A Method of Parameter Estimation for Stochastic Distributed Parameter Systems and its Applications to Seismic Profiles Identification

Abstract

Bearing in mind an application to the identification of seismic profiles, e.g., the oil exploration survey, this taper gives a feasible method for estimating parameters of a class of distributed parameter systems modeled by the one-dimensional hyperbolic partial differential equation with stochastic boundary input. Fast, the theoretical aspect of existence and uniqueness conditions of the solution to the basic equation is discussed in a Kilbert space. Secondly, a method for estimating the system parameter is developed within the framework of the maximum likelihood ratio principle. An example of practical applications is finally shown, including estimation of the reflection coefficients in layered media by using reflected seismic wave data.