and z axes are found to be very similar within each array element's active region. The focus moving effect prediction from the effective element model is verified by water tank ultrasound field hydrophone measurements of the on-axis z fields from elements of an array disposed in a fluid filled dome.

View all works in Cristin

• Arnestad, Håvard; Rindal, Ole Marius Hoel; Austeng, Andreas & Näsholm, Sven Peter (2024). Estimation of probability densities in ultrasound imaging.
• Han, Chaoran; Arnestad, Håvard; Austeng, Andreas & Näsholm, Sven Peter (2024). Spectral estimation inspired by a non-linear beamformer: Insights into null-subtraction imaging.
• Solberg, Celine Marie; Brissaud, Quentin & Näsholm, Sven Peter (2024). Preliminary assessments of the global detectability of venusquakes from a balloon platform. Show summary

  (presented on-site by Celine Marie Solberg)

• Brissaud, Quentin; Näsholm, Sven Peter & Solberg, Celine Marie (2024). Assumptions and uncertainties when simulating seismo-acoustic wave propagation on Venus.
• Sufayan, Mulani; Näsholm, Sven Peter & Austeng, Andreas (2024). Fourier Migration Based Beamforming Method For Medical Ultrasound Imaging.
• Sotoodeh Ziksari, Mahsa; Näsholm, Sven Peter & Austeng, Andreas (2024). Adaptive beamforming for high frame-rate ultrasound imaging.
• Giuliacci, Kety; Bailo, Daniele; Michalek, Jan; Paciello, Rossana; Vinciarelli, Valerio & Goffi, Claudio [Show all 20 contributors for this article] (2023). A FAIR approach for the integration of scientific services in the Geo-INQUIRE initiative. Show summary

  In recent years, there has been a growing trend in science towards data integration, with the purpose of using multidisciplinary data and products to foster new methodological approaches and scientific discoveries. One of the many projects that have emerged is the Geosphere INfrastructures for QUestions into Integrated REsearch (Geo-INQUIRE). Geo-INQUIRE started in October 2022 and benefits from a unique consortium of 51 partners consisting of major national research institutes, universities, national geological surveys, and European consortia. Geo-INQUIRE aims to overcome cross-domain barriers, especially in land-sea-atmosphere environments. To achieve this goal, it has set out to integrate the resources and capacities of the major research infrastructures (RIs) involved with geosphere observations, namely EPOS, EMSO, ARISE, ECCSEL, and ChEESE. By making available its enhanced data, product, and service portfolio, it will enable the next generation of scientists to carry out leading-edge research addressing societal challenges from a multidisciplinary perspective, making intelligent use of these resources to encourage curiosity-driven research. In order to achieve curiosity-driven advanced scientific results across domains, the project aims at providing integrated access to harmonised data, data products, software and services from different RIs services to a broader community of users. To identify services provided by RIs a comprehensive survey was conducted. The collected information included basic details, points of contact, and the technical status of the service (e.g., accessibility, API structure, response formats, data representations, and the standard of metadata describing the service). Furthermore, the survey also assessed the presence of licenses and documentation related to both the service and the provided data, ultimately providing an overview of the technology readiness level and the level of integrability of the services, with the goal of validating the “FAIRness of the services”. This contribution describes the landscape analysis conducted and the technical solutions being adopted to integrate such a wealth of heterogeneous resources. These solutions are based on the FAIR metadata approach successfully applied in the EPOS context.

• Brissaud, Quentin; Näsholm, Sven Peter; Turquet, Antoine; Kaschwich, Tina & Solberg, Celine Marie (2023). The AIR project: Leveraging balloon pressure data for planetary exploration . Show summary

  Our understanding of Earth’s internal structure comes primarily from seismic waves that provide important constraints on subsurface seismic-velocity properties. However, traditional inversion methods cannot be implemented in regions of limited seismic-station coverage, in particular on Venus due to its harsh surface conditions but also in remote Earth regions. This lack of seismic data greatly limits our understanding of Venus’ origin and evolution and Earth’s subsurface. However, the mechanical coupling between the ground and its atmosphere enables the seismic energy to be transmitted into the atmosphere as low-frequency acoustic waves carrying information about the seismic source and the subsurface properties. While infrasound is traditionally recorded at ground-based stations, which suffers from the same in-situ deployment limitations as seismic stations, recent studies have demonstrated that balloon platforms can be used to monitor seismic activity from the atmosphere at a low operational cost. Balloon-borne seismology is a new dynamic field considered to be the only way to investigate Venus’ interior. However, inversion methods for balloon-borne infrasound data are lacking and the coupling between seismic and acoustic waves in realistic media is poorly understood. Taking advantage of historical balloon pressure data, the newly granted project Airborne Inversion of Rayleigh waves (AIR), will address these key theoretical and practical issues by analyzing and modeling these seismically-induced infrasound signatures to retrieve the source and subsurface properties. In this contribution, we will present the project objectives and recent progress in balloon seismology and infrasound modeling.

• Holm, Sverre; Chandrasekaran, Sri Nivas & Näsholm, Sven Peter (2023). Finding wave equations for sediment acoustics theories. Show summary

  The two main theories for wave propagation in sediments, the Extended Biot theory and the Viscous Grain Shearing (VGS) theory, have been formulated in terms of dispersion equations only. Some have considered the lack of a wave equation to be a weakness that may indicate lack of a physical basis for these theories. In the Biot theory, it is the frequency-dependent viscodynamic operator which models viscous boundary effects in pores that poses the problem. It can be formulated as a ratio of Bessel functions for circular pores and as a ratio of tanh-functions for a 2D parallel plane duct. There is no simple equivalent time domain operator for use in the wave equation. In both geometries, the factor may, however, be approximated well with (1 + icω)1/2, where c is a constant. This factor also appears in the Cole-Davidson dielectric theory for complex media. The equivalent time domain operator, the fractional pseudo-differential operator, enables the formulation of wave equations for all three wave modes. The same operator turns out to be central for transforming the dispersion relations of the VGS theory to time-space wave equations. These wave equations enable a closer study of properties of the medium models than that obtained from dispersion relations alone.

• Näsholm, Sven Peter; Arnestad, Håvard; Austeng, Andreas & Rindal, Ole Marius Hoel (2023). Calculating the generalized contrast-to-noise ratio using kernel density estimation. Show summary

  The histogram-based generalized contrast-to-noise ratio (gCNR) evaluates how well image regions with different intensity can be distinguished. The gCNR is defined as ‘one minus the overlap region’ of normalized histograms from two regions. Histogram-based gCNR depends on user parameters like bin size and bin offset, but there are also approaches to robustify the histogram calculation. Kernel density estimation (KDE) is a well-established alternative to histograms to estimate probability density functions (PDFs), and is generally considered to be more robust. We suggest replacing histograms with KDE in gCNR calculations.

