Direct Observations of Surface‐Wave Eigenfunctions at the Homestake 3D Array

Despite the theory for both Rayleigh and Love waves being well accepted and the theoretical predictions accurately matching observations, the direct observation of their quantifiable decay with depth has never been measured in the Earth's crust. In this work, we present observations of the quantifiable decay with depth of surface-wave eigenfunctions. This is done by making direct observations of both Rayleigh-wave and Love-wave eigenfunction amplitudes over a range of depths using data collected at the 3D Homestake array for a suite of nearby mine blasts. Observations of amplitudes over a range of frequencies from 0.4 to 1.2 Hz are consistent with theoretical eigenfunction predictions. They show a clear exponential decay of amplitudes with increasing depth and a reversal in sign of the radial-component Rayleigh-wave eigenfunction at large depths, as predicted for fundamental-mode Rayleigh waves. Minor discrepancies between the observed eigenfunctions and those predicted using estimates of the local velocity structure suggest that the observed eigenfunctions could be used to improve the velocity model. Our results confirm that both Rayleigh and Love waves have the depth dependence that they have long been assumed to have. This is an important direct validation of a classic theoretical result in geophysics and provides new observational evidence that classical seismological surface-wave theory can be used to accurately infer properties of Earth structure and earthquake sources.