Applications of a New Inverse Method to Nondestructive Evaluation

When a wave impinges upon an irregularity in an otherwise homogeneous medium, the wave is deformed in a manner which 1s characteristic of the irregularity. This is the basis of a method of nondestructive evaluation of materials. Problems in which one seeks information about material prooerties from scattered waves are known as inverse problems. Traditionally, such problems are analyzed either by cataloging many solutions of direct problems and comparing the results of a given experiment with catalogs, or by attempting to solve the relevant equation of wave properties backwards in time. In contrast, we formulate the inverse problem as an equation or system of equations in which one of the unknowns is a function which directly characterizes the i rregularity to be detennined. Under the assumption of small sized anomalies or small changes in media properties, our system reduces to a single linear integral equation for this "characteristic" function. In many cases of practical interest, this equation admits closed form solutions. Even under the constraints of practical limitations on the data, information about the irregularity can be deduced. As an example, we consider the case of a void in a solid probed by acoustic waves. We show how high frequency data can be directly processed to yield the actual shape of the anomaly in a region of the surface covered by specular reflect ion of the probe. In the low frequency case, we show how to directly process the data to yield the volume, centroid, and "products of inertia" of the void.