Seismic wavelet shape-oriented reflectivity inversion method

Abstract

Abstract Reflectivity inversion plays a pivotal role in reservoir prediction. Conventional sparse-spike deconvolution assumes that the reflectivity (reflection coefficient) is sparse, which is solved based on the l1 norm. However, the restricted isometry property (RIP) of wavelet matrix and seismic effective bandwidth limits the accuracy of the sparse-spike reflectivity inversion. Consequently, we investigate the connection between seismic amplitude shape and reflectivity. When the reflectivity contains more non-zero values, the wavelet bandwidth within the effective seismic data bandwidth approaches a limit corresponding to the Sinc wavelet, where the main-lobe amplitude closely approximates the reflectivity. Conversely, when the reflectivity has fewer non-zero values, a wavelet with a smaller sidelobe provides a more accurate approximation of the reflectivity. In this paper, we propose a high-resolution inversion optimization method based on joint l2 norm and l1 norm constraints. By parameter tuning, we construct the Sinc wavelet or the wavelet with a weak-sidelobe corresponding to the seismic spectrum. Subsequently, we determine the extremum to approximate the reflectivity. To mitigate the RIP condition's constraints, we employ the l2 norm to balance the l1 norm (joint constraint) by introducing l2 norm with low-pass filtering characteristics. This approach yields more accurate reflectivity estimates. By taking the extremum, this approach yields more accurate reflectivity estimates. The synthetic test demonstrates that our method achieves better reflectivity inversion accuracy compared to sparse-spike inversion with l1–l2 norm constraint. Furthermore, field tests indicate that the proposed reflectivity inversion method not only can better match the well curve, but also exhibits excellent resolution.