Correlation of nonisotropically distributed ballistic scalar diffuse waves in two dimensions.

Abstract

Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Greens function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed this. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and constructed impressive tomographic maps of seismic wave velocity, and even detected fractional secular changes in seismic wave speed at a level of 0.0001. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The usual wave field used in long-period seismology is due to distant ocean storms and is, even in the presence of scattering, not isotropic. Here an asymptotic evaluation of the effect, on apparent travel time in a correlation waveform, is made of nonisotropic distributions of ballistic specific intensity. It is shown that for station pairs separated by one or more wavelengths, that the effect is small. A formula is derived permitting estimations of error, and corrections to travel times. It is successfully compared to errors seen in synthetic waveforms.