Modelling curved surface wave paths: membrane surface wave synthetics, Geophys

Earth's heterogeneity near the surface is so severe that surface waves with period 20 s exhibit complicated propagation effects such as curved paths and multiple rays. In order to take account of these effects, a new method to analyse surface waves is developed. The method, which we call the membrane surface wave method, is an approximation to the Green's function method in a 3-D medium and is valid for a laterally, smoothly varying media. We also present the formulae to invert the seismograms. As an example, we apply the method to a preliminary California model. Use of the method for the forward calculation shows that heterogeneity in the model is so severe that the wavefront due to the Whittier Narrows earthquake is split in two by the time it feaches the San Francisco Bay area. The kernels in the inverse formula to the six Berkeley stations show curved paths, multipathings and finite wavelength effects and visually demonstrate how waves sample the medium. The method is attractive in that these complications cause no problems in its application. Key words: inversion, seismograms, surface waves.