The propagation of seismic waves in fractured rocks is greatly influenced by the fracture system and fluid content. Seismic anisotropy varies with frequency and fluid saturation. Previous theories on frequency-dependent anisotropy (FDA) are mostly limited to the assumption of single-phase fluid, whereas almost all reservoirs are usually partially or fully saturated with one or more fluids. The inelasticity, heterogeneity, and anisotropy exhibited by real earth media seriously challenge the traditional theory of uniform fully elastic media. Therefore, based on the Chapman elastic theory, we consider the viscoelastic model, the relative mobility of saturated fluids, and the coupled effects of commonly independently considered squirt flow and patch effects on the frequency-dependent anisotropic seismic wave propagation in viscoelastic media. By calculating the frequency-dependent anisotropic elastic coefficients of two-phase immiscible fluid-saturated fractured rocks, a new viscoelastic Chapman extension model for FDA in partially saturated rocks, which includes the unified seismic wave propagation effects of squirt flow and patch effects, is constructed. The effect of relative permeability is significant, and compared to the case of complete saturation, the effective fluid mobility in partially saturated rocks may be lower, which may lead to nonmonotonic changes in elastic modulus and water saturation. Numerical experiments are conducted on our viscoelastic Chapman extension model to discuss the coupling effects of squirt flow and patch effects on the FDA of viscoelastic media in cracked rocks with partially saturated reservoirs, under the conditions of no fractures and the existence of fractures. The simulation results of the P-wave modulus, P-wave velocity, and anisotropy parameters confirm the validity of our method and model. We link the anisotropy of viscoelastic media with fluid flow parameters in fractures, which is conducive to improving the understanding of frequency-dependent seismic anisotropy in partially saturated rocks with fractures and the combination of seismology and reservoir engineering.

For high frequencies, traditional programs based on quasi-static assumptions fail to accurately simulate radio-magnetotelluric (RMT) responses because displacement currents become significant and cannot be disregarded. However, 3D RMT forward modeling that accounts for diffusion and wave phenomena, especially in anisotropic media, remains underexplored. We have developed an open-source 3D anisotropic forward-modeling algorithm for RMT data, em3d-MT, using an edge-based finite-element (FE) method. Unlike existing 3D RMT modeling algorithms, em3d-MT solves full-wave Maxwell’s equations considering conduction and displacement currents. The program considers the effects of arbitrary anisotropy in electrical conductivity and dielectric permittivity, alongside an advanced 3D geologic modeling workflow with unstructured tetrahedral meshes, to accurately simulate RMT responses of complex geologic models. The FE linear system of equations is solved using a direct solver and a double-layer parallel scheme to improve computational efficiency. We validate the accuracy of em3d-MT using layered-earth and 3D benchmark models. We then analyze the RMT responses of a 3D block model with varying dielectric permittivity and anisotropic parameters. Finally, we apply em3d-MT to the modeling of a complex anisotropic coal mine goaf model to demonstrate its effectiveness in real-world scenarios. Numerical results confirm that em3d-MT can accurately simulate the coupled behavior of diffusive and wave fields, revealing the significant influence of dielectric permittivity and its anisotropic effects on RMT data.

Euler deconvolution is a widely used automatic or semi-automatic method for potential field data. However, it yields many spurious solutions that complicate interpretation and must be reduced, eliminated, recognized, or ignored during interpretation. This study proposes a post-processing algorithm that converts Euler solutions produced by tensor Euler deconvolution of gravity data with an unprescribed structural index into probability values (p values) using the B-spline series density estimation (BSS) method. The p values of the Euler solution set form a probability density distribution on the estimation grid. The BSS method relies on the fact that while spurious solutions are sparse and ubiquitous, Euler deconvolution yields many similar or duplicate solutions, which may tightly cluster near real sources. The p values of the Euler solution clusters form multi-layered isosurfaces that can be used to discriminate neighboring target sources because the p values of spurious solutions are vanishingly small, making it simple to remove their interference from the probability density distribution. In all synthetic cases, the geometric outlines of anomaly sources are estimated from probability density isosurfaces approximating synthetic model parameters. The BSS method was then applied to airborne gravity data from Mount Milligan, British Columbia, Canada. Subsequently, results from synthetic models and field data show that the proposed method can successfully localize meaningful geological targets.

The resistivity distribution obtained from traditional inversion methods for magnetotelluric (MT) data often lacks clarity, making it difficult to delineate boundaries between host media and anomalous targets. To address this, we developed a novel three-dimensional (3-D) MT inversion approach based on the multinary transformation of model parameters. This method transforms the model resistivity distribution into a desired step-function-like form, enabling explicit identification of interfaces between geological units. The sharpness of the recovered resistivity model is controlled by the standard deviation of the multinary transformation’s error function, and an adaptive technique is introduced to adjust this parameter during the inversion process to account for deviations between true and discrete values in the multinary space. The inversion problem is solved using a data-space Gauss-Newton approach, which enhances memory efficiency and convergence speed. Additionally, unstructured tetrahedral meshes are utilized to accurately model rugged topography and complex geoelectric structures. Synthetic model studies demonstrate the superiority of the adaptive multinary inversion over conventional maximum smoothness inversion and fixed standard deviation multinary inversion. Finally, the method is applied to image subsurface resistivity in the northwest Geysers geothermal field in California, USA, showcasing its effectiveness.

For three-dimensional (3D) controlled-source electromagnetic (CSEM) inversion, generating accurate predicted data requires forward calculation with a dense mesh near measurement points and in areas of complex topography to ensure reliable electric field calculations. In contrast, inversion typically uses a coarser mesh, given the limited spatial resolution of the parameters and the associated computational cost. To accommodate the different mesh requirements of forward modeling and inversion, we decouple the forward and inversion meshes using a nested mesh scheme. In this scheme, a relatively coarse mesh is used for inversion, while a dense mesh for forward modeling is generated by subdividing the inversion cells. The Gauss–Newton method is employed to solve the inversion problem due to its fast convergence. By transforming the inversion problem from model space to data space, the computational memory requirements are reduced, allowing the model update to be solved using a direct solver. We demonstrate the effectiveness of the developed inversion scheme by several synthetic models.