Leading-order seismic imaging using curvelets

Curvelets are plausible candidates for simultaneous compressionofseismicdata,theirimages,andtheimagingoperator itself. We show that with curvelets, the leading-order approximation in angular frequency, horizontal wavenumber, and migrated location to common-offset CO Kirchhoff depth migration becomes a simple transformation of coordinates of curvelets in the data, combined with amplitude scaling. This transformation is calculated using map migration, whichemploysthelocalslopesfromthecurveletdecomposition of the data. Because the data can be compressed using curvelets, the transformation needs to be calculated for relatively few curvelets only. Numerical examples for homogeneous media show that using the leading-order approximationonlyprovidesagoodapproximationtoCOmigrationfor moderate propagation times.As the traveltime increases and raysdivergebeyondthespatialsupportofacurvelet;however, the leading-order approximation is no longer accurate enough. This shows the need for correction beyond leading order,evenforhomogeneousmedia.

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