Normal mode multiplet coupling along a dispersion branch

Abstract

Summary We investigate normal mode multiplet coupling along the fundamental spheroidal mode branch using three different numerical methods. A suite of 300 synthetic vertical accelerograms computed using the great-circle approximation and the first-order subspace-projection algorithm are compared with accurate accelerograms computed using a Rayleigh-Ritz variational method. In each case, the accelerograms are computed by summing the responses of the hybrid multiplets 0S10–10S55; the resulting waveforms correspond to mantle Rayleigh waves with periods between 150 and 600 s. The great-circle approximation correctly represents all but 5 per cent of the waveform variance produced by the degree-8 model of upper mantle heterogeneity M84A, for each of the sequentially arriving wavegroups R1-R6. For a contrived model with a modest amount of additional heterogeneity up to degree 20, the relative great-circle error is substantially greater, approximately 30 per cent. The first-order subspace-projection algorithm requires an order of magnitude more computer time than the great-circle approximation; however it is much more accurate. For the first arriving wavegroup R1, it correctly represents all but 2 per cent of the waveform variance produced by model M84A; this relative error decreases for subsequent wavegroups to less than 1 per cent for R2 and less than 0.2 per cent for R3. For the contrived degree-20 model, the relative subspace-projection error is 6 per cent for R1, 1.5 per cent for R2 and 0.9 per cent for R3; the relative error is less for the later arriving wavegroups because of the increasing effect of the lateral heterogeneity as well as the more rapid attenuation of the higher frequency multiplets that are not as well modelled by the approximation.