Extension of the spatial autocorrelation (SPAC) method to mixed-component correlations of surface waves

Geophysical Journal International
By: , and 



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.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Extension of the spatial autocorrelation (SPAC) method to mixed-component correlations of surface waves
Series title Geophysical Journal International
DOI 10.1111/j.1365-246X.2012.05597.x
Volume 191
Issue 1
Year Published 2012
Language English
Publisher Wiley
Publisher location Hoboken, NJ
Contributing office(s) Volcano Hazards Program, Volcano Science Center
Description 18 p.
Larger Work Type Article
Larger Work Subtype Journal Article
Larger Work Title Geophysical Journal International
First page 189
Last page 206
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