The Reflection Inverse Problem for Acoustic Waves

: We study an acoustic model of the inverse problem of reflection seismology. A straightforward best-fit formulation of this problem has been used by several investigators as the basis for numerical solution of this problem, but typically fails when coupled with local optimization algorithms. We give an explanation for this failure, and suggest a relaxation of the best-fit formulation which may be more amenable to quasi-Newton optimization. Our analysis relies on linearization and on a high-frequency (Fourier Integral) approximation to the scattered field.