Odd Kolbjørnsen

• Martinsen, Iver; Ricaud, Benjamin; Wade, David; Kolbjørnsen, Odd & Godtliebsen, Fred (2025). The Fossil Frontier: An answer to the 3-billion fossil question. Artificial Intelligence in Geosciences. 7(1). doi: 10.1016/j.aiig.2025.100184. Fulltekst i vitenarkiv
• Oliver, Dean; Sætrom, Jon; Skorstad, Arne; Saksvik, Trond & Kolbjørnsen, Odd (2025). Robust multi-objective production optimization with CO2 emissions reduction. Geoenergy Science and Engineering. ISSN 2949-8929. 251. doi: 10.1016/j.geoen.2025.213845. Fulltekst i vitenarkiv Vis sammendrag

  In this paper, we describe an efficient methodology for simultaneously maximizing the expected profitability of oil field production and minimizing the expected emission of greenhouse gasses associated with the production through optimizing controls of the reservoir injection and production wells. Instead of simply minimizing water production and injection as is often done as a surrogate for energy consumption, we use an emissions calculator to account for the energy efficiency of the injection and compression system. Because our approach to minimization is efficient, we are able to account for uncertainty in geology during the minimization and to use the operational simulation model for the field. The most common approach to solving for Pareto optimal solutions is through some type of scalarization of the optimization problem. In this study, we apply the weighted-sum method, which despite its limitations when applied to problems with feasible regions for objective outcomes that are not convex provides Pareto optimal solutions at a relatively low cost. Finally, we apply the methodology to the problem of well controls for a three-well field in the Norwegian Sea with platform facilities shared by another field. The reservoir model has 330,000 active cells with an active aquifer. The emissions calculator uses pump characteristics to account for fuel usage attributed to water injection. Gas compression, water treatment, and base energy costs are estimated by calibration of allocated energy usage to historical production data. The expectation of the objective functions is approximated by the sample average of the objective functions over the ensemble of 50 history-matched model realizations. Control variables are the injector and producer rates over one-month intervals. The Stochastic Simplex Approximate Gradient (StoSAG) method was used to estimate the gradient of the scalarized objective function and a quasi-Newton method (BFGS) was used for minimization. Results showed that moderately large reductions in CO2 emissions from a reference case optimized purely for profitability could be obtained at the cost of modest reductions in NPV. Larger reductions in CO emissions were costlier. Additionally, the optimized reservoir production strategies were not intuitively obvious, indicating that a formal multi-objective optimization approach was beneficial.

• Aasan, Marius; Kolbjørnsen, Odd; Solberg, Anne H Schistad & Rivera, Adín Ramírez (2025). A Spitting Image: Modular Superpixel Tokenization in Vision Transformers. Lecture Notes in Computer Science (LNCS). ISSN 0302-9743. 15641, s. 124–142. doi: 10.1007/978-3-031-93806-1_11. Fulltekst i vitenarkiv Vis sammendrag

  Vision Transformer (ViT) architectures traditionally employ a grid-based approach to tokenization independent of the semantic content of an image. We propose a modular superpixel tokenization strategy which decouples tokenization and feature extraction; a shift from contemporary approaches where these are treated as an undifferentiated whole. Using on-line content-aware tokenization and scale- and shape-invariant positional embeddings, we perform experiments and ablations that contrast our approach with patch-based tokenization and randomized partitions as baselines. We show that our method significantly improves the faithfulness of attributions, gives pixel-level granularity on zero-shot unsupervised dense prediction tasks, while maintaining predictive performance in classification tasks. Our approach provides a modular tokenization framework commensurable with standard architectures, extending the space of ViTs to a larger class of semantically-rich models.

