Prestack inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is the estimation of elastic parameters in the thin layers and weak reflectors. To improve the resolution and the accuracy of the inversion results, we introduced the difference of L1 and L2 norms as a nearly unbiased approximation of the sparsity of a vector, denoted as the L1−2 norm, to the prestack inversion. The nonconvex penalty function of the L1−2 norm can be decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem can be solved efficiently by the alternating direction method of multipliers. Compared with the L1 norm regularization, the L1−2 minimization can reconstruct reflectivities more accurately. In addition, the f-x predictive filtering was introduced to guarantee the lateral continuity of the location and the amplitude of the reflectivity series. The generalized linear inversion and f-x predictive filtering are combined for stable elastic impedance inversion results, and three parameters of P-wave velocity, S-wave velocity, and density can be inverted with the Bayesian linearized amplitude variation with offset inversion. The inversion results of synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and accuracy of the inversion results.

The natural damping effect of the Earth typically results in significant distortion of seismic waveforms, which greatly diminishes the precise of subsequent processes such as parameter inversion, migration imaging, and reservoir description. Compensating for this attenuation is crucial to achieving precise underground parameter measurements. While inversion or imaging techniques that rely on wave path compensation have the potential to address attenuation effects better, they encounter challenges, including heightened demands for input models, rapidly escalating algorithm intricacy, and computational burdens. Consequently, developing novel attenuation compensation methods that balance computational efficiency and accuracy is important in enhancing the precision of exploring complex reservoirs. This study utilizes a groundbreaking convolutional neural network, which integrates an attention mechanism and residual learning. This network establishes an inherent link between attenuated seismic data and their non-attenuated counterparts, effectively accomplishing data-driven compensation for seismic data attenuation. The more advanced acoustic (non-attenuated) full waveform inversion or reverse time migration framework is directly applied to enhance the modeling or imaging of attenuated seismic data with improved accuracy and efficiency. Simulation data and actual test results confirm that the suggested Q-compensation approach successfully enhances the amplitude of deep structural reflection signals, rectifies phase distortion induced by attenuation, and widens the seismic frequency range. This mitigates issues like the cycle-skipping problem associated with low-frequency absence in traditional FWI and the numerical instability and increased computational complexity found in attenuation compensation FWI. Furthermore, the imaging profile’s resolution is further heightened due to the effective attenuation correction and enhancement of high-frequency components.

Seismic acoustic impedance inversion plays an important role in reservoir prediction. However, single-trace inversion methods often suffer from spatial discontinuities and instability due to poor-quality seismic records with spatially variable signal-to-noise ratios or missing traces. The specified hyperparameters for seismic inversion cannot be suitable to all seismic traces and subsurface structures. In addition, conventional multichannel inversion imposes lateral continuity with a prespecified mathematical model. However, the inversion results constrained with specified lateral regularization are inferior when the subsurface situations violate the hypothesis. A data-driven multichannel acoustic impedance inversion method with patch-ordering regularization is introduced, in which the spatial correlation of seismic reflection is used. The method decomposes the seismic profile into patches and constructs the patch-ordering matrix based on the similarity among seismic patches to record the impedance structural extension. So the patch-ordering matrix can record the spatial extension of the acoustic impedance. Then, a simple regularization with difference operators of varying weights can reduce the random noise presented in the inverted impedance profile, stabilize the inversion result, and enhance the spatial continuity of the layer extension. The objective function for multichannel poststack seismic impedance inversion can be constructed by integrating the observed seismic record and the spatial continuity in the form of patch-ordering regularization, and it can be solved effectively with the limited-memory BFGS algorithm. The synthetic and field data tests illustrate the improvement of accuracy and lateral continuity of inverted results with our method, compared to conventional model-based inversion results.

Bayesian linearized inversion (BLI) stands out as an exceptional stochastic inversion method in the realms of geophysics and remote sensing. It excels in estimating inversion results and assessing their uncertainty with remarkable efficiency. However, one of the challenges faced by BLI lies in the inversion of its core matrix. To surmount this limitation, an innovative dimension reduction strategy is proposed based on the discrete cosine transform (DCT), thus formulating a rapid BLI approach termed DCT-BLI. Within this method, the DCT-based reduction strategy effectively compresses a large sparse matrix by extracting its essential information, transforming the inversion of this sizable matrix into the inversion of a reduced-size counterpart. A compression factor (CF), defined as the size ratio of matrices after and before reduction, quantifies the extent of matrix reduction. DCT-BLI integrates the strengths of both BLI and the DCT-based reduction strategy. Leveraging this reduction approach, DCT-BLI tackles the challenge of inverting its sizable core matrix. Through the synthetic and field data tests, DCT-BLI exhibits clear superiority over BLI in terms of efficiency, and the DCT-based reduction method achieves a remarkable two-thirds reduction in the core matrix size of BLI without compromising inversion accuracy.

High-resolution prestack inversion combining the well-logging and seismic data is a significant geophysical task, and can be achieved by two kinds of stochastic inversion approaches, the geostatistical inversion (GSI) and Bayesian linearized inversion (BLI). Nevertheless, the existing GSI is restricted by the heavy iteration calculation. Although BLI can avoid this issue, it suffers from the large core matrix inverse. A fast multi-Gaussian inversion (FMG_INV) is proposed herein to achieve the well-log and seismic combined inversion with higher efficiency than GSI and BLI. FMG_INV is derived from prestack BLI, which requires a large core matrix inverse. However, FMG_INV utilizes a simplification strategy and reduces the core matrix dimension of BLI. This improvement is presented under the assumption of statistical independence between well-logging and seismic data, which relieves the issue of large matrix inverse in BLI to a great extent. Moreover, the spatial and statistical correlation between different parameters in prestack stochastic inversion is presented by a multi-Gaussian distribution and may reduce inversion accuracy, and FMG_INV solves this problem by a novel decorrelation strategy. One-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) field tests and a synthetic data test are given herein to verify the effectiveness of FMG_INV. 1D and 2D tests of traditional BLI are also conducted for comparison. The results demonstrate that FMG_INV achieves the same satisfying inversion accuracy and resolution with BLI but much lower time consumption than BLI.

Bayesian inversion is capable of integrating seismic data, well-log data, and geological data to obtain a posterior probability distribution function (PPDF) of elastic parameters. Due to the absorption of strata, amplitude attenuation and phase distortion inevitably occur during the propagation of seismic wave, resulting in low resolution of seismic data. The traditional linear Bayesian inversion method is based on the stationary convolution model, and amplitude compensation and phase correction are needed to be conducted in advance. Uncertainties exist in both compensation and inversion, and the inversion results cannot account for the uncertainties in the directly observed seismic data resulting in accurate inversion results. To estimate uncertainty more accurately and improve inversion accuracy, in this article, we develop a nonstationary prestack linear Bayesian stochastic inversion (NSPLBSI) method. Through the proposed method, prior information from well-log data can be effectively introduced to constrain inversion. Compensation and inversion are integrated into one procedure, which can estimate the posterior uncertainties more accurately directly from seismic data compared with traditional two-step inversion methods, i.e., first compensating attenuation and second performing inversion. Also, more accurate inversion results are obtained. In order to verify the rationality and effectiveness of our proposed method, we conduct inversions using synthetic seismic data on the Marmousi model and a field seismic dataset. Numerical examples show that it can not only compensate amplitude well but also obtain high-precision inversion results with smaller prediction interval.