When are noise correlation amplitudes useful?

Victor C. Tsai, & Zhongwen Zhan

Published September 2012, SCEC Contribution #2058

Cross correlation of ambient seismic noise is known to result in time series from
which station‐station travel‐time measurements can be made. Part of the reason that these
cross‐correlation travel‐time measurements are reliable is that there exists a theoretical
framework that quantifies how these travel times depend on the features of the ambient
noise. However, corresponding theoretical results do not currently exist to describe
how the amplitudes of the cross correlation depend on such features. For example,
currently it is not possible to take a given distribution of noise sources and calculate the
cross correlation amplitudes one would expect from such a distribution. Here, we provide a
ray‐theoretical framework for calculating cross correlations. This framework differs
from previous work in that it explicitly accounts for attenuation as well as the spatial
distribution of sources and therefore can address the issue of quantifying amplitudes in
noise correlation measurements. After introducing the general framework, we apply it to
two specific problems. First, we show that we can quantify the amplitudes of coherency
measurements, and find that the decay of coherency with station‐station spacing depends
crucially on the distribution of noise sources. We suggest that researchers interested in
performing attenuation measurements from noise coherency should first determine how
the dominant sources of noise are distributed. Second, we show that we can quantify the
signal‐to‐noise ratio of noise correlations more precisely than previous work, and that
these signal‐to‐noise ratios can be estimated for given situations prior to the deployment of
seismometers. It is expected that there are applications of the theoretical framework
beyond the two specific cases considered, but these applications await future work.

Tsai, V. C., & Zhan, Z. (2012, 9). When are noise correlation amplitudes useful?. Poster Presentation at SCEC Annual Meeting 2012. doi: doi:10.1029/2011JB008483.