Odd Kolbjørnsen

• 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 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), s R75- R87 . doi: 10.1190/geo2015-0314.1
• Kolbjørnsen, Odd; Buland, Arild; Hauge, Ragnar; Røe, Per; Jullum, Martin; Metcalfe, Richard William & Skjæveland, Øyvind (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 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.

• 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 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.

• 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
• Hauge, Vera Louise & Kolbjørnsen, Odd (2014). Spatial Resolution in Bayesian Inversion of Gravimetric Data, In EAGE2014 (ed.),  Conference proceedings. 76th EAGE Conference & Exhibition.  European Association of Geoscientists and Engineers.  ISBN 978-90-73834-89-7.  We D202 02. Show summary

  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 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.

• 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 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.

• 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
• 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 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.

• 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
• 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
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). A 3D Ray-based Pulse Estimation for Seismic Inversion of PSDM Data, In 2010 EAGE (ed.),  72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010 Barcelona.  European Association of Geoscientists and Engineers.  ISBN 978-90-73781-86-3.  A031.
• 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
• 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
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2008). Markov Mesh Simulations with Data Conditioning through Indicator Kriging, In Julian M. Ortiz & Xavier Emery (ed.),  Proceedings of the Eight International Geostatistics Congress.  GECAMIN.  ISBN 978-956-8504-17-5.  Chapter.  s 257 - 266
• Kolbjørnsen, Odd & Stien, Marita (2008). D-vine Creation of Non-Gaussian Random Field, In Julian Ortiz & Xavier Emery (ed.),  Procedings of the Eight International Geostatistics Congress Volume 1.  GECAMIN.  ISBN 978-956-8504-18-2.  Chapter.  s 399 - 408
• Manzocchi, T; Carter, JN; Skorstad, Arne; Fjellvoll, Bjørn; Stephen, KD; Howell, JA; Matthews, JD; Walsh, JJ; Nepveu, M; Bos, C; Cole, J; Egberts, P; Flint, S; Hern, C; Holden, Lars; Hovland, H; Jackson, H; Kolbjørnsen, Odd; MacDonald, A; Nell, PAR; Onyeagoro, K; Strand, J; Syversveen, Anne Randi; Tchistiakov, A; Yang, C; Yielding, G & Zimmerman, RW (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 . doi: 10.1144/​1354-079307-790 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.

• 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
• 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
• Tveranger, Jan; Howell, John Anthony; Aanonsen, Sigurd Ivar; Kolbjørnsen, Odd; Semshaug, Siv Lise; Skorstad, Arne & Ottesen, Signe (2008). Assessing structural controls on reservoir performance in different stratigraphic settings, In A Robinson; P. Griffiths; J. Hegre & A. Muggeridge (ed.),  The future of geological modelling in hydrocarbon development.  Geological Society of London.  ISBN 978-1862392663.  Chapter.  s 51 - 66
• 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 Society of Petroleum Engineers SPE (ed.),  SPE Annual Technical Conference and Exhibition, 11-14 November 2007, Anaheim, California, U.S.A.  Society of Petroleum Engineers.  ISBN 978-1-55563-148-2.  Chapter.
• Skorstad, Arne; Kolbjørnsen, Odd; Drottning, Åsmund; Gjøystdal, Håvar & Huseby, Olaf Kr. (2006). Combining saturation changes and 4D seismic for updating reservoir characterizations. SPE Reservoir Evaluation and Engineering.  ISSN 1094-6470.  9 . doi: 10.2118/106366-PA Show summary

  Elastic seismic inversion is a tool frequently used in analysis of seismic data. Elastic inversion relies on a simplified seismic model and generally produces 3D cubes for compressional-wave velocity, shear-wave velocity, and density. By applying rock-physics theory, such volumes may be interpreted in terms of lithology and fluid properties. Understanding the robustness of forward and inverse techniques is important when deciding the amount of information carried by seismic data. This paper suggests a simple method to update a reservoir characterization by comparing 4D-seismic data with flow simulations on an existing characterization conditioned on the base-survey data. The ability to use results from a 4D-seismic survey in reservoir characterization depends on several aspects. To investigate this, a loop that performs independent forward seismic modeling and elastic inversion at two time stages has been established. In the workflow, a synthetic reservoir is generated from which data are extracted. The task is to reconstruct the reservoir on the basis of these data. By working on a realistic synthetic reservoir, full knowledge of the reservoir characteristics is achieved. This makes the evaluation of the questions regarding the fundamental dependency between the seismic and petrophysical domains stronger. The synthetic reservoir is an ideal case, where properties are known to an accuracy never achieved in an applied situation. It can therefore be used to investigate the theoretical limitations of the information content in the seismic data. The deviations in water and oil production between the reference and predicted reservoir were significantly decreased by use of 4D-seismic data in addition to the 3D inverted elastic parameters.

