On the Properties of Higher-Order Ambient Field Correlation

Yixiao Sheng, Nori Nakata, & Gregory C. Beroza

Submitted August 12, 2017, SCEC Contribution #7522, 2017 SCEC Annual Meeting Poster #031 (PDF)

Higher order cross-correlations, like C3 (correlation of the coda of correlation), of the ambient seismic field, is observed to yield more symmetric, and thus more accurate Green’s functions (GFs) than direct, first order correlation (C1). This is attributed to the widely accepted argument that the wavefield of the correlation coda is more diffuse than that of the ambient noise.

This explanation of C3–that the C1 coda is more diffuse–is inconsistent with our observations. If the coda wavefield is diffuse, C3+, constructed by using the causal part of C1 (or C3-, from flipped anti-causal part of C1), should be symmetric itself. Our observations show that GFs from C3+ are asymmetric, while C3- GFs appear to be symmetric to C3+ GFs and show up on the other side. Evenly distributed virtual source stations should lead to more symmetric GFs, which is also inconsistent with our observations that symmetry is obtained for station pairs even at the edge of a virtual source array, that is, when the distribution of virtual source stations is highly asymmetric.

We use modal theory, which considers the cross-talk between degenerate modes, to explain our observations. The pattern of cross-talk is consistent on the causal and anti-causal part of C1. It is the cross-correlation of the cross-talk terms that give rise to signals showing up on C3 GFs, which therefore should be more sensitive to the distribution of the sources or scatters, rather than the secondary virtual source stations. As we flip the anti-causal codas to construct C3-s, the orientation pattern is flipped, leading to the relatively symmetric behavior of C3- and C3+ GFs. As a result, C3 GFs, the summation of C3- and C3+ GFs, appear to be symmetric.

Numerical simulations with homogeneous velocity model confirm that, only using the ballistic wavefield yields symmetric C2 (correlation of correlation, no coda with homogeneous velocity) and the symmetry arises from flipping the anti-causal parts of C1s rather than the diffusive nature of the wavefield. Cross-correlation results on a linear array in southern California further support our interpretation.

We propose to exploit the cross-talk through a modified C3 technique, which we refer to as ‘pre-stack C3’ that simply constructs C3 from each single time window before stacking to finalize the results. Our tests show the pre-stack C3 method significantly improves the SNR and shows promise for extending the correlation results to higher frequency.

Key Words
ambient noise; higher-order correlation

Sheng, Y., Nakata, N., & Beroza, G. C. (2017, 08). On the Properties of Higher-Order Ambient Field Correlation. Poster Presentation at 2017 SCEC Annual Meeting.

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