Seismic deblending

Deblending of a continuously blended common-receiver gather.

• True model: the unblended gather.

• Operator: pylops.waveeqprocessing.BlendingContinuous, with sources fired every overlap * nt samples plus a random jitter in the ignition times (drawn with a fixed seed).

• Data: the blended (continuous) recording, plus optional white Gaussian noise (noise_std, also drawn with a fixed seed).

All solvers promote sparsity in the same dictionary, an overlapping patched f-k transform (pylops.signalprocessing.Patch2D of FFT2D), either in synthesis form (inversion for the f-k coefficients) or in analysis form (inversion for the data, with the regularizer applied to its f-k transform). Thresholds decay with the iterations (continuation).

Solvers compared:

Solver	Formulation
Acc. Proximal Gradient	L1 or L0 regularized least squares, synthesis or analysis, solved with the accelerated proximal gradient algorithm (PyProximal)
POCS	L1 or L0 regularization with exact data consistency, synthesis or analysis, alternating thresholding and projection onto the data-consistent affine set (PyProximal HQS)
ADMM	L1 or L0 regularization with exact data consistency, synthesis or analysis, solved with ADMM (PyProximal)
PrimalDual	L1 or L0 regularization with exact data consistency, synthesis or analysis, solved with the primal-dual algorithm (PyProximal)

Source: benchmarks/seismic_deblending.

Results

Raw results: results/seismic_deblending.csv.

Mobil AVO

Mobil AVO common-receiver gather, continuously blended.

The gather has 60 sources and 960 time samples (4 ms sampling). Sources are fired every overlap * nt samples with a random jitter of +/-1 s in the ignition times.

Dataset parameters: noise_std=0, overlap=0.5, seed=42

Rank	Solver	Parameters	MAE	PSNR [dB]	Time [s]	Figure
1	POCS	formulation=analysis, regularizer=l0	0.7726	48.46	3.285	view
2	Acc. Proximal Gradient	formulation=analysis, regularizer=l1	0.9025	47.20	2.514	view
3	ADMM	formulation=analysis, regularizer=l1	0.9217	47.02	4.252	view
4	ADMM	formulation=analysis, regularizer=l0	0.9083	46.85	2.547	view
5	POCS	formulation=analysis, regularizer=l1	0.9884	46.58	4.671	view
6	PrimalDual	formulation=analysis, regularizer=l0	1.098	46.20	3.561	view
7	Acc. Proximal Gradient	formulation=analysis, regularizer=l0	1.006	46.03	1.310	view
8	POCS	formulation=synthesis, regularizer=l0	1.171	45.71	10.140	view
9	Acc. Proximal Gradient	formulation=synthesis, regularizer=l1	1.216	45.51	2.922	view
10	POCS	formulation=synthesis, regularizer=l1	1.196	45.43	11.756	view
11	ADMM	formulation=synthesis, regularizer=l1	1.198	45.37	10.889	view
12	PrimalDual	formulation=synthesis, regularizer=l1	1.405	44.07	9.376	view
13	PrimalDual	formulation=analysis, regularizer=l1	1.421	43.55	3.495	view
14	Acc. Proximal Gradient	formulation=synthesis, regularizer=l0	1.733	43.17	1.573	view
15	ADMM	formulation=synthesis, regularizer=l0	2.35	40.19	10.805	view
16	PrimalDual	formulation=synthesis, regularizer=l0	2.771	37.55	9.649	view