Modelling of laterally trapped surface waves with application to Rayleigh waves in the Hawaiian swell

Abstract

SUMMARY A method for synthetizing surface wave seismograms in anelastic 2-D structures is presented. It is based on the local mode coupling method, extended here to allow for propagation in any direction, and especially in the symmetry direction of the structure. This implies including both homogeneous and inhomogeneous waves in the wavefield representation. The complex wavenumbers of inhomogeneous waves require that a dual space of modes and a new bi-orthonormality relation between modes are defined. Combinations of local modes which are not singular for modes having an horizontal turning point in the 2-D structure are used as a basis for wavefield decomposition. This allows calculation of the propagation and coupling characteristics of homogeneous and inhomogeneous waves with a single set of equations. The mode coupling matrices are then combined with source terms and boundary conditions to yield synthetic seismograms with a procedure similar to the one used in the reflectivity method in 1-D structures. The method is applied to model Rayleigh wave fundamental modes propagating along the Hawaiian chain, in order to refine the interpretation of phase velocities measured for this area by LCvCque (1991). The a priori reheated and thinner lithosphere under the chain acts as lateral low-velocity waveguide where Rayleigh waves are trapped. We show that this waveguide has three lateral free modes in the period range 20 to 150 s. Synthetic seismograms for different source-receiver configurations are presented. The influence of the source-type, epicentral distance and channel width on the waveguide's amplification power is examined in the frequency domain. Apparent phase velocities between two stations situated in the middle of the channel are calculated, and the influence of the outer parts of the waveguide on these velocities is analysed. It is found that the velocities measured by LCvCque are probably influenced at 20 to 30 per cent by the normal lithosphere outside the reheated channel.