Curvelet‐domain multiple elimination with sparseness constraints

Abstract

Predictive multiple suppression methods consist of two main steps: a prediction step, in which multiples are predicted from the seismic data, and a subtraction step, in which the predicted multiples are matched with the true multiples in the data. The last step appears crucial in practice: an incorrect adaptive subtraction method will cause multiples to be sub-optimally subtracted or primaries being distorted, or both. Therefore, we propose a new domain for separation of primaries and multiples via the Curvelet transform. This transform maps the data into almost orthogonal localized events with a directional and spatialtemporal component. The multiples are suppressed by thresholding the input data at those Curvelet components where the predicted multiples have large amplitudes. In this way the more traditional filtering of predicted multiples to fit the input data is avoided. An initial field data example shows a considerable improvement in multiple suppression.

Similarity index for seismic data sets using adaptive curvelets

“…It works by dividing the spatial content of images into different frequency bands representing unique scale and directional features. It has shown performance advantages in seismic denoising (Oueity et al (2009)), multiple suppression (Herrmann et al (2004)), compressed sensing retrieval (Herrmann et al (2012)), and seismic imaging (Douma and de Hoop (2007)).…”

An iterative curvelet thresholding algorithm for seismic random noise attenuation

“…It combines the advantages of ridgelet and wavelet transforms which are good at expressing the characteristics of lines or points, respectively, and uses the unique characteristics of multiscale analysis (Huang, 2007;Zhao, 2007;Wu, 2008). Herrmann and Verschuur (2004) and Herrman et al (2007) gave reports on curvelet-based multiple removal, curvelet-and wavelet-based AVO inversion, and so on, and proposed a new concept of curvelet-based seismic data processing. Huub and Masarten (2004) discussed pre-migration in the curvelet domain.…”

Sparse adaptive template matching and filtering for 2D seismic images with dual-tree wavelets and proximal methods

“…As a result, multiscale geometric transforms such as curvelet frames [10][11][12] have been employed in geophysical processing. Indeed, 2D matching filters resemble directional filters [13].…”