Marine seismic multiple suppression moves to a self-supervised network: no smoothness constraint, better weak-signal and waveform preservation

The adaptive subtraction step of multiple suppression no longer depends on a hand-set smoothness constraint; a self-supervised neural network learns the nonlinear mapping from the predicted multiple model to the observed full wavefield directly. Previously the subtraction step of SRME typically used a fixed-length stationary least-squares matching filter, or a non-stationary regression filter whose local smoothness was imposed by a triangle-smoothing operator, and the latter was limited where signal energy varies rapidly in space. On a set of synthetic examples and one field dataset, PDL is compared with the classical non-stationary least-squares matching filter: PDL leaves fewer multiple residuals and preserves weak primaries better, and the synthetic case reports mean squared error and structural similarity, both favoring PDL over the classical method.

Training is governed by the adaptive matching filtering equation, with the loss being the matching misfit between multiple samples and noise-contaminated data samples, so no manual labels are needed. The method uses a patching scheme that cuts a moderately sized seismic profile and an initial multiple model into many patches according to patch size and shift size, supplying the number of training samples mainstream deep-learning platforms require. The first synthetic example is 751 by 121 samples with patch size and shift size of 10 and 1; the second, the Pluto dataset, is 1126 by 818 with 32 and 8; the Viking Graben field data are 1500 by 120 by 1012 at 4 ms sampling with 64 and 8, and the network has two dense layers.

Because optimization runs by backpropagation without a local smoothness constraint, PDL captures rapidly oscillating local variations, while batch size constrains gradient updates in a non-local way to keep training stable. In the traditional non-stationary matching filter, smoothness is guaranteed by the triangle-smoothing shaping operator of shaping regularization, and that assumption limits matching in highly non-stationary settings. On a noisy scatter-point fitting benchmark, the PDL fitted curve beats regularized non-stationary regression, with the difference clearest at the edge points; in noise tests at signal-to-noise ratios of 5 dB and 10 dB, performance degrades as noise rises but multiples are still suppressed.

The demonstrated scope is 2D seismic profiles: two synthetic examples and one field dataset from the Viking Graben, all with multiple subtraction performed in the common-offset domain and compared against the classical non-stationary least-squares matching filter. The authors recommend a parameter sensitivity analysis of patch size and shift size before processing, and note the method suits domains where events are relatively flat.

The authors note PDL has limited ability to suppress ambient noise and suggest denoising the input first; in noise tests performance degrades as the noise level rises. For complex structures, the patching scheme needs a small shift size to guarantee holistic recovery, which raises computational cost, and the authors say they will develop a scheme balancing efficiency and accuracy for large-scale 3D applications.