Wavelet domain linear inversion with application to well logging

Abstract

Solving linear inversion problems in geophysics is a major challenge when dealing with non-stationary data. Certain non-stationary data sets can be shown to lie in Besov function spaces and are characterized by their smoothness (differentiability) and two other parameters. This information can be input into an inverse problem by posing the problem in the wavelet domain. Contrary to Fourier transforms, wavelets form an unconditional basis for Besov spaces, allowing for a new generation of linear inversion schemes which incorporate smoothness information more precisely. As an example inversion is performed on smoothed and subsampled well log data.