A constrained-based optimization approach for seismic data recovery ...

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May 9, 2014 - CONTEXT. GENERAL SCHEME. RESULTS. CONCLUSION. A constrained-based optimization approach for seismic data recovery problems.
I NTRODUCTION

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G ENERAL SCHEME

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A constrained-based optimization approach for seismic data recovery problems ICASSP 2014 — SS5: Seismic signal processing M-Q. PHAM, L. DUVAL* IFP Energies nouvelles 1 et 4 av. de Bois-Pr´eau, 92852 Rueil-Malmaison - France C. CHAUX Univ. Aix-Marseille, I2M UMR CNRS 7373 39 rue F. Joliot-Curie, 13453 Marseille - France J-C. PESQUET Univ. Paris-Est, LIGM UMR CNRS 8049 5 bd Descartes, 77454 Marne-la-Vall´ee - France

4-9 May 2014

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I NTRODUCTION

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The fast way ◮ ◮

Here: signal = primary; disturbance = multiples Use of approximate disturbance models (given) ◮





Two aims: ◮ ◮



to recover highly under-determined signals to alleviate and fasten hyper-parameter determination

An entwined approach: ◮ ◮



similar to acoustic echo cancellation, speech dereverberation, pattern matching. . . imperfect models: adaptation (and regularization) required

pragmatic: with geophysically-sound functions/models heuristic: explore other suitable penalties/constraints

Focus on the “sparsity” term (signal wavelet coefficients)

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I NTRODUCTION

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Outline I NTRODUCTION C ONTEXT Seismic data Problem formulation G ENERAL SCHEME MAP estimation Hyperplane constraints R ESULTS Synthetic data Real data C ONCLUSION

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I NTRODUCTION

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Seismic data propagation & acquisition Hydrophone •







Towed streamer •





Primaries + multiple reflection disturbances 4 / 17

I NTRODUCTION

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Multiple problem formulation

z(n) |{z}

observed signal

¯(n) + |{z} ¯s(n) + y b(n) = |{z} |{z} multiple

primary

noise

where ◮

n: time index (somehow related to underground depth)



z = (z(n) )0≤n

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