Wavelet transform inversion with prior scale information

The concept of scale is of central importance in all problems related to the interpretation of earth data. Inversion of geophysical data does not at present, however, allow the incorporation of scale-dependent information directly. This article presents an application of the wavelet transform to traveltime inversion where we are specifically concerned with the selection and application of a priori scale information in the wavelet domain to reconstruct tomographic models. Because of the nature of the problem, the wavelet basis chosen for this example is the Haar basis. The results are compared with the classic damped least-squares (DLS) method, which is a special case of the wavelet transform approach when all the scales are treated equally. We show that with scale-dependent prior information, most of the artifacts created by the DLS technique are diminished considerably.