Solid Earth Physics and Computational Geoscience
The Solid Earth Physics and Computational Geoscience Group at the Niels Bohr Institute is engaged in inverse theory and algorithm development for the solution of complex problems in the study of the Earth's interior. Of particular interest to us is the integration of quantitative geophysical and geological models and the related computational challenges.
Our projects span from largescale planetary studies to Earth resource exploration, including drinking water, geothermal energy and mineral resources. All these activities share common themes that continue to fascinate us: nonlinear inverse problems, the search for feasible solutions, probabilistic Earth models, and the complex flow of information from uncertain observations, through numerical modeling, to final interpretions and decisions.
Probabilistic approach for risk assessment of CO_{2} Storage
One of the possible postproduction utilization of abandoned hydrocarbon fields in the North Sea fields is to use them as reservoirs for CO_{2} storage. There are several advantages in doing so: the reservoirs are already discovered and the wells needed to access them are in place.
However, CO_{2} storage requires a careful risk assessment, based on integrated data analysis where all uncertainties are correctly balanced. In an ideal approach, the analysis must evaluate risks related to capture, transport and storage, the associated CO_{2} migration mechanisms and pathways, as well as effects on atmosphere, soil, groundwater, and surface water. Each component in this chain of investigations must be based on all available data for the considered CO_{2} storage scenario, and the best possible probabilistic model for data uncertainties.
Current methods try to reach these ideal goals, but have severe limitations in the analysis of reservoir properties. Probabilistic analysis of geoscientific data and production data is not based on physically correct error propagation methods. Instead, statistical predictions about the reservoir are only based on (1) large geological data bases, or (2) subjective expert assessments of geophysical and geological data. Prediction models about the overburden are nearly nonexisting. These limitations may have significant consequences for the appraisal of possible caprock failures, releases through induced or existing faults, displacement into nontarget formations, or well leakage. Furthermore, a miscalculation of these factors may have a dramatic consequence on the evaluation of migration scenarios and their short and longterm consequences.
The aim of this pilot project is to investigate and describe how a risk analysis system based on a consistent, probabilistic approach to geophysical/geostatistical inversion and flow data analysis can be developed.
RESPROB [20182021] Probabilistic Geomodelling of Groundwater Resources
funded by Free Research Council (Technology and Production)
Groundwater mapping in Denmark is internationally acknowledged and regarded as a benchmark approach. Massive amounts of data (well logs, geophysical, geo and hydrological data) have been collected. Today these data are combined in a deterministic sequential workflow, where, typically, a single final model represents all available information. While successful, this workflow has some limitations: There is no way to ensure the final model consistency with all information at hand, and there is no way to ensure correct uncertainty quantification. The main goal of RESPROB is to develop a probabilistic data integration workflow that allows consistent integration of welllog, geophysical and geological data. The resulting probabilistic geomodel should be efficient tool for endusers for informed, datadriven, decision making and for risk assessment.
A PhD position (located at Niels Bohr Institute) and a PostDoc position (GEUS/University of Aarhus) will be offered as part of the project.
Collaborators and contact:
Niels Bohr Institute, University of Copenhagen [contact: Thomas Mejer Hansen(tmeha@nbi.ku.dk)]
GEUS [contact: Flemming Jørgensen (flj@geus.dk)]
Dept. of Geosciences, Aarhus University [contact: Niels Bøie Christensen (nbc@geo.au.dk)]
University of Cagliary [contact: Giulio Vignoli (gv@unica.it)]
USGS, Denver, [contact: Burke J. Minsley (bminsley@usgs.com)]
LOCRETA [20182020] Seismic modelling and optimal inversion
With this initiative we strive to improve seismic imaging of key features, which are determining for the reservoir properties of the lower Cretaceous sediment package, i.e. characteristic, alternating (cyclic?) lithologies as well as faults and fractures. We employ forward fullwaveform modelling for improved understanding of origin and characterization of seismic arrivals occurring from such key features, and we build fullwaveform inversion (FWI) schemes aimed particularly at resolution of such elements. The FWI schemes will be constrained by geological and rock physical prior knowledge (including results from other work packages of this proposal) and special emphasis will be on formulating the inversion schemes in a geostatistical framework, which provides realistic distributions and uncertainties of key seismic and/or rock physical parameters. We draw on existing collaboration with international leading experts in this research field.
Collaborators and contact:
Niels Bohr Institute, University of Copenhagen, Department of Geosciences and Natural Resource Management (IGN), University of Copenhagen. Geological Survey of Denmark And Greenland (GEUS), DTU Civil Engineering
[contact: Klaus Mosegaard (mosegaard@nbi.ku.dk)]
Outcrop Analog Studies of Chalk [20172020]
The goal is to build reservoir models spanning heterogeneities from millimeters to hundreds of meters, thereby providing a link between structural and depositional elements of widely different scales. In a crossdisciplinary effort, we combine geological, geophysical and geostatistical methods to identify different lengthscale regimes. Statistical models will be developed for each regime and combined to one multiscale model to be compared with North Sea data sets. Geostatistical models provide not only spatial estimates of rock properties with uncertainties and correlations, they also provide a framework for consistent updating of existing reservoir models with new information, as well as the necessary information needed to upscale a reservoir model to coarser grids to facilitate reservoir simulations.
Collaborators and contact:
Niels Bohr Institute, University of Copenhagen, Natural History Museum of Denmark, University of Copenhagen, Department of Geosciences and Natural Resource Management (IGN), University of Copenhagen.
[contact: Klaus Mosegaard (mosegaard@nbi.ku.dk)]
2018  

