The influence of noise sources on cross-correlation amplitudes

TL;DR

This paper investigates how different noise source distributions affect seismic cross-correlation measurements, emphasizing the importance of source modeling for interpreting wave attenuation and inverting source distributions.

Contribution

It demonstrates the impact of spatially complex noise sources on cross-correlation signals and proposes a method to invert for source distribution using waveform energy.

Findings

Cross correlations are generally not Green's functions and depend on source distribution.

Waveform energy can be used to invert for source distribution.

Accurate interpretation of cross-correlation energy requires knowledge of source distribution.

Abstract

We use analytical examples and asymptotic forms to examine the mathematical structure and physical meaning of the seismic cross correlation measurement. We show that in general, cross correlations are not Green's functions of medium, and may be very different depending on the source distribution. The modeling of noise sources using spatial distributions as opposed to discrete collections of sources is emphasized. When stations are illuminated by spatially complex source distributions, cross correlations show arrivals at a variety of time lags, from zero to the maximum surface-wave arrival time. Here, we demonstrate the possibility of inverting for the source distribution using the energy of the full cross-correlation waveform. The interplay between the source distribution and wave attenuation in determining the functional dependence of cross correlation energies on station-pair distance is quantified. Without question, energies contain information about wave attenuation. However, the accurate interpretation of such measurements is tightly connected to the knowledge of the source distribution.