Odd Kolbjørnsen

• Greiner, Thomas André Larsen; Lie, Jan Erik; Kolbjørnsen, Odd; Evensen, Andreas Kjelsrud; Nilsen, Espen Harris & Zhao, Hao [Show all 8 contributors for this article] (2021). Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction. Geophysics. ISSN 0016-8033. 87(2). doi: 10.1190/geo2021-0099.1. Full text in Research Archive Show summary

  In 3D marine seismic acquisition, the seismic wavefield is not sampled uniformly in the spatial directions. This leads to a seismic wavefield consisting of irregularly and sparsely populated traces with large gaps between consecutive sail-lines especially in the near-offsets. The problem of reconstructing the complete seismic wavefield from a subsampled and incomplete wavefield, is formulated as an underdetermined inverse problem. We investigate unsupervised deep learning based on a convolutional neural network (CNN) for multidimensional wavefield reconstruction of irregularly populated traces defined on a regular grid. The proposed network is based on an encoder-decoder architecture with an overcomplete latent representation, including appropriate regularization penalties to stabilize the solution. We proposed a combination of penalties, which consists of the L2-norm penalty on the network parameters, and a first- and second-order total-variation (TV) penalty on the model. We demonstrate the performance of the proposed method on broad-band synthetic data, and field data represented by constant-offset gathers from a source-over-cable data set from the Barents Sea. In the field data example we compare the results to a full production flow from a contractor company, which is based on a 5D Fourier interpolation approach. In this example, our approach displays improved reconstruction of the wavefield with less noise in the sparse near-offsets compared to the industry approach, which leads to improved structural definition of the near offsets in the migrated sections.

• Sandnes, Anders T.; Grimstad, Bjarne Andre & Kolbjørnsen, Odd (2021). Multi-task learning for virtual flow metering. Knowledge-Based Systems. ISSN 0950-7051. 232, p. 1–10. doi: 10.1016/j.knosys.2021.107458.
• Grimstad, Bjarne Andre; Hotvedt, Mathilde; Sandnes, Anders Thoresen; Kolbjørnsen, Odd & Imsland, Lars Struen (2021). Bayesian neural networks for virtual flow metering: An empirical study. Applied Soft Computing. ISSN 1568-4946. 112. doi: 10.1016/j.asoc.2021.107776.
• Greiner, Thomas Larsen; Hlebnikov, Volodya; Lie, Jan Erik; Kolbjørnsen, Odd; Kjeldsrud Evensen, Andreas & Harris Nilsen, Espen [Show all 8 contributors for this article] (2020). Cross-streamer wavefield reconstruction through wavelet domain. Geophysics. ISSN 0016-8033. 85(6), p. V457–V471. doi: 10.1190/geo2019-0771.1. Full text in Research Archive
• Bugge, Aina Juell; Lie, Jan Erik; Evensen, Andreas Kjelsrud; Nilsen, Espen Harris; Kolbjørnsen, Odd & Faleide, Jan Inge (2020). Data-driven identification of stratigraphic units in 3D seismic data usin hierarchical density-based clustering. Geophysics. ISSN 0016-8033. 85(5), p. IM15–IM26. doi: 10.1190/geo2019-0413.1.
• Kolbjørnsen, Odd; Buland, Arild; Hauge, Ragnar; Røe, Per; Ndingwan, Abel Onana & Aker, Eyvind (2020). Bayesian seismic inversion for stratigraphic horizon, lithology, and fluid prediction. Geophysics. ISSN 0016-8033. 85(3), p. R207–R221. doi: 10.1190/geo2019-0170.1. Full text in Research Archive Show summary

  We have developed an efficient methodology for Bayesian prediction of lithology and pore fluid, and layer-bounding horizons, in which we include and use spatial geologic prior knowledge such as vertical ordering of stratigraphic layers, possible lithologies and fluids within each stratigraphic layer, and layer thicknesses. The solution includes probabilities for lithologies and fluids and horizons and their associated uncertainties. The computational cost related to the inversion of large-scale, spatially coupled models is a severe challenge. Our approach is to evaluate all possible lithology and fluid configurations within a local neighborhood around each sample point and combine these into a consistent result for the complete trace. We use a one-step nonstationary Markov prior model for lithology and fluid probabilities. This enables prediction of horizon times, which we couple laterally to decrease the uncertainty. We have tested the algorithm on a synthetic case, in which we compare the inverted lithology and fluid probabilities to results from other algorithms. We have also run the algorithm on a real case, in which we find that we can make high-resolution predictions of horizons, even for horizons within tuning distance from each other. The methodology gives accurate predictions and has a performance making it suitable for full-field inversions.