• Kjønsberg, Heidi; Hauge, Ragnar; Nilsen, Carl-Inge Colombo; Ndingwan, Abel Onana & Kolbjørnsen, Odd (2024). Bayesian seismic 4D inversion for lithology and fluid prediction. Geophysics. ISSN 0016-8033. 89(6), s. R551–R567. doi: 10.1190/GEO2024-0092.1. Fulltekst i vitenarkiv Vis sammendrag

  Seismic data acquired at different times over the same area can provide insight into changes in an oil/gas reservoir. Probabilities for pore fluid will typically change, whereas the lithology remains stable over time. This implies significant correlations across the vintages. We develop a methodology for the Bayesian prediction of joint probabilities for discrete lithology-fluid classes (LFCs) for two vintages, simultaneously considering the seismic amplitude-variation-with-offset data of both vintages. By taking into account the cross-vintage correlations of elastic and seismic properties, the simultaneous inversion ensures that the individual results of both vintages, as well as their differences, are consistent and constrained by the seismic data of both vintages. The method relies on prior geologic knowledge of stratigraphic layering, the possible lithologies and fluids within each layer, and the possible cross-vintage changes in lithology and pore fluid. Multiple LFCs can be used to represent different strengths of dynamic cross-vintage changes. We test the algorithm on a synthetic data set and data from the Edvard Grieg field in the central North Sea. Synthetic results demonstrate that the algorithm is able to use dual-vintage data together with a prior model specifying their correlations to calculate joint LFC posterior probabilities for both vintages with a lower degree of uncertainty than independent single-vintage inversions. The Edvard Grieg results indicate that the underlying model is sufficiently general to explain 4D variations in seismic data using a reasonably simple prior model of 4D LFC changes.

• Sandnes, Anders Thoresen; Grimstad, Bjarne André & Kolbjørnsen, Odd (2024). Multi-task neural networks by learned contextual inputs. Neural Networks. ISSN 0893-6080. 179. doi: 10.1016/j.neunet.2024.106528. Fulltekst i vitenarkiv Vis sammendrag

  This paper explores learned-context neural networks. It is a multi-task learning architecture based on a fully shared neural network and an augmented input vector containing trainable task parameters. The architecture is interesting due to its powerful task adaption mechanism, which facilitates a low-dimensional task parameter space. Theoretically, we show that a scalar task parameter is sufficient for universal approximation of all tasks, which is not necessarily the case for more common architectures. Empirically it is shown that, for homogeneous tasks, the dimension of the task parameter may vary with the complexity of the tasks, but a small task parameter space is generally viable. The task parameter space is found to be well-behaved, which simplifies workflows related to updating models as new data arrives, and learning new tasks with the shared parameters are frozen. Additionally, the architecture displays robustness towards datasets where tasks have few data points. The architecture’s performance is compared to similar neural network architectures on ten datasets, with competitive results.

• Sanchis, Charlotte Juliette Semin & Kolbjørnsen, Odd (2023). Sampling-Free Bayesian Inference for Local Refinement in Linear Inversion Problems with a Latent Target Property. IEEE Transactions on Geoscience and Remote Sensing. ISSN 0196-2892. 61. doi: 10.1109/TGRS.2023.3301717. Fulltekst i vitenarkiv Vis sammendrag

  We present a sampling-free probabilistic inversion of latent target property based on the principles of expectation propagation where we estimate the joint distribution of the target variable in a local region. The prior model matches the prior distribution in the local-focused region but integrates our model parameters outside the focus region using approximate distributions. The approximate distribution includes large spatial structure information while maintaining the dimension of the inversion small. In addition, we map and solve the inversion into a new feature space where we can exclude components where the data have little influence, thereby decreasing the dimensionality of the inversion, and therefore, the inversion runtime. We test the method on seismic amplitude-versus-offset (AVO) inversion examples for the prediction of facies classes, as well as on the estimation of vuggy porosity in computed tomography (CT) images of core from a carbonate reservoir. We demonstrate that our method achieves good-quality predictions while significantly reducing the computational demand, making it particularly interesting to run large-scale inversion studies.

• Greiner, Thomas Larsen; Lie, Jan Erik; Kolbjørnsen, Odd; Evensen, Andreas Kjelsrud; Nilsen, Espen Harris & Zhao, Hao [Vis alle 8 forfattere av denne artikkelen] (2021). Unsupervised deep learning with higher-order total-variation regularization for multidimensional seismic data reconstruction. Geophysics. ISSN 0016-8033. 87(2), s. 59–73. doi: 10.1190/geo2021-0099.1. Fulltekst i vitenarkiv Vis sammendrag

  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.

