Full Waveform Inversion for Seismic Velocity and Anelastic Losses in Heterogeneous Structures

Abstract

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic at- tenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the in- verse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to a variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propaga- tion model in which the intrinsic energy-dissipating nature of the soil medium is mod- eled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regulariza- tion functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multi- ple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to re- main within the basin of attraction of the global minimum. We illustrate the metho- dology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.