Abstract
Using ambient seismic noise for imaging subsurface structure dates back to the development of the spatial autocorrelation (SPAC) method in the 1950s. We present a theoretical analysis of the SPAC method for multicomponent recordings of surface waves to determine the complete 3 × 3 matrix of correlations between all pairs of three-component motions, called the correlation matrix. In the case of isotropic incidence, when either Rayleigh or Love waves arrive from all directions with equal power, the only non-zero off-diagonal terms in the matrix are the vertical-radial (ZR) and radial-vertical (RZ) correlations in the presence of Rayleigh waves. Such combinations were not considered in the development of the SPAC method. The method originally addressed the vertical-vertical (ZZ), RR and TT correlations, hence the name spatial autocorrelation. The theoretical expressions we derive for the ZR and RZ correlations offer additional ways to measure Rayleigh wave dispersion within the SPAC framework. Expanding on the results for isotropic incidence, we derive the complete correlation matrix in the case of generally anisotropic incidence. We show that the ZR and RZ correlations have advantageous properties in the presence of an out-of-plane directional wavefield compared to ZZ and RR correlations. We apply the results for mixed-component correlations to a data set from Akutan Volcano, Alaska and find consistent estimates of Rayleigh wave phase velocity from ZR compared to ZZ correlations. This work together with the recently discovered connections between the SPAC method and time-domain correlations of ambient noise provide further insights into the retrieval of surface wave Green's functions from seismic noise.
Highlights
Seismologists often encounter signals that do not exhibit distinct P- or S-wave phase arrivals
We show that the ZR and RZ correlations have advantageous properties in the presence of an out-of-plane directional wavefield compared to ZZ and RR correlations
Aki’s spatial autocorrelation (SPAC) method has subsequently been used to study shallow subsurface structure using wavefields composed of microseisms (Okada 2003) and volcanic tremor (Ferrazzini et al 1991; Chouet 1996; Chouet et al 1998; Saccorotti et al 2003)
Summary
Seismologists often encounter signals that do not exhibit distinct P- or S-wave phase arrivals. In the presence of an isotropic noise field, Nakahara (2006) connected the Fourier transform of the time-domain ambient noise correlation and the spectral correlation coefficient from the SPAC method. In the case of an anisotropic noise field, Nakahara (2006) derived expressions for time-domain ambient noise correlations drawing on results derived in the field of acoustics (Cox 1973; Teal et al 2002) Through these studies, the SPAC method and time-domain correlations have been shown to be different but largely equivalent ways of using ambient noise to gain information on the structure of the subsurface. We extend the SPAC method to the complete matrix of correlation coefficients and compare the result to time-domain correlations between three-component instruments. With data from two broadband seismometers at Akutan Volcano, Alaska, we use ZR correlations to obtain Rayleigh wave dispersion curve measurements within the SPAC methodology that are complementary to measurements from ZZ correlations
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