• Amezcua, Javier & Näsholm, Sven Peter (2023). Using satellite data assimilation techniques to combine infrasound observations and a full ray-tracing model to constrain atmospheric variables.
• Vorobeva, Ekaterina; Assink, Jelle D.; Chunchuzov, Igor; Renkwitz, Toralf; Espy, Patrick Joseph & Näsholm, Sven Peter (2023). Using infrasound from explosions for probing internal gravity waves in the middle atmosphere.
• Eggen, Mari Dahl; Midtfjord, Alise Danielle; Vorobeva, Ekaterina; Benth, Fred Espen; Hupe, Patrick & Brissaud, Quentin [Show all 10 contributors for this article] (2023). Using a machine learning and stochastics-founded model to provide near real-time stratospheric polar vortex diagnostics based on high-latitude infrasound data. Show summary

  Acoustic waves below the frequency limit of human hearing - infrasound - can travel for thousands of kilometres in the atmosphere. The global propagation signature of infrasound is highly sensitive to the wind structure of the stratosphere. This work exploits processed continuous data from three high-latitude infrasound stations to characterize an aspect of the stratospheric polar vortex. Concretely, a mapping is developed which takes the infrasound data from these three stations as input and outputs an estimate of the polar cap zonal mean wind averaged over 60-90 degrees in latitude at the 1 hPa pressure level. This stratospheric diagnostic information is relevant to, for example, sudden stratospheric warming assessment and sub-seasonal prediction. The considered acoustic data is within a low-frequency regime globally dominated by so-called microbarom infrasound, which is continuously radiated into the atmosphere due to nonlinear interaction between counter-propagating ocean surface waves. We trained a stochastics-based machine learning model (delay-SDE-net) to map between a time series of five years (2014-2018) of processed infrasound data and the ERA5 (reanalysis-based) daily average polar cap wind at 1 hPa for the same period. The ERA5 data was hence treated as ground-truth. In the prediction, the delay-SDE-net utilizes time-lagged inputs and their dependencies, as well as the day of the year to account for seasonal differences. In the validation phase, the input was the 2019 and 2020 infrasound time series, and the model inference results in an estimate of the daily average polar cap wind time-series. This result was then compared to the ERA5 representation of the stratospheric diagnostic time-series for the same period. The applied machine learning model is based on stochastics and allows for an interpretable approach to estimate the aleatoric and epistemic prediction uncertainties. It is found that the mapping, which is only informed of the trained model, the day of year, and the infrasound data from three stations, generates a 1 hPa polar cap average wind estimate with a prediction error standard deviation of around 10 m/s compared to ERA5. Focus should be put on the winter months because this is when the coupling between the stratosphere and the troposphere can mostly influence the surface conditions and provide additional prediction skill, in particular during strong and weak stratospheric polar vortex regimes. The infrasound data is available in real-time, and we discuss how the developed approach can be extended to provide near real-time stratospheric polar vortex diagnostics.

• Näsholm, Sven Peter; Amezcua, Javier; Assink, Jelle D.; Belova, Evgenia; Blixt, Mårten & Brissaud, Quentin [Show all 16 contributors for this article] (2023). Summarizing the research of the MADEIRA project - Middle atmosphere dynamics: exploiting infrasound using a multidisciplinary approach at high latitudes.
• Forestier, Edouard; Näsholm, Sven Peter; Brissaud, Quentin & Pichon, Alexis Le (2023). Rapid estimation of ground-to-ground infrasonic transmission loss using a recurrent neural network (RNN) trained on simulations through realistic atmosphere model specifications.
• Näsholm, Sven Peter; Brissaud, Quentin; Vorobeva, Ekaterina & Eggen, Mari Dahl (2023). Introduction to Infrasound and Atmospheric Sensing.
• Brissaud, Quentin; Schweitzer, Johannes; Näsholm, Sven Peter; Vorobeva, Ekaterina & Eggen, Mari Dahl (2023). Infrasound arrays as probes for atmospheric and ice dynamics in polar regions.
• Hupe, Patrick; Vergoz, Julien; Listowski, Constantino; Pichon, Alexis Le; Milton A., Garcés & Marchetti, Emanuele [Show all 16 contributors for this article] (2023). IMS observations of infrasound and acoustic-gravity waves produced by the January 2022 volcanic eruption of Hunga, Tonga: A global analysis.
• Vorobeva, Ekaterina; Assink, Jelle D.; Belova, Evgenia; Latteck, Ralph; Espy, Patrick Joseph & Baumgarten, Gerd [Show all 9 contributors for this article] (2023). Probing internal gravity waves in the middle atmosphere using infrasound from explosions.
• Näsholm, Sven Peter (2023). Measuring winds we cannot measure using sound we cannot hear?
• Turquet, Antoine Leo; Brissaud, Quentin; Näsholm, Sven Peter; Alvizuri, Celso; Kero, Johan & Listowski, Constantino [Show all 8 contributors for this article] (2023). Constraining Moment-Tensor and Source Depth of a Mine Quake Using Local Infrasound Data.
• Vergoz, Julien; Pichon, Alexis Le; Pilger, Christoph; Listowski, Constantino; Marchetti, Emanuele & Ceranna, Lars [Show all 16 contributors for this article] (2023). International Monitoring System Observations of Infrasound and Acoustic Gravity Waves Produced by the January 2022 Volcanic Eruption of Hunga, Tonga: A Global Analysis.
• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2023). Bounding the beampattern of acoustic arrays using interval arithmetic.
• Arnestad, Håvard; Gereb, Gabor; Lønmo, Tor Inge Birkenes; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Bounding the beampattern of acoustic arrays using interval arithmetic.
• Arnestad, Håvard; Austeng, Andreas; Näsholm, Sven Peter & Rindal, Ole Marius Hoel (2022). The Effect of Retrospective Transmit Focusing on Minimum Variance Beamforming.
• Gereb, Gabor; Hansen, Roy Edgar; Austeng, Andreas; Lønmo, Tor Inge Birkenes; Näsholm, Sven Peter & Rindal, Ole Marius Hoel (2022). Ultrasound Beamformer Benchmarking Pipeline.
• Gereb, Gabor; Hansen, Roy Edgar; Lønmo, Tor Inge Birkenes; Näsholm, Sven Peter; Austeng, Andreas & Rindal, Ole Marius Hoel (2022). Improving Sonar Surveying of Subsea Cables and Pipelines with Adaptive Beamforming. Show summary

  Background, Motivation and Objective Safe and efficient transportation of offshore energy requires well-maintained underwater infrastructure, no matter if the energy source is fossil, wind, sun, or wave. Subsea cables and pipelines can be efficiently surveyed using sonar systems mounted on surface or underwater vehicles. Adaptive array signal processing methods are increasingly explored to improve image quality and detection or estimation accuracy in specific survey scenarios. However, adaptive methods can be sensitive to the context they are used in. Therefore, choosing the right beamforming approach from the available candidates requires extensive testing in various scenarios, which is often not feasible out at sea. Statement of Contribution/Methods Realistic simulation of complex underwater scenarios has been previously demonstrated using the Field II Ultrasound Simulation Program in combination with the open access package UltraSound ToolBox (USTB). We use Field II to create digital twins of water column images from pipeline surveys, and then modify parameters such as the layout, depth, and SNR to extend the scope of testing. We add multiple realizations of random noise to the signal and then use USTB to beamform the data with different techniques. On the beamformed data we perform estimation of multiple parameters such as the position and size of the pipe and the seabed depth around it. Finally, using the known ground truth of the model, we compare the bias and variance of the estimations made using images reconstructed by different beamformers. Results/Discussion Following on the results of previous studies demonstrating the benefits of adaptive beamforming in sonar bathymetry, we present a benchmark study of adaptive beamforming techniques such as Low Complexity Adaptive (LCA) and Capon Minimum Variance (MVDR). Comparison with the Coherence Factor (CF) method is made as well. We use Delay-and-Sum (DAS) as a reference with various apodizations. We provide quantitative performance assessment based on the statistical distribution of the estimations with reference to the ground truth in different scenarios.

