Abstract
The inverse problem in geophysics is the determination of the inhomogeneous structure of an elastic medium from experimental observations. In this presentation, we first briefly review the Gelfand-Levitan and the Marchenko methods for the solution of the related quantum inverse problem. In these approaches, as well as in the methods for the geophysical problem we will discuss, the desired information is recovered from the solution of certain integral equations. Next, we consider the construction of a computational scheme for the inversion of geophysical data based on one of the methods. We will further show that the resulting algorithm is stable under small perturbations to the data. We will finally demonstrate the inversion scheme by inverting noiseless and noise-corrupted synthetic seismograms.
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