Multichannel adaptive deconvolution based on streaming prediction-error filter

Introduction

Thin interbedded reservoirs and subtle reservoirs with complex lithology are becoming key areas of seismic exploration and development. Conventional seismic data is difficult to accurately characterize the thin reservoir, therefore, improvement of seismic resolution is a persistent problem in seismic exploration. Two major categories improving the vertical resolution of seismic data include deconvolution (Margrave et al., 2011; ver der Baan, 2008,2012; Li et al., 2013) and inverse Q filtering (Wang, 2006,2002), and those techniques can effectively broaden the frequency bandwidth and improve the accuracy of seismic data interpretation, especially in the identification of thin reservoir. The inverse Q filtering method compensates the attenuation of wave amplitude and fixes the phase distortion caused by the absorption of subsurface media; however, the correction depends on the accuracy of the quality factor Q. Predictive deconvolution method improves the resolution of seismic data by compressing seismic wavelet, which depends on the assumptions of minimal phase wavelet and whitening reflection coefficients. Thus, predictive deconvolution is suitable for vibroseis seismic data (Ristow and Jurczyk, 1975).

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.

Multichannel adaptive deconvolution based on streaming prediction-error filter