ELSEVIER Wave Motion 20 (1994) 33-39 Ik An inverse problem in low-frequency scattering by an ellipsoidally embossed surface George Dassios Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, and Institute of Chemical Engineering and High Temperature Chemical Processes, GR 261 10 Patras, Greece R.J. Lucas 1 Department of Mathematical Sciences, Loyola University of Chicago, Chicago, IL 60626, USA Received 19 August 1993; revised 21 January 1994 Abstract The inverse problem for plane wave excitation of a small soft ellipsoidal boss on a rigid base plane is considered. It is shown that one measurement of the leading order low-frequency coefficient of the real part of the specular scattering amplitude and four measurements of the second order coefficient are sufficient to specify the semiaxes of the boss and its orientation. The leading order terms of the scattering amplitude for the boss plus base plane are obtained from that of the ellipsoid by an image technique, and the first two terms of the real part are used to solve the inverse problem. 1. Introduction The problems that arise in scattering theory can usually be categorized as being of either the direct or the inverse type. For the direct problem one attempts to determine the field scattered by an isonified obstacle as a function of its relevant characteristics, e.g., size, shape, and orientation, which are assumed known. On the other hand, for the inverse problem one tries to infer these characteristics from a knowledge of the response of the scatterer to the exciting field. The direct problem for the scattering of an acoustic wave by a base plane having one or more bosses (protuberances) has been discussed in detail in the literature. In particular Twersky [1-4] considered the plane wave excitation of distributions of relatively arbitrary bosses on rigid or free (pressure release) base planes using an image technique. This work was subsequently applied to ellipsoidally embossed surfaces in both the low [5] and high-frequency [6,7] domains, as well as to point source excitation [8]. Corresponding author. 0165-2125/94/$07.00 (~ 1994 Elsevier Science B.V. All rights reserved SSDIOI65-2125(94)OOOI2-T