• Belova, Evgenia; Barabash, Victoria; Godin, Oleg A.; Kero, Johan; Näsholm, Sven Peter & Vorobeva, Ekaterina [Show all 7 contributors for this article] (2022). Infrasound as a Probable Cause of Fast-travelling Polar Mesosphere Winter Echoes. Show summary

  Polar mesosphere winter echoes (PMWE) are relatively strong signals from 50-80 km altitudes observed by radars operating at a broad frequency range, at polar latitudes during the equinox and winter seasons. A majority of PMWE can be explained by the neutral air turbulence with or without the presence of charged small particles (presumably meteor smoke particles). However, in some cases strong, quasi-specular radar echoes with high horizontal speeds exceeding 350-400 m/s were observed (Kirkwood et al., 2006; Kirkwood, 2007). Since atmospheric scatterers moving with velocities of hundreds of m/s cannot be attributed to the atmospheric turbulence or nano particles moving with the wind, there is a need to understand what are the physical mechanisms that can generate such PMWE. We consider three recent PMWE events, when the signals travelling with high horizontal velocities above 300 m/s were measured by the 52 MHz atmospheric radar ESRAD located at Esrange, near Kiruna in northern Sweden. We propose four mechanisms of generation of such PMWE that involves microbaroms, i.e. infrasound waves at 0.1 - 0.35 Hz frequencies created by ocean swell. These mechanisms are (i) generation of viscous waves, (ii) generation of thermal waves, (iii) direct contributions of infrasound, and (iv) generation of secondary waves at sound dissipation and they necessarily accompany sound propagation in inhomogeneous, thermally conducting and viscous fluid (air). The infrasound measurements at the IS37 station located about 170 km north-west from the ESRAD radar, modelled maps of the microbarom sources, infrasound propagation conditions and ionospheric conditions for three PMWE events support the proposed mechanisms.

• Näsholm, Sven Peter (2022). Infralydbasert karakterisering av vind i den midtre atmosfæren. Show summary

  Lyd i lavere frekvenser enn mennesket kan høre – infralyd – forplanter seg over lange avstander (opp til tusenvis av kilometer) i den midtre atmosfæren og blir deretter registrert av et globalt nettverk av bakkebaserte instrumenter. Disse akustiske bølgene bringer med seg informasjon om dynamikken i den øvre stratosfæren (opp til cirka 50 km høyde) der det er få andre muligheter å måle vind. Vi forteller om vår forskning knyttet til assimilering av infralyddata i atmosfæremodeller og vår ambisjon om å bidra til en forbedret langtidsværvarsling.

• Rindal, Ole Marius Hoel; Näsholm, Sven Peter; Hansen, Roy Edgar & Austeng, Andreas (2022). Compensating Dynamic Range Alterations from Adaptive Beamforming using Histogram Matching.
• Rindal, Ole Marius Hoel; Näsholm, Sven Peter; Hansen, Roy Edgar & Austeng, Andreas (2022). Image Enhancement Using Capon Minimum Variance Adaptive Beamforming in Synthetic Aperture Sonar.
• Austeng, Andreas; Näsholm, Sven Peter; Hansen, Roy Edgar & Rindal, Ole Marius Hoel (2022). Spatial Aperture Coherence with Synthetic Transmit Focusing in SAS.
• Dando, Benjamin; Iranpour, Kamran; Wüstefeld, Andreas; Näsholm, Sven Peter; Baird, Alan F. & Oye, Volker (2022). Designing the next generation of seismic arrays using fibre optic DAS. Show summary

  While seismic arrays have been in use since the 1950s and are currently a vital part of the IMS, they have fundamentally consisted of single or 3-component seismometers to measure the ground motion at a discrete set of locations known as the array elements. With the advent of Distributed Acoustic Sensing (DAS) within the last two decades, there is currently great interest in exploring the potential seismological applications. In contrast to traditional seismometers, DAS measures the deformation (e.g. strain-rate) along the length of a fibre optic cable with great flexibility in the number of measurements that can be taken and where they are taken along a given cable layout. Applying such technology to seismic arrays offers an exciting opportunity to design array configurations that were previously impractical with individual seismometers. However, the use of DAS requires special consideration of its unique signal characteristics, which include insensitivity of P-waves arriving broadside to the fibre optic cable. In this paper we present a design study for the installation of a new fibre optical cable at the site of the existing NORES seismic array in Norway – a 1.4 km aperture array located within a subarray of IMS station PS27 (NOA). We demonstrate through the modelling of DAS-specific array response functions how to optimize a new seismic array for regional seismic monitoring, highlighting the importance of incorporating DAS directivity effects. The final design will be installed in 2022 supplementing the current NORES array and will provide a unique data set that could lead to a new generation of DAS seismic arrays for both regional and global seismic monitoring.

• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2022). Stochastic Modeling of Stratospheric Temperature. Show summary

  This study suggests a stochastic model for time series of daily zonal (circumpolar) mean stratospheric temperature at a given pressure level. It can be seen as an extension of previous studies which have developed stochastic models for surface temperatures. The proposed model is a combination of a deterministic seasonality function and a Lévy-driven multidimensional Ornstein–Uhlenbeck process, which is a mean-reverting stochastic process. More specifically, the deseasonalized temperature model is an order 4 continuous-time autoregressive model, meaning that the stratospheric temperature is modeled to be directly dependent on the temperature over four preceding days, while the model’s longer-range memory stems from its recursive nature. This study is based on temperature data from the European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis model product. The residuals of the autoregressive model are well represented by normal inverse Gaussian-distributed random variables scaled with a time-dependent volatility function. A monthly variability in speed of mean reversion of stratospheric temperature is found, hence suggesting a generalization of the fourth-order continuous-time autoregressive model. A stochastic stratospheric temperature model, as proposed in this paper, can be used in geophysical analyses to improve the understanding of stratospheric dynamics. In particular, such characterizations of stratospheric temperature may be a step towards greater insight in modeling and prediction of large-scale middle atmospheric events, such as sudden stratospheric warming. Through stratosphere–troposphere coupling, the stratosphere is hence a source of extended tropospheric predictability at weekly to monthly timescales, which is of great importance in several societal and industry sectors.

