The introduction of rock physics models allows us to fully utilize pre-stack seismic data for inversion, thereby obtaining more comprehensive information about the subsurface media. However, the increase in the number of parameters to be inverted in the elastic impedance equation, which is based on the reflection coefficient equation, as well as the varying contributions of different parameters to the reflection coefficient, have also increased the difficulty of the inversion. Consequently, to ensure the stability of multi-parameter inversion, the two-step inversion method has been widely applied. That is, firstly, perform elastic impedance inversion to obtain elastic impedance information under different incident angles and azimuthal angles, and then use elastic impedance as input for the next step of multi-parameter inversion.Elastic impedance, as an extension of acoustic impedance inversion technology, has become very mature, but there are still problems such as non-uniqueness of solutions, insufficient resolution, and insufficient sparsity of the solution. This article introduces the hyper-Laplacian blocky constraint into the inversion process. This is commonly used in the field of signal and image processing. It can avoid the issue of 0-norm differentiation and also allow for the selection of the optimal p-value according to the characteristics of the data itself, ensuring a certain degree of stability while obtaining higher resolution in the inversion results. At the same time, a linearized approximate PP wave reflection coefficient equation is introduced to obtain the inversion results of elastic impedance directly from the seismic data. First, the derivation of a linearized elastic impedance approximation equation is carried out, and its accuracy is analyzed. Subsequently, based on the Bayesian theory, the objective function of elastic impedance inversion with the introduction of the differentiable hyper-Laplacian blocky constraint is derived. The iterative reweighted least squares method is chosen to solve the objective function to obtain the elastic impedance inversion results. Finally, the results of the new method are compared with those obtained by traditional methods to verify the accuracy and stability of the method. Both the correlation coefficient and the comparison of elastic impedance curves effectively demonstrate that the inversion results obtained by the proposed method are better than those of the traditional inversion results constrained by L₁ norm and L₂ norm. By applying the new method to the inversion of both synthetic data and real data, its effectiveness and feasibility have been proved. Therefore it can be widely applied in the inversion process of elastic impedance, providing more reliable and comprehensive information for subsequent multi-parameter inversion.

Injecting supercritical CO₂ into underground reservoir space significantly alters the properties of the sequestered area, resulting in obvious time-lapse responses on post-stack seismic data. Time-lapse wave impedance inversion is an effective method to identify reservoir changes by calculating differential wave impedance with post-stack time-lapse differential data. Since reservoir parameters lapse are usually localized, the differential wave impedance often displays clear, block-like features, meaning that the reflectivity of differential wave impedance tends to exhibit sparsity. And due to the insufficient sparsity of the L₂ or L₁ regularization constraint term used in the conventional time-lapse wave impedance inversion method, it results in the problem of unclear boundary delineation in time-lapse difference imaging. In this paper, we propose to add L_1-2 norms with stronger sparsity-promoting characteristics as a prior constraint into the differential wave impedance inversion to enhance the clarity of the inversion results at the boundary clarity. The L_1-2 norm constraint improves the sharpness of the inversion results, especially at impedance interfaces. Through model testing and analysis, it is found that the L_1-2 norm constraint provides the highest inversion resolution in the vertical direction when compared to L₁ and L₂ norms. Additionally, in order to overcome the problem of poor transverse continuity of the inversion results that may be caused by using the single-channel inversion method, this paper adopts the f-x filtering method for result enhancement. By applying the proposed method to the model data and the CO₂ geological storage data in the deep saline layer of Sleipner, Norway, it is shown that the time-lapse wave impedance inversion method based on the constraints of L_1-2 norms can characterize the time-lapse seismic differential response efficiently and accurately, and it can be used as a means to monitor the CO₂ geological storage.