Wavelet domain linear inversion with application to well logging
Author(s)
Kane, Jonathan
Herrmann, Felix
Toksoz, M. Nafi
Date Issued
2001
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;2001-05
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.
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