A statistical analysis for an inverse acoustic problem in estimating spatially varying sound velocity

A simple inverse acoustic algorithm using the Levenberg-Marquardt method is developed to estimate the sound velocity held as a function of depth from the transient measurements of the wave displacement at some suitable locations. The inverse calculations are performed based on the simulated exact and inexact measurement data to show the validity of the present study. Moreover, statistical analysis will also be considered here to determine both the best measurement position anti the 99% confidence hounds. Results show that the accuracy of the estimated sound velocity and its sensitivity to the measurement errors depend on the number of measurement data, as well as the measured positions. The reliable inverse solutions can be obtained only when these two factors are chosen properly.