Frequency-space migration in practice

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

The basis of the steep-dip implicit algorithms is the dispersion relation of equation (18). Finite-difference schemes with steep-dip accuracy are implemented conveniently in the frequency-space domain. An important advantage of the implicit method is its exceptional ability to handle velocity variations, whether vertical or lateral. Its accuracy for the lateral velocity problem results from the fact that the time shift associated with the thin-lens term (equation 16b) can be implemented exactly in the frequency domain. For these reasons, the algorithm is most appropriate for depth migration to image targets beneath complex structures (earth imaging in depth).

The frequency-space, sometimes referred to as ω − x or f − x, migration also has the important operational advantage that each frequency can be processed separately. This property can reduce computer memory requirements significantly and, thus, decrease input-output operations for large data sets. Also, in frequency-space migration, some accuracy features can be conveniently implemented. For example, wave extrapolation can be limited to a specified signal bandwidth. Each frequency component can, in principle, be downward continued using an optimum depth step size that yields a minimum acceptable phase error, leading to a minimum amount of dispersive noise on the migrated section.

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Frequency-space migration in practice
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