[pdf]  Hansen, T.M., Vu. L.T., Mosegaard, K., and Cordua, K. S. (2018) Multiple point statistical simulation using uncertain (soft) conditional data. Copmuters and Geosciences (114), May 2018, Pages 110. https://doi.org/10.1016/j.cageo.2018.01.017. 
[pdf]  Madsen. R.B., and Hansen, T.M. (2018) Estimation and accounting for the modeling error in probabilistic linearized AVO inversion. Geophysics, 2018. 83(2), 601606. doi:10.1190/geo20170404.1. 
2017  
[pdf]  Efficient Monte Carlo sampling of inverse problems using a Neural Network based forward  applied to GPR crosshole traveltime inversion Hansen, T.M. and Cordua, K.S. Geophysical Journal International, 211(2), 2017, 15241533.. doi:10.1093/gji/ggx380. 
[pdf]  Multiplepoint statistical simulation for hydrogeological models: 3D training image development and conditioning strategies Høyer, A.S, Vignoli, G., Hansen, T.M., Vu, L.T., Keefer, D.A., and Jørgensen, F. Hydrology and Earth System Sciences, 2017, 21(12), 60696089. doi:10.5194/hess2016567. 
[pdf]  On inferring the noise in probabilistic seismic AVO inversion using hierarchical Bayes. Madsen. R.B., Zunino, A., and Hansen, T.M. SEG Technical Program Expanded Abstracts 2017. Society of Exploration Geophysicists, 2017. 601606. doi:10.1190/segam201717725822.1. 
[pdf]  Automatic mapping of base of aquifer – A case study from Morill Nebraska. Gulbrandsen, M.L., Ball. L., Minsley, B., and Hansen, T.M., 2017 Interpretation 5(2), p. doi:10.1190/INT20160195.1 
[pdf]  Smart Interpretation  Automatic geological interpretations based on supervised statistical models. Gulbrandsen, M.L., Cordua. K.S., Bach, T., and Hansen, T.M., 2017 Computational Geosciences 21(3), pp 427440. doi:10.1007/s1059601796218. 
[pdf]  SemiAutomatic Mapping of Permafrost in the Yukon Flats  Alaska. Gulbrandsen, M.L., Minsley, B., Ball. L., and Hansen, T.M., 2016. Geophysical Research Letters 43(13), pp 1213112137. doi:10.1002/2016GL071334. 
[pdf]  Mixedpoint geostatistical simulation: A combination of two and multiplepoint geostatistics. Cordua. K.S., Hansen, T.M., Gulbrandsen, M.L., Barnes, C., and Mosegaard, K., 2016 Geophysical Research Letters 43(17), pp 90309037.. doi:10.1002/2016GL070348. 
2016  
Revealing multiple geological scenarios through unsupervised clustering of posterior realizations from reflection seismic inversion. Gulbrandsen, M.L., Cordua. K.S., Hansen, T.M., and Mosegaard, K. in Geostatistics Valencia 2016, Editors: GómezHernández, J.J., RodrigoIlarri, J., RodrigoClavero, M.E., Cassiraga, E., VargasGuzmán, J.A. (Eds.) 

