Two unconventional approaches to electromagnetic inversion: hierarchical Bayesian inversion and inverse scattering series
Name:
Kwon_mines_0052N_10252.pdf
Size:
2.724Mb
Format:
PDF
Description:
Two unconventional approaches ...
Advisor
Snieder, Roel, 1958-Date issued
2013Keywords
inverse scattering seriesBayesian inversion
Inversion (Geophysics)
Bayesian statistical decision theory
Electromagnetism
Seismic waves -- Speed
Electric conductivity
Hydrocarbon reservoirs
Metadata
Show full item recordAbstract
Electromagnetic methods are effective complementary tools, when combined with seismic exploration, for the delineation of a hydrocarbon reservoir, because electromagnetic methods provide extra information about, for example, electric conductivity, which is an important property for the economic evaluation of reservoirs. In this study, we analyze unconventional approaches of electromagnetic inversion: hierarchical Bayesian inversion and inverse scattering series. We apply the hierarchical Bayesian inversion to the uncertainty analysis for the joint inversion and utilize rock-physics models to integrate these two disparate data sets. The study shows that the uncertainties in the seismic wave velocity and electric conductivity play a more significant role in the variation of posterior uncertainty than do the seismic and CSEM data noise. The numerical simulations also show that the uncertainty in porosity is most affected by the uncertainty in seismic wave velocity and that the uncertainty in water saturation is most influenced by the uncertainty in electric conductivity. The framework of the uncertainty analysis presented in this study can be utilized to effectively reduce the uncertainty of the porosity and water saturation derived from integration of seismic and CSEM data. We also study the feasibility of the inverse scattering series, which can effectively resolve the nonlinearity of an inverse problem, for the interpretation of electromagnetic data. The application of the inverse scattering series has been limited because the series converges when the reference model sufficiently close to the true model. This study quantifies convergence conditions of the inverse scattering series and suggests a different approach of the inverse series, the modified inverse scattering series, which guarantees the convergence of the series and facilitates the choice of a reference model.Rights
Copyright of the original work is retained by the author.Collections
Related items
Showing items related by title, author, creator and subject.
-
Buried penny-shaped cracksPenny-shaped cracks are commonly used mathematical models, generally used in the field of fracture mechanics. One specific application is the modeling of micro-structures, within elastic materials. From a purely mathematical perspective, a penny-shaped crack can be described as a flat, disk-shaped crack. In this work, we consider the buried penny-shaped crack problem, consisting of a single crack, buried below the surface of a half-space. Specifically, the flat surface of the crack is taken to be parallel to the boundary, and the radius of the crack is held constant. The primary point of interest in this problem is the depth dependence of the stress intensity factor, which characterizes the fracture conditions near the tip of the crack. Determining the stress intensity factor for this problem is reduced to solving a pair of dual integral equations, specifically looking at these equations evaluated at the upper bound of integration. These equations were amenable to numerical solution, where the distance between the crack and the boundary was allowed to become small. The values of these equations, at the upper bound of integration, both tend toward 0. Based on the numerical results, the stress intensity factors for this problem were dependent on the depth at which the penny-shaped crack is buried.
-
Waveform-based velocity estimation from reflection seismic dataThe objective of this thesis is to investigate new methods in reflection seismology for estimating subsurface velocity models accurately and efficiently. Full waveform inversion (FWI) is a state-of-the-art approach that can yield high-resolution models. However, multiple problems, including high computational cost, spurious local minima and possible geologically-implausible solutions, have prevented widespread applications of FWI for reflection data. These problems correspond to the fact that we in practice must estimate numerous model parameters with inadequate data (e.g., limited aperture, insufficient low frequencies). To tackle the problems and achieve the goal of this thesis, I develop image-guided sparse-model FWI (IGFWI) and wave-equation reflection traveltime inversion (WERTI). IGFWI uses subsurface structures to constrain the inversion of a sparse model. I extract the subsurface structures from migrated seismic images. With the structures, I construct a sparse model, which can, with substantially fewer parameters, explain the subsurface in a geologically plausible way. The IGFWI optimization problem is then formulated with respect to the sparse model that is constrained by structures. With fewer parameters, IGFWI converges faster in fewer iterations than does conventional FWI; with structural constraints, estimated models are geologically plausible; with a sparse representation of the model, blocky updates mitigate the lack of low frequencies. I solve IGFWI using a image-guided conjugate-gradient method. With respect to the sparse model, I explicitly compute a projected Hessian matrix and its inverse using a projected BFGS (P-BFGS) method. Compared to the classic limited-memory BFGS (L-BFGS) method, P-BFGS substantially saves both computational time and memory, due to fewer model parameters of the sparse model. With the P-BFGS method, I propose an efficient quasi-Newton method to solve large-scale inversion problems, such as FWI. I also introduce WERTI to recover the low-wavenumber velocity background, and thereby mitigate local minima in reflection FWI with insufficient low frequencies. By alternating between WERTI and FWI, we can overcome the velocity-depth ambiguity in reflection traveltime inversion and estimate both the low- and high-wavenumber components of velocity models using only high-frequency reflection data .
-
Parts-based geophysical inversion with application to water flooding interface detection and geological facies detectionI built parts-based and manifold based mathematical learning model for the geophysical inverse problem and I applied this approach to two problems. One is related to the detection of the oil-water encroachment front during the water flooding of an oil reservoir. In this application, I propose a new 4D inversion approach based on the Gauss-Newton approach to invert time-lapse cross-well resistance data. The goal of this study is to image the position of the oil-water encroachment front in a heterogeneous clayey sand reservoir. This approach is based on explicitly connecting the change of resistivity to the petrophysical properties controlling the position of the front (porosity and permeability) and to the saturation of the water phase through a petrophysical resistivity model accounting for bulk and surface conductivity contributions and saturation. The distributions of the permeability and porosity are also inverted using the time-lapse resistivity data in order to better reconstruct the position of the oil water encroachment front. In our synthetic test case, we get a better position of the front with the by-products of porosity and permeability inferences near the flow trajectory and close to the wells. The numerical simulations show that the position of the front is recovered well but the distribution of the recovered porosity and permeability is only fair. A comparison with a commercial code based on a classical Gauss-Newton approach with no information provided by the two-phase flow model fails to recover the position of the front. The new approach could be also used for the time-lapse monitoring of various processes in both geothermal fields and oil and gas reservoirs using a combination of geophysical methods. A paper has been published in Geophysical Journal International on this topic and I am the first author of this paper. The second application is related to the detection of geological facies boundaries and their deforation to satisfy to geophysica data and prior distributions. We pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case study, performing a joint inversion of gravity and galvanometric resistivity data with the stations all located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to deform the facies boundaries preserving prior topological properties of the facies throughout the inversion. With the additional help of prior facies petrophysical relationships, topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The result of the inversion technique is encouraging when applied to a second synthetic case study, showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries. A paper has been submitted to Geophysics on this topic and I am the first author of this paper. During this thesis, I also worked on the time lapse inversion problem of gravity data in collaboration with Marios Karaoulis and a paper was published in Geophysical Journal international on this topic. I also worked on the time-lapse inversion of cross-well geophysical data (seismic and resistivity) using both a structural approach named the cross-gradient approach and a petrophysical approach. A paper was published in Geophysics on this topic.
