Multichannel deconvolution, MCD, in geophysics and helioseismology

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.