Investigating Fine Structures of the Earth’s Interior Based on Spectral-element Seismic-wave Simulations

One of the ultimate goals in the studies of seismic waves is to utilize the entire records of seismograms and exploit these waveforms to map the heterogeneity and anisotropy in the Earth's interior. An important technique towards this goal is full waveform inversion (FWI), which often combines accurate numerical solvers of wave equations with gradient-based iterative model updates. Meanwhile, the model resolved by seismic tomography using the relatively low-frequency component of seismograms is only an equivalent smooth one (i.e., homogenized model) of the complex geological structures (i.e., the Earth). In this thesis, we first present the application of homogenization theory to transversely isotropic models and demonstrate the computational efficiency gained from using effective media in forward seismic wave simulations. An efficient wave-equation solver is vital to FWI as forward modeling is repeatedly used to compute accurate synthetics for the updated model to match the observations. Full numerical solvers based on spectral-element method (SEM) are desirable in this task of resolving fine-scale structures, but the associated computational cost can be prohibitive when the simulation frequency becomes high. Hybrid method can be used to reduce the computational cost by restricting the 2D/3D numerical solver to the target region where complex structures reside. We present the framework of an SEM-based two-way hybrid method where the target region can be anywhere inside the Earth. This two-way hybrid method can help map detailed heterogeneities in the lowermost mantle with the unprecedented resolution of FWI. As part of the work in this thesis to investigate fine-scale structures, we have also systematically measured the apparent splitting of vertically and horizontally polarized diffracted S waves along the core-mantle boundary (CMB) based on cross-correlation traveltimes, choosing Aleutian and west Africa as the study regions. Waveform simulations based upon SEM demonstrate that the SHdiff/SVdiff apparent splitting times from isotropic effects are comparable in magnitude to those from actual observations. These apparent splittings should be attributed to the different SHdiff and SVdiff sensitivities even in isotropic Earth models. Therefore, 1D and 3D isotropic effects, rather than intrinsic anisotropy, need to be first incorporated in the interpretation of SHdiff/SVdiff apparent splitting.Ph.D