• Vergoz, Julien; Le Pichon, Alexis; Listowski, Constantino; Hupe, Patrick; Pilger, Christian & Peter, Gaebler [Show all 15 contributors for this article] (2022). A global analysis of deep infrasound produced by the January 2022 eruption of Hunga volcano. Show summary

  The eruption of Hunga volcano, Tonga is the most energetic event recorded by the infrasound component of the global International Monitoring System (IMS). Infrasound, acoustic-gravity and Lamb waves were recorded by all 53 operational stations after circling four times the globe. The atmospheric waves recorded globally exhibit amplitude and period comparable to the ones observed following the 1883 Krakatoa eruptions. In the context of the future verification of the Comprehensive Nuclear-Test-Ban Treaty, this event provides a prominent milestone for studying in detail infrasound propagation around the globe for almost one week as well as for calibrating the performance of the IMS network in a broad frequency band.

• Näsholm, Sven Peter; Iranpour, Kamran; Wüstefeld, Andreas; Dando, Benjamin; Baird, Alan F. & Oye, Volker (2022). Array signal processing on distributed acoustic sensing data: directivity effects in slowness space. Show summary

  Distributed Acoustic Sensing (DAS) involves the transmission of laser pulses along a fiber-optic cable. These pulses are backscattered at fiber inhomogeneities and again detected by the same interrogator unit that emits the pulses. Elastic deformation along the fiber causes phase shifts in the backscattered laser pulses which are converted to spatially averaged strain measurements, typically at regular fiber intervals. DAS systems provide the potential to employ array processing algorithms. However, there are certain differences between DAS and conventional sensors. The current paper is focused on taking these differences into account. While seismic sensors typically record the directional particle displacement, velocity, or acceleration, the DAS axial strain is inherently proportional to the spatial gradient of the axial cable displacement. DAS is therefore insensitive to broadside displacement, e.g., broadside P-waves. In classical delay-and-sum beamforming, the array response function is the far-field response on a horizontal slowness (or wavenumber) grid. However, for geometrically non-linear DAS layouts, the angle between wavefront and cable varies, requiring the analysis of a steered response that varies with the direction of arrival. This contrasts with the traditional array response function which is given in terms of slowness difference between arrival and steering. This paper provides a framework for DAS steered response estimation accounting also for cable directivity and gauge-length averaging – hereby demonstrating the applicability of DAS in array seismology and to assess DAS design aspects. It bridges a gap between DAS and array theory frameworks and communities, facilitating increased employment of DAS as a seismic array.

• Gereb, Gabor; Hansen, Roy Edgar; Lønmo, Tor Inge Birkenes; Näsholm, Sven Peter & Austeng, Andreas (2022). Underwater pipeline detection and localisation using multibeam echo sounder in a resolution limited case.
• Arnestad, Håvard; Gereb, Gabor; Birkenes Lønmo, Tor Inge; Kirkebø, Jan Egil; Austeng, Andreas & Näsholm, Sven Peter (2022). Sonar array beampattern bounds: tolerance analysis using interval arithmetic. Show summary

  The framework of interval arithmetic (IA) and its extension to complex numbers has in the last decade been applied as a tool for finding robust tolerance bounds of antenna arrays. The IA framework complements statistical methods, as inclusive upper and lower bounds of the beampattern are obtained directly, only assuming error bounds on specifically chosen array parameters. Recently, beampattern synthesis for sonar arrays subject to amplitude excitation errors has been extended from linear arrays with omnidirectional elements to non-linear arrays with directive elements. In this work, we demonstrate that the analysis can be developed further to include both amplitude and phase errors. Moreover, we account for error bounds in element position and orientation, thus representing a more comprehensive method for evaluating the worst-case performance due to uncertainty bounds in a multitude of design parameters. For this purpose, we have created an open-source MATLAB toolbox to calculate beampattern bounds for an array with bounded error tolerances. The toolbox features an object oriented library of interval classes and an interactive graphical user interface with easily configurable settings, where results for different interval representations are shown along with their corresponding bounds. The beampattern bounds of a sonar array is illustrated through an example.

• Amezcua, Javier; Näsholm, Sven Peter & Vera Rodriguez, Ismael (2022). Constraining middle and upper atmospheric variables by assimilating measurements from infrasound propagation. Show summary

  When an infrasound wave travels through the atmosphere, it is affected by the atmospheric variables it encounters (e.g. temperature and winds) in its path. When the wave is detected, the integrated effect of these variables along the trajectory of the wave affects measured quantities such as apparent velocity, backazimuth angle and travel time. Data assimilation combines background atmospheric information with observations to get a better estimate (analysis) of atmospheric variables. In this work, we use the ensemble Kalman filter --with the 10-member ERA-5 reanalysis as background-- to assimilate integrated infrasound observations from the Hukkakero explosions detected by the ARCES array. This process helps get better estimates of atmospheric variables, specially in the stratosphere and lower mesosphere. For each explosion, this process has three steps: (i) the mapping of each of the 10 atmospheric profiles into observation space using the Infra-GA wave propagation model, (ii) the application of the filer equations in observation space, and (c) the mapping back to the space of model variables. The results of these experiments are compared to the Copernicus Artic Regional Reanalysis Service.

• Brissaud, Quentin; Näsholm, Sven Peter & Turquet, Antoine Leo (2021). Predicting infrasound transmission loss using deep learning. Show summary

  Modeling the spatial distribution of infrasound attenuation (or transmission loss, TL) from surface sources is key to understanding and interpreting observations at ground-based stations. Such predictions enable the reliable assessment of infrasound source characteristics such as ground pressure levels associated with earthquakes, volcanic explosion properties, yield of nuclear and non-nuclear explosions, and ocean-generated microbaroms wavefields. However, the computational cost associated with current full-waveform modeling tools, such as Parabolic Equation (PE) codes, often prevents the exploration of a large parameter space, i.e., variations in wind models, source frequency, and source location, when deriving reliable estimates of source or atmospheric properties — in particular for real-time and near-real-time applications. Therefore, many studies rely on analytical regression heuristic TL equations that neglect complex vertical wind variations and the range-dependent variation in the atmospheric properties. This introduces significant uncertainties in the predicted TL. In this contribution, we propose a deep-learning model trained on a large set of simulated wavefields using PE simulations and ERA5 re-analysis atmospheric models to predict infrasound amplitudes up to 1000 km from the source, also accounting for arbitrarily large vertical and horizontal wind variations. Given an atmospheric model, our new modeling framework provides a fast (0.05 s runtime) and reliable (<5 dB error on average, compared to PE simulations) estimate of the infrasound TL. This work paves the way for real-time monitoring and characterization of infrasound sources such as active volcanoes and man-made explosions. We also see a potential for this approach to be incorporated into frameworks that invert for infrasound source locations, and into studies where infrasound datasets are exploited to constrain atmospheric and numerical weather prediction models.

