This article is concerned with the problem of seismic inversion in the presence of model uncertainty. In a recent article (Askan et al., 2007), we described an inverse adjoint 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 that govern 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 was modeled by a set of standard linear solids. Assuming no information was initially available on the target shear-wave velocity distribution, we employed a homogeneous shear-wave velocity profile as the initial guess. In practice, some information is usually available. The purpose of the present article is to modify our nonlinear inversion method to start from an initial velocity model, and include a priori information regarding the initial model parameters in the misfit (objective) function. To represent model uncertainties, given an initial velocity model, in addition to the data misfit term in our objective function, we include an L2-normed weighting term, which quantifies the model estimation errors, independently of the measured data. We use total variation (TV) regularization to overcome ill posedness. 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.

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