Curvelet‐based ground roll removal

Abstract

We have effectively identified and removed ground roll through a twostep process. The first step is to identify the major components of the ground roll through various methods including multiscale separation, directional or frequency filtering or by any other method that identifies the ground roll. Given this estimate for ground roll, the recorded signal is separated during the second step through a block-coordinate relaxation method that seeks the sparsest set for weighted curvelet coefficients of the ground roll and the sought-after reflectivity. The combination of these two methods allows us to separate out the ground roll signal while preserving the reflector information. Since our method is iterative, we have control of the separation process. We successfully tested our algorithm on a real data set with a complex ground roll and reflector structure.

Data adaptive ground-roll attenuation via sparsity promotion

“…Because reflections and ground-roll in common shot gathers are both inspired by the same source and obey the wave equation, it is hard to find two proper signal representations that separate these two signal components without any prior information on their characteristics. Following the ideas of Herrmann et al (2007a) and Yarham et al (2006), we thus take weighted sparse constraints instead of the simple sparse constraints in the problem P 1 , and meanwhile use the same overcomplete dictionary A = A 1 = A 2 for representing both signal components:…”

“…Adopting the similar signal separation model as Yarham et al (2006) used, we make use of the coherency of reflection events and propose a data-adaptive ground-roll attenuation method. The separation process is applied on a trace-to-trace basis and thus is capable for the data unequally spaced along the offset axis.…”

“…A successful separation of events with different shapes is obtained whenever the signal model assumptions hold. Yarham et al (2006) utilize some approximate signal predictions to model the to-be-separated signals and exploit the sparseness of certain signal representations in curvelet transform domain. With reasonable predictions of both signal components, this separation scheme removes most ground-roll energy while preserving reflections.…”

Seismic data analysis with dual-tree M-band wavelet transforms

“…However, despites their achievements, traditional approaches based on discrete and separable (both for computational purposes) wavelets fail at efficiently representing directional or higher dimensional data features, such as line or plane singularities, especially in severe noise conditions. Subsequent extensions to wavelets (multiscale pyramids, curvelets [YaTrHe04][Do06], contourlets, bandlets) have recently generated tremendous theoretical and practical interests. They feature local and multiscale properties associated with a certain amount of redundancy, which may represent an issue for huge datasets processing.…”

“…A recent work has proposed a curvelet domain thresholding technique [YaTrHe04]. The infinite support of curvelets and their redundancy may limit their performance in some applications.…”