Velocity and density profiles of a layered acoustic medium from common source‐point data

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Abstract
An inverse scattering theory is presented for the unique reconstruction of the density and velocity profiles of a layered acoustic half‐space from common source‐point surface data. The point source is either impulsive or is capable of vibrating at two arbitrary frequencies. An additional datum for the unique reconstruction of these profiles is an estimate of either the highest or lowest velocity within the inhomogeneous acoustic half‐space. Two direct (noniterative) inversion algorithms are developed which construct the density and velocity profiles of the inhomogeneous half‐space from these data. Analytical examples are presented in which all steps in the inversion algorithms are analytically determined. Finally, the paper discusses the potential application of the theory to real seismic data.

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