Sparse impedance inversion is widely applied for hydrocarbon prediction. Due to the low sparseness of traditional sparse constraints, pseudolayer and low-resolution problems still exist. To overcome this barrier, an impedance inversion method based on the reweighted L1-norm sparse constraint is proposed. Different from the traditional L1-norm constraint, which considers the location information of impedance boundaries, the reweighted L1-norm uses the amplitude information of impedance boundaries. The amplitude information can improve the sparseness, which helps inversion obtain more precise boundaries of impedance and weaken the pseudolayer phenomenon. Both the reweighted L1-norm constraint and initial model constraint are used to construct the objective function. The alternating direction method of multipliers (ADMM) algorithm is utilized to obtain the inversion algorithm. Both synthetic and field data tests prove that the impedance boundary of the proposed method is more accurate, and the pseudolayer phenomenon is weakened.

The inversion of reservoir elastic parameters and fracture parameters is of great significance to oil and gas production. In shale reservoirs with inclined fractures, using the reflection coefficient equation of vertical fractures or horizontal fractures under the vertical transverse isotropy (VTI) background has certain limitations. For this reason, based on the linear-slip model, this article establishes the approximate stiffness matrix of the monoclinic medium with a set of inclined fractures under the background of VTI and combines the Born scattering theory to further derive the PP-wave linear reflection coefficient equation of the monoclinic medium. The equation includes parameters, such as Young’s modulus, Poisson’s ratio, density, fracture weaknesses, and bedding weaknesses. Then, a rock physics model that comprehensively considers horizontal bedding and inclined fractures is established, and the influence of the inclination of the fractures on the reflection coefficient is analyzed. Finally, taking the advantage of Bayesian theory, the fracture weakness inversion method based on the azimuth amplitude difference is established, and the inversion accuracy is improved by adding Cauchy constraints and smoothing model regularization terms. Then, take the fracture weaknesses as inputs to invert the parameters, such as Young’s modulus, Poisson’s ratio, density, and bedding weaknesses. The inversion results of theoretical data show that the method can invert the fracture information well, and it can also be effectively applied to low-to-medium signal-to-noise ratio (SNR) data. The inversion results of theoretical and actual data prove that the inversion equation derived in this article can be used to obtain more accurate elastic and fracture parameters in fractured shale reservoirs.

Most of the current 3D reservoir porosity estimation methods are based on analyzing the elastic parameters inverted from seismic data. It is well-known that elastic parameters vary with the pore structure parameters such as the pore aspect ratio, consolidation coefficient, and critical porosity. Thus, we may obtain inaccurate 3D porosity estimation if the chosen rock-physics model fails to properly address the effects of the pore structure parameters on the elastic parameters. However, most of the current rock-physics models only consider one pore structure parameter such as the pore aspect ratio or the consolidation coefficient. To consider the effect of multiple pore structure parameters on the elastic parameters, we have developed a comprehensive pore structure (CPS) parameter set that is generalized from current popular rock-physics models. The new CPS set is based on the first-order approximation of current rock-physics models that consider the effect of the pore aspect ratio on the elastic parameters. The new CPS set can accurately simulate the behavior of current rock-physics models that consider the effect of pore structure parameters on the elastic parameters. To demonstrate the effectiveness of the proposed parameters in porosity estimation, we use a theoretical model to demonstrate that our CPS parameter set properly addresses the effect of pore aspect ratio on elastic parameters such as velocity and porosity. Then, we obtain a 3D porosity estimation for a tight sand reservoir by applying it seismic data. We also predict the porosity of the tight sand reservoir using a neural network algorithm and a rock-physics model that is commonly used in porosity estimation. The comparison demonstrates that the predicted porosity has a higher correlation with the porosity logs at blind well locations.

Seismic data interpolation and denoising play vital roles in obtaining complete and clean data in seismic data processing. Seismic data usually miss along various spatial axes and always mix with random noise. To obtain complete and clean seismic data, reconstruction technology can interpolate missing data and attenuate random noise. A nonsubsampled contourlet transform (NSCT) is an effective transform to obtain multiscale and multidirection sparse domain data for compression sensing interpolation and denoising. However, conventional iterative shrinkage/thresholding (IT) cannot handle ill-posed and ill-conditioned equations for solving linear inverse problem. We present a two-step iterative log thresholding (TwILT) method to overcome ill-posed and ill-conditioned problems and improve the convergence rate and solution accuracy, which can interpolate and denoise seismic data simultaneously in the NSCT framework. First, we use the NSCT to convert the seismic missing data with random noise to sparse domain. Then, we apply the TwILT algorithm to interpolate and denoise data in sparse domain. The result of each iteration is based on the results of the previous two iterations, which can accelerate convergence rate. In addition, log thresholding can further improve convergence rate and solution accuracy. Finally, we use inverse NSCT to obtain the interpolated and denoised seismic data. The new method can reconstruct the irregularly missing data and attenuate random noise to obtain complete and clean seismic data with high accuracy, which is crucial for seismic imaging and inversion. We demonstrate the applicability and effectiveness of this simultaneous interpolation and denoising technique with successful applications to both synthetic and field data examples.

The brittleness index (BI) is an essential parameter for evaluating rock brittleness, which can effectively guide artificial hydraulic fracturing for shale gas exploitation. However, some conventional brittleness indexes often fall short when applied to shale reservoirs with low permeability, low porosity, and high total organic carbon (TOC) content, we proposed a novel brittleness index more sensitive to brittle rock fractions, porosity, and organic matter content, which was corroborated via the constructed petrophysical modeling method for shale reservoirs. Considering the disadvantage of accumulating error in the indirect calculation of elasticity parameters, we further derived a new PP-wave reflection coefficient approximation equation incorporating the novel BI, Young’s modulus, and density, named the BYD reflection coefficient approximation equation. Rigorous validation against the exact Zoeppritz equation by four classes of amplitude versus offset (AVO) seismic response models underlines its accuracy and reliability. Furthermore, we enhanced the seismic inversion algorithm using the reweighted L _P (RL _P ) quasinorm, surpassing the sparsity of the L _P quasinorm. The nonlinear optimization problem was solved by the alternating direction method of multipliers (ADMM) and the L _P quasinorm iterative shrinkage thresholding algorithm (ISTA). Three sets of model tests with different noises have demonstrated the rationality and robustness of the inversion method. Finally, the 3D seismic inversion of the novel BI parameter applied to a gas-bearing shale reservoir in Sichuan Basin, China, confirmed its effectiveness in characterizing brittleness distribution, facilitating optimal shale gas exploitation.

To completely use large incident angle seismic data and improve the accuracy of amplitude-variation-with-offset inversion, especially for density information, we have derived second-order approximate expressions of the P- and SV-wave reflection coefficients at the solid/solid media interface. Vectors and Hessian matrices are used to describe the first- and second-order terms of the approximate expressions. The second-order approximations are then rewritten in a simple form. Furthermore, different pseudosecond-order approximations with different power series of the ray parameter p are derived based on the Taylor expansion of the second-order approximation of the P-wave reflection coefficient for the incident P wave (PP-wave reflection coefficient) according to the ray parameter p. By establishing four different single-phase medium models, we have verified that the accuracies of the second-order approximate expressions were remarkably higher than those of the first-order approximations. Furthermore, the pseudo p2 second-order approximation of the PP-wave reflection coefficient is highly consistent with the exact analytical expression.