• Kolbjørnsen, Odd; Evensen, Andreas Kjelsrud; Nilsen, Espen Harris & Lie, Jan Erik (2019). Digital superresolution in seismic AVO inversion. The Leading Edge. ISSN 1070-485X. 38(10), p. 742–820. doi: 10.1190/tle38100791.1. Full text in Research Archive
• Kolbjørnsen, Odd & Evensen, Andreas Kjelsrud (2019). Digital superresolution in seismic amplitude processing. SEG technical program expanded abstracts. ISSN 1949-4645. doi: 10.1190/segam2019-3214317.1. Full text in Research Archive
• Greiner, Thomas Larsen; Kolbjørnsen, Odd; Lie, Jan Erik; Harris Nilsen, Espen; Kjeldsrud Evensen, Andreas & Gelius, Leiv-J. (2019). Cross-streamer wavefield interpolation using deep convolutional networks. In SEG, . (Eds.), SEG Technical Program Expanded Abstracts 2019. SEG. ISSN 0916160009. p. 2207–2211. doi: https%3A/doi.org/10.1190/segam2019-3214009.1. Full text in Research Archive
• Ndingwan, Abel Onana; Kolbjørnsen, Odd; Straith, Knut Richard & Bjerke, Morten D. (2018). Deciphering the seismic signature of the Edvard Grieg field, North Sea. SEG technical program expanded abstracts. ISSN 1949-4645. doi: 10.1190/segam2018-2994746.1. Full text in Research Archive
• Vigsnes, Maria; Kolbjørnsen, Odd; Hauge, Vera Louise; Dahle, Pål & Abrahamsen, Petter (2017). Fast and Accurate Approximation to Kriging Using Common Data Neighborhoods. Mathematical Geosciences. ISSN 1874-8961. 49(5), p. 619–634. doi: 10.1007/s11004-016-9665-7. Show summary

  Unknown values of a random field can be predicted from observed data using kriging. As data sets grow in size, the computation times become large. To facilitate kriging with large data sets, an approximation where the kriging is performed in sub-segments with common data neighborhoods has been developed. It is shown how the accuracy of the approximation can be controlled by increasing the common data neighborhood. For four different variograms, it is shown how large the data neighborhoods must be to get an accuracy below a chosen threshold, and how much faster these calculations are compared to the kriging where all data are used. Provided that variogram ranges are small compared to the domain of interest, kriging with common data neighborhoods provides excellent speed-ups (2–40) while maintaining high numerical accuracy. Results are presented both for data neighborhoods where the neighborhoods are the same for all sub-segments, and data neighborhoods where the neighborhoods are adapted to fit the data densities around the sub-segments. Kriging in sub-segments with common data neighborhoods is well suited for parallelization and the speed-up is almost linear in the number of threads. A comparison is made to the widely used moving neighborhood approach. It is demonstrated that the accuracy of the moving neighborhood approach can be poor and that computational speed can be slow compared to kriging with common data neighborhoods.

• Jullum, Martin & Kolbjørnsen, Odd (2016). A Gaussian-based framework for local Bayesian inversion of geophysical data to rock properties. Geophysics. ISSN 0016-8033. 81(3), p. R75–R87. doi: 10.1190/geo2015-0314.1.
• Kolbjørnsen, Odd; Buland, Arild; Hauge, Ragnar; Røe, Per; Jullum, Martin & Metcalfe, Richard William [Show all 7 contributors for this article] (2016). Bayesian AVO inversion to rock properties using a local neighborhood in a spatial prior model. The Leading Edge. ISSN 1070-485X. 35(5), p. 431–436. doi: 10.1190/tle35050431.1. Show summary

  The spatial structure of the subsurface is an important factor when interpreting seismic data. The Bayesian methodology is a valuable tool for integrating these spatial relations in the inversion process as it merges the information together and assesses the uncertainty of the model. In the everyday use of the Bayesian methodology, however, the computational cost is a challenge. We describe a new approach that utilizes a local neighborhood to include the spatial constraints and assess the uncertainties in the inversion using fast and parallelizable computations. The approach is applicable for both discrete lithology-fluid prediction and estimation of rock properties, such as porosity and saturation.

