Full Anelastic Waveform Inversion Including Model Uncertainties

Aysegul Askan, & Jacobo Bielak

In Preparation 2007, SCEC Contribution #1093

In a recent article, we described an inverse anelastic wave propagation algorithm for determining the crustal velocity and attenuation properties of basins in earthquake-prone regions. We formulated the tomography problem as a constrained optimization problem where the constraints are the partial and the ordinary differential equations (PDE and ODE, respectively) describing the anelastic wave propagation from the source to the receivers. We employed a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. We assumed that no information was initially available on the target shear wave velocity distribution, and we began the inversion process with a homogeneous shear wave velocity profile as the initial guess. In practice, some information is usually available. To treat such cases, in this paper, we modify our nonlinear inversion method to start from an initial velocity model, by including a-priori information regarding the initial model parameters in the misfit (objective) function. To represent model uncertainties, given a prior velocity model, in addition to the data misfit term in our objective function, we include an L�-normed weighting term, which quantifies the model estimation errors independent of the measured data.

To overcome rank deficiency and ill-conditioning issues, we use total variation regularization. The problem of multiple minima is not encountered in the present inversion technique since the inversion process starts with an a-priori model that is already in the attraction basin of the global minimum of the inverse problem.

We illustrate the methodology with pseudo-observed data from two-dimensional sedimentary models of the San Fernando Valley, using a source model with an antiplane slip function.

Askan, A., & Bielak, J. (2007). Full Anelastic Waveform Inversion Including Model Uncertainties. Not yet decided, (in preparation).