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 doe s not at present, however, allow the incorporation of scale-dependent information directly. This article presents an application of the wave let transform to traveltime inversion where we are specifically concer ned with the selection and application of a priori scale information i n the wavelet domain to reconstruct tomographic models. Because of the nature of the problem, the wavelet basis chosen for this example is t he 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 s cale-dependent prior information, most of the artifacts created by the DLS technique are diminished considerably.