• Jullum, Martin & Kolbjørnsen, Odd (2015). A Gaussian-based framework for local Bayesian inversion of geophysical data to rock properties. Geophysics. ISSN 0016-8033. 81(3), p. R75–R87. doi: 10.1190/GEO2015-0314.1.
• Hauge, Vera Louise & Kolbjørnsen, Odd (2015). Bayesian inversion of gravimetric data and assessment of CO2 dissolution in the Utsira Formation. Interpretation. ISSN 2324-8858. 3(2), p. SP1–SP10. doi: 10.1190/INT-2014-0193.1. Show summary

  Offshore gravimetric monitoring has been introduced as a complement to seismic monitoring of fields with moving fluids. The Sleipner field in the North Sea is a fully operational carbon capture and storage facility, where CO2 is injected for storage. Gravimetric measurements are one of the geophysical monitoring methods applied, and the data have been used to estimate the in situ density and dissolution of the CO2. We defined a Bayesian inversion of gravimetric data, and we used this to analyze gravimetric data at Sleipner field. In our approach, we included spatial uncertainty in the model and performed a Bayesian analysis of the in situ CO2 density and dissolution. We also analyzed the impact of mass changes due to gas production from the Ty Formation. Our estimates were comparable with published results.

• Hauge, Vera Louise & Kolbjørnsen, Odd (2014). Spatial Resolution in Bayesian Inversion of Gravimetric Data. In EAGE2014, (Eds.), Conference proceedings. 76th EAGE Conference & Exhibition. European Association of Geoscientists and Engineers (EAGE). ISSN 978-90-73834-89-7. doi: 10.3997/2214-4609.20141001.
• Kolbjørnsen, Odd; Stien, Marita; Kjønsberg, Heidi; Fjellvoll, Bjørn & Abrahamsen, Petter (2013). Using Multiple Grids in Markov Mesh Facies Modeling. Mathematical Geosciences. ISSN 1874-8961. 46(2), p. 205–225. doi: 10.1007/s11004-013-9499-5. Show summary

  A multigrid Markov mesh model for geological facies is formulated by defining a hierarchy of nested grids and defining a Markov mesh model for each of these grids. The facies probabilities in the Markov mesh models are formulated as generalized linear models that combine functions of the grid values in a sequential neighborhood. The parameters in the generalized linear model for each grid are estimated from the training image. During simulation, the coarse patterns are first laid out, and by simulating increasingly finer grids we are able to recreate patterns at different scales. The method is applied to several tests cases and results are compared to the training image and the results of a commercially available snesim algorithm. In each test case, simulation results are compared qualitatively by visual inspection, and quantitatively by using volume fractions, and an upscaled permeability tensor. When compared to the training image, the method produces results that only have a few percent deviation from the values of the training image. When compared with the snesim algorithm the results in general have the same quality. The largest computational cost in the multigrid Markov mesh is the estimation of model parameters from the training image. This is of comparable CPU time to that of creating one snesim realization. The simulation of one realization is typically ten times faster than the estimation.

• Hammer, Hugo Lewi; Kolbjørnsen, Odd; Tjelmeland, Håkon & Buland, Arild (2012). Lithology and fluid prediction from prestack seismic data using a Bayesian model with Markov process prior. Geophysical Prospecting. ISSN 0016-8025. 60(3), p. 500–515. doi: 10.1111/j.1365-2478.2011.01012.x.
• Buland, Arild & Kolbjørnsen, Odd (2012). Bayesian inversion of CSEM and magnetotelluric data. Geophysics. ISSN 0016-8033. 77(1), p. E33–E42. doi: 10.1190/GEO2010-0298.1. Show summary

