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Incoherent noise suppression and deconvolution using curvelet-domain sparsity Vishal, Kumar


Curvelets are a recently introduced transform domain that belongs to a family of multiscale and also multidirectional data expansions. As such, curvelets can be applied to resolution of the issues of complicated seismic wavefronts. We make use of this multiscale, multidirectional and hence sparsifying ability of the curvelet transform to suppress incoherent noise from crustal data where the signal-to-noise ratio is low and to develop an improved deconvolution procedure. Incoherent noise present in seismic reflection data corrupts the quality of the signal and can often lead to misinterpretation. The curvelet domain lends itself particularly well for denoising because coherent seismic energy maps to a relatively small number of significant curvelet coefficients while incoherent energy is spread more or less evenly amongst all curvelet coefficients. Following standard processing of crustal reflection data, we apply our curvelet denoising algorithm to deep reflection data. In terms of enhancing the coherent energy and removing incoherent noise, curvelets perform better than the F-X prediction method. We also use the curvelet transform to exploit the continuity along reflectors for cases in which the assumption of spiky reflectivity may not hold. We show that such type of seismic reflectivity is sparse in the curvelet-domain. This curvelet-domain compression of reflectivity opens new perspectives towards solving classical problems in seismic processing, including the deconvolution problem. We present a formulation that seeks curvelet-domain sparsity for non-spiky reflectivity. Comparing the results with those obtained from sparse spike deconvolution, curvelets perform better than the latter by recovering the frequency components, which get degraded by convolution operator and noise.

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