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Efficient modeling and waveform inversion of multicomponent seismic data for anisotropic media
Sethi, Harpreet Singh
Sethi, Harpreet Singh
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2023
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2024-10-23
Abstract
Accurate modeling of elastic wavefields is crucial for seismic imaging and inversion applications. Incorrect handling of the boundary conditions can distort the wavefield solutions, especially the horizontal displacement and velocity components, which may have serious implications for elastic reverse time migration (ERTM) and elastic full-waveform inversion (EFWI). For ERTM and EFWI, another important factor to consider is the computational speed of the modeling engine because inefficient algorithms are impractical for industrial applications. This thesis aims to develop efficient elastic wave propagators using mimetic finite-difference (MFD) operators and fully staggered grids (FSGs). Also, I present an EFWI framework based on these propagators and discuss inversion strategies for estimating the parameters of coupled fluid/solid VTI (transversely isotropic with a vertical symmetry axis) media using multicomponent ocean-bottom data.
First, I develop a graphics processing unit (GPU)-based MFD+FSG algorithm to efficiently model elastic wavefields in anisotropic media. The CUDA Aware MPI framework is used to handle communication across GPU nodes. The weak- and strong-scaling tests on up to eight DGX NVIDIA A100 nodes (64 GPUs in total) demonstrate the efficiency of the algorithm. Numerical tests for large-scale anisotropic models with more than 1.7$\times$10$^{\rm 10}$ grid points indicate that the algorithm achieves a quasilinear computational speedup with over 98\% efficiency. Comparison with results from the spectral-element method (SEM) demonstrates the high accuracy of the algorithm.
Next, this methodology is extended to a coupled fluid/solid medium to accurately handle the boundary conditions at the seafloor for marine seismic applications. Numerical experiments reveal wavefield distortions caused by erroneously assuming the seafloor to be a welded boundary. The proposed algorithm is also less computationally expensive than the conventional ``welded" approach, and comparisons with SEM solutions again confirm the accuracy of the MFD+FSG implementation.
For handling nonflat bathymetric surfaces, I use a vertically deformed coordinate system to transform the irregular grid into a regular Cartesian grid in a generalized coordinate system. Then, a tensorial approach is employed to directly solve the wave equation in the transformed coordinate system. A semianalytic coordinate mapping is employed for computationally- and memory-efficient implementation of the fluid/solid boundary conditions. Numerical tests confirm that the MFD+FSG algorithm can accurately handle undulating bathymetric surfaces overlying structurally complex anisotropic
media.
Then, I develop a framework for anisotropic elastic full-waveform inversion of multicomponent ocean-bottom data using the coupled fluid/solid MFD+FSG propagator. The adjoint fluid/solid coupled system and the gradient of the objective function are derived by employing the adjoint-state method. Several inversion strategies using individual data components and their combinations are investigated using a multiscale algorithm. Synthetic tests show that using a sequential strategy by operating with a single data component at a time improves the overall accuracy of the inverted parameters. Also, the inversion benefits from including the horizontal displacement or particle-velocity components, especially for heterogeneous underwater models.
Finally, I develop a mesh-free approach for solving the acoustic wave equation using physics-informed neural networks (PINNs). The physical laws governing the partial differential equations (PDEs) are used as regularization terms in the loss function. The initial conditions are enforced in a hard manner instead of including them as an additional regularization term. A Fourier neural network (FNN) is used to address the spectral bias commonly observed in PINNs based on fully connected neural networks (FCNNs). The developed PINN approach is not as prone to numerical errors and is less restrictive than the traditional numerical methods such as the MFD+FSG method developed in this thesis. It provides a potential alternative for wavefield modeling in imaging and waveform-inversion algorithms.
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