• 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. Fulltekst i vitenarkiv Vis sammendrag

  Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. Encouraging results and advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). Data-driven VFMs are developed in the small data regime, where it is important to question the uncertainty and robustness of models. The modeling of uncertainty may help to build trust in models, which is a prerequisite for industrial applications. The contribution of this paper is the introduction of a probabilistic VFM based on Bayesian neural networks. Uncertainty in the model and measurements is described, and the paper shows how to perform approximate Bayesian inference using variational inference. The method is studied by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where an average error of 4%–6% and 8%–13% is achieved for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. Prediction performance and uncertainty calibration is explored in detail and discussed in light of four data challenges. The findings motivate the development of alternative strategies to improve the robustness of data-driven VFMs.

• Sandnes, Anders Thoresen; Grimstad, Bjarne Andre & Kolbjørnsen, Odd (2021). Multi-task learning for virtual flow metering. Knowledge-Based Systems. ISSN 0950-7051. 232, s. 1–10. doi: 10.1016/j.knosys.2021.107458. Fulltekst i vitenarkiv Vis sammendrag

  Virtual flow metering (VFM) is a cost-effective and non-intrusive technology for inferring multiphase flow rates in petroleum assets. Inferences about flow rates are fundamental to decision support systems that operators extensively rely on. Data-driven VFM, where mechanistic models are replaced with machine learning models, has recently gained attention due to its promise of lower maintenance costs. While excellent performances in small sample studies have been reported in the literature, there is still considerable doubt about the robustness of data-driven VFM. In this paper, we propose a new multi-task learning (MTL) architecture for data-driven VFM. Our method differs from previous methods in that it enables learning across oil and gas wells. We study the method by modeling 55 wells from four petroleum assets and compare the results with two single-task baseline models. Our findings show that MTL improves robustness over single-task methods, without sacrificing performance. MTL yields a 25%–50% error reduction on average for the assets where single-task architectures are struggling.

• 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), s. IM15–IM26. doi: 10.1190/geo2019-0413.1. Fulltekst i vitenarkiv
• 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), s. R207–R221. doi: 10.1190/geo2019-0170.1. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Greiner, Thomas Larsen; Hlebnikov, Volodya; Lie, Jan Erik; Kolbjørnsen, Odd; Evensen, Andreas Kjeldsrud & Nilsen, Espen Harris [Vis alle 8 forfattere av denne artikkelen] (2020). Cross-streamer wavefield reconstruction through wavelet domain. Geophysics. ISSN 0016-8033. 85(6), s. V457–V471. doi: 10.1190/geo2019-0771.1. Fulltekst i vitenarkiv Vis sammendrag

  Seismic exploration in complex geologic settings and shallow geologic targets has led to a demand for higher spatial and temporal resolution in the final migrated image. Conventional marine seismic and wide-azimuth data acquisition lack near-offset coverage, which limits imaging in these settings. A new marine source-over-cable survey, with split-spread configuration, known as TopSeis, was introduced in 2017 to address the shallow-target problem. However, wavefield reconstruction in the near offsets is challenging in the shallow part of the seismic record due to the high temporal frequencies and coarse sampling that leads to severe spatial aliasing. We have investigated deep learning as a tool for the reconstruction problem, beyond spatial aliasing. Our method is based on a convolutional neural network (CNN) approach trained in the wavelet domain that is used to reconstruct the wavefield across the streamers. We determine the performance of the proposed method on broadband synthetic data and TopSeis field data from the Barents Sea. From our synthetic example, we find that the CNN can be learned in the inline direction and applied in the crossline direction, and that the approach preserves the characteristics of the geologic model in the migrated section. In addition, we compare our method to an industry-standard Fourier-based interpolation method, in which the CNN approach shows an improvement in the root-mean-square (rms) error close to a factor of two. In our field data example, we find that the approach reconstructs the wavefield across the streamers in the shot domain, and it displays promising characteristics of a reconstructed 3D wavefield.

