How to choose a subset of frequencies in frequency-domain finite-difference migration

Details How to choose a subset of frequencies in frequency-domain finite-difference migration How to choose a subset of frequencies in frequency-domain finite-difference migration

Sep 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004geoji.158..801m&link_type=abstract

Geophysical Journal International, Volume 158, Issue 3, pp. 801-812.

Astronomy and Astrophysics

Astronomy

13

Finite-Differences, Frequency Domain, Migration

Scientific paper

Finite-difference migration with the two-way wave equation can be accelerated by an order of magnitude if the frequency domain rather than the time domain is used. This gain is mainly accomplished by using a subset of the available frequencies. The implicit assumption is that the data have a certain amount of redundancy in the frequency domain.
The choice of frequencies cannot be arbitrary. If the frequencies are chosen with a constant increment and their spacing is too large, the well-known wrap-around that occurs when transforming back to the time domain will also show up in the migration to the depth domain, albeit in a more subtle way. Because migration involves propagation in a given background velocity model and summation over shots and receivers, the effects of wrap-around may disappear even when the Nyquist theorem is not obeyed.
We have studied these effects analytically for the constant-velocity case and determined sampling conditions that avoid wrap-around artefacts. The conditions depend on the velocity, depth of the migration grid and offset range. They show that the spacing between subsequent frequencies can be larger than the inverse of the time range prescribed by the Nyquist theorem. A 2-D example has been used to test the validity of these conditions for a more realistic velocity model. Finite-difference migration with the one-way wave equation shows a similar behaviour.

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