Identification of physical properties in geology, hydrology and ecology

Abstract

This thesis presents the details of a new method for approximating the solution to inverse problems for the identification of position dependent coefficients in differential equations from observations on the boundary of the problem domain. The method is based on the classical Backus-Gilbert method, first introduced in geophysics, but employs this idea in a new way to coefficient inverse problems. The method can be used for identifying one or more coefficients in either ordinary or partial differential equations. Inverse problems of this sort are prevalent in diverse areas including geology, hydrology and ecology where physical properties of a system must be determined indirectly from experimental data. Several examples are provided to illustrate how the method can be applied for identification of such things as electrical, thermal and hydraulic properties.