[pdf,www]  MPSLIB: A C++ class for sequential simulation of multiplepoint statistical models. Hansen, T.M., Vu. L.T., and Bach, T. in SoftwareX, doi:10.1016/j.softx.2016.07.001. 
[pdf]  Probabilistic Integration of GeoInformation. Hansen, T.M., Cordua. K.S., Zunino, A., and Mosegaard, K. in Integrated Imaging of the Earth: Theory and Applications, pp 93116. ISBN:9781118929056. 
[]  Inverse Methods: Problem Formulation and Probabilistic Solutions. Mosegaard, K. and Hansen, T.M. in Integrated Imaging of the Earth: Theory and Applications, pp 928 ISBN:9781118929056. 
[]  Constitution and Structure of Earth’s Mantle: Insights from Mineral Physics and Seismology. Zunino, A., Khan, A., Cupillard, P., and Mosegaard, K. in Integrated Imaging of the Earth: Theory and Applications, pp 219244 ISBN:9781118929056. 
2015  
[pdf]  A general probabilistic approach for inference of Gaussian model parameters from noisy data of point and volume support. Hansen, T.M., Cordua. K.S., and Mosegaard, K. Mathematical Geosciences 47(7), pp 843865. published online 092014. doi:10.1007/s1100401495675 An example application using the SIPPI Matlab toolbox 
[pdf]  Monte Carlo reservoir analysis combining seismic reflection data and informed priors. Zunino, A., Mosegaard, K., Lange, K., Melnikova, Y., and Hansen, T.M. Geophysics 80(1), pp R31–R41, 2014. doi:10.1190/geo20140052.1 
2014  
[pdf]  History Matching through a Smooth Formulation of MultiplePoint Statistics. Melnikova,. Y., Zunino, A., Lange, K., Cordua, K. S., and Mosegaard, K. Mathematical Geosciences, May, 2014. doi:10.1007/s110040149537y 
[pdf]  Improving the pattern reproducibility of multiplepointbased prior models using frequency matching. Cordua, K. S., Hansen, T.M., and Mosegaard, K. Mathematical Geosciences, April 2014. doi:10.1007/s1100401495314 
[pdf]  Accounting for imperfect forward modeling in geophysical inverse problems  exemplified for cross hole tomography. Hansen, T.M., Cordua, K. S., Jacobsen, B. J., and Mosegaard, K. Geophsyics, 79(3) H1H21, 2014. doi:10.1190/geo20130215.1 
2013  
[pdf,code]  SIPPI : A Matlab toolbox for Sampling the solution to Inverse Problems with complex Prior Information: Part 1  Methodology. Hansen, T.M., Cordua, K. S., Looms. M.C., and Mosegaard, K. Computers & Geosciences, 52, 470480, 2013. doi:10.1016/j.cageo.2012.09.004. SIPPI Matlab toolbox 
[pdf, code]  SIPPI : A Matlab toolbox for Sampling the solution to Inverse Problems with complex Prior Information: Part 2  Application to cross hole GPR tomography. T.M., Cordua, K. S., Looms. M.C., and Mosegaard, K. Computers & Geosciences, 52, 481492480, 2013. doi:10.1016/j.cageo.2012.09.001. SIPPI Matlab toolbox 
Modeling and detection of oil in sea water. Xenaki, A., Gerstoft, P., and Mosegaard, K. Journal of the Acoustical Society of America, 134(4), pp 27902798, 2013. doi:10.1121/1.4818897. 

2012  
[pdf]  A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information. Lange, K., Frydendall, J., Cordua, K. S., Hansen, T.M., Melnikova, Y., and Mosegaard, K. Mathematical Geosciences, 44(7), 783803, 2012. doi:10.1007/s1100401294172. 
[pdf]  Monte Carlo Full Waveform Inversion of Crosshol GPR Data Using Multiplepoint Geostatistical a Priori Information. Cordua, K. S., Hansen, T. M., and Mosegaard, K., Geophysics, 77(2), pp H19H31, 2012. doi:10.1190/geo20110170.1. 
[pdf ]  Inverse problems with nontrivial priors  Efficient solution through Sequential Gibbs Sampling. Hansen, T. M., Cordua, K. S., and Mosegaard, K. Computational Geosciences, 16(3), pp 593611, 2012. doi:10.1007/s1059601192711 We thank Ian Lynam for allowing us to use one of his Neojaponsime patterns.

