Browsing by Subject "Inverse theory"

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A mixed forward/inverse modeling framework for earthquake deformation problems
(2023-08-11) Puel, Simone; Becker, Thorsten W.; Lavier, Luc; Ghattas, Omar; Hesse, Marc A; Johnson, Kaj M
Subduction is responsible for the most powerful earthquakes and dangerous volcanic eruptions, resulting in significant human casualties and economic losses. However, the prediction of these natural events remains challenging due to an incomplete understanding of the underlying physics that govern these phenomena. Key questions persist regarding stress accumulation and dissipation, rock behavior under extreme pressure and temperature, and the influence of fluids and melt in these processes. Recent advancements in space geodesy and seismic networks have enabled the measurement of seismic responses and surface displacements, revealing the complex dynamics of subduction zones. To enhance our comprehension of these processes, computational modeling that integrates various types of observations and constraints is crucial. This can be achieved through forward modeling, where model parameters are adjusted to better fit the observations, or through inverse modeling, which extracts critical parameters and the underlying physical mechanisms directly from the data. However, a comprehensive numerical physics-based modeling framework that combines both forward and inverse capabilities, using adjoints, within a unified infrastructure is currently lacking. The objective of this dissertation is to address this gap by developing an open-source, flexible, transparent, and easily extendable framework capable of handling multi-physics coupled problems. This framework will also drive the advancement of innovative techniques for analyzing earthquake systems. It introduces a novel implementation of fault discontinuity within the finite-element model, an improved fault slip inversion method that does not require Green’s function computations, and a novel approach to infer material structure solely from surface displacement data, eliminating the need for seismic velocity analysis. Furthermore, by incorporating these approaches, it offers a novel joint inversion of surface geodetic data, facilitating the simultaneous recovery of subduction zone structure and coseismic slip distribution. This provides valuable insights into the interplay between heterogeneous material structure and fault processes. As a demonstration, the framework successfully recovers the coseismic slip distribution and subduction zone structure by inverting the coseismic surface displacements recorded during the 2011 M9 Tohoku-oki earthquake in Japan. The results reveal weaker material beneath several volcanoes in the same region where local coseismic subsidence was reported during the earthquake. Accounting for heterogeneity in fault slip inversions is crucial for accurately matching the surface displacement data, as suggested by previous studies. Overall, the proposed framework represents a significant advancement in subduction zone modeling, providing a comprehensive tool for understanding and analyzing these complex phenomena, thereby paving the way for improved hazard assessment and risk mitigation strategies.
Diffraction imaging by path-summation migration
(2018-08-07) Merzlikin, Dmitrii; Fomel, Sergey B.; Foster, Douglas J; Ghattas, Omar; Meckel, Timothy A; Sen, Mrinal K
Unconventional reservoir characterization requires accurate and high-resolution subsurface images to detect small-scale geological features controlling the production efficiency. Diffraction imaging techniques provide higher lateral resolution images in comparison with the results of conventional reflection imaging and highlight direct responses of such subsurface discontinuities as faults, channel edges, fracture swarms and pinch-outs, distribution of which can be crucial for reservoir development decisions. There are three major challenges in diffraction imaging: reflection/diffraction separation, imaging of diffractions, and de-noising of diffractions. I develop a diffraction imaging workflow based on least-squares inversion and path-summation migration to address these challenges and to improve the robustness of diffraction imaging. Conventional reflection images are dominated by high-energy reflections, which mask diffractions. The challenge of diffraction/reflection separation is to extract diffracted energy by suppressing reflections. Diffraction on an edge has both reflective and diffractive components. Both components should be preserved to generate a diffraction image. I develop azimuthal plane-wave destruction workflow (AzPWD) to account for edge diffraction signatures. The method suppresses high-energy reflections and preserves edge diffractions by orienting plane wave destruction (PWD) filter perpendicular to the edge. Edge orientations are also determined and can be utilized for the interpretation. Diffraction imaging is based on conventional imaging operators tailored towards reflections. I develop analytical expressions for path-summation integral diffraction imaging, which naturally incorporates diffraction apex stationarity under time migration velocity perturbation. This approach allows for determining diffraction likelihood distribution with the approximate cost of only two fast Fourier transforms in a velocity-model-independent fashion. I also develop double-path-summation framework for automatic migration velocity analysis based on diffractions, which does not require picking. Diffraction images are prone to noise and contain reflection remainders after application of reflection-diffraction separation procedure. I address this problem using least-squares migration. I define the inverted forward modeling operator as the chain of three operators: Kirchhoff modeling, plane-wave destruction and path-summation integral filter. This chain of operators accounts for diffraction energy contribution to the least-squares migration misfit dominated by reflections. I propose to use sparsity constraints to penalize diffractions with spiky and intermittent distributions. Reflections are regularized using smoothing along the dominant local slopes in the image domain. I use a shaping regularization framework. The approach decomposes input data into diffractions, reflections and noise. I extend the proposed chain inversion approach to 3D to account for edge diffraction responses by replacing PWD with AzPWD in forward modeling. I penalize edge diffractions using both sparsity constraints and anisotropic diffusion. The first regularization extracts diffractive component of the edge response whereas the second one enforces continuity along the edge to account for the reflective component. Proposed inversion schemes address the challenge of diffraction de-noising and can be treated as imaging operators tailored towards diffractions and extracting edge diffractions in an iterative fashion. The developed workflows allow for diffraction extraction from reflections and noise and for accurate focusing of diffracted energy. Numerous synthetic and field data examples are used to test the performance of the proposed methods. The tests confirm their effectiveness.