• 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), s. 742–820. doi: 10.1190/tle38100791.1. Fulltekst i vitenarkiv Vis sammendrag

  The sparseness promoted by the total variation norm is utilized to achieve superresolution amplitude-variation-with-offset (AVO) inversion. The total variation norm promotes solutions that have constant values within unspecified regions and thus are well suited for an earth model consisting of layers bounded by faults and erosion surfaces. Algorithmic developments from digital image and video restoration are utilized to solve the geophysical problem. A spatial point spread function is used to model the resulting effect of wave propagation, migration, and processing. The methodology is compared to current alternatives and discussed in the context of AVO inversion. Good results are obtained in a Barents Sea test case.

• Greiner, Thomas Larsen; Kolbjørnsen, Odd; Lie, Jan Erik; Nilsen, Espen Harris; Evensen, Andreas Kjeldsrud & Gelius, Leiv-J. (2019). Cross-streamer wavefield interpolation using deep convolutional networks. I SEG, . (Red.), SEG Technical Program Expanded Abstracts 2019. SEG. ISSN 9780916160005. s. 2207–2211. doi: 10.1190/segam2019-3214009.1. Fulltekst i vitenarkiv Vis sammendrag

  Seismic exploration in complex geological settings and shallow geological targets has led to a demand for higher spatial and temporal resolution in the final migrated image. Seismic data from conventional marine acquisition lacks near offset and wide azimuth data, which limits imaging in these settings. In addition, large streamer separation introduce aliasing of spatial frequencies across the streamers. A new marine survey configuration, known as TopSeis, was introduced in 2017 in order to address the shallow-target problem. However, introduction of near offset data has shown to be challenging for interpolation and regularization, using conventional methods. In this paper, we investigate deep learning as a tool for interpolation beyond spatial aliasing across the streamers, in the shot domain. The proposed method is based on imaging techniques from single-image super resolution (SISR). The model architecture consist of a deep convolutional neural network (CNN) and a periodic resampling layer for upscaling to the non-aliased wavefield. We demonstrate the performance of proposed method on representative broad-band synthetic data and TopSeis field data from the Barents Sea.

• Kolbjørnsen, Odd & Evensen, Andreas Kjelsrud (2019). Digital superresolution in seismic amplitude processing. SEG technical program expanded abstracts. doi: 10.1190/segam2019-3214317.1. Fulltekst i vitenarkiv Vis sammendrag

  We describe a method for geophysical inversion of seismic amplitude data, we argue that this type of inversion is a natural extension of the processing flow. The methodology is related to digital image-video restoration and single image superresolution. It formulates the inverse problem in term of a regularization and solve it by an augmented Lagrangian approach. It can be seen as an extension of 1D sparse spike inversion to 3D. The approach impose weak geological constraints through the gradient of the earth parameter and is thus particular useful in the exploration setting, and regions with little well control. We test three different regularizations in a synthetic example, and show how this is used for a data set acquired in the Barents sea. We find that the anisotropic total variation regularizer is robust and efficient when it comes to restoring earth models, and outperform the weighted L2 norm when it comes to reproducing discontinuities along smooth edges.

• 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. doi: 10.1190/segam2018-2994746.1. Fulltekst i vitenarkiv Vis sammendrag

  We present a case of seismic reservoir characterization within a multi-source depositional setting. To resolve issues of non-uniqueness between intrinsic reservoir properties and the seismic data, we use a probabilistic approach. Stochastic rock physics relationships are used to establish a link between elastic parameters and various lithology classes. We highlight the importance of concurrently using multiple lithological prior models to achieve an improved understanding of the seismic response of the Edvard Grieg field. Application of a one-step inversion approach, which assesses the direct conditional (posterior) distribution of elastic parameters, yields improved reservoir prediction particularly in regions where the reservoir sandstones are thin. Quantitative prediction and interpretation of impedances and lithology volumes is done in light of selected models and associated uncertainties.

