Joint estimation of elastic and petrophysical properties from seismic data and quantification of their uncertainties are critical aspects of reservoir characterization studies. The ensemble smoother with multiple data assimilation (ES-MDA) is proving to be a valuable tool for generating a reliable set of reservoir properties by matching simulated seismic responses with available observations. However, in standard implementations of ES-MDA, when the ensemble size is small, spurious correlations can arise in the cross covariances of model parameters and seismic data, leading to erroneous parameter updates in inappropriate regions. To mitigate this problem, this article introduces ES-MDA in conjunction with covariance localization (CL), termed ES-MDA_CL, which aims to reduce the impact of spurious covariance resulting from small ensembles and provide inversion results with robust error estimation. In the ES-MDA_CL framework, the model parameters are initially generated perturbatively by geostatistical simulations and subsequently updated while constrained by seismic data. The introduction of CL reduces the size of the initial ensembles, thereby increasing the computational efficiency of the entire inversion process. Through synthetic and field data tests, ES-MDA_CL demonstrates satisfactory inversion results with more reasonable computational times compared to ES-MDA. The proposed methodology enables the generation of inversion results with robust uncertainty estimation and holds promise for application to a wide range of geophysical challenges.

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.

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. The 1-D, 2-D, and 3-D field tests and a synthetic data test are given herein to verify the effectiveness of FMG_INV. The 1-D and 2-D 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.

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 (CNN), which integrates an attention mechanism and residual learning. This network establishes an inherent link between attenuated seismic data and their nonattenuated counterparts, effectively accomplishing data-driven compensation for seismic data attenuation. The more advanced acoustic (nonattenuated) full-waveform inversion (FWI) 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 such as 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.

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.