HR: 13:45h
AN: S33A-02    [Abstracts]
TI: Common-Offset Pre-Stack Time Migration Using Curvelets
AU: * Douma, H
EM: huub@dix.mines.edu
AF: Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, 924 16th Street, Golden, CO 80401-1887 United States
AU: de Hoop, M V
EM: mdehoop@dix.mines.edu
AF: Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, 924 16th Street, Golden, CO 80401-1887 United States
AB: Recently, in the field of applied harmonic analysis, curvelets have been introduced in an effort to combine geometry and multiscale analysis. Roughly speaking, curvelets are 2D extensions to wavelets. It has been shown that curvelets in essence provide optimal sparsification of objects that are twice continuously differentiable (C²) with discontinuities along C² edges. In addition, it was recently shown that curvelets in essence optimally sparsify certain Fourier Integral Operators (FIO). Because the seismic imaging operator belongs to this class of FIO, and since the singularities in reflection seismic data lie mainly along smooth curves, curvelets are plausible candidates for simultaneous sparsification of seismic data and the imaging operator. The geometry of seismic imaging is determined by map migration. Since map migration makes explicit use of the directions (or slopes) in the data, and since curvelets have directions associated with them, map migration can be used to determine the transformation from a curvelet in the data domain to a curvelet in the image domain. This transformation consists of a translation, rotation and dilation of the curvelet. We show the use of map migration to image seismic data using curvelets, and treat common-offset (CO) pre-stack time migration as an example. We present synthetic data examples of CO pre-stack time migration using curvelets, where we use the aforementioned transformation.
DE: 0902 Computational methods, seismic
DE: 0910 Data processing
DE: 0935 Seismic methods (3025)
SC: Seismology [S]
MN: 2005 Joint Assembly