• 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), s. 619–634. doi: 10.1007/s11004-016-9665-7. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Kolbjørnsen, Odd; Buland, Arild; Hauge, Ragnar; Røe, Per; Jullum, Martin & Metcalfe, Richard William [Vis alle 7 forfattere av denne artikkelen] (2016). Bayesian AVO inversion to rock properties using a local neighborhood in a spatial prior model. The Leading Edge. ISSN 1070-485X. 35(5), s. 431–436. doi: 10.1190/tle35050431.1. Fulltekst i vitenarkiv Vis sammendrag

  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 (2016). A Gaussian-based framework for local Bayesian inversion of geophysical data to rock properties. Geophysics. ISSN 0016-8033. 81(3), s. R75–R87. doi: 10.1190/geo2015-0314.1. Fulltekst i vitenarkiv
• 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), s. R75–R87. doi: 10.1190/GEO2015-0314.1. Fulltekst i vitenarkiv
• 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), s. SP1–SP10. doi: 10.1190/INT-2014-0193.1. Fulltekst i vitenarkiv Vis sammendrag

  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. I EAGE2014 (Red.), Conference proceedings. 76th EAGE Conference & Exhibition. European Association of Geoscientists and Engineers (EAGE). ISSN 9789073834897. doi: 10.3997/2214-4609.20141001. Fulltekst i vitenarkiv Vis sammendrag

  CO_2 capture and storage of CO_2 in geological structures are important parts in reaching the targets of the International Energy Agency on cutting CO_2 emissions related to energy. Quantitative description 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 CO_2 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; Stien, Marita; Kjønsberg, Heidi; Fjellvoll, Bjørn & Abrahamsen, Petter (2013). Using Multiple Grids in Markov Mesh Facies Modeling. Mathematical Geosciences. ISSN 1874-8961. 46(2), s. 205–225. doi: 10.1007/s11004-013-9499-5. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Buland, Arild & Kolbjørnsen, Odd (2012). Bayesian inversion of CSEM and magnetotelluric data. Geophysics. ISSN 0016-8033. 77(1), s. E33–E42. doi: 10.1190/GEO2010-0298.1. Fulltekst i vitenarkiv Vis sammendrag

  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), s. E21–E31. doi: 10.1190/GEO2010-0300.1. Fulltekst i vitenarkiv Vis sammendrag

  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.

• 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), s. 500–515. doi: 10.1111/j.1365-2478.2011.01012.x. Fulltekst i vitenarkiv
• Buland, Arild; Kolbjørnsen, Odd & Carter, Andrew J. (2011). Bayesian Dix inversion. Geophysics. ISSN 0016-8033. 76(2), s. R15–R22. doi: 10.1190/1.3552596. Fulltekst i vitenarkiv
• Stien, Marita & Kolbjørnsen, Odd (2011). Facies Modeling Using a Markov Mesh Model Specification. Mathematical Geosciences. ISSN 1874-8961. 43(6), s. 611–624. doi: 10.1007/s11004-011-9350-9. Fulltekst i vitenarkiv
• Kjønsberg, Heidi; Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2010). Bayesian Monte Carlo method for seismic predrill prospect assessment. Geophysics. ISSN 0016-8033. 75(2), s. O9–O19. doi: 10.1190/1.3339678. Fulltekst i vitenarkiv
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). A 3D Ray-based Pulse Estimation for Seismic Inversion of PSDM Data. I EAGE, 2010 (Red.), 72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010 Barcelona. European Association of Geoscientists and Engineers (EAGE). ISSN 9789073781863. Fulltekst i vitenarkiv
• 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, s. 45–54. Fulltekst i vitenarkiv
• 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), s. C13–C21. doi: 10.1190/1.2842150. Fulltekst i vitenarkiv
• Manzocchi, T; Carter, JN; Skorstad, Arne; Fjellvoll, Bjørn; Stephen, KD & Howell, JA [Vis alle 27 forfattere av denne artikkelen] (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), s. 3–15. Fulltekst i vitenarkiv Vis sammendrag

  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.

