A numerical algorithm for remote sensing of density profiles of a simple ocean model by acoustic pulses

Abstract

An iterative algorithm for solving nonlinear inverse problems in remote sensing of density profiles of a simple ocean model by using acoustic pulses is developed. Here the adiabatic sound velocity is assumed to be proportional to the inverse square root of the density. The basic idea of this new algorithm is that first, the original pulse problem in the time domain is reduced to a continuous wave problem in the frequency domain and then the nonlinear inverse problem in the frequency domain is solved by a hybrid of a Newton-like iterative method, Backus and Gilbert linear inversion technique, and the finite difference method. This new computational algorithm is tested by numerical simulations with given data from 10 different frequencies and is found to give excellent results. The effects of taking data from various frequency ranges and of the contaminating instrument and ambient noise on the accuracy and efficiency of numerical computation are investigated. It is found that the low frequency data are preferred over the data from the high frequency spectrum. Under favorable conditions, the maximum pointwise numerical error of the density profile ϱ( x) is less than 5% of the total variation of the density profile, ρ tv =|Max ρ( x) − Min ρ( x)|. Better result can be achieved if a large number of data are available and more efforts are made in the numerical computation.