Full waveform inversion for seismic velocity and anelastic losses in heterogeneous structures

The objective of this thesis is to solve the inverse viscoelastic wave propagation problem for determining the crustal velocity and attenuation properties of basins in earthquake-prone regions. Given a heterogeneous medium with known dimensions, a predefined seismic source, and measurements at receiver locations, the goal is to determine the elastic and viscoelastic properties of the heterogeneous medium. The inverse problem is formulated as a constrained optimization problem where the constraints are the partial, (PDE) and the ordinary (ODE) differential equations describing the viscoelastic wave propagation from the source to the receivers.; The performance of the seismic waveform inversion problem depends on the fidelity of the forward model used to describe the wave propagation. In this work, we employ an improved wave propagation model where the intrinsic energy dissipating nature of soil medium is modeled by a set of standard linear solids.; The well-known inherent challenges of inverse wave propagation algorithms encountered in this work are rank deficiency and multiple minima. To overcome rank deficiency, we add a regularization functional to the objective function for penalizing high frequency material perturbations. To treat multiple minima, we make use of a multiscale algorithm that employs spatial domain decomposition for the optimizer to remain within the attraction basin of the global minimum. As illustration of the methodology, we present high resolution results for two-dimensional sedimentary models of the San Fernando Valley, under SH wave excitation. We perform inversions both for the seismic velocity and the damping model using synthetic waveforms at the observer locations as pseudo-observed data. Results prove to be encouraging for future inversion attempts using actual observations.