  We describe a time-resolved monitoring technique for heterogeneous media. Our
approach is based on the spatial variations of the cross-coherence of coda
waveforms acquired at fixed positions but at different dates. To locate and
characterize a weak change that occurred between successive acquisitions, we
use a maximum likelihood approach combined with a diffusive propagation model.
We illustrate this technique, called LOCADIFF, with numerical simulations. In
several illustrative examples, we show that the change can be located with a
precision of a few wavelengths and its effective scattering cross-section can
be retrieved. The precision of the method depending on the number of source
receiver pairs, time window in the coda, and errors in the propagation model is
investigated. Limits of applications of the technique to real-world experiments
are discussed.
