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

Computational Seismology Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 aaskan{at}andrew.cmu.edu

Volkan Akcelik

Stanford Linear Accelerator Center, Stanford University, Menlo Park, California 94025 volkan{at}slac.stanford.edu

Jacobo Bielak

Computational Seismology Laboratory, Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 jbielak{at}cmu.edu

Omar Ghattas

Jackson School of Geosciences, Department of Mechanical Engineering, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712 omar{at}ices.utexas.edu

^* Present Address: Department of Civil Engineering, Middle East Technical University, Ankara, 06531, Turkey.

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse 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 propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled 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 regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology 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.

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				A. Askan and J. Bielak Full Anelastic Waveform Tomography Including Model Uncertainty Bulletin of the Seismological Society of America, December 1, 2008; 98(6): 2975 - 2989. [Abstract] [Full Text] [PDF]