LEADING-ORDER SEISMIC IMAGING USING CURVELETS

Abstract

We show that with curvelets the leading-order approximation (in angular frequency, horizontal wavenumber, and migrated location) to Kirchhoff depth-migration becomes a simple transformation of the coordinates of the curvelets in the data, combined with amplitude scaling. This transformation is calculated using map migration, which uses the local slopes provided by the curvelet decomposition of the data. We verify the accuracy of the method using numerical examples for homogeneous media. These examples indicate that using the leading-order approximation only provides a good approximation to common-offset migration when rays do not diverge beyond the spatial support of a curvelet, but looses accuracy when they diverge beyond this support. This shows the need for correction beyond leading order, even for homogeneous media when the data contains diffracted waves. We proceed to show how correction beyond the leading order can be accounted.