In coda wave interferometry, one records multiply scattered waves at a limited number of receivers to infer changes in the medium over time. With this technique, we have determined the nonlinear dependence of the seismic velocity in granite on temperature and the associated acoustic emissions. This technique can be used in warning mode, to detect the presence of temporal changes in the medium, or in diagnostic mode, where the temporal change in the medium is quantified.

[1] The coda of seismic waves consists of that part of the signal after the directly arriving phases. In a finite medium, or in one that is strongly heterogeneous, the coda is dominated by waves which have repeatedly sampled the medium. Small changes in a medium which may have no detectable influence on the first arrivals are amplified by this repeated sampling and may thus be detectable in the coda. We refer to this use of multiple-sampling coda waveforms as coda wave interferometry. We have exploited ultrasonic coda waves to monitor time-varying rock properties in a laboratory environment. We have studied the dependence of velocity on uniaxial stress in Berea sandstone, the temperature dependence of velocity in granite and in aluminum, and the change in velocity due to an increase of water saturation in sandstone. There are many other possible applications of coda wave interferometry in geophysics, including dam and volcano monitoring, time-lapse reservoir characterization, earthquake relocation, and stress monitoring in mining and rock physics.

SUMMARY Coda waves are highly sensitive to changes in the subsurface; we use this sensitivity to monitor small stress changes in an underground mine. We apply coda wave interferometry to seismic data excited by a hammer source, collected at an experimental hard rock mine in Idaho Springs, CO. We carried out a controlled stress‐change experiment in a mine pillar and we show how coda wave interferometry can be used to monitor the in situ stress change with modest hardware requirements.

Some experiments are conveniently performed in the time domain, some in the frequency domain, and some use a hybrid approach. Does the domain make any difference in the ultimate resolution of the experiment? Or can the details of the experiment always be tweaked so that the different approaches give the same answer? We consider a simple optics experiment and consider both time and frequency measurements and take into account the influence of noise, finite dynamic range, attenuation, and the duration of the measurement.

Multiply scattered waves are extremely sensitive to small changes of the medium through which these waves have propagated. Coda Wave Interferometry [Science 295, 2253–2255 (2002)] is a new technique that utilizes multiply scattered waves in the time domain to monitor small changes in media. This is applied to ultrasonic waves that were recorded in a granite sample that was subjected to a change in temperature. Velocity perturbations of about 0.1% can be detected with this technique with an accuracy of about 0.02%. A multiply scattered wave in an elastic medium has traveled part of its trajectory as a P-wave and part as an S-wave. A model for the equilibration of P- and S-waves is presented. This model is used to extend the theory of coda wave interferometry to include elastic wave propagation. [Work was partially supported by the NSF (EAR-0106668 and EAR-0111804), by the U.S. Army Research Office (DAAG55-98-1-0070), and by the sponsors of the Consortium Project on Seismic Inverse Methods for Complex Structures at the Center for Wave Phenomena.]