Partitions among elastic waves for dynamic surface loads in a layered medium

Abstract

SUMMARY The relationship between the Green's function and the average correlations of the elastic displacements within a diffuse field has been firmly established. The energies of horizontal and vertical motion in such a field are proportional to the imaginary part of the corresponding diagonal components of the Green's tensor for coincident source and receiver. Given this remarkable connection, we examine the partitions of elastic waves due to dynamic horizontal and vertical surface loads in a layered elastic media. The elastic radiation characteristics for horizontally layered media are much more complicated than for the homogeneous half-space. While the corresponding power partitions of the different types of waves in a half-space do not vary with respect to frequency, even in an elastic medium consisting of layers over a half-space, the modal structure shows strong variations in the frequency, mainly around the main peak and the minimum of the horizontal-to-vertical spectral ratio (HVSR). Using a test model with a moderately high impedance contrast, we find that most of the energy density of the horizontal displacements is concentrated in the fundamental mode of the Love waves, reaching ∼80 per cent of the power in the horizontal components. The vertical displacement of the P-SV body waves reaches a maximum of ∼85 per cent, while the fundamental mode of Rayleigh waves reaches a maximum of ∼99 per cent of the available power in the vertical motion. With this analysis, it is possible to analyse the multimodal effects in the dispersion diagrams and explicitly relate the partition of the energy density with the dispersion curves and the HVSR under the diffuse field assumption.