Abstract
A hybrid forward modeling method is presented which combines the Born series and the boundary integral equation (BIE) methods. An earth model is first divided into two portions, a large and not too interesting part (such as the background layering) to be treated by an efficient ray tracing or matrix propagator method, and a small part (such as a complicated reef or gas-bearing sand lens) which will be treated by a highly accurate BIE method. Then, the scattered fields from each part are coupled together by extrapolation operators and their interactions are summed up in a Born series. For notational convenience this method will be denoted as a generalized Born series (GBS). The GBS has five important features: (1) It allows the combination of the BIE method with fast modeling techniques. As an illustration, we present numerical results of coupling BIE's with matrix propagator methods, ray tracing methods, and BIE methods for (respectively) scatterers embedded in plane layered media, scatterers embedded in irregularly layered media, and multibody scatterers. (2) Each term of the GBS has a clear physical significance so that we can interpret the genesis of anomalous events in the seismogram. (3) The GBS is more efficient than the normal BIE approach when Gaussian elimination is used to invert the matrices. (4) The GBS is a fast interactive modeling tool when the configuration of the scatterers, sources or receivers are iteratively changed. (5) For arbitrarily layered media the GBS is somewhat akin to a generalization of the Bremmer series for flat layers. The main disadvantage of this method is that the convergence rate of the GBS is difficult to quantify. However, many of our numerical examples suggest that convergence is very fast for certain classes of models.