Simultaneous Linearized Inversion of Velocity and Density Profiles for Multidimensional Acoustic Media
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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The multidimensional inverse scattering problem for an acoustic medium is considered within the homogeneous background Born approximation. The medium is probed by wide-band plane wave sources, and the scattered field is observed along straight-line receiver arrays. The objective is to reconstruct simultaneously the velocity and density profiles of the medium. The time traces observed at the receivers are appropriately filtered to obtain generalized projections of the velocity and density scattering potentials, which are related to the velocity and density perturbations of the medium with respect to their nominal values. The generalized projections are weighted integrals of the scattering potentials in two dimensions the weighting functions are concentrated along parabolas, in three dimensions they are concentrated over circular paraboloids. The reconstruction problem for the generalized projections is formulated in a way similar to the problem of x-ray, or straight-line tomography. The solution is expressed as a back-projection operation followed by a two or three dimensional space-invariant filtering operation. In the Fourier domain, the resulting image is a linear combination of the velocity and density scattering potentials, where the coefficients depend on the angle of incidence of the probing wave. Therefore, two or more different angles of incidence are necessary to reconstruct the velocity and density scattering potentials separately.
- Numerical Mathematics