• Soleng, Harald Heimtun; Syversveen, Anne Randi & Kolbjørnsen, Odd (2006). Comparing Facies Realizations: Defining Metrices on Realization Space, In  Proceedings of the 10th European Conference in the Mathematics of Oil Recovery.  European Association of Geoscientists & Engineers.  ISBN 978-90-73781-47-4.  A014.
• Dahle, Pål; Kolbjørnsen, Odd & Abrahamsen, Petter (2005). When can shape and scale parameters of a 3D variogram be estimated?, In Oy Leuangthong & Clayton V. Deutsch (ed.),  Geostatistics Banff 2004.  Springer.  ISBN 978-1-4020-3515-9.  Theory and selected topics.  s 949 - 958 Show summary

  We have used a method of least squares to fit full 3D variogram models to data, and have tested it on data taken from Gaussian random fields. The empirical variogram estimates are made using various lag grid definitions and the best of these grids is identified. Our results suggest that some 200 vertical wells are needed for obtaining reliable estimates of the azimuth and dip anisotropy angles, while some 50 wells seem sufficient for the horizontal ranges and the sill. For the vertical range 10 wells are sufficient.

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

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• Kolbjørnsen, Odd; Ndingwan, Abel Onana; Straith, Knut Richard; Aker, Eyvind & Røe, Per (2017). Deciphering the seismic AVO response of the reservoir at Edvard Grieg.
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2017). From Volume to Value – a tool for decision support v 1.3. Documentation and user manual.. NR-notat. SAND/03/2017.
• Røe, Per & Kolbjørnsen, Odd (2017). Comparison of one- and two-step seismic inversion for lithology and fluid prediction.
• Røe, Per & Kolbjørnsen, Odd (2017). Rock physics depth trends in PCube+ - Possible ways of integrating trends in PCube and PCube+. NR-notat. SAND/14/2017.
• Jullum, Martin; Hjort, Nils Lid & Kolbjørnsen, Odd (2016). New focused approaches to topics within model selection and approximate Bayesian inversion.
• 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 (2014). 4D inversion of seismic travel-times. NR-notat. SAND/07/14.
• Olsen, Håvard Goodwin & Kolbjørnsen, Odd (2014). Modelling the H2S filters and SOx emissions at Kårstø Driftsmodell v2.0. NR-notat. SAND/02/2014.
• Dahle, Pål; Nesvold, Erik; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2013). CRAVA User Manual version 2.0. NR-notat. SAND/07/2013.
• Georgsen, Frode; Myrseth, Inge & Kolbjørnsen, Odd (2013). Volume and Gas Quality Uncertainty Study for Gassco Transport Plan 2013. NR-notat. SAND/09/2013.
• Hauge, Vera Louise & Kolbjørnsen, Odd (2013). Inversion of gravimetric data. NR-notat. SAND/08/13.
• Kolbjørnsen, Odd; Ulvmoen, Marit; Hauge, Vera Louise; Hauge, Ragnar; Fjellvoll, Bjørn; Jensen, Erling Hugo; Johansen, Tor Arne; Dvorkin, Jack; Mavko, Gary; Furre, Anne-Kari & Johnston, David (2013). Monitoring Geological CO2 storage.
• Myrseth, Inge & Kolbjørnsen, Odd (2013). Monitoring the H2S filters and SOx emissions at Kårstø. NR-notat. SAND/04/13.
• Ulvmoen, Marit & Kolbjørnsen, Odd (2013). Bayesian lithology/scenario-contact prediction from seismic data. NR-notat. SAND/01/13.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2012). CRAVA User Manual version 1.1. NR-notat. SAND/02/2012.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2012). CRAVA User Manual version 1.2. NR-notat. SAND/05/2012.
• Kolbjørnsen, Odd (2012). Interpretation of saturation and porosity from inverted 4D seismic parameters. NR-notat. SAND/03/12.
• Kolbjørnsen, Odd (2012). Using 3D inversion schemes to solve 4D inverse problems. NR-notat. SAND/04/12.
• 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), s 83- 86
• Abrahamsen, Petter; Fjellvoll, Bjørn; Hauge, Ragnar & Kolbjørnsen, Odd (2011). Geostatistics course.
• Dahle, Pål; Fjellvoll, Bjørn; Georgsen, Frode; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2011). CRAVA User Manual version 1.1. NR-notat. SAND/03/11.
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2011). Making a 4D seismic prior model from rock physics relations. NR-notat. SAND/22/2011. 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.