• Turquet, Antoine Leo; Brissaud, Quentin; Kero, Johan; Näsholm, Sven Peter; Le Pichon, Alexis & Listowski, Constantino [Show all 7 contributors for this article] (2021). Near and Far-Field Seismo-Acoustic Analysis of Mb 4.9 Mining Induced Earthquake Nearby Kiruna, Sweden .
• Turquet, Antoine Leo; Brissaud, Quentin; Kero, Johan; Näsholm, Sven Peter; Kværna, Tormod & Le Pichon, Alexis [Show all 7 contributors for this article] (2021). Seismo-acoustic analysis of Mw 4.2 mining induced earthquake nearby Kiruna, Sweden.
• Turquet, Antoine Leo; Brissaud, Quentin; Näsholm, Sven Peter; Kero, Johan; Kværna, Tormod & Listowski, C. [Show all 7 contributors for this article] (2021). Near and far-field seismo-acoustic analysis of mb 4.9 mining induced earthquake nearby Kiruna, Sweden.
• Turquet, Antoine Leo; Brissaud, Quentin; Kero, Johan; Näsholm, Sven Peter; Kværna, Tormod & Le Pichon, Alexis [Show all 7 contributors for this article] (2021). Insights from mb4.9 Kiruna Minequake (Sweden) - 18 May 2020.
• Eggen, Mari Dahl; Dahl, Kristina Rognlien; Näsholm, Sven Peter & Mæland, Steffen (2021). Stochastic modelling of stratospheric temperature.
• Vorobeva, Ekaterina; De Carlo, Marine; Näsholm, Sven Peter; Le Pichon, Alexis & Espy, Patrick Joseph (2021). A vespagram-based approach in application to atmospheric remote sensing.
• Vorobeva, Ekaterina; De Carlo, Marine; Näsholm, Sven Peter; Le Pichon, Alexis & Espy, Patrick Joseph (2021). A vespagram-based approach to assess microbarom radiation and propagation models.
• Vorobeva, Ekaterina; De Carlo, Marine; Näsholm, Sven Peter; Le Pichon, Alexis & Espy, Patrick Joseph (2021). Vespagram-based approach for microbarom radiation and propagation model assessment using infrasound recordings.
• Vera Rodriguez, Ismael; Näsholm, Sven Peter; Brissaud, Quentin; Turquet, Antoine Leo & Le Pichon, Alexis (2021). Estimation of infrasound-consistent wind and temperature atmospheric profiles from model ensembles in North Scandinavia. Show summary

  Atmospheric reanalysis models rely on the assimilation of direct and indirect measurements of different properties of the atmosphere. A better representation of the upper stratosphere in these models, especially for winds, can contribute to enhanced numerical weather predictions on weekly to monthly timescales. Thus, in the current work, we consider the problem of estimating an updated atmospheric model to become consistent with a set of infrasound array observations of travel-time, backazimuth, and apparent velocity.

• Amezcua, Javier; Näsholm, Sven Peter; Blixt, Erik Mårten & Charlton–Perez, Andrew (2020). Assimilation of Atmospheric Infrasound Data to Constrain Winds using an EnKF.
• Näsholm, Sven Peter (2020). Probing middle atmospheric winds using infrasound recorded at ground-based arrays.
• Näsholm, Sven Peter (2020). Probing middle atmospheric winds using infrasound recorded at ground-based arrays.
• Vera Rodriguez, Ismael; Näsholm, Sven Peter; Turquet, Antoine Leo & Evers, Läslo G. (2020). Climatology reflected by infrasound travel-times sampling the stratosphere in its transition between summer and winter.
• Belova, Evgenia; Näsholm, Sven Peter; Vorobeva, Ekaterina; Godin, Oleg A. & Barabash, Victoria (2020). Polar Mesosphere Winter Echoes and their relation to infrasound.
• Amezcua, Javier; Näsholm, Sven Peter; Blixt, Erik Mårten & Charlton-Perez, Andrew (2020). Assimilation of atmospheric infrasound data to constrain tropospheric and stratospheric winds.
• Vera Rodriguez, Ismael; Näsholm, Sven Peter & Le Pichon, Alexis (2020). Atmospheric model calibration using infrasound waves from explosions.
• Vorobeva, Ekaterina; De Carlo, Marine; Näsholm, Sven Peter & Le Pichon, Alexis (2020). Vespagram-based approach for benchmarking microbarom models and observations.
• Turquet, Antoine Léo; Kero, Johan; Brissaud, Quentin; Näsholm, Sven Peter; Kværna, Tormod & Le Pichon, Alexis (2020). In-depth seismo-acoustic analysis of mining-induced Mw 4.9 Kiruna earthquake.
• Näsholm, Sven Peter; Vorobeva, Ekaterina; Le Pichon, Alexis; Orsolini, Yvan; Turquet, Antoine Leo & Hibbins, Robert [Show all 10 contributors for this article] (2020). Semidiurnal tidal signatures in microbarom infrasound array measurements.
• Vorobeva, Ekaterina; Näsholm, Sven Peter; Espy, Patrick Joseph; Orsolini, Yvan & Hibbins, Robert (2020). Wind estimates in the mesosphere - lower thermosphere retrieved from infrasound data.
• Millet, Christophe; Ribstein, Bruno & Näsholm, Sven Peter (2019). Learning about small-scale atmospheric structures through recurrent infrasound events.
• Le Pichon, Alexis; De Carlo, Marine; Vergoz, Julien; Näsholm, Sven Peter; Espy, Patrick Joseph & Hibbins, Robert [Show all 7 contributors for this article] (2019). Characterizing middle atmosphere variability using ocean ambient noise as recorded by a regional infrasound network.
• Le Pichon, Alexis; De Carlo, Marine; Näsholm, Sven Peter; Kero, Johan; Ceranna, Lars & Hupe, Patrick [Show all 7 contributors for this article] (2019). Characterizing ocean ambient noise using a regional infrasound network: a sensitivity analysis.
• Dinescu, Raluca; Chica, Daniela; Schweitzer, Johannes; Näsholm, Sven Peter; Popa, Michaela & Ionescu, Constantin (2019). Monitoring man-made hazards using data recorded with the Romanian seismic and infrasonic arrays. Show summary

  Seismic events observed with the Romanian Seismic Network, operated by the National Institute for Earth Physics, are produced by various sources: earthquakes, mining and quarry blasts, thunderstorms, atmospheric and underground explosions. To monitor man-made seismic sources, data recorded by the Romanian seismic and infrasonic arrays deployed at Plostina seismo-acoustic site (PLOR and IPLOR stations) and at Bucovina seismo-acoustic site (BURAR and BURARI stations) are jointly analyzed in order to build an efficient tool for discrimination between anthropogenic and natural events, i.e. between explosions and tectonic earthquakes. At the same time, our work supports the attempt to clean the Romanian seismic catalogue from non-tectonic events. A specific methodology for the seismo-acoustic analysis has been developed. The main analysis steps consist of: (1) selection of natural and artificial reference events detected by seismo-acoustic arrays considered; (2) analysis of the infrasound detections using standard array processing methods – array data processing software “ep” – provided by NORSAR, in order to extract the signal features (backazimuth, apparent velocity, frequency content, amplitude, SNR); (3) analysis of the seismic detections using the same array data processing software, in order to extract the characteristics of their seismic signature (waveform shape, frequency content, amplitude, particle motion; (4) combination of the infrasonic detections with seismic ones in order to associate them with the reference events based on comparison of the backazimuth estimates and arrival time measurements with the theoretical/expected values and taking in account the effect of the atmospheric propagation conditions; (5) identification of the near-surface explosions produced in the local quarries using the analyzed seismo-acoustic signals and discrimination between these blasts and tectonic earthquakes. In the future we aim to extract templates of the seismo-acoustic signals generated by the man-made explosions and compare them with the continuously recorded waveforms in order to develop an automatic event identification process.

