Surface waves across 2‐D structures: a method based on coupled local modes

Abstract

The propagation of surface waves across 2‐D structures is treated by a coupled‐mode approach, expressing the wavefield as a laterally varying sum of local modes. The propagation direction may differ from normal incidence to the 2‐D structure. The continuity conditions across tilted interfaces, including a fluid‐solid interface, are fulfilled by transforming the part of the continuity condition related to the slope into a volume force. The lateral heterogeneity introduces energy transfers between modes, including transfers between Love and Rayleigh waves, leading to a lateral variation of the different mode‐amplitude coefficients. This variation is described by a first‐order coupling equation which is established using the orthogonality properties of the local modes. The coupling matrix is cast into a form where the role of the lateral derivatives of the elastic constants and density appears explicitly. This method can be applied to a wide variety of structures since no restriction has to be put on the rate or the extent of the lateral variation in the model. Copyright © 1988, Wiley Blackwell. All rights reserved