TY - JOUR

T1 - Multichannel deconvolution, MCD, in geophysics and helioseismology

AU - Jacobsen, B.H.

AU - Møller, I.

AU - Jensen, J.M.

AU - Effersø, F.

N1 - Funding Information:
Acknowgements. This work was supported by The Danish Natural Science Research Council, Aarhus University, and Theoretical Astrophysics Center (Copenhagen/Aarhus). Helioseismic data were made available to us by Thomas L. Duvall, Stanford University, and electrical welllog data by Kurt Soerensen, Aarhus University. Calculations in Fig. 3c used a geoelectrical finite difference code made available by Douglas W. Oldenburg, University of British Columbia.

PY - 1999

Y1 - 1999

N2 - Whenever data sampling is regular along a coordinate in space and/or time, it is relevant to look for approximate shift invariance which casts the forward problem into a convolution formulation. The resulting computations may be speeded up significantly through the Fourier transform. For nonlinear problems the Born approximation in horizontally stratified media leads to just such a result. In many cases the noise is well approximated by a stationary process, and it turns out that the resulting inverse solution is then a multi-channel deconvolution. This formulation allows very fast inversion in the periodic approximation of densely sampled high volume data sets. New applications within geophysical well logging, continuous geoelectrical sounding/profiling, and 3D helioseismic tomography demonstrate the wide applicability of this method.

AB - Whenever data sampling is regular along a coordinate in space and/or time, it is relevant to look for approximate shift invariance which casts the forward problem into a convolution formulation. The resulting computations may be speeded up significantly through the Fourier transform. For nonlinear problems the Born approximation in horizontally stratified media leads to just such a result. In many cases the noise is well approximated by a stationary process, and it turns out that the resulting inverse solution is then a multi-channel deconvolution. This formulation allows very fast inversion in the periodic approximation of densely sampled high volume data sets. New applications within geophysical well logging, continuous geoelectrical sounding/profiling, and 3D helioseismic tomography demonstrate the wide applicability of this method.

UR - http://www.scopus.com/inward/record.url?scp=0032781775&partnerID=8YFLogxK

U2 - 10.1016/S1464-1895(99)00021-6

DO - 10.1016/S1464-1895(99)00021-6

M3 - Article

AN - SCOPUS:0032781775

VL - 24

SP - 215

EP - 220

JO - Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy

JF - Physics and Chemistry of the Earth, Part A: Solid Earth and Geodesy

SN - 1464-1895

IS - 3

ER -