Adaptive multiple subtraction with wavelet-based complex unary Wiener filters

Abstract

Adaptive subtraction is a key element in predictive multiple-suppression methods. It minimizes misalignments and amplitude differences between modeled and actual multiples, and thus reduces multiple contamination in the dataset after subtraction. Due to the high crosscorrelation between their waveform, the main challenge resides in attenuating multiples without distorting primaries. As they overlap on a wide frequency range, we split this wide-band problem into a set of more tractable narrow-band filter designs, using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via complex, single-sample (unary) Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation and, despite its simplicity, narrows the gap between 1D and standard adaptive 2D methods on field data * .

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

“…3 displays a recorded seismic data with a partially appearing primary (arrows) and the estimated primaries obtained by 1D version [8] and by 2D version. We refer to [6] for template construction. The outcome is displayed in the cropped square zone from recorded seismic data only.…”

“…In the latter case, the given wavelets yield the primal tree, the dual being obtained by the Hilbert transform of the aforementioned wavelets. The constraint bounds ( ( ) ∈{1,..., } and ) are computed empirically on i) real signals for synthetic data and ii) estimated signals using [6] for real data.…”

“…The multidimensionality of the filters is thought to ensure lateral continuity in seismic events. A quite opposite direction was taken in [6], with an emphasis on a frequencyand shift-insensitive complex wavelet transform frame, associated with simple unary (one-tap) complex filters, in 1D only. Counter-intuitively, it was able to perform similarly to more classical 2D matching techniques.…”

Internal multiple adaptive subtraction using Huber norm

“…The predicted multiple model then has the same amplitude and phase after matching filtering, thus helping to remove internal multiples (Araújo, 1994;Berkhout, 1997;Ikelle et al, 2002;Cao and McMechan, 2011). Traditional matching filters are always calculated by a residual minimized algorithm in L 2 -norm or L 1 -norm (Chapman and Barrodale, 1983;Guitton and Verschuur, 2004;Fomel, 2009;Wang et al, 2009;Ventosa et al, 2012). However, when the internal multiple strongly interferes with primary energy, these methods are difficult to deal with internal multiple subtraction (Luo et al, 2007).…”

Seismic multiple removal with a primal-dual proximal algorithm

“…Model-based multiple removal is one of the industry standard techniques. It consists of estimating a realistic template of the multiples, which is subsequently adapted in amplitude, delay and frequency by timevarying matched filtering techniques, for instance in a wavelet or curvelet domain, see [6,7] and references therein. When highly complicated propagation paths occur (dashed lines in Fig.…”