Passive seismic imaging applied to synthetic data

James Rickett and Jon Claerbout

james@sep.stanford.edu, jon@sep.stanford.edu

ABSTRACT

It can be shown that for a 1-D Earth model illuminated by random plane waves from below, the cross-correlation of noise traces recorded at two points on the surface is the same as what would be recorded if one location contained a shot and the other a receiver. If this is true for real data, it could provide a way of building `pseudo-reflection seismograms' from background noise, which could then be processed and used for imaging. This conjecture is tested on synthetic data from simple 1-D and point diffractor models, and in all cases, the kinematics of observed events appear to be correct. The signal to noise ratio was found to increase as $\sqrt{n}$, where n is the length of the time series. The number of incident plane waves does not directly affect the signal to noise ratio; however, each plane wave contributes only its own slowness to the common shot domain, so that if complete hyperbolas are to be imaged then upcoming waves must be incident from all angles.