• Kjønsberg, Heidi; Stien, Marita; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Abrahamsen, Petter (2011). Methods of the Markov Mesh Multi-Grid Module in RMS. NR-notat. SAND/21/2010.
• Kolbjørnsen, Odd (2011). H2S Challenges upstream Kårstø. NR-notat. SAND/24/2011.
• Kolbjørnsen, Odd (2011). Technicalities in the windowed PCUBE implementation. NR-notat. SAND/26/2011.
• Kolbjørnsen, Odd; Hauge, Ragnar & Buland, Arild (2011). Including facies geometry in lithology and fluid prediction. NR-notat. SAND/12/2011.
• Kolbjørnsen, Odd & Kjønsberg, Heidi (2011). Joint 4D inversion of multiple data sources for CO2 monitoring. NR-notat. SAND/20/2011. 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.

• Røe, Per; Hauge, Ragnar; Drange-Espeland, Maren; Kolbjørnsen, Odd & Skjæveland, Øyvind (2011). PCube 2010 arbeidsbeskrivelse. NR-notat. SAND/02/2011.
• Røe, Per; Hauge, Vera Louise; Hauge, Ragnar; Drange-Espeland, Maren & Kolbjørnsen, Odd (2011). PCube 2011 Arbeidsbeskrivelse. NR-notat. SAND/21/2011.
• Dahle, Pål; Fjellvoll, Bjørn; Hauge, Ragnar; Kolbjørnsen, Odd; Syversveen, Anne Randi & Ulvmoen, Marit (2010). CRAVA USer Manual version 0.9.6. NR-notat. SAND/04/2009.
• Georgsen, Frode; Kolbjørnsen, Odd & Lecomte, Isabelle (2010). The effect of illumination on source pulse estimation for PSDM seismic data. NR-notat. SAND/10/10.
• Hauge, Ragnar & Kolbjørnsen, Odd (2010). CRAVA course for NORSAR.
• Kolbjørnsen, Odd; Hauge, Ragnar & Ng, Sebastian (2010). Deriving Deterministic Facies Probabilities from Stochastic Inversion.
• Kolbjørnsen, Odd; Syversveen, Anne Randi & Hauge, Ragnar (2010). From Volume to Value - a tool for decision support. Documentation and user manual - revised edition. NR-notat. SAND/19/2010.
• 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.
• Stien, Marita; Georgsen, Frode; Hauge, Ragnar & Kolbjørnsen, Odd (2010). Computation of horizon gradients from seismic. NR-notat. SAND/11/10.
• Stien, Marita & Kolbjørnsen, Odd (2010). Markov mesh model specification for facies modeling. NR-notat. SAND/09/10.
• Abrahamsen, Petter; Fjellvoll, Bjørn; Kolbjørnsen, Odd & Skorstad, Arne (2009). Geostatistics course.
• Kjønsberg, Heidi; Fjellvoll, Bjørn; Abrahamsen, Petter; Kolbjørnsen, Odd & Stien, Marita (2009). Methods of the Multipoint Module in RMS. NR-notat. SAND/09/09.
• Kjønsberg, Heidi; Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2009). Integrating Stochastic Rock Physics in Seismic Pre-drill Prospect Risk and Reservoir Quality Assessment.
• Buland, Arild; Kolbjørnsen, Odd & Hauge, Ragnar (2008). Fast Bayesian Seismic Prestack Inversion with Consistent Coupling to Rock Physics.
• Fjellvoll, Bjørn; Hammer, Hugo Lewi; Kolbjørnsen, Odd & Skorstad, Arne (2008). Geostatistics course.
• Førland, Maren Drange; Hauge, Ragnar & Kolbjørnsen, Odd (2008). Approximate likelihood computations for conditioning facies to seismic amplitudes. NR-notat. SAND/15/08.
• Georgsen, Frode & Kolbjørnsen, Odd (2008). Simple SIMPLI Inversion. NR-notat. SAND/08/08.
• 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; Hauge, Ragnar; Lie, Tove & Jørstad, Arild (2008). Palisade - quantifying risk. Digital Energy journal.
• Kjønsberg, Heidi & Kolbjørnsen, Odd (2008). Markov Mesh Simulations with Data Conditioning through Indicator Kriging.
• Kjønsberg, Heidi; Kolbjørnsen, Odd; Stien, Marita & Abrahamsen, Petter (2008). Main Results of the Multipoint Project. NR-notat. NR/SAND/13/2008. 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.

