The Lg-wave phase, which is of considerable interest for nuclear discrimination problems, is normally observed after propagation through a few hundred kilometres. This phase is dominantly guided in the crustal waveguide, which is known to be a region with a very significant horizontal variability in properties.
The effect of heterogeneous crustal structures on Lg waves has been determined by using a “coupled-mode” technique in which the local seismic wavefield in the real medium is expressed as a horizontally varying combination of the modal eigenfunctions of a stratified reference structure. Departures of the seismic properties in the medium from those of the reference medium lead to coupling between the various amplitude coefficients in the modal expansion. The evolution of these modal weighting factors with horizontal position are described by a coupled set of ordinary differential equations. This approach provides a calculation scheme for studying guided wave propagation over extended distances, at frequencies of 1 Hz and above. The heterogeneity models that have been used are two-dimensional and calculations are carried out for one frequency at a time.
A sequence of models with varying levels of heterogeneity have been considered in order to determine the merits and limitations of the computation scheme. The coupled mode technique works well with heterogeneous models in which the local seismic velocities differ from the stratified reference model by up to two per cent and there are no significant distortions of the main discontinuities (e.g., the crust-mantle boundary). The approach can be used for higher levels of heterogeneity and with distorted interfaces but a large number of modes needs to be considered with consequent high computation costs. If the level of heterogeneity is not too large, the interaction between modes can be restricted, rather than extending over the whole mode set, with consequent reduction in computation cost.
One of the major effects of crustal heterogeneity is to introduce the possibility of smearing out the main amplitude peak in the Lg wave train over a band of group velocities. As a result, an effective measure of the energy content of the Lg waves will be to consider the integrated amplitude along the trace between group velocities of 3.6 and 3.3 km/sec. The effects of heterogeneity vary between different parts of the Lg wave train and the representation of the wavefield in terms of modal contributions allow a detailed analysis in terms of the group velocity components, which can be illustrated by constructing theoretical seismograms (with a narrow bandwidth in frequency) for the heterogeneous models.