[Title]
Adaptive filtering in the complex wavelet domain with unary filters: application to multiple suppression in geophysics
Presenter: Laurent Duval (IFPEN)
Co-authors: Sergi Ventosa (IPGP), Irène Huard, Sylvian Le Roy, Antonio Pica (CGG Veritas), Hérald Rabeson (IFPEN)

[Background]
Geophysical signal processing addresses the extraction of relevant information present in seismic data. In reflection seismology, seismic waves propagate through the subsurface medium. The portion of seismic wave fields recorded at the surface forms seismic traces, whose primary reflections at geological interfaces and propagation-related distortions inform about the subsurface structure. Many types of disturbances affect seismic signals. Consequently, geophysics has nurtured several signal processing tools, including robust, l1-promoted deconvolution, or complex, continuous wavelet transforms. 

[Scope]
Multiple reflections, corresponding to seismic waves bouncing betwixt layers, are one of the most severe types of interferences. They are somehow related to the notion of echoes. With a priori information and assumptions, along with additional processing, one may build different models, approximately matching multiple reflections. The main challenge resides in performing adaptive filtering on the models, allowing subsequent subtraction from the noisy data, to recover useful primary reflection information.

[Focus]
Due to the high cross-correlation between primary and multiple reflections, attenuating the latter without distorting the former is a complicated problem. The talk deals with a recently proposed technique for joint multiple model-based adaptive subtraction. Since signals and disturbances 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 local time and frequency supports, and can correct small and large misalignment errors through phase and integer delay corrections. This approach greatly simplifies the matching filter estimation. Despite its simplicity, it compares promisingly with standard industrial methods on field seismic data. 
Joint work between IFP Energies nouvelles and CGGVeritas.
http://library.seg.org/doi/abs/10.1190/geo2011-0318.1
http://arxiv.org/abs/1108.4674

[Keywords]
geophysics, echoes, signal processing, adaptive filtering, wavelet transform, Wiener filter

[Biography]
Laurent Duval conducts research in signal processing and image analysis at IFP Energies nouvelles with applications to geosciences, material characterization, chemical analysis, and engine diagnosis. His research interests are in the area of non-stationnary digital signal and image processing, with a special emphasis on wavelets and time-frequency techniques, and their applications to denoising, detection, filtering, and data compression.