• Kolbjørnsen, Odd & Almendral-Vazquez, Ariel (2008). EM inversion software, USER MANUAL. NR-notat. SAND/11/08.
• Kolbjørnsen, Odd; Almendral-Vazquez, Ariel & Buland, Arild (2008). Bayesian common midpoint inversion for controlled source electromagnetics. NR-notat. SAND/12/08.
• Kolbjørnsen, Odd; Buland, Arild & Hauge, Ragnar (2008). Method of Modelling A Subterranean Region of the Earth.
• 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.
• Stien, Marita; Hauge, Ragnar; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). Modification of the Snesim Algorithm. NR-notat. SAND/09/08.
• Stien, Marita; Kjønsberg, Heidi; Kolbjørnsen, Odd & Abrahamsen, Petter (2008). An implementation of conditional Markov mesh simulation with parameter estimation. NR-notat. SAND/04/2008.
• Stien, Marita & Kolbjørnsen, Odd (2008). D-vine Creation of Non-Gaussian Random Fields. NR-notat. SAND/07/08.
• Abrahamsen, Petter; Fjellvoll, Bjørn; Kolbjørnsen, Odd; Skorstad, Arne & Hauge, Ragnar (2007). Geostatistics course.
• Buland, Arild; Kolbjørnsen, Odd & Hauge, Ragnar (2007). Fast Bayesian prediction of lithology and fluid classes and rock properties from seismic data.
• Dahle, Pål; Hauge, Ragnar; Kolbjørnsen, Odd; Della Rossa, Ernesto; Luoni, Fabio & Marini, Alfonso Junio (2007). Geostatistical AVO Inversion on a Deep-water Oil Field.
• Hauge, Ragnar; Kolbjørnsen, Odd & Buland, Arild (2007). Feasibility of lithology and fluid prediction from seismic data.
• 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".
• Kolbjørnsen, Odd; Hauge, Ragnar & Buland, Arild (2007). Depth-to-time conversion errors in Bayesian seismic wavelet estimation.
• Røe, Per; Syversveen, Anne Randi; Kolbjørnsen, Odd & Hauge, Ragnar (2007). Generating facies probability cubes using filtered wells. NR-notat. SAND/17/07.
• Stien, Marita; Hauge, Ragnar & Kolbjørnsen, Odd (2007). Robust selection of simulations from geostatistical inversion project. NR-notat. SAND/01/07.
• Stien, Marita; Kolbjørnsen, Odd; Hauge, Ragnar & Abrahamsen, Petter (2007). Modification of the SNESIM algorithm.
• Dahle, Pål; Hauge, Ragnar & Kolbjørnsen, Odd (2006). Geostatistical Inversion Using the CRAVA Program. NR-notat. SAND/02/06.
• Dahle, Pål; Hauge, Ragnar; Kolbjørnsen, Odd & Pham, Nam Hoai (2006). Geostatistical AVO inversion on Smørbukk Sør.
• Drottning, Åsmund; Lecomte, Isabelle; Gjøystdal, Håvar; Skorstad, Arne; Kolbjørnsen, Odd & Huseby, Olaf (2006). Modeling the Seismic Response to Production. A Closer Look at the Sensitivity to Overburden, Survey, Rock Physics Model and Seismic Modeling Approach.
• Dahle, Pål; Hauge, Ragnar; Kolbjørnsen, Odd & Pham, Nam Hoai (2005). Bayesian AVO Inversion and Application to a Case Study.
• Hauge, Ragnar; Kjønsberg, Heidi & Kolbjørnsen, Odd (2005). Validation and comparison of integral approximations used in pCube. NR-notat. SAND/15/05.

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