Abstract
In this paper, we present an interactive modeling scheme, which is based upon perturbing the surface boundary integral equations about a reference model in which the Green’s function is known. This Green’s function is computed by a boundary integral equation (BIE) method. The new perturbed equation can be efficiently solved by a Born series and for convenience is designated as the perturbed Born series (PBS). The PBS differs from the series solution to the familiar Lippmann–Schwinger integrals in that it solves a boundary integral which is computationally inexpensive compared to the prohibitively expensive volume integral of Lippmann–Schwinger. For small enough perturbations about the reference model, the PBS will converge quickly for any given source frequency, scatterer size, or contrast in impedance across an interface. The PBS can therefore be used to efficiently compute the dynamic, as well as static, responses to a series of models iteratively perturbed about a reference model. The disadvantage of the PBS is that the convergence rate is not easy to predict and decreases with an increase in scatterer size, source frequency, and perturbations about the reference model.