High resolution prestack nonstationary AVA inversion: Part 1 - Theory

Xintao Chai*, Shangxu Wang, Xian Wei, Xiangcui Meng, Jingnan Li, Hanjun Yin, Yang Qiao, and Ming Ma China University of Petroleum, State Key Laboratory of Petroleum Resources and Prospecting, CNPC Key Laboratory of Geophysical Exploration Summary In this paper, a nonstationary AVA (NAVA) inversion method for field nonstationary prestack data is proposed, in which the nonstationarity is due to the Q attenuation and dispersion effects. The deabsorption preprocessing is then needless, as the NAVA inversion performs AVA inversion and deabsorption simultaneously. Namely, the NAVA inversion integrates the two-step procedure of “inverse Q filtering followed by the AVA inversion” into a single operation. The highlights of the NAVA inversion are that it avoids the intrinsic numerical instability of inverse Q filtering and directly extracts high-resolution parameters from the nonstationary prestack data. Using some synthetic noise-free and noisy data results (presented in the followed paper, see Part 2), it is shown that this completely novel methodology (the NAVA inversion) generates superior results compared to the traditional approach of “performing inverse Q filtering followed by the AVA inversion”. Introduction Recently, prestack seismic inversion has been used extensively and plays an important role in hydrocarbon exploration, due to the fact that prestack seismic data contain more information than poststack data because the amplitude variation with offset or angle (AVO or AVA) phenomenon is related to P-wave velocity VP, S-wave velocity VS, and density ρ contrasts above and below the boundaries. AVA inversion has served as a foundation for extracting parameters and achieved remarkable advances. However, there are still problems with the AVA inversions. The conventional AVA inversion methods are based on the convolutional model (e.g., Buland and Omre, 2003; Downton and Ursenbach, 2006; Russell and Hampson, 2006; Alemie and Sacchi, 2011; Chai et al., 2013; Perez et al., 2013) and a linearized approximation of the Zoeppritz equation (e.g., Aki and Richards, 1980; Shuey, 1985). However, the convolutional model assumes a stationary propagating wavelet. A wavelet is considered stationary if its amplitude and phase spectra do not change as it propagates. Conversely, nonstationary wavelets propagate in a way that changes their Fourier spectra. A seismic trace represented by the sum of nonstationary wavelets is by itself nonstationary (Chai et al., 2014). The stationarity assumption facilitates application of the conventional AVA inversion, but does not realistically reflect the prestack data which are essentially nonstationary because of wavefront divergence, anelastic attenuation and dispersion, and other effects. Here, we primarily address nonstationarity caused by attenuation and dispersion (i.e., the so-called Q effects). Our novel idea is illustrated in Figure 1. Conventional AVA inversion for nonstationary prestack data (Figure 1b) requires us to first compensate for the Q-filtering effects (or the deabsorption preprocessing) by inverse Q filtering. However, the attenuation correction for inverse Q filtering is inherently unstable (Wang, 2006) (see Figure 1c, Problem 1), and the gain-limited inverse Q filtering cannot effectively compensate the severely attenuated highfrequency components (Chai et al., 2014) (comparing Figure 1d and 1a, Problem 2). Thus, we propose the NAVA inversion for field nonstationary prestack data. It performs the AVA inversion and deabsorption simultaneously. Namely, we integrate the two-step procedure of “inverse Q filtering followed by the AVA inversion” into a single operation. One highlight of the NAVA inversion is that it avoids the intrinsic instability of inverse Q filtering. Or simpler, we extend the poststack nonstationary sparse reflectivity inversion (NSRI) (Chai et al., 2014) to the prestack seismic data. The reconstructed stationary prestack data from the NAVA inversion results (e.g., Figure 1a) can also be used for poststack inversion, attributes analysis, etc. c) d)