• De Carlo, Marine; Le Pichon, Alexis; Ardhuin, Fabrice; Näsholm, Sven Peter & Smets, Pieter (2019). Evaluating microbaroms source models in finite ocean depth: comparison with IMS station observations.
• Blixt, Erik Mårten; Näsholm, Sven Peter; Gibbons, Steven John & Kværna, Tormod (2019). Estimating tropospheric and stratospheric large-scale wind components using infrasound from explosions.
• Blanc, Elisabeth; Hauchecorne, Alain; Keckhut, Philippe; Le Pichon, Alexis; Baumgarten, Gerd & Stober, Gunter [Show all 23 contributors for this article] (2019). Atmospheric dynamics from near ground to near Earth space: The ARISE project.
• Blanc, Elisabeth; Le Pichon, Alexis; Pilger, Christoph; Hupe, Patrick; Ceranna, Lars & Marchetti, Emanuele [Show all 12 contributors for this article] (2019). ARISE project: infrasound monitoring for civil applications.
• Näsholm, Sven Peter; Assink, Jelle; Blixt, Erik Mårten; De Carlo, Marine; Evers, Läslo Gerardus & Gibbons, Steven John [Show all 11 contributors for this article] (2019). Observations of microbarom-generated infrasound in Northern Norway during three different sudden stratospheric warmings .
• Näsholm, Sven Peter (2019). Observations of microbarom-generated infrasound in Northern Norway during three different sudden stratospheric warmings.
• Gibbons, Steven John; Kværna, Tormod & Näsholm, Sven Peter (2019). CTBT Seismic Monitoring in Far East Asia using Coherent and Incoherent Array Processing.
• Marine, De Carlo; Le Pichon, Alexis; Vergoz, Julien; Ardhuin, Fabrice; Näsholm, Sven Peter & Ceranna, Lars [Show all 8 contributors for this article] (2019). Characterizing coherent ambient noise in the North Atlantic and Barents sea regions.
• Blixt, Erik Mårten; Charlton–Perez, Andrew; Evers, Läslo Gerardus; Gibbons, Steven John; Kværna, Tormod & Näsholm, Sven Peter [Show all 7 contributors for this article] (2019). Cross-wind effects on infrasound waves partially reflected at stratospheric altitudes.
• Näsholm, Sven Peter (2019). Exploiting low-frequency acoustic waves to probe middle atmospheric dynamics.
• Näsholm, Sven Peter (2019). NORSAR: Vi lytter til jorden for et sikrere samfunn.
• Näsholm, Sven Peter; Assink, Jelle; Blixt, Erik Mårten; De Carlo, Marine; Evers, Läslo G. & Gibbons, Steven John [Show all 11 contributors for this article] (2019). Observations of microbarom-generated infrasound in Northern Norway during three different sudden stratospheric warmings .
• Näsholm, Sven Peter; Assink, Jelle; Blanc, Elisabeth; Blixt, Erik Mårten; Claud, Chantal & Gibbons, Steven John [Show all 13 contributors for this article] (2018). Infrasonic signatures of polar lows - Comparing a decade of polar low tracks to infrasonic detection backazimuths.
• Näsholm, Sven Peter; Blixt, Erik Mårten; Gibbons, Steven John; Stettner, Felix Benedikt & Kværna, Tormod (2018). Interpreting explosive acoustic arrivals at the ARCES seismic array in the context of atmospheric cross-winds.
• Le Pichon, Alexis; Arnal, Thibault; Blixt, Erik Mårten; Näsholm, Sven Peter; Kero, Johan & Ceranna, Lars [Show all 7 contributors for this article] (2018). Characterizing ocean ambient noise using a regional infrasound network.
• Gibbons, Steven John; Näsholm, Sven Peter; Blixt, Erik Mårten & Kværna, Tormod (2018). Measuring infrasonic wavefronts over large aperture sensor arrays.
• Blixt, Erik Mårten; Näsholm, Sven Peter; Stettner, Felix Benedikt & Kværna, Tormod (2018). Cross-wind effects on infrasound propagation.
• Blixt, Erik Mårten; Näsholm, Sven Peter; Kværna, Tormod & Gibbons, Steven John (2018). Multi-station study of the cross-wind effect on infrasound propagation.
• Gibbons, Steven John; Kværna, Tormod; Näsholm, Sven Peter & Mykkeltveit, Svein (2018). Seismic Monitoring of the North Korea Nuclear Test-Site to Low Magnitude Using Seismic Pattern Detectors .
• Kühn, Daniela; Heimann, Sebastian; Näsholm, Sven Peter; Dando, Benjamin; Gharti, Hom Nath & Ruigrok, Elmer (2017). Uncertainties in moment tensor estimation for induced earthquakes illustrated at the example of the Groningen gas field, Netherlands.
• Lambert, Simon; Chatelin, Simon; Näsholm, Sven Peter; Jugé, Lauriane; Garteiser, Philippe & ter Beek, Leon [Show all 12 contributors for this article] (2013). Sub-Voxel Micro-Architecture Assessment by Scattering of Mechanical Shear Waves.
• Lambert, Simon; Chatelin, Simon; Näsholm, Sven Peter; Jugé, Lauriane; Garteiser, Philippe & ter Beek, Leon [Show all 12 contributors for this article] (2012). Sub-Voxel Micro-Architecture Assessment by Scattering of Mechanical Shear.
• Chatelin, Simon; Lambert, Simon; Jugé, Lauriane; Cai, Xing; Näsholm, Sven Peter & Vilgrain, Valérie [Show all 12 contributors for this article] (2012). Measured elasticity and its frequency dependence are sensitive to tissue microarchitecture in MR Elastography.
• Lambert, Simon; Chatelin, Simon; Näsholm, Sven Peter; Holm, Sverre & Sinkus, Ralph (2012). Sub-Voxel Micro-Architecture Assessment by Diffusion of Mechanical Shear.
• Näsholm, Sven Peter & Holm, Sverre (2012). A Fractional Acoustic Wave Equation from Multiple Relaxation Loss and Conservation Laws.
• Holm, Sverre; Näsholm, Sven Peter & Sinkus, Ralph (2012). Fractional acoustic wave equations from constitutive equations.
• Sinkus, Ralph; Holm, Sverre; Guzina, Bojan B.; Näsholm, Sven Peter; Garteiser, Philippe & Doblas, S [Show all 8 contributors for this article] (2011). Revealing the origin of attenuation in tissue: pure absorption or multiple scattering?
• Prieur, Fabrice Jean Gabriel; Näsholm, Sven Peter; Austeng, Andreas & Holm, Sverre (2011). Second harmonic imaging with echo-sounders: measurements and preliminary results.
• Prieur, Fabrice Jean Gabriel; Näsholm, Sven Peter; Austeng, Andreas & Holm, Sverre (2010). Second harmonic imaging a possibility with sonar?
• Prieur, Fabrice Jean Gabriel; Näsholm, Sven Peter; Austeng, Andreas & Holm, Sverre (2010). Exploiting nonlinear propagation in echo sounders and sonar. Full text in Research Archive
• Måsøy, Svein-Erik; Tangen, Thor Andreas; Standal, Øyvind; Deibele, Jochen; Näsholm, Sven Peter & Hansen, Rune [Show all 8 contributors for this article] (2009). SURF imaging - Acoustics from a dual-frequency band annular array.
• Måsøy, Svein-Erik; Tangen, Thor Andreas; Standal, Øyvind; Deibele, Jochen; Näsholm, Sven Peter & Hansen, Rune [Show all 8 contributors for this article] (2009). SURF imaging - A real time dual-frequency band ultrasound system.
• Måsøy, Svein-Erik; Tangen, Thor Andreas; Standal, Øyvind; Deibele, Jochen; Näsholm, Sven Peter & Hansen, Rune [Show all 8 contributors for this article] (2009). SURF imaging - Acoustics from a dual-frequency band annular array.
• Måsøy, Svein-Erik; Tangen, Thor Andreas; Standal, Øyvind; Deibele, Jochen; Näsholm, Sven Peter & Hansen, Rune [Show all 8 contributors for this article] (2009). SURF imaging - A real time dual-frequency band ultrasound system.
• Näsholm, Sven Peter; Kaupang, Halvard; Måsøy, Svein-Erik; Hansen, Rune & Angelsen, Bjørn Atle J. (2008). A simulation study on SURF reverberation suppression in an aberrating medium.
• Måsøy, Svein-Erik; Hansen, Rune; Angelsen, Anders; Kaupang, Halvard; Tangen, Thor Andreas & Standal, Øyvind [Show all 9 contributors for this article] (2008). SURF IMAGING – High-frequency ultrasound contrast agent imaging in patients with prostate cancer. Show summary