  We have developed a Bayesian methodology for inversion of controlled source electromagnetic (CSEM) data and magnetotelluric (MT) data. The inversion method provided optimal solutions and also the associated uncertainty for any sets of electric and magnetic components and frequencies from CSEM and MT data. The method is based on a 1D forward modeling method for the electromagnetic (EM) response for a plane-layered anisotropic earth model. The inversion method was also designed to invert common midpoint (CMP)-sorted data along a 2D earth profile assuming locally horizontal models in each CMP position. The inversion procedure simulates from the posterior distribution using a Markov chain Monte Carlo (McMC) approach based on the Metropolis-Hastings algorithm. The method that we use integrates available geologic prior knowledge with the information in the electromagnetic data such that the prior model stabilizes and constrains the inversion according to the described knowledge. The synthetic examples demonstrated that inclusion of more data generally improves the inversion results. Compared to inversion of the inline electric component only, inclusion of broadside and magnetic components and an extended set of frequency components moderately decreased the uncertainty of the inversion. The results were strongly dependent on the prior knowledge imposed by the prior distribution. The prior knowledge about the background resistivity model surrounding the target was highly important for a successful and reliable inversion result.

• Kolbjørnsen, Odd; Hauge, Ragnar; Drange-Espeland, Maren & Buland, Arild (2012). Model-based fluid factor for controlled source electromagnetic data. Geophysics. ISSN 0016-8033. 77(1), p. E21–E31. doi: 10.1190/GEO2010-0300.1. Show summary

  We have developed a new Bayesian methodology for use of controlled source electromagnetic (CSEM) data in prospect risking. The methodology modifies the probability for hydrocarbon presence based on the information in the CSEM data. This is done by identifying the linear combination of the data where the weighted sum provides the optimal separation of cases with and without hydrocarbons. The weighted sum of the CSEM data is a model-based parallel to the well-known fluid factor used in seismic amplitude analysis. The optimal weighting is constructed based on forward modeling of models with and without hydrocarbons. We further compute the statistical distributions of the fluid factor with and without hydrocarbon presence, and use these distributions to compute the value of CSEM data and update the probability for hydrocarbon presence. The method does not involve inversion for the complete resistivity model but computes the chance of hydrocarbon presence directly. The method was tested on data from Troll, where it provided evidence for hydrocarbon presence, and on another data set, where it provided evidence against hydrocarbons. These real case examples showed the importance of rock physical knowledge. Improved control on the rock properties leads to stronger conclusions and higher value of the CSEM data. The proposed model-based approach is fast and robust.

• Stien, Marita & Kolbjørnsen, Odd (2011). Facies Modeling Using a Markov Mesh Model Specification. Mathematical Geosciences. ISSN 1874-8961. 43(6), p. 611–624. doi: 10.1007/s11004-011-9350-9.
• Buland, Arild; Kolbjørnsen, Odd & Carter, Andrew J. (2011). Bayesian Dix inversion. Geophysics. ISSN 0016-8033. 76(2), p. R15–R22. doi: 10.1190/1.3552596.
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). A 3D Ray-based Pulse Estimation for Seismic Inversion of PSDM Data. In EAGE, 2010 (Eds.), 72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010 Barcelona. European Association of Geoscientists and Engineers (EAGE). ISSN 978-90-73781-86-3.
• Kjønsberg, Heidi; Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2010). Bayesian Monte Carlo method for seismic predrill prospect assessment. Geophysics. ISSN 0016-8033. 75(2), p. O9–O19. doi: 10.1190/1.3339678.
• Tveranger, Jan; Howell, John Anthony; Aanonsen, Sigurd Ivar; Kolbjørnsen, Odd; Semshaug, Siv Lise & Skorstad, Arne [Show all 7 contributors for this article] (2008). Assessing structural controls on reservoir performance in different stratigraphic settings. In Robinson, A; Griffiths, P.; Hegre, J. & Muggeridge, A. (Ed.), The future of geological modelling in hydrocarbon development. Geological Society of London. ISSN 978-1862392663. p. 51–66.
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2008). Markov Mesh Simulations with Data Conditioning through Indicator Kriging. In Ortiz, Julian M. & Emery, Xavier (Ed.), Proceedings of the Eight International Geostatistics Congress. GECAMIN. ISSN 978-956-8504-17-5. p. 257–266.
• Kolbjørnsen, Odd & Stien, Marita (2008). D-vine Creation of Non-Gaussian Random Field. In Ortiz, Julian & Emery, Xavier (Ed.), Procedings of the Eight International Geostatistics Congress Volume 1. GECAMIN. ISSN 978-956-8504-18-2. p. 399–408.
• Skorstad, Arne; Kolbjørnsen, Odd; Manzocchi, Tom; Carter, Jonathan N. & Howell, John (2008). Combined effects of structural, stratigraphic and well controls on production variability in faulted shallow marine reservoirs. Petroleum Geoscience. ISSN 1354-0793. 14.01.2012, p. 45–54.
• Buland, Arild; Kolbjørnsen, Odd; Hauge, Ragnar; Skjæveland, Øyvind & Duffaut, Kenneth (2008). Bayesian lithology and fluid prediction from seismic prestack data. Geophysics. ISSN 0016-8033. 73(3), p. C13–C21. doi: 10.1190/1.2842150.
• Skorstad, Arne; Kolbjørnsen, Odd; Manzocchi, T; Carter, Jonathan N. & Howell, John Anthony (2008). Combined effects of structural, stratigraphic and well controls on production variability in faulted shallow-marine reservoirs. Petroleum Geoscience. ISSN 1354-0793. 14(1), p. 45–54.
• Manzocchi, T; Carter, JN; Skorstad, Arne; Fjellvoll, Bjørn; Stephen, KD & Howell, JA [Show all 27 contributors for this article] (2008). Sensitivity of the impact of geological uncertainty on production from faulted and unfaulted shallow-marine oil reservoirs: objectives and methods. Petroleum Geoscience. ISSN 1354-0793. 14(1), p. 3–15. Show summary

