L_1–2 minimization for P- and S-impedance inversion

Abstract

Amplitude variation with offset (AVO) inversion has been widely used in reservoir characterization to predict lithology and fluids. However, some existing AVO inversion methods that use [Formula: see text] norm regularization may not obtain the block boundary of subsurface layers because the AVO inversion is a severely ill-posed problem. To obtain sparse and accurate solutions, we have introduced the [Formula: see text] minimization method as an alternative to [Formula: see text] norm regularization. We used [Formula: see text] minimization for simultaneous P- and S-impedance inversion from prestack seismic data. We first derived the forward problem with multiangles and set up the inversion objective function with constraints of a priori low-frequency information obtained from well-log data. Then, we introduced minimization of the difference of [Formula: see text] and [Formula: see text] norms, denoted as [Formula: see text] minimization, to solve this objective function. The nonconvex penalty function of the [Formula: see text] minimization method is decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem is solved by the alternating direction method of multipliers. Compared to [Formula: see text] norm regularization, the results indicate that [Formula: see text] minimization has superior performance over [Formula: see text] norm regularization in promoting blocky/sparse solutions. Tests on synthetic and field data indicate that our method can provide sparser and more accurate P- and S-impedance inversion results. The overall results confirm that our method has great potential in the detection and identification of fluids.

Mechanochemical Synthesis of Solid Catalysts and Application in Catalytic Reaction

“…Nie et al. found the above strategy was suitable to prepare noble metal/meso‐Al 2 O 3 catalysts [36] . Aluminium isopropoxide, P123 and acetylacetonate platinum were mixed in a reactor and ball milled for 0.5 h, followed by calcination at 400 °C.…”

Prestack Seismic Inversion via Nonconvex L1-2 Regularization

“…Previous work in this area indicates that this reservoir formation, known as the Pearl River Formation, is characterized by shallow deltaic deposits. This formation is deeply buried, structurally complex, and exhibits significant lateral variation [12]. Based on the results of our model experiments, separated the seismic data into three angle ranges: 3 • -15 • , 18 • -30 • , and 33 • -45 • .…”

“…Certain types of a priori information, such as structural and well-log data, significantly improve the stability of the inversion by providing useful constraints for the model results. According to [12,30], there are two types of useful a priori information: (1) low-frequency data that adhere to a (0, c 2 low ) Gaussian distribution and (2) constraints on the sparsity of the estimated parameter. The low-frequency information, which is independent of the seismic data and is typically obtained by interpolating and extrapolating the horizon and well-log data, is used to enhance the lateral continuity of the inversion.…”

“…Those methods are sensitive to noise and the amount and quality of the observational data used in the inversion. To improve the stability of the inversion method, Nie et al proposed a novel P/S impedance inversion used in conjunction with L 1−2 regularization, and they demonstrated the applicability and feasibility of their method, however, which method also faces difficulties in producing accurate density values [12].…”

Seismic inversion with L2,0-norm joint-sparse constraint on multi-trace impedance model

“…L 2,0 -norm is a joint-sparse measure or row-sparse 14 , which can not only measure the conventional sparsity with L 0 -norm in vertical direction, but also measure the lateral continuity with L 2 -norm in lateral direction. The joint-sparse or row-sparse has promoted the sparse signal representation and compressed sensing recovery 22 , 23 and has been applied in many science fields, such as target detection 24 , color image restoration 25 , hyperspectral image processing 26 , art restoration 27 , feature extraction 28 , and applied geophysics 29 . Then, we use a split Bregman algorithm to solve the L 2,0 -norm joint-sparse constrained objective function.…”