  A dual-band method for ultrasound contrast agent detection is demonstrated in vivo in patients with prostate cancer. The method is named Second-Order UltRasound Field Imaging, with the acronym SURF Imaging. It relies on simultaneously transmitting two ultrasound pulses with a large separation in frequency. Here, a low-frequency pulse of 0.9 MHz is combined with a high-frequency pulse of 7.5 MHz. The low-frequency pulse is used to manipulate the properties of the contrast agent, and the high-frequency pulse is used for high-resolution contrast imaging. An annular array capable of transmitting the low- and high-frequency pulses simultaneously was constructed and fitted to a mechanically scanned probe used in a GE Vingmed System 5 ultrasound scanner. The scanner was modified and adapted for the dual-band transmit technique. In-house software was written for post-processing of recorded IQ-data, thus real-time imaging was not possible. Generally, the method decouples the contrast agent detection frequency from the resonance frequency of the microbubbles, allowing imaging at clinically-high frequencies. The low-frequency pulse is used (e.g. 0.5-2 MHz) to manipulate the properties of the contrast agent around its resonance frequency, changing the back-scattering from the high-frequency pulse (e.g. 3-14 MHz) which is used for high-resolution detection. The general principle of insonifying ultrasound contrast agents with the above described pulse complex is also known as Radial Modulation Imaging in the literature. Here, the name SURF Imaging is used to recognize the fact that transmitting such a pulse complex also infers changes in the forward generated tissue nonlinearities which needs to be accounted for. The low-frequency manipulation pulse generates a local change in the speed of sound experienced by the high-frequency pulse. In the data presented here, this effect is estimated and compensated in the obtained images. The results present contrast-processed B-mode images from patients enrolled in an ongoing pilot study aimed at imaging prostate cancer using ultrasound contrast agents. The study is approved by the local ethics committee and the patients provide written informed consent. The obtained images show contrast agent detection in the prostate with a transmit frequency of 7.5 MHz, demonstrating that SURF imaging works well in a clinical setting. Due to scanner limitations in IQ-data storage, wash-in curves were not possible to obtain. Images displaying Maximum Intensity Projections (MIP) are presented, demonstrating areas of high contrast activity in regions with positive biopsy findings in patients with locally advanced prostate cancer (T3) and aggressive growth patterns (Gleason score 9). The results demonstrate the potential of SURF Imaging as an ultrasound contrast detection technique in a clinical setting for high ultrasound frequencies.

• Måsøy, Svein-Erik; Kaupang, Halvard; Tangen, Thor Andreas; Standal, Øyvind; Näsholm, Sven Peter & Johansen, Tonni Franke [Show all 8 contributors for this article] (2007). SURF IMAGING – IN VIVO DEMONSTRATION OF AN ULTRASOUND CONTRAST AGENT DETECTION TECHNIQUE IN PATIENTS WITH PROSTATE CANCER AND THYROID NODULES. Show summary

  A dual-band method for ultrasound contrast agent detection is demonstrated in vivo in patients with prostate cancer and thyroid nodules. The method is named Second-Order UltRasound Field Imaging, with the acronym SURF Imaging. It relies on simultaneously transmitting two ultrasound pulses with a large separation in frequency. Here, a low-frequency pulse of 0.9 MHz is combined with a high-frequency pulse of 7.5 MHz. The low-frequency pulse is used to manipulate the properties of the contrast agent, and the high-frequency pulse is used for high-resolution contrast imaging. An annular array capable of transmitting the low- and high-frequency pulses simultaneously was constructed and fitted to a mechanically scanned probe used in a GE Vingmed System 5 ultrasound scanner. The scanner was modified and adapted for the dual-band transmit technique. In-house software was written for post-processing of recorded IQ-data, thus real-time imaging was not possible. Generally, the method decouples the contrast agent detection frequency from the resonance frequency of the microbubbles, allowing imaging at clinically-high frequencies. The low-frequency pulse is used (e.g. 0.5-2 MHz) to manipulate the properties of the contrast agent around its resonance frequency, changing the back-scattering from the high-frequency pulse (e.g. 3-14 MHz) which is used for high-resolution detection. The general principle of insonifying ultrasound contrast agents with the above described pulse complex is also known as Radial Modulation Imaging in the literature. Here, the name SURF Imaging is used to recognize the fact that transmitting such a pulse complex also infers changes in the forward generated tissue nonlinearities which needs to be accounted for. The low-frequency manipulation pulse generates a local change in the speed of sound experienced by the high-frequency pulse. In the data presented here, this effect is estimated and compensated in the obtained images. The results present contrast-processed B-mode images from patients enrolled in two ongoing pilot studies, aimed at imaging prostate cancer and thyroid nodules respectively. The studies are approved by the local ethics committee and the patients provide written informed consent. The obtained images show contrast agent detection in both cases, demonstrating that SURF imaging works well in a clinical setting. For the studied thyroid nodules, contrast-to-tissue ratios ranging from 15-20 dB was obtained, and wash-in curves of contrast agents within a region-of-interest are presented. For the prostate cases, due to scanner limitations in IQ-data storage, wash-in curves were not possible to obtain. Images displaying Maximum Intensity Projections are shown for both categories of patients. The results demonstrate the potential of SURF Imaging as an ultrasound contrast detection technique in a clinical setting for high ultrasound frequencies.