  Estimates of recovery from oil fields are often found to be significantly in error, and the multidisciplinary SAIGUP modelling project has focused on the problem by assessing the influence of geological factors on production in a large suite of synthetic shallow-marine reservoir models. Over 400 progradational shallow-marine reservoirs, ranging from comparatively simple, parallel, wave-dominated shorelines through to laterally heterogeneous, lobate, river-dominated systems with abundant low-angle clinoforms, were generated as a function of sedimentological input conditioned to natural data. These sedimentological models were combined with structural models sharing a common overall form but consisting of three different fault systems with variable fault density and fault permeability characteristics and a common unfaulted end-member. Different sets of relative permeability functions applied on a facies-by-facies basis were calculated as a function of different lamina-scale properties and upscaling algorithms to establish the uncertainty in production introduced through the upscaling process. Different fault-related upscaling assumptions were also included in some models. A waterflood production mechanism was simulated using up to five different sets of well locations, resulting in simulated production behaviour for over 35 000 full-field reservoir models. The model reservoirs are typical of many North Sea examples, with total production ranging from c. 15×106 m3 to 35×106 m3, and recovery factors of between 30% and 55%. A variety of analytical methods were applied. Formal statistical methods quantified the relative influences of individual input parameters and parameter combinations on production measures. Various measures of reservoir heterogeneity were tested for their ability to discriminate reservoir performance. This paper gives a summary of the modelling and analyses described in more detail in the remainder of this thematic set of papers.

• Hollund, Knut Utne; Kolbjørnsen, Odd; Syversveen, Anne Randi; Lie, Tove & Jørstad, Arild (2007). Using "Fast Models" for Selecting the Right Decision - A Norwegian North Sea Case Study. In SPE, Society of Petroleum Engineers (Eds.), SPE Annual Technical Conference and Exhibition, 11-14 November 2007, Anaheim, California, U.S.A. Society of Petroleum Engineers. ISSN 978-1-55563-148-2.

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• Abrahamsen, Petter; Kolbjørnsen, Odd & Hauge, Ragnar (2012). Geostatistics Oslo 2012. Springer. ISBN 978-94-007-4152-2. 573 p.

