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![]() | Multichannel adaptive deconvolution based on streaming prediction-error filter | ![]() |
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Prediction-error filtering (PEF) or least-square inverse filtering has been applied in seismic deconvolution for decades, and it has proved its effectiveness for resolution improvement and multiple elimination. The theory of predictive deconvolution was introduced by Robinson (1967,1957). Peacock and Treitel (1969) proved the effectiveness of predictive deconvolution for enhancing resolution and suppressing periodic multiples. To take full advantage of the spatial characteristics of seismic data and suppress noise, several authors developed multichannel predictive deconvolution (Claerbout, 1992; Porsani and Ursin, 2007; Li et al., 2016). The traditional deconvolution method is designed under the assumption of stationary data and becomes less effective because seismic data are nonstationary in nature. Clark (1968) proposed a nonstationary deconvolution in time domain based on optimal Wiener filtering. Wang (1969) gave the criteria for determining the optimal length of the filtering window on the assumption of a piecewise stationary. Griffiths et al. (1977) proposed an adaptive predictive deconvolution method that adaptively updates the filter coefficients for each data point. Koehler and Taner (1985) proposed a generalized mathematical theory of time-varying deconvolution and used the conjugate gradient algorithm to calculate the filter coefficients. Prasad and Mahalanabis (1980) compared three adaptive deconvolution methods and demonstrated that all three methods perform better than traditional predictive deconvolution when dealing with nonstationary data. Liu and Fomel (2011) obtained smoothly nonstationary PEF coefficients by solving a global regularized least-squared problem, however, iterative approach leads to slow computation speed and high memory cost. Fomel and Claerbout (2016) proposed the concept of streaming computation, which can adaptively update the filter coefficients without iteration, and the properties of nonstationary representation and low computational cost are useful for the single-channel deconvolution model and random noise attenuation of seismic data (Liu and Li, 2018). To improve the resolution effectively for nonstationary seismic data, in this paper, we design a multichannel adaptive deconvolution method based on the streaming prediction error filter in time-space domain. The time and space constraints added to the objective function can guarantee the continuity of deconvolution results in space direction, and the relationship between the prediction step and wavelet frequency reasonably improve the fidelity of the reflection coefficients in the deconvolution result.
This paper is organized as follows. First, we introduce the streaming computation for adaptive PEF. Then, we propose the improved streaming PEF method that involves spatial constraints and time-varying prediction step. Finally, the synthetic data and real data are used to demonstrate that the proposed method can be effective and efficient in vertical resolution improvement of nonstationary seismic data.
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![]() | Multichannel adaptive deconvolution based on streaming prediction-error filter | ![]() |
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