• 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), s. 45–54. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Abrahamsen, Petter; Kolbjørnsen, Odd & Hauge, Ragnar (2012). Geostatistics Oslo 2012. Springer. ISBN 9789400741522. 573 s. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Aasan, Marius; Kolbjørnsen, Odd; Solberg, Anne H Schistad & Rivera, Adín Ramírez (2024). A Spitting Image: Modular Superpixel Tokenization in Vision Transformers. Fulltekst i vitenarkiv
• Aasan, Marius; Kolbjørnsen, Odd; Solberg, Anne H Schistad & Rivera, Adín Ramírez (2024). A Spitting Image: Modular Tokenization in Vision Transformers. Fulltekst i vitenarkiv
• Aasan, Marius; Kolbjørnsen, Odd; Solberg, Anne H Schistad & Rivera, Adín Ramírez (2024). A Spitting Image: Modular Superpixel Tokenization in Vision Transformers. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd (2023). Convolutional computations for local Bayesian approximations in linear inverse problems. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd & Sanchis, Charlotte Juliette (2022). Sample free inference for Bayesian inverse problems, a local approximation. Fulltekst i vitenarkiv
• Aasan, Marius; Rivera, Adín Ramírez; Kolbjørnsen, Odd & Solberg, Anne H Schistad (2022). An Information Metric for Partitions on Images using Lattice Theoretic Entropy. Fulltekst i vitenarkiv
• Røe, Per; Kolbjørnsen, Odd & Hauge, Ragnar (2019). Comparison of one- and two-step seismic inversion for Lithology and Fluid prediction. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd & Evensen, Andreas Kjelsrud (2019). Digital superresolution in seismic amplitude processing. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• Ndingwan, Abel Onana; Kolbjørnsen, Odd; Straith, Knut Richard & Bjerke, Morten (2018). Deciphering the seismic signature of the Edvard Grieg field, North Sea. Fulltekst i vitenarkiv
• Røe, Per & Kolbjørnsen, Odd (2017). Comparison of one- and two-step seismic inversion for lithology and fluid prediction. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd; Ndingwan, Abel Onana; Straith, Knut Richard; Aker, Eyvind & Røe, Per (2017). Deciphering the seismic AVO response of the reservoir at Edvard Grieg. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• Vigsnes, Maria; Abrahamsen, Petter; Hauge, Vera Louise & Kolbjørnsen, Odd (2015). Efficient Neighborhoods for Kriging with Numerous Data. Fulltekst i vitenarkiv Vis sammendrag

  Kriging is a data interpolation method that can be used to populate regular grids from data scattered in space, and requires the solution of a linear equation system the size of the number of data. When the data is numerous the speed of the calculation is slow. In this paper we propose to divide the regular grid into rectangular sub-segments and let all the grid cells in each sub-segment share a common data neighborhood. The advantage of this approach is that the number of data in the neighborhoods can be small compared to the complete dataset and it is possible to reuse some of the computations for all grid cells in each sub-segment. We show that the precision can be controlled through selection of neighbourhood size, and that the speed of the calculations can be optimized through selection of subsegment size. We show that this is an efficient method for kriging when number of data is huge, giving a significant speed-up even for high data densities and precisions.

• Jullum, Martin & Kolbjørnsen, Odd (2015). An Approximate Bayesian Inversion Framework based on Local-gaussian Likelihoods. Fulltekst i vitenarkiv
• Hauge, Vera Louise & Kolbjørnsen, Odd (2014). Spatial Resolution in Bayesian Inversion of Gravimetric Data. Fulltekst i vitenarkiv Vis sammendrag

