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Tensorial elastodynamics and acoustodynamics for generalized seismic migration and inversion applications
Konuk, Tugrul
Konuk, Tugrul
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2022
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Abstract
Numerical solutions of elastodynamics and acoustodynamics form the key computational kernels for a wide variety of earth imaging and inversion problems within the exploration, microseismic, and earthquake seismology communities. The main driver is the need to accurately model and reproduce full-wavefield solutions, which represent the main computational effort for such applications as elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI). However, real-life scenarios often require computing solutions for computational domains characterized by non-Cartesian geometry (e.g., free-surface topography). The majority of the available modeling and imaging applications assume Cartesian meshes, which face significant challenges in obtaining stable and accurate numerical wave-equation solutions due to difficulties in representing curvilinear geological interfaces.
Many difficulties associated with curvilinear solution geometries can be precluded by abandoning the Cartesian coordinate system and obtaining numerical elastodynamics solutions directly on a coordinate system conformal to the irregular topologies encountered in real-world applications. I propose a novel tensorial strategy for generalized modeling and least-squares reverse time migration (E-LSRTM) of elastic multi-component seismic data in arbitrarily heterogeneous and anisotropic media for generalized geometries (e.g., conformal to complex free-surface topography or bathymetry). The proposed methods have computational complexities comparable to those of their Cartesian counterparts and lead to more accurate numerical solutions and subsurface model estimates than are possible with Cartesian meshes, especially when considering the irregular computational geometries. I validate the tensorial approach with realistic numerical modeling and imaging examples, which demonstrate that the proposed solution can simulate anisotropic elastodynamic field solutions on irregular geometries and is thus a reliable tool for anisotropic elastic modeling, imaging and inversion applications in generalized computational domains.
I also extend the tensorial approach to time-varying scenarios, develop a new 3D acoustic wave equation formulation appropriate for time-varying solution domains (e.g., waves at the ocean-air interface), and propose a numerical mimetic finite-difference time-domain (MFDTD) approach that accurately simulates seismic wave propagation on a "moving mesh''. I present numerical examples that demonstrate that the developed MFDTD method can accurately simulate seismic wavefield propagation on a moving mesh for significant wave heights of 5m and beyond and is thus a reliable tool for applications involving modeling, processing, imaging and inversion of seismic data acquired in rough seas.
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