HR: 09:30h
AN: H21G-07    [Abstracts]
TI: Markov chain Monte Carlo based Approaches for Inverse Problems
AU: * Chen, J
EM: jchen@lbl.gov
AF: Lawrence Berkeley National Lab, MS 90-1116 1 Cyclotron Road, Berkeley, CA 94720 United States
AU: * Chen, J
EM: jchen@lbl.gov
AF: Department of Civil and Environmental Eng., University of California, Berkeley, CA 94720
AU: Hoverten, M
EM: GMHoversten@lbl.gov
AF: Lawrence Berkeley National Lab, MS 90-1116 1 Cyclotron Road, Berkeley, CA 94720 United States
AU: Vasco, D
EM: DWVasco@lbl.gov
AF: Lawrence Berkeley National Lab, MS 90-1116 1 Cyclotron Road, Berkeley, CA 94720 United States
AU: Hou, Z
EM: hou@berkeley.edu
AF: Department of Civil and Environmental Eng., University of California, Berkeley, CA 94720
AU: Rubin, Y
EM: rubin@ce.berkeley.edu
AF: Department of Civil and Environmental Eng., University of California, Berkeley, CA 94720
AB: Inverse modeling of heterogeneous subsurface systems is difficult. One of the main challenges is the lack of effective and flexible inversion methods that can handle complex practical situations, which may be characterized by non-Gaussian likelihood functions and prior distributions, multiple local optimal solutions, as well as nonlinearity and non-uniqueness of the relationships between parameters and measurements. This study presents a Markov chain Monte Carlo (MCMC) based approach for inverting complex data sets. This approach includes three major steps: (1) Build a stochastic model within the Bayesian framework; (2) Generate many samples from the joint posterior distribution using MCMC methods; (3) Make inferences about unknown parameters from the generated samples. The use of MCMC methods makes our approach very flexible for solving complex inversion problems. First, we can virtually use any types of likelihood functions and prior distributions in the Bayesian model. This allows us to build inversion models primarily based on complex practical situations. Second, MCMC methods are well suitable for parallel computing. This allows us to incorporate computationally intensive forward simulation models into the inversion procedures and allows us to avoid being trapped in multiple local modes of the joint posterior distribution. Finally, MCMC methods generate many samples of unknown parameters. This allows for quantification of uncertainty in estimation of each unknown parameter. To demonstrate our approach, we applied it on geophysical seismic and electromagnetic (EM) data for estimating porosity and natural gas saturation in deepwater gas reservoir. Conventional techniques (such as seismic methods) for gas exploration often suffer a large degree of uncertainty because seismic properties of a medium are not sensitive to gas saturation in the medium. In contrast, electrical properties of a medium are very sensitive to gas saturation. Therefore, EM techniques have the potential of providing information for reducing the uncertainty. We explore in this study the combined use of seismic and EM data using MCMC methods based on layered reservoir models. We consider gas saturation and porosity in each layer of the reservoir, seismic velocities and density in the layers below and above the reservoir, and electrical conductivity in the overburden as random variables. We consider pre-stack seismic amplitude versus offsets (AVO) measurements in a given time window and the amplitudes and phases of the recorded electrical field as data. Using the Bayes' theorem, we get the joint posterior distribution function of all the unknowns. Using MCMC sampling methods, we obtain many samples for each of the unknowns. We demonstrate the efficiency of the developed model for joint inversion of seismic AVO and EM data, and the benefits of incorporating EM data into gas saturation estimation, using two case studies, one is a synthetic case study, and the other is a field case study. Results show that the incorporation of EM data reduces the uncertainty within estimation of both gas saturation and porosity.
DE: 0520 Data analysis: algorithms and implementation
DE: 0619 Electromagnetic theory
DE: 1829 Groundwater hydrology
DE: 3265 Stochastic processes (3235, 4468, 4475, 7857)
DE: 3275 Uncertainty quantification (1873)
SC: Hydrology [H]
MN: Fall Meeting 2005