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APPLICATION OF THE PARTIAL KARHUNEN‐LOÈVE TRANSFORM TO SUPPRESS RANDOM NOISE IN SEISMIC SECTIONS 1
Author(s) -
ALYAHYA KAMAL M.
Publication year - 1991
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1991.tb00302.x
Subject(s) - interpolation (computer graphics) , noise (video) , fourier transform , karhunen–loève theorem , algorithm , data processing , geology , wiener filter , mathematics , computer science , mathematical analysis , artificial intelligence , motion (physics) , image (mathematics) , operating system
A bstract The Karhunen‐Loève (K–L) transform is an effective technique for suppressing spatially uncorrelated noise, but because of its high computational cost, fast transforms, such as the Fourier transform, have been more favoured. Two techniques that combine to make the K–L transform feasible for seismic data processing are discussed. The first technique filters the data for limited dips. For each dip, linear moveout is applied to the seismic sections so that events with this dip are made flat. By interpolation, we can include dips that are fractions of a sample/trace. After linear moveout, zero‐lag K–L filtering is applied followed, by inverse linear moveout; the results from all dips are added to form the final filtered data. The second technique is blocking, in which the seismic section is divided into blocks small enough for each block to be processed using relatively small matrices; the processed blocks are assembled to form the final filtered section. Using a combination of these techniques, seismic sections can be filtered at a reasonable cost using the K‐L transform.