  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 [Vis alle 11 forfattere av denne artikkelen] (2013). Monitoring Geological CO2 storage. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd; MacDonald, Alister; Skorstad, Arne & Berg, Thomas (2012). Estimating the Cloud Transform. Fulltekst i vitenarkiv
• Nair, Krishnakumar Narayanan; Kolbjørnsen, Odd & Skorstad, Arne (2012). Seismic inversion and its applications in reservoir characterization. First Break. ISSN 0263-5046. 30(3), s. 83–86. Fulltekst i vitenarkiv
• Abrahamsen, Petter; Fjellvoll, Bjørn; Hauge, Ragnar & Kolbjørnsen, Odd (2011). Geostatistics course. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• Hauge, Ragnar & Kolbjørnsen, Odd (2010). CRAVA course for NORSAR. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd; Hauge, Ragnar & Ng, Sebastian (2010). Deriving Deterministic Facies Probabilities from Stochastic Inversion. Fulltekst i vitenarkiv
• Kjønsberg, Heidi; Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2009). Integrating Stochastic Rock Physics in Seismic Pre-drill Prospect Risk and Reservoir Quality Assessment. Fulltekst i vitenarkiv
• Abrahamsen, Petter; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Skorstad, Arne (2009). Geostatistics course. Fulltekst i vitenarkiv
• Fjellvoll, Bjørn; Hammer, Hugo Lewi; Kolbjørnsen, Odd & Skorstad, Arne (2008). Geostatistics course. Fulltekst i vitenarkiv
• Hollund, Knut Utne; Kolbjørnsen, Odd; Hauge, Ragnar; Lie, Tove & Jørstad, Arild (2008). Palisade - quantifying risk. Digital Energy journal. Fulltekst i vitenarkiv
• Hollund, Knut Utne; Kolbjørnsen, Odd; Hauge, Ragnar; Lie, Tove & Jørstad, Arild (2008). From Geological Knowledge to Good Decisions using @Risk models. Fulltekst i vitenarkiv
• Ng, Sebastian; Dahle, Pål; Hauge, Ragnar & Kolbjørnsen, Odd (2008). Estimation of facies probabilities on the Snorre field using AVA inversion. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd & Stien, Marita (2008). D-vine Creation of Non-Gaussian Random Field, twopoint interactions to the limit. Fulltekst i vitenarkiv
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2017). From Volume to Value – a tool for decision support v 1.3. Documentation and user manual. Norsk Regnesentral. Fulltekst i vitenarkiv
• Røe, Per & Kolbjørnsen, Odd (2017). Rock physics depth trends in PCube+ - Possible ways of integrating trends in PCube and PCube+. Norsk Regnesentral. Fulltekst i vitenarkiv
• Jullum, Martin; Hjort, Nils Lid & Kolbjørnsen, Odd (2016). New focused approaches to topics within model selection and approximate Bayesian inversion. Universitetet i Oslo. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd & Ulvmoen, Marit (2014). 4D inversion of seismic travel-times. Norsk Regnesentral. Fulltekst i vitenarkiv
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2014). Modelling the H2S filters and SOx emissions at Kårstø Driftsmodell v2.0. Norsk Regnesentral Oslo. Fulltekst i vitenarkiv
• Myrseth, Inge & Kolbjørnsen, Odd (2013). Monitoring the H2S filters and SOx emissions at Kårstø. Norsk Regnesentral. Fulltekst i vitenarkiv
• Ulvmoen, Marit & Kolbjørnsen, Odd (2013). Bayesian lithology/scenario-contact prediction from seismic data. Norsk Regnesentral. Fulltekst i vitenarkiv
• Dahle, Pål; Nesvold, Erik; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar & Kolbjørnsen, Odd [Vis alle 8 forfattere av denne artikkelen] (2013). CRAVA User Manual version 2.0. Norsk Regnesentral Oslo. Fulltekst i vitenarkiv
• Georgsen, Frode; Myrseth, Inge & Kolbjørnsen, Odd (2013). Volume and Gas Quality Uncertainty Study for Gassco Transport Plan 2013. Norsk Regnesentral. Fulltekst i vitenarkiv
• Hauge, Vera Louise & Kolbjørnsen, Odd (2013). Inversion of gravimetric data. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd (2012). Using 3D inversion schemes to solve 4D inverse problems. Norsk Regnesentral. Fulltekst i vitenarkiv Vis sammendrag

  Seismic data observed at a given point in time are sensitive to the elastic parameters at this time. A Bayesian 3D inversion computes the posterior of the elastic parameters at that moment in time. In 4D inversion data at multiple time steps are collected, in order to investigate changes in elastic parameters. One option is to investigate each time step individually, and consider the differences, this approach ignore the temporal correlation of data. We use a Kalman filter approach to model the time correlations; in this approach we must separate the model for static and dynamic parameters. The current inversion methodology does not account for this separation. In the current note we show how we merge and split static and dynamic parameters, when conditioning to the current data set. This enables us to incorporate the standard inversion methodology for solving the 4D problem.

