A Coupled Local‐Mode Analysis of Surface‐Wave Propagation In A Laterally Heterogeneous Waveguide

We consider surface‐wave propagation in a laterally heterogeneous waveguide based upon coupled local modes, which are the eigenfunctions of a laterally homogeneous waveguide with a vertical structure identical to that of the laterally heterogeneous waveguide at the horizontal location of interest. Energy transfer from one overtone to another is expressed in terms of local‐mode amplitude coefficients which determine the surface‐wave amplitude. the amplitude coeffieients can be determined from a system of first‐order partial‐differential equations. In particular, we investigate the nature of forward‐coupled Love and Rayleigh waves along a given surface‐wave trajectory. We demonstrate that overtone coupling is determined by lateral gradients in density, elastic parameters, and topography on discontinuities, and that the coupling strength is on the order of the ratio of the lateral change in the model parameters to the squared wavenumber spacing and fluctuates with a wavelength on the order of 2ω over this spacing. the theory allows for topography on solid‐solid as well as fluid‐solid boundaries. When overtone coupling is ignored the results are reduced to traditional surface‐wave JWKB theory.