An inverse method for obtaining the attenuation profile and small variations in the sound speed and density profiles of the ocean bottom

Abstract

The acoustic properties of marine sediments have a direct effect on the propagation of sound in the ocean. In the frequency range of interest (50 - 500 Hz) the sediment can be modelled as a fluid. Assuming horizontal stratification of the ocean bottom, the acoustic parameters of interest are the compressional wave speed, the compressional wave attenuation and density as a function of depth. An inverse method based on a perturbation technique is presented in this thesis for the determination of these parameters. A monochromatic source experiment is proposed because of the desirability of such an experiment for determining the acoustic properties of an anelastic medium. The input information is the plane wave reflection coerricent as a function of the angle of incidence at a fixed frequency. A nonlinear integral equation relating the variations of these acoustic properties from a known reference value to the plane wave reflection coefficient is derived. This is then linearised using the Born approximation. The region of validity of the Born approximation is derived and based on this the optimum angular aperture for the input data is obtained. The linearised integral equation is a Fredholm integral equation of the first kind. An acceptable stable solution of the integral equation is obtained by imposing a priori constraints on the solution. The inversion method is tested using synthetic data and inversions are carried out for various examples of the attenuation coefficient profile and the sound speed profile. The results obtained with noise free data show good agreement between the true profiles and the reconstructed profiles. The resolution obtainable with the data set is studied using the resolving power theory of Backus and Gilbert and the inversion method is shown to provide adequate resolution. The effect of additive noise in data is examined and inversions performed with noisy data yielded stable acceptable results.