• Kolbjørnsen, Odd (2012). Interpretation of saturation and porosity from inverted 4D seismic parameters. Norsk Regnesentral. Fulltekst i vitenarkiv Vis sammendrag

  In this note we propose two alternative approaches for stochastic rock physics inversion of 4D seismic data. Both methods use the approach of approximate local marginal likelihood coming from a Bayesian inversion scheme. We describe the concept of approximate local marginal likelihood, and put forward arguments for the approach, using arguments from the linear estimation methods, bounding of error, and also a more heuristic argument through information theory. Within the framework we propose two alternative approximations, which differ with respect to which level we use the approximation. The fastest and simplest approach applies the concept of local approximate marginal likelihood directly to porosity and saturation, the slightly more time consuming approach applies the concept of approximate local marginal likelihood to the seismic parameters and will give more accurate results for porosity and saturation.

• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Vis alle 7 forfattere av denne artikkelen] (2012). CRAVA User Manual version 1.2. Norsk Regnesentral. Fulltekst i vitenarkiv
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Vis alle 7 forfattere av denne artikkelen] (2012). CRAVA User Manual version 1.1. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2011). Making a 4D seismic prior model from rock physics relations. Norsk Regnesentral. Fulltekst i vitenarkiv Vis sammendrag

  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. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Røe, Per; Hauge, Ragnar; Drange-Espeland, Maren; Kolbjørnsen, Odd & Skjæveland, Øyvind (2011). PCube 2010 arbeidsbeskrivelse. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd; Hauge, Ragnar & Buland, Arild (2011). Including facies geometry in lithology and fluid prediction. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd (2011). Technicalities in the windowed PCUBE implementation. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kolbjørnsen, Odd (2011). H2S Challenges upstream Kårstø. Norsk Regnesentral. Fulltekst i vitenarkiv
• Røe, Per; Hauge, Vera Louise; Hauge, Ragnar; Drange-Espeland, Maren & Kolbjørnsen, Odd (2011). PCube 2011 Arbeidsbeskrivelse. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kjønsberg, Heidi; Stien, Marita; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Abrahamsen, Petter (2011). Methods of the Markov Mesh Multi-Grid Module in RMS. Norsk Regnesentral. Fulltekst i vitenarkiv
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd & Syversveen, Anne Randi [Vis alle 7 forfattere av denne artikkelen] (2011). CRAVA User Manual version 1.1. Norsk Regnesentral. Fulltekst i vitenarkiv
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). The effect of illumination on source pulse estimation for PSDM seismic data. Norsk Regnesentral. Fulltekst i vitenarkiv
• Dahle, Pål; Fjellvoll, Bjørn; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2010). CRAVA USer Manual version 0.9.6. Norsk Regnesentral. Fulltekst i vitenarkiv
• 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. Fulltekst i vitenarkiv
• Stien, Marita; Georgsen, Frode; Hauge, Ragnar & Kolbjørnsen, Odd (2010). Computation of horizon gradients from seismic. Norsk Regnesentral. Fulltekst i vitenarkiv
• Stien, Marita & Kolbjørnsen, Odd (2010). Markov mesh model specification for facies modeling. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kjønsberg, Heidi; Fjellvoll, Bjørn; Abrahamsen, Petter; Kolbjørnsen, Odd & Stien, Marita (2009). Methods of the Multipoint Module in RMS. Norsk Regnesentral. Fulltekst i vitenarkiv
• Stien, Marita; Kjønsberg, Heidi; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). An implementation of conditional Markov mesh simulation with parameter estimation. Norsk Regnesentral. Fulltekst i vitenarkiv
• Stien, Marita & Kolbjørnsen, Odd (2008). D-vine Creation of Non-Gaussian Random Fields. Norsk Regnesentral. Fulltekst i vitenarkiv
• Kjønsberg, Heidi; Kolbjørnsen, Odd; Stien, Marita & Abrahamsen, Petter (2008). Main Results of the Multipoint Project. Norsk Regnesentral. Fulltekst i vitenarkiv Vis sammendrag

  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.

• Stien, Marita; Hauge, Ragnar; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). Modification of the Snesim Algorithm. Norsk Regnesentral. Fulltekst i vitenarkiv
• Førland, Maren Drange; Hauge, Ragnar & Kolbjørnsen, Odd (2008). Approximate likelihood computations for conditioning facies to seismic amplitudes. Norsk Regnesentral. Fulltekst i vitenarkiv

Se alle arbeider i NVA