Coherence‐Based Approaches for Estimating the Composition of the Seismic Wavefield

Abstract

As new techniques exploiting the Earth's ambient seismic noise field are developed and applied, such as for the observation of temporal changes in seismic velocity structure, it is crucial to quantify the precision with which wave‐type measurements can be made. This work uses array data at the Homestake mine in Lead, South Dakota, and an array at Sweetwater, Texas, to consider two aspects that control this precision: the types of seismic wave contributing to the ambient noise field at microseism frequencies and the effect of array geometry. Both are quantified using measurements of wavefield coherence between stations in combination with Wiener filters. We find a strong seasonal change between body‐wave and surface‐wave content. Regarding the inclusion of underground stations, we quantify the lower limit to which the ambient noise field can be characterized and reproduced; the applications of the Wiener filters are about 4 times more successful in reproducing ambient noise waveforms when underground stations are included in the array, resulting in predictions of seismic time series with less than a 1% residual, and are ultimately limited by the geometry and aperture of the array, as well as by temporal variations in the seismic field. We discuss the implications of these results for the geophysics community performing ambient seismic noise studies, as well as for the cancellation of seismic Newtonian gravity noise in ground‐based, sub‐Hertz, gravitational‐wave detectors.

Simulations of Gravitoelastic Correlations for the Sardinian Candidate Site of the Einstein Telescope

“…Even if we do not know the wave composition of a seismic field at a site, it is still reasonable in many cases to assume that Rayleigh waves dominate the normal surface displacement at frequencies in the range 1–20 Hz produced by surface or near‐surface seismic sources (Bonnefoy‐Claudet et al, 2006; Mooney, 1976). Only at exceptionally quiet (necessarily remote) surface sites or underground sites, body wave content is expected to be significant or dominant in this band (however, mode content can change significantly with time if due to natural sources; Coughlin et al, 2019).…”

A Linear Inversion Approach to Measuring the Composition and Directionality of the Seismic Noise Field

“…In particular, we will examine the modal composition and directionality of oceanic microseism. In a past publication, we have shown evidence based on coherence across different seismic stations that when microseism is weak, the seismic field at low frequencies (0.2-0.4 Hz) appears to be dominated by body waves, while when microseism is strong, Rayleigh waves appear to dominate [50]. However, the evidence provided was indirect, as it was based on evaluating how quickly the coherence between stations drops off as a function of distance (i.e., more quickly for Rayleigh waves, less quickly for body waves), and did not attempt to directly estimate the various noise amplitudes.…”

“…whereΩ = (cos φ, sin φ) depicts the wave propagation direction (with φ = 0 corresponding to eastward propagation), x 1,2 are the locations of the two stations, and v is the Rayleigh wave speed that was studied and measured in [45,50]. The comparison is performed using a likelihood maximization method, yielding the preferred wave propagation direction φ = 2.4 ± 0.7 • , i.e., nearly eastward propagation.…”

“…We calculate 128 s Hanning-windowed Fourier transforms and use these to generate inter-station and inter-channel cross-spectral densities, which we evaluate at 0.2 Hz. For the inversion, we assume velocities of 3500 m/s for R waves, 7000 m/s for P waves, and 5000 m/s for S waves, based on past studies of velocities and Rayleigh eigenfunctions [45,50]. We average together 45 of the 128 s cross-spectral densities and use the resulting spectrum estimated from 1.6 h worth of data as Y when performing the recoveries.…”

Terrestrial gravity fluctuations

“…There are however hardly any underground array measurements to characterize the seismic field in terms of mode composition. An exception is the last underground array measurements at the former Homestake mine in South Dakota, USA (Mandic et al 2018;Coughlin et al 2018a). This is mostly due to the fact that these experiments are very costly, and seismic stations have to be maintained under unusual conditions (humidity, temperature, dust, …).…”