Waveform Inversion for Estimating Subsurface Properties: Phase-encoding Strategies, Optimization Methods, Interparameter Tradeoffs Quantification and Reduction

Wenyong Pan

This thesis concerns seismic full-waveform inversion (FWI) techniques for estimating subsurface properties. FWI approaches promise to provide high-resolution estimates of subsurface parameters using full wavefield information. However, FWI also suffers from a series of obstacles including extensive computation requirements, slow convergence rate, cycle-skipping, interparameter tradeoffs, etc. This thesis focuses on developing advanced phase-encoding and optimizations methods for accelerating FWI, quantifying and reducing the interparameter tradeoffs in multiparameter FWI.

Iteratively minimizing the objective function and updating the models gives rise to high computational costs. In this thesis, I have developed phase-encoding approaches for constructing gradient and Hessian diagonals in the τ-ρ domain for accelerating FWI. Most of FWI applications employ gradient-based methods for updating the models by assuming the Hessian to be an identity matrix, which suffer from slow convergence rate. In this thesis, advanced second-order optimizations (i.e., l-BFGS and Hessian-free methods) are developed for improving the convergence rate. Different preconditioning strategies are examined for accelerating Hessian-free Gauss-Newton FWI.

Simultaneously reconstructing multiple physical parameters suffers from parameter crosstalk, a dificulty arising from inherent ambiguities among different physical parameters. Quantifying the coupling effects of different physical parameters is an essential part of multiparameter FWI. Most parameter resolution studies are based on scattering patterns. Ambiguities appear between different physical parameters if their scattering patterns overlap over a certain range of scattering angles. Scattering patterns of isotropic-elastic parameters with various parameterizations are derived in this thesis. The interparameter contamination kernels are introduced to explain the origins of interparameter tradeoffs. A novel inversion strategy with approximate contamination kernels is developed for providing more convincing density estimations in isotropic-elastic FWI. Synthetic examples and realistic seismic dataset examples are given to verify the effectiveness of this inversion strategy. Performances of different parameterizations for isotropic-elastic FWI are also examined.

This thesis also demonstrates that applying inverse multiparameter Hessian to precondiii tion the gradients is able to suppress the unwanted interparameter contaminations. 3D scattering patterns of elastic constants in general anisotropic media are given. The second-order term in multiparameter Hessian, which accounts for multiparameter second-order scattering, can be constructed with adjoint-state approach. Newton-based methods are applied to reconstruct the elastic constants in anisotropic (HTI) media.