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Adaptive subtraction is a key element in predictive multiple-suppressionmethods. It minimizes misalignments and amplitude differences between modeledand actual multiples, and thus reduces multiple contamination in the datasetafter subtraction. Due to the high cross-correlation between their waveform,the main challenge resides in attenuating multiples without distortingprimaries. As they overlap on a wide frequency range, we split this wide-bandproblem into a set of more tractable narrow-band filter designs, using a 1Dcomplex wavelet frame. This decomposition enables a single-pass adaptivesubtraction via complex, single-sample (unary) Wiener filters, consistentlyestimated on overlapping windows in a complex wavelet transformed domain. Eachunary filter compensates amplitude differences within its frequency support,and can correct small and large misalignment errors through phase and integerdelay corrections. This approach greatly simplifies the matching filterestimation and, despite its simplicity, narrows the gap between 1D and standardadaptive 2D methods on field data.

Adaptive multiple subtraction with wavelet-based complex unary Wiener filters