Sparse Multichannel Blind Deconvolution of Seismic Data via Spectral Projected-Gradient

Abstract

In this work, an efficient numerical scheme is presented for seismic blind deconvolution in a multichannel scenario. The proposed method iterate with two steps: first, wavelet estimation across all channels and second, refinement of the reflectivity estimate simultaneously in all channels using sparse deconvolution. The reflectivity update step is formulated as a basis pursuit denoising problem and a sparse solution is obtained with the spectral projected-gradient algorithm -faithfulness to the recorded traces is constrained by the measured noise level. Wavelet re-estimation has a closed form solution when performed in the frequency domain by finding the minimum energy wavelet common to all channels. Nothing is assumed known about the wavelet apart from its time duration. In tests with both synthetic and real data, the method yields sparse reflectivity series and stable wavelet estimates results compared to existing methods with significantly less computational effort.

Distributed Blind Deconvolution of Seismic Signals Under Sparsity Constraints in Sensor Networks

“…However, both source wavelet and reflectivity are usually unknown such that blind approaches are required. As proposed by [4] one can separate the blind deconvolution into a stage of wavelet estimation and reflectivity estimation. We make use of the same approach here but extend it for distributed operation.…”

“…Based on the system models introduced in Section 2 we aim at estimating both the source wavelet w and the reflectivity vectors hj in a distributed fashion within the network. As proposed in [4] for the centralized case, we can separate the problem into two steps: one step is an estimation of the wavelet w and the other one is the estimation of the reflectivity hj. Let us first introduce the wavelet estimation.…”

“…Hence, blind deconvolution algorithms are needed that recover both the source signal and the reflectivity profile. In the past, a lot of research has been contributed to the field of blind seismic deconvolution, see [3,4] and references therein. In particular, sparse multichannel blind deconvolution (SMBD) methods have shown promising performance results for the reflectivity estimation.…”

“…In particular, sparse multichannel blind deconvolution (SMBD) methods have shown promising performance results for the reflectivity estimation. The recent work of [4] uses an iterative algorithm that alternates between wavelet and reflectivity estimation. The wavelet estimation is conducted in the frequency domain whereas the reflectivity estimation is done in the time domain to exploit sparsity in the reflectivity's impulse response.…”

“…However, all of these state-of-the-art deconvolution methods consider a centralized operation. Our paper proposes a distributed blind deconvolution algorithm inspired by [4]. Both wavelet and reflectivity estimation are conducted in a distributed fashion within the seismic network such that each sensor in the network obtains an estimate of the impulse response of its corresponding reflectivity.…”