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• Greiner, Thomas Larsen; Kolbjørnsen, Odd; Lie, Jan Erik; Nilsen, Espen Harris; Evensen, Andreas Kjelsrud & Gelius, Leiv-J. (2019). Cross-streamer wavefield interpolation using deep convolutional neural network.
• Kolbjørnsen, Odd & Evensen, Andreas Kjelsrud (2019). Digital superresolution in seismic amplitude processing.
• Kolbjørnsen, Odd; Dahle, Pål; Bjerke, Morten D.; Bakke, Beate A. & Straith, Knut Richard (2019). Using Deep Directional Resistivity for Model Selection and Uncertainty Reduction in the Edvard Grieg Depth Conversion.
• Røe, Per; Kolbjørnsen, Odd & Hauge, Ragnar (2019). Comparison of one- and two-step seismic inversion for Lithology and Fluid prediction.
• Ndingwan, Abel Onana; Kolbjørnsen, Odd; Straith, Knut Richard & Bjerke, Morten (2018). Deciphering the seismic signature of the Edvard Grieg field, North Sea.
• Kolbjørnsen, Odd; Ndingwan, Abel Onana; Straith, Knut Richard; Aker, Eyvind & Røe, Per (2017). Deciphering the seismic AVO response of the reservoir at Edvard Grieg .
• Røe, Per & Kolbjørnsen, Odd (2017). Comparison of one- and two-step seismic inversion for lithology and fluid prediction.
• Skjæveland, Øyvind M.; Metcalfe, Richard William; Kolbjørnsen, Odd; Røe, Per & Hauge, Ragnar (2016). Pcube+ - high-resolution horizon update by prestack inversion, a Statfjord case history.
• Jullum, Martin & Kolbjørnsen, Odd (2015). An Approximate Bayesian Inversion Framework based on Local-gaussian Likelihoods.
• Vigsnes, Maria; Abrahamsen, Petter; Hauge, Vera Louise & Kolbjørnsen, Odd (2015). Efficient Neighborhoods for Kriging with Numerous Data.
• Hauge, Vera Louise & Kolbjørnsen, Odd (2014). Spatial Resolution in Bayesian Inversion of Gravimetric Data. Show summary

  CO2 capture and storage of CO2 in geological structures are important parts in reaching the targets of the International Energy Agency on cutting CO2 emissions related to energy. Quantitative descriptions of the development of an underground gas plume is important both to ensure public safety and to gain general support for underground storage. Methods for a quantitative prediction of the distributions of the subsurface CO2 are developed, using statistical models as a key tool for integrating data within physical models. In this presentation Bayesian inversion of gravimetric data is described and through an example with synthetic data we illustrate the power of the method. We quantify what we learn from the data in terms of best estimate and what remains undetermined by providing the uncertainty. This knowledge is crucial for integrating gravimetric data in a joint inversion with seismic data. The results show that the gravimetric data carry information about low-frequent components in the density change and that gravimetric inversion alone is not sufficient for inferring local details. However, the data can verify properties on a larger scale, such as average density change.

