Spectral properties of the interference head wave

Abstract

The interference head wave propagating through a sediment with a linear sound speed gradient is studied as a function of the parameter zeta, which is itself a function of acoustic frequency f, sediment sound speed and its gradient, and range. For zeta<1 the amplitude spectrum of the interference head waves goes as |S(f)|/f, where S(f) is the source spectrum. For increasing zeta beyond unity a more complicated modulation of S(f) ensues, which is explained by a channel transfer function H1(f), constructed analytically from a summation of terms involving zeroth-order refracted waves (referred to as a ray approach). For zeta greater than or approximately equal to 2 this summation compares well with a wave theory result for the interference head wave involving a fluid-fluid boundary. The amplitude spectrum of the interference head wave in the absence of sediment attenuation is |S(f)| x |H1(f)| and it is essential to know these to obtain an estimate of sediment attenuation from field observations. Examples of |S(f)| x |H1(f)| are presented for which H1(f) is computed directly using the ray approach and indirectly using the parabolic wave equation. A brief discussion on the application of these results towards the inversion of sediment attenuation is given.