Linear Inversion of Band-Limited Reflection Seismograms
- 1 October 1986
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Scientific and Statistical Computing
- Vol. 7 (4), 1307-1330
- https://doi.org/10.1137/0907087
Abstract
We present a method for the linear inversion (deconvolution) of band-limited reflection seismograms. A large convolution problem is first broken up into a sequence of smaller problems. Each small problem is then posed as an optimization problem to resolve the ambiguity presented by the band-limited nature of the data. A new cost functional is proposed that allows robust profile reconstruction in the presence of noise. An algorithm for minimizing the cost functional is described. We present numerical experiments which simulate data interpretation using this procedure.This publication has 6 references indexed in Scilit:
- Recovery of the acoustic impedance from reflection seismogramsGeophysics, 1983
- Impedance profile inversion via the first transport equationJournal of Mathematical Analysis and Applications, 1983
- Reconstruction of a sparse spike train from a portion of its spectrum and application to high‐resolution deconvolutionGeophysics, 1981
- Deconvolution with the ℓ1 normGeophysics, 1979
- Minimization Techniques for Piecewise Differentiable Functions: The $l_1$ Solution to an Overdetermined Linear SystemSIAM Journal on Numerical Analysis, 1978
- ROBUST MODELING WITH ERRATIC DATAGeophysics, 1973