An Estimation Method of Impulse Response and its Application

Abstract

The estimation of linear filter from observed time series of input x₁(t) and output x₂(t) is considered. Following Burg's algorithm for maximum entropy method, a new technique is developed in this paper, where the impulse response of the filter as well as the correlation functions of x₁ and x₂ are simultaneously estimated.
The method is applied to the analysis of elastic wave response of rock samples (granite). It is shown that the dispersion of P-wave phase velocity amounts to 4 percent of the non-dispersive velocity. It is comparable to the value expected from the attenuation property: Q=10-20 and Kramers-Kronig causality relation.