• Kolbjørnsen, Odd; Ulvmoen, Marit; Hauge, Vera Louise; Hauge, Ragnar; Fjellvoll, Bjørn & Jensen, Erling Hugo [Show all 11 contributors for this article] (2013). Monitoring Geological CO2 storage.
• Kolbjørnsen, Odd; MacDonald, Alister; Skorstad, Arne & Berg, Thomas (2012). Estimating the Cloud Transform.
• Nair, Krishnakumar Narayanan; Kolbjørnsen, Odd & Skorstad, Arne (2012). Seismic inversion and its applications in reservoir characterization. First Break. ISSN 0263-5046. 30(3), p. 83–86.
• Abrahamsen, Petter; Fjellvoll, Bjørn; Hauge, Ragnar & Kolbjørnsen, Odd (2011). Geostatistics course.
• Kolbjørnsen, Odd; Hauge, Ragnar & Ng, Sebastian (2010). Deriving Deterministic Facies Probabilities from Stochastic Inversion.
• Nivlet, Phillippe; Ng, Sebastian; Hetle, Mari -Anne; Hauge, Ragnar; Dahle, Pål & Kolbjørnsen, Odd (2010). Integration of seismic data and uncertainties in the facies model; application to the Snorre field.
• Hauge, Ragnar & Kolbjørnsen, Odd (2010). CRAVA course for NORSAR.
• Kjønsberg, Heidi; Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2009). Integrating Stochastic Rock Physics in Seismic Pre-drill Prospect Risk and Reservoir Quality Assessment.
• Abrahamsen, Petter; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Skorstad, Arne (2009). Geostatistics course.
• Buland, Arild; Kolbjørnsen, Odd & Hauge, Ragnar (2008). Fast Bayesian Seismic Prestack Inversion with Consistent Coupling to Rock Physics.
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2008). Markov Mesh Simulations with Data Conditioning through Indicator Kriging.
• Kolbjørnsen, Odd & Stien, Marita (2008). D-vine Creation of Non-Gaussian Random Field, twopoint interactions to the limit.
• Ng, Sebastian; Dahle, Pål; Hauge, Ragnar & Kolbjørnsen, Odd (2008). Estimation of facies probabilities on the Snorre field using AVA inversion.
• Hollund, Knut Utne; Kolbjørnsen, Odd; Hauge, Ragnar; Lie, Tove & Jørstad, Arild (2008). Palisade - quantifying risk. Digital Energy journal.
• Fjellvoll, Bjørn; Hammer, Hugo Lewi; Kolbjørnsen, Odd & Skorstad, Arne (2008). Geostatistics course.
• Hollund, Knut Utne; Kolbjørnsen, Odd; Hauge, Ragnar; Lie, Tove & Jørstad, Arild (2008). From Geological Knowledge to Good Decisions using @Risk models.
• Hollund, Knut Utne; Kolbjørnsen, Odd; Syversveen, Anne Randi; Jørstad, Arild & Lie, Tove (2007). Using "Fast models" for Making the Right Decision - A Norwegian North Sea Case".
• Røe, Per & Kolbjørnsen, Odd (2017). Rock physics depth trends in PCube+ - Possible ways of integrating trends in PCube and PCube+. Norsk Regnesentral.
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2017). From Volume to Value – a tool for decision support v 1.3. Documentation and user manual. Norsk Regnesentral.
• Jullum, Martin; Hjort, Nils Lid & Kolbjørnsen, Odd (2016). New focused approaches to topics within model selection and approximate Bayesian inversion. Faculty of Mathematics and Natural Sciences, University of Oslo.
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2014). Modelling the H2S filters and SOx emissions at Kårstø Driftsmodell v2.0. Norsk Regnesentral Oslo.
• Kolbjørnsen, Odd & Ulvmoen, Marit (2014). 4D inversion of seismic travel-times. Norsk Regnesentral.
• Dahle, Pål; Nesvold, Erik; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar & Kolbjørnsen, Odd [Show all 8 contributors for this article] (2013). CRAVA User Manual version 2.0. Norsk Regnesentral Oslo. 2013(SAND/07/2013).
• Myrseth, Inge & Kolbjørnsen, Odd (2013). Monitoring the H2S filters and SOx emissions at Kårstø. Norsk Regnesentral.
• Georgsen, Frode; Myrseth, Inge & Kolbjørnsen, Odd (2013). Volume and Gas Quality Uncertainty Study for Gassco Transport Plan 2013. Norsk Regnesentral.
• Hauge, Vera Louise & Kolbjørnsen, Odd (2013). Inversion of gravimetric data. Norsk Regnesentral.
• Ulvmoen, Marit & Kolbjørnsen, Odd (2013). Bayesian lithology/scenario-contact prediction from seismic data. Norsk Regnesentral.
• Kolbjørnsen, Odd (2012). Using 3D inversion schemes to solve 4D inverse problems. Norsk Regnesentral.
• Kolbjørnsen, Odd (2012). Interpretation of saturation and porosity from inverted 4D seismic parameters. Norsk Regnesentral.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Show all 7 contributors for this article] (2012). CRAVA User Manual version 1.2. Norsk Regnesentral.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Show all 7 contributors for this article] (2012). CRAVA User Manual version 1.1. Norsk Regnesentral.
• Kjønsberg, Heidi; Stien, Marita; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Abrahamsen, Petter (2011). Methods of the Markov Mesh Multi-Grid Module in RMS. Norsk Regnesentral.
• Røe, Per; Hauge, Ragnar; Drange-Espeland, Maren ; Kolbjørnsen, Odd & Skjæveland, Øyvind (2011). PCube 2010 arbeidsbeskrivelse. Norsk Regnesentral.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Show all 7 contributors for this article] (2011). CRAVA User Manual version 1.1. Norsk Regnesentral.
• Kolbjørnsen, Odd; Hauge, Ragnar & Buland, Arild (2011). Including facies geometry in lithology and fluid prediction. Norsk Regnesentral.
• Røe, Per; Hauge, Vera Louise; Hauge, Ragnar; Drange-Espeland, Maren & Kolbjørnsen, Odd (2011). PCube 2011 Arbeidsbeskrivelse. Norsk Regnesentral.
• Kolbjørnsen, Odd (2011). Technicalities in the windowed PCUBE implementation. Norsk Regnesentral.
• Kolbjørnsen, Odd (2011). H2S Challenges upstream Kårstø. Norsk Regnesentral.
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2011). Making a 4D seismic prior model from rock physics relations. Norsk Regnesentral. Show summary

  This note describes how to find a prior 4D model for seismic parameters from an underlying rock physics model. The main ideas are expressed in terms of the Markov property for the dependency between different time steps, time locality in the sense that the seismic parameters at any time instance are found from the rock physics parameters as they are at that same time instance, and the use of Gaussian-linear models.

