The Rytov approximation, which expresses phase residuals as an explicit function of the slowness perturbations, is also a Generalized Radon T ransform (GRT). Using Beylkin's formalism, we deriv e the corresponding iiverse GRT to give the slo wness model as an explicit function of the phase residuals. This expression is used to deduce the resolution limits of trav eltime tomograms as a function of source frequency and source-receiver geometry. Its validity is restricted to arbitrary models with smooth variations in v elocity, where theelocity variations must be at least 3 times longer than the characteristic source wavelength. The formula sho ws that the slowness resolution limits of an anomaly can be computed by estimating the intersection area of the wavepaths that visit it. Using this procedure, resolution limits are obtained for several types of trav eltime data: controlled source data in a crosswjll experiment, data from a refraction experiment, and earth-quak e data using the Preliminary Reference Earth Model (PREM).
ASJC Scopus subject areas
- Geotechnical Engineering and Engineering Geology