Adaptive seismic multiple removal with complex wavelet (paper)

The November-December 2012 issue of Geophysics (Volume 77, Issue 6) features (at last) a recent work performed on model-based, adaptive multiple removal in seismic. The concept is illustrated on the figure to the left. Signal obtained from direct reflections of interest (blue) are mixing with other waves bouncing between layers (red). They look alike except for differential attenuation in the frequency domains, different slopes in CMP gathers. Those interested could have a look at the booklet Seismic multiple removal techniques: past, present and future by Eric J. (Dirk) Verschuur. Those more patient may want to waiting for Seismic Multiple Elimination Techniques, by the same author, which should be published in June 2013.As the problem is quite complex per se, hundred of papers have been devoted to multiple elimination techniques, since the January 1948 special issue of Geophysics. A common approach consists in first computing one or several approximate models of the multiple reflections, and then trying to adaptively substract the model from the data. Such techniques usually combine an adapted representation (Fourier, Radon, different breeds of wavelets) and a matching or separation technique. The one we finally published resides at one end of the representation/matching spectrum, to cope with the industrial partner requirements. A somewhat redundant complex wavelet tranform (and yes, combining a Morlet wavelet frame and the complex trace, so to say) and a very simple sliding window 1-tap adaptive filter estimation on the complex scalogram, to adapt and remove a template disturbance signal from the original seismic trace. Maybe not the most theoretically proven approach, but a decent, fancy blend of complex wavelets and adaptive filtering, and some industrialized code that works. And a milestone in a nice collaborative venture, especially with Sergi Ventosa, now at IPGP. And finally published (took 1.5 years). So here it is:

Adaptive multiple subtraction with wavelet-based complex unary Wiener filters (arxiv, doi, page), Geophysics, 2012, November-December

Sergi Ventosa, Sylvain Le Roy, Irène Huard, Antonio Pica, Hérald Rabeson, Patrice Ricarte, Laurent Duval

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. The challenge consists in attenuating multiples without distorting primaries, despite the high cross-correlation between their waveform. For this purpose, this complicated wide-band problem is decomposed into a set of more tractable narrow-band problems using a 1D complex wavelet frame. This decomposition enables a single-pass adaptive subtraction via single-sample (unary) complex Wiener filters, consistently estimated on overlapping windows in a complex wavelet transformed domain. Each unary filter compensates amplitude differences within its frequency support, and rectifies more robustly small and large misalignment errors through phase and integer delay corrections . This approach greatly simplifies the matching filter estimation and, despite its simplicity, compares promisingly with standard adaptive 2D methods, on both synthetic and field data.

The preprint version is available, with nice color figures, under the umbrella of Arxiv. Next in line: explore other ends of the matching/transform spectrum. Comments welcome.