• Kolbjørnsen, Odd & Kjønsberg, Heidi (2011). Joint 4D inversion of multiple data sources for CO2 monitoring. Norsk Regnesentral. Show summary

  This note discusses the general framework of 4D inversion with multiple data-sources, phrased as a filtering and smoothing problem. Statistically this is formulated as a Markov process prior distribution, with multi-dimensional state variables. This is a well-established field, and the purpose of the current paper is twofold; to recapture the general equations and relations of the filtering and smoothing theory for Markov processes; and to outline the general framework we will work under in the NFR funded MonCO2 project.

• Stien, Marita & Kolbjørnsen, Odd (2010). Markov mesh model specification for facies modeling. Norsk Regnesentral.
• Stien, Marita; Georgsen, Frode; Hauge, Ragnar & Kolbjørnsen, Odd (2010). Computation of horizon gradients from seismic. Norsk Regnesentral.
• Kolbjørnsen, Odd; Syversveen, Anne Randi & Hauge, Ragnar (2010). From Volume to Value - a tool for decision support. Documentation and user manual - revised edition. Norsk Regnesentral.
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). The effect of illumination on source pulse estimation for PSDM seismic data. Norsk Regnesentral.
• Dahle, Pål; Fjellvoll, Bjørn; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2010). CRAVA USer Manual version 0.9.6. Norsk Regnesentral.
• Kjønsberg, Heidi; Fjellvoll, Bjørn; Abrahamsen, Petter; Kolbjørnsen, Odd & Stien, Marita (2009). Methods of the Multipoint Module in RMS. Norsk Regnesentral.
• Stien, Marita; Hauge, Ragnar; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). Modification of the Snesim Algorithm. Norsk Regnesentral.
• Førland, Maren Drange; Hauge, Ragnar & Kolbjørnsen, Odd (2008). Approximate likelihood computations for conditioning facies to seismic amplitudes. Norsk Regnesentral.
• Kolbjørnsen, Odd & Almendral-Vazquez, Ariel (2008). EM inversion software, USER MANUAL. Norsk Regnesentral.
• Kolbjørnsen, Odd; Almendral-Vazquez, Ariel & Buland, Arild (2008). Bayesian common midpoint inversion for controlled source electromagnetics. Norsk Regnesentral.
• Kjønsberg, Heidi; Kolbjørnsen, Odd; Stien, Marita & Abrahamsen, Petter (2008). Main Results of the Multipoint Project. Norsk Regnesentral. Show summary

  The aim of this project is to develop new and improved methods for modelling geological facies by combining the efficiency of multipoint methods with the robustness and consistency of Markov random field methods. It is a goal to develop software tools and test new methods on real cases and data. The project started in 2006 and is planned to finish in December 2008. The project is a mutually beneficial collaboration between the Norwegian Computing Center, the Norwegian University of Science and Technology and Stanford University. It is sponsored by the Research Council of Norway, ENI and StatoilHydro. The industry partners have contributed with valuable input for the discussions as well as useful guidelines for the choice of research topics. In this document we first provide a short summary of the main achievements in the project. This is followed by an introduction to multiple point methods and a somewhat more detailed account of each theme of the project.

• Georgsen, Frode & Kolbjørnsen, Odd (2008). Simple SIMPLI Inversion. Norsk Regnesentral.
• Stien, Marita & Kolbjørnsen, Odd (2008). D-vine Creation of Non-Gaussian Random Fields. Norsk Regnesentral.
• Stien, Marita; Kjønsberg, Heidi; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). An implementation of conditional Markov mesh simulation with parameter estimation. Norsk Regnesentral.
• Røe, Per; Syversveen, Anne Randi; Kolbjørnsen, Odd & Hauge, Ragnar (2007). Generating facies probability cubes using filtered wells. Norsk Regnesentral.
• Stien, Marita; Hauge, Ragnar & Kolbjørnsen, Odd (2007). Robust selection of simulations from geostatistical inversion project. Norsk Regnesentral.

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