ALBERT

Description: 〈span〉〈div〉ABSTRACT〈/div〉Acoustic impedance (AI) inversion is of great interest because it extracts information regarding rock properties from seismic data and has successful applications in reservoir characterization. During wave propagation, anelastic attenuation and dispersion always occur because the subsurface is not perfectly elastic, thereby diminishing the seismic resolution. AI inversion based on the convolutional model requires that the input data be free of attenuation effects; otherwise, low-resolution results are inevitable. The intrinsic instability that occurs while compensating for the anelastic effects via inverse Q filtering is notorious. The gain-limit inverse Q filtering method cannot compensate for strongly attenuated high-frequency components. A nonstationary sparse reflectivity inversion (NSRI) method can estimate the reflectivity series from attenuated seismic data without the instability issue. Although AI is obtainable from an inverted reflectivity series through recursion, small inaccuracies in the reflectivity series can result in large perturbations in the AI result because of the cumulative effects. To address these issues, we have developed a Q-compensated AI inversion method that directly retrieves high-resolution AI from attenuated seismic data without prior inverse Q filtering based on the theory of NSRI and AI inversion. This approach circumvents the intrinsic instability of inverse Q filtering by integrating the Q filtering operator into the convolutional model and solving the inverse problem iteratively. This approach also avoids the ill-conditioned nature of the recursion scheme for transforming an inverted reflectivity series to AI. Experiments on a benchmark Marmousi2 model validate the feasibility and capabilities of our method. Applications to two field data sets verify that the inversion results generated by our approach are mostly consistent with the well logs.〈/span〉

Description: Seismic data are nonstationary due to subsurface anelastic attenuation and dispersion effects. These effects, also referred to as the earth’s Q -filtering effects, can diminish seismic resolution. We previously developed a method of nonstationary sparse reflectivity inversion (NSRI) for resolution enhancement, which avoids the intrinsic instability associated with inverse Q filtering and generates superior Q compensation results. Applying NSRI to data sets that contain multiples (addressing surface-related multiples only) requires a demultiple preprocessing step because NSRI cannot distinguish primaries from multiples and will treat them as interference convolved with incorrect Q values. However, multiples contain information about subsurface properties. To use information carried by multiples, with the feedback model and NSRI theory, we adapt NSRI to the context of nonstationary seismic data with surface-related multiples. Consequently, not only are the benefits of NSRI (e.g., circumventing the intrinsic instability associated with inverse Q filtering) extended, but also multiples are considered. Our method is limited to be a 1D implementation. Theoretical and numerical analyses verify that given a wavelet, the input Q values primarily affect the inverted reflectivities and exert little effect on the estimated multiples; i.e., multiple estimation need not consider Q filtering effects explicitly. However, there are benefits for NSRI considering multiples. The periodicity and amplitude of the multiples imply the position of the reflectivities and amplitude of the wavelet. Multiples assist in overcoming scaling and shifting ambiguities of conventional problems in which multiples are not considered. Experiments using a 1D algorithm on a synthetic data set, the publicly available Pluto 1.5 data set, and a marine data set support the aforementioned findings and reveal the stability, capabilities, and limitations of the proposed method.