• Hansen, Rune; Måsøy, Svein-Erik; Näsholm, Sven Peter; Standal, Øyvind; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2007). SURF imaging for ultrasound contrast agents.
• Hansen, Rune; Måsøy, Svein-Erik; Standal, Øyvind; Näsholm, Sven Peter; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2007). Improving contrast agent detection with SURF imaging.
• Kaupang, Halvard; Näsholm, Sven Peter; Måsøy, Svein-Erik & Angelsen, Bjørn Atle J. (2007). Sound Field Simulation Activities.
• Hansen, Rune; Johansen, Tonni Franke; Måsøy, Svein-Erik; Näsholm, Sven Peter; Standal, Øyvind & Angelsen, Bjørn Atle J. (2006). SURF - A better method to detect ultrasound contrast agents and micro-calcifications.
• Måsøy, Svein-Erik; Hansen, Rune; Näsholm, Sven Peter; Standal, Øyvind; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2006). SURF IMAGING – A METHOD FOR HIGH FREQUENCY ULTRASOUND CONTRAST AGENT DETECTION.
• Måsøy, Svein-Erik; Näsholm, Sven Peter; Standal, Øyvind; Johansen, Tonni Franke; Hansen, Rune & Angelsen, Bjørn Atle J. (2006). ACOUSTIC NOISE IN MEDICAL ULTRASOUND IMAGING – CHALLENGES AND SOLUTIONS.
• Näsholm, Sven Peter; Hansen, Rune; Måsøy, Svein-Erik; Standal, Øyvind; Johansen, Tonni Franke & Angelsen, Bjørn (2006). Reverberation suppression using SURF as an alternative to second harmonic.
• Näsholm, Sven Peter; Johansen, Tonni Franke & Angelsen, Bjørn Atle J. (2004). Effect of a Curved Dome on the Effective Foci of an Annular Array - Numerical Simulations and Experimental Measurements. Show summary

  A numerical method to estimate the {effective focus} and {effective aperture} changes when a geometrically pre-focused ultrasound annular array is placed inside a curved fluid filled dome is developed. The method is based on ray tracing. The {effective element} hypothesis and our numerical method to calculate it are verified by comparing simulated ultrasound fields for the following two cases: 1) The {real elements} in the inhomogeneous dome fluid/dome plastic/tissue medium. 2) The {effective elements} in a homogeneous medium. The ultrasonic fields both along the x- and z axes are found to be very similar within each array element's active region. The focus moving effect prediction from the effective element model is verified by water tank ultrasound field hydrophone measurements of the on-axis z fields from elements of an array disposed in a fluid filled dome.

• Kühn, Daniela; Goertz-Allmann, Bettina; Albaric, Julie; Bohloli, Bahman; Braathen, A. & Brenguier, Florent [Show all 22 contributors for this article] (2017). Final project report to KMB project 224880: SafeCO2 II 2013-2016 Investigation of induced seismicity and aseismic deformation in response to CO2 injection and related pressure changes . Final project report to industry partners, NORSAR report no. 16-022.
• Näsholm, Sven Peter & Angelsen, Bjørn Atle J. (2008). Ultrasound beams for enhanced image quality. Norges teknisk-naturvitenskapelige universitet, Det medisinske fakultet. ISSN 978-82-471-9144-6. Show summary

  The contents of this thesis consider new methods for generating ultrasound beams for enhanced image quality in medical imaging. The results presented are produced through computer simulations. The thesis consists of an introductory chapter and four papers, which are all intended to be individually readable. Chapter 1 gives a brief overview of ultrasound and medical ultrasound imaging, as well as different aspects of ultrasound image quality and acoustic noise. A non-linear wave equation is presented and analyzed. This equation describes ultrasound propagation within, and interaction with tissue. In Paper A, a transducer annular array design method is presented. The method involves a geometric pre-focusing, which may vary between the array elements. This is useful for producing narrow receive beams within a large imaging depth window. It is advantageous for avoiding problems that occur when combining high frequencies and large receive apertures when utilizing the conventional equal-area design method. Paper B introduces a method to produce synthetic transmit beams that are useful for suppression of reverberation noise caused by multiple scattering of the forward-propagating imaging pulse. This is done through combination of two transmit pulse complexes denoted Second order UltRasound Field (SURF). Each such complex consists of a conventional high-frequency imaging pulse added to a low-frequency sound-speed manipulation pulse. The SURF transmit beam is generated by forming the difference between the propagated fields, filtered around the imaging frequency. This beam has suppressed amplitude near the transducer, where a reflection-generating body-wall is often present during in vivo imaging. Furthermore, a method to produce a combined second-harmonic pulse inversion (PI) and SURF beam is also presented, here denoted SURF-PI. Two imaging setups are defined for which the feasibility of the method is tested through simulations in case of propagation through homogeneous tissue. SURF beams and combined SURF-PI beams are compared to fundamental imaging and PI imaging beams for the two setups. The SURF-PI beams are the most suppressed in the near-field, followed by the approximately equally suppressed SURF and PI beams. The signal level within the imaging depth region becomes higher for SURF than for PI. In Paper C, two signal processing methods for further adjustment of the SURF beams are introduced. This is achieved through post-processing, either by application of a time-shift, or of a general filter, to one of the propagated fields. The processing is done prior to carrying out the subtraction that is done to form the SURF beam. This provides a flexible way of adjustment to choose the depth position where the scattering sources wished to be suppressed are located. Different adjustments may be realized without need for re-transmission or resumed propagation of the SURF pulse complexes. The post-processing methods are applied to a dataset generated for Paper B. Adjusted transmit beam examples are presented and their reverberation suppression abilities are compared to non-adjusted SURF. In Paper D, the feasibility study of the SURF beam generation as presented in Paper B, and its post-processing adjustment as presented in Paper C, are enlarged to include propagation within an inhomogeneous medium where a body-wall model producing severe aberration delays is present. It is shown that both the generation of the SURF beams and the post-processing adjustment are attainable under the modeled conditions.

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