Linear inverse problems in wave motion: non-self-adjoint integral equations of the first kind

Summary form only given. In the study of linear inverse problems, integral equations of the first kind play an important role. In many applications, the inversion of these integral equations is widely used to produce estimates of media parameters and geometries in areas as diverse as geophysical prospecting, medical imaging, and nondestructive evaluation. The authors interests an in wave motion and, in particular, in applications to geophysical exploration. A Fredholm integral equation of the first kind arises, for example, in the employment of the Born approximation in geophysics. In this paper, we consider the characteristics of the first kind integral equations and their solution(s) under the assumption that the integral operator is compact, but not necessarily self-adjoint.