2011  
[]  Mosegaard, K., 2011. Quest for consistency, symmetry and simplicity : The Legacy of Albert Tarantola, Geophysics, 76, pp. W51W61. doi:10.1190/geo20100328.1 
2010  
[pdf]  Mosegaard, K., 2010. Albert Tarantola Memorial, The Leading Edge (), pp 874875. 
[]  Looms, M. C., Hansen, T. M., Cordua, K. S., Nielsen, L., Jensen, K. H., Binley, A., 2010. Geostatistical inference using crosshole groundpenetrating radar : Geostatistical inference using GPR, Geophysics, 75(6), pp J29J41. doi:10.1190/1.3496001 
[]  Nielsen, L., Looms, M. C., Hansen, T. M., Cordua, K. S., Stemmerik, L., 2010. Estimation of Chalk Heterogeneity from Stochastic Modeling Conditioned by Crosshole GPR Traveltimes and Log Data, in Advances in NearSurface Seismology and GroundPenetrating Radar, eds. Miller, R., Bradford, J., and Holliger, K., Society of Exploration Geophysicists, Tulsa, Oklahoma, ISBN: 9781560802242 , pp 379396. 10.1190/1.9781560802259.ch23 
[pdf]  Hansen, T. M., Mosegaard, K., and Schiøtt, C. R., 2010. Kriging interpolation in seismic attribute space applied to the South Arne Field, North Sea. Geophysics, 75(6), pp 3141.doi:10.1190/1.3494280 
2008  
[pdf]  Hansen, T. M., Mosegaard, K., PedersenTatalovic, R., Uldall, A., and Jacobsen, N. L., 2008. Attribute guided well log interpolation. Geophysics, 73(6), pp R83R95.doi:10.1190/1.2996302 
[pdf]  PedersenTatalovic, R., Uldall, A., Jacobsen, N.L., Hansen, T.M., and Mosegaard, K., 2008. Event Based Low Frequency Impedance Modelling using Well Logs and Seismic Attributes. The Leading Edge 27(5), pp 592603. 
[pdf]  Hansen, T. M., Looms, M. C., and Nielsen, L., 2008. Infering the subsurface structural covariance model using corss boreborehole ground penetrating radar tomography. Vadose Zone Journal, special issue on Ground Penetrating Radar in Hydrogeophysics 7(1), pp 249262. doi:10.2136/vzj2006.0144 
[pdf,code]  Hansen, T. M. and Mosegaard, K., 2008. VISIM : Sequential simulation for linear inverse problems, Computers and Geosciences 34(1), pp 5376, doi:10.1016/j.cageo.2007.02.003. If you intend to use VISIM please visit http://imgp.imm.dtu.dk/visim.php

2006  
[pdf]  Hansen T. M., Journel A. G, Tarantola A., and Mosegaard, K., 2006. Linear Inverse Gaussian Theory and Geostatistics, Geophysics 71(6), pp R101R111. doi:10.1190/1.2345195 
Software developed by Solid Earth Physics and Geostatistics
SIPPI
A Matlab toolbox for Sampling the solution to inverse problems with complex a priori models.
Source Code: http://github.com/cultpenguin/sippi
Documentation: https://cultpenguin.gitbooks.io/sippi/content/
See Hansen et al. 2013a,b (http://dx.doi.org/10.1016/j.cageo.2012.09.004, http://dx.doi.org/10.1016/j.cageo.2012.09.001)
MPSlib
A C++ class for MultiplePoint based sequential Simulation.
Source code: https://github.com/ergosimulation/mpslib, http://ergosimulation.github.io/mpslib/
Documentation: https://cultpenguin.gitbooks.io/mpslib/content/
See Hansen et al. 2016. (https://doi.org/10.1016/j.softx.2016.07.001)
Developed in collaboration with IGIS.
PHEMGP
The use of phase equilibrium calculations to compute physical properties of rocks has become commonplace in geophysical modeling. Typically, the phase equilibrium calculations are used to construct twodimensional tables of rock properties as a function of pressure and temperature. Phemgp is a Fortran program that can be used to assemble a threedimensional table that accounts for compositional variations from twodimensional tables.
Source Code: https://github.com/inverseproblem/Phemgp
See Zunino et al., 2011 (https://doi.org/10.1029/2010GC003304)
mGstat
Geostatistical toolbox for Matlab : Contains native Matlab functions and Matlab interfaces to gstat, snesim and sgems.
Source Code and documentation: http://github.com/cultpenguin/mgstat
SegyMAT
A Matlab toolbox for reading, writing and editing SEGY formatted files.
Source Code: http://github.com/cultpenguin/segymat
Documentation: https://cultpenguin.gitbooks.io/segymat/content/
VISIM
A FOTRAN 77 code for sequential Simulation conditioned to noisy data of mixed support.
Source Code: https://github.com/cultpenguin/mGstat/tree/master/visim/visim_src
See Hansen and Mosegaard, 2008. (http://dx.doi.org/10.1016/j.cageo.2007.02.003)
MPM
2D elastic finite difference waveform modeling. Especially efficent when simulation the elastic response from a target zone.
Source code: https://github.com/cultpenguin/mpm
See Hansen and Jacobsen, 2008 (https://doi.org/10.1016/S00983004(01)001133)
Centre secretary (web, communication, coordination, guests), pice@nbi.ku.dk
Staff
Name  Title  Phone  

Ayzenberg, Alena  Postdoc  +45 35324153  
Jóhannsson, Óli D.  PhD  
Khoshkholgh, Sarouyeh  Research assistant  +45 35333327  
Mosegaard, Klaus  Professor  +45 21 66 45 66  
Youssof, Mohammad  Postdoc  +45 35332169 
Enrolled PhD student
Name  Title  Phone  

Iris Fernandes  PhD Student  iris@nbi.ku.dk 
Students
Name  Titel 

Klaus Ortving Lindholmer  MSc. Student 
Niels Fabrin Nymand  MSc. Student 
Yifan Liu  MSc. Student 