Curvelet-based seismic data processing: a multiscale and nonlinear approach

In this letter, the solutions to three seismic processing problems are presented that exploit the multiscale and multi-angular properties of the curvelet transform. Data regularization, multiple removal, and restoration of migration amplitudes are all formulated in terms of a sparsity promoting program that employs the high degree of sparsity attained by curvelets on seismic data and images. For each problem the same nonlinear program is solved, simultaneously minimizing the data misfit and the one norm (`1) on the desired curveletdomain solution. Parsimony of curvelets on seismic wavefields and images of the sedimentary crust with wavefront-like features underlies the successful solution of these problems and is a clear indication of the broad applicability of this transform in exploration seismology. ∗Seismic Laboratory for Imaging and Modeling, Department of Earth and Ocean Sciences, University of British Columbia, 6339 Stores Road, Vancouver, V6T 1Z4, BC, Canada †Jilin University, 2699 Qianjin street, Changchun, 130012, China. Visiting the University of British