Modeling scatterers embedded in plane-layered media by a hybrid Haskell-Thomson and boundary integral equation method

A hybrid Haskell-Thomson and boundary integral equation (BIE) method is formulated which can model the acoustic or elastic response of scatterers embedded in plane-layered media. The scatterers can have an arbitrary smooth shape but must not intersect layer interfaces. The Green's function of the scatterer is computed by BIEs in the (x, z, w) domain and the Green's function of the layers is computed by a Haskell-Thomson method in the (kxz, w) domain. Their fields are coupled by the appropriate combination of FFTs and extrapolation operators and are finally summed up in a Born series. For notational convenience this hybrid method will be called a generalized Born series (GBS) method. Two advantages of the GBS method are (1) it is more efficient than finite elements or finite differences for small scatterers embedded in thickly layered media, and (2) no artificial side reflections are generated from the infinitely extended plane interfaces. The disadvantages are (1) the convergence rate of the GBS depends on the model and is unknown a priori, and (2) the computation time increases with the size of the scatterer.