Inverse scattering in a stratified medium

Abstract

A point harmonic source at frequencies ω1 and ω2 is located in the region z < 0, where both the sound-speed and density profiles are known. These two profiles are recovered from a measurement of the pressure field for all r at some fixed depth z < 0 at the two frequencies. Trace formula methods are used. The following assumptions are needed. First, c(z) and ρ(z) approach c1, ρ1 as z→ − ∞ and c2, ρ2 as z→ + ∞, and although c2, ρ2 are not known, it must be known that c2⩾c1. Second, the angular frequencies ω1 and ω2 must excite no proper modes, i.e., only the continuous spectrum is excited. Third, the sound speed c(z) may be complex, but c1 and c2 must be real. If c(z) also depends on frequency and the form of the dependence is known, say c(z) = cR(z) + iωλ(z), cl(z), then cR(z), cl(z), λ (z) can be recovered along with the density. If the density is known and c(z) is real then only one frequency is required. Two numerical examples are given, using parameters associated with ocean bottom sediments.