Accurate characterization of fracture attributes and in-situ stress fields is critical for optimizing horizontal well placement and hydraulic fracturing strategies in fractured shale gas reservoirs. This study introduces a novel model-constrained damped least-squares amplitude variation with angle of incidence and azimuth (AVAZ) inversion method to predict pore pressure and horizontal stresses. By integrating generalized Hooke’s law with Schoenberg’s linear-slip model, horizontal stress equations are derived for horizontally transversely isotropic (HTI) media. Pore pressure estimation is established through a vertical stress sensitivity parameter linked to porosity via a critical porosity model. A saturated stiffness matrix incorporating this parameter and fracture weakness parameters is developed. The P-wave reflection coefficient is formulated using a coupled scattering function and perturbed stiffness matrix, integrating five key parameters: fluid bulk modulus, porosity-dependent vertical stress sensitivity, rock P-wave modulus, fluid modulus-density product, and fracture density. A multi-parameter inversion algorithm is proposed to simultaneously estimate pore pressure, maximum, and minimum horizontal stresses. Validation with field data demonstrates that this method provides reliable estimates of pore pressure and horizontal stresses.

For magnetic inversion, recovering the location and boundaries of causative bodies is challenging. In this study, we propose an improved magnetic inversion method based on the L1 norm of the model and its gradients total variation (TV1). Four weights for the L1 norm and TV1 penalties are introduced in the L1-TV1 inversion, and their effects are discussed comprehensively. These weights are crucial for the inversion, controlling the shape, boundaries, and resolution of the resultant model. Based on extensive synthetic model tests, appropriate parameters are given to achieve good inversion performance. Numerical experiments demonstrate that the proposed approach can reproduce a consistent model with the real solution. Finally, we apply this method to the inversion of the actual data in the Yeshan region, east Jiangsu Province, China, and successfully image the underground magnetic structure.

Salt domes are favorable geological structures associated with hydrocarbon reservoirs and critical mineral resources. Currently, imaging salt diapir subsurface structures has received widespread attention. The gravity method has been widely used to interpret salt structures due to the significant density contrast between salts and surrounding sediments. However, complex mass sources at different depths challenge the interpretation of the gravity data over salt domes. In this study, we put forward the mixed L1 and L2 norm regularized inversion of the gravity data observed on the surface to image the 3-D subsurface structure of salt domes. The synthetic tests demonstrate that the mixed norm regularization inversion of gravity data can effectively recover subsurface complex density anomalies similar to salt dome structures. The practical application in the Vinton Salt Dome reveals a shallow high-density caprock and a deep low-density salt core beneath Vinton Dome, greatly enriching the underground structure information of the study area. It demonstrates that the mixed norm regularized inversion is a valuable interpretation technique for detecting and delineating salt structures.

Fracture weaknesses are two important parameters to describe the characteristics of reservoir fracture-induced anisotropy. Accurate estimation for fracture weaknesses is of great significance for seismic exploration and characterization of naturally fractured reservoir, especially for gas-bearing reservoir. Linear seismic inversion based on Bayesian theory can fuse prior information. And the inverse problem is solved in the form of the posterior probability density function (PDF) to obtain the maximum posterior solution. Based on the PP-wave reflection coefficient in a transversely isotropic medium with a horizontal symmetry axis (HTI), we first construct forward models in different domains by using the convolution model. Then, we select a relatively good initial model to realize the seismic inversion in time domain, frequency domain, and joint time-frequency domain, respectively. Next, a relatively poor initial model is selected to estimate the low-frequency components in Laplace-Fourier domain, and the final estimation is compared with the traditional approach. Finally, both synthetic and real data are used to verify the feasibility of inversion approaches in different domains. The anti-noise ability of estimated fracture weaknesses in time domain is stronger than those of frequency-domain inversion. The joint time-frequency inversion inherits the advantages of strong anti-noise ability of time-domain inversion and retains the excellent characteristics of high resolution of frequency-domain inversion, it balances between improving the resolution of seismic inversion and suppressing random noise. The estimation of low-frequency components for fracture weaknesses in Laplace-Fourier domain can reduce the dependence of seismic inversion on the initial model and improve the estimated accuracy.

Gravity gradient data are sensitive to local density anomalies in regional geological structures. Compared with the inversion of one component of the gravity field, joint inversion of the gravity gradient tensor data can provide more constraint information, reduce the non-uniqueness, and improve the reliability of inversions. This study developed a joint inversion of gravity gradient tensor data based on the coordinate descent algorithm. A model function based on mixed L1 and L2 norms is used to constrain the joint inversion. The synthetic model tests show that the proposed method can effectively image the location of density anomalies with proper amplitude. Finally, this joint inversion method is applied to the gravity gradient tensor data observed over the Vinton Dome in Louisiana, USA. The results reveal a high-density caprock consistent with the geological information, proving the ability of this method to process the actual data.

Fracture weakness is one of the most important anisotropic parameters used to characterize the fractures and identify the fluids. The model of horizontal transversely isotropic (HTI) medium is usually utilized in seismic azimuthal inversion for the fracture weaknesses. Low-frequency component of fracture weaknesses plays a significant role in seismic fracture characterization and fluid identification due to the deficiency of low-frequency component in acquired seismic azimuthal data. The commonly used approaches to estimate low-frequency component include the smoothing model constraints and the damped wave field in complex-frequency domain. Following the Bayesian framework, we propose a novel approach used for compensating the low-frequency component of fracture weaknesses in Laplace-Fourier domain. Firstly, we reconstruct the seismic forward solver in Laplace-Fourier domain to obtain the low-frequency component of fracture weaknesses. Then, we propose a method of seismic azimuth-difference inversion for fracture weaknesses in Laplace-Fourier domain in a Bayesian framework. Finally, both synthetic and field data examples are used to demonstrate the superiority and stability of the proposed inversion approach. Compared with the conventional inversion approach, the proposed approach can reduce the dependence on the initial model of model parameters and weaken the effect of missing low-frequency components of fracture weaknesses in azimuthal seismic data, and it may help to improve the inversion accuracy of fracture weaknesses and reduce the uncertainty of inversion results.