Full-waveform inversion (FWI) is a powerful tool to reconstruct subsurface geophysical parameters with high resolution. As 3D surveys become widely implemented, corresponding 3D processing techniques are required to solve complex geological cases, while a large amount of computation is the most challenging problem. We propose an adaptive variable-grid 3D FWI on graphics processing unit devices to improve computational efficiency without losing accuracy. The irregular-grid discretization strategy is based on a dispersion relation, and the grid size adapts to depth, velocity, and frequency automatically. According to the transformed grid coordinates, we derive a modified acoustic wave equation and apply it to full wavefield simulation. The 3D variable-grid modeling is conducted on several 3D models to validate its feasibility, accuracy and efficiency. Then we apply the proposed modeling method to full-waveform inversion for source and residual wavefield propagation. It is demonstrated that the adaptive variable-grid FWI is capable of decreasing computing time and memory requirements. From the inversion results of the 3D SEG/EAGE overthrust model, our method retains inversion accuracy when recovering both thrust and channels.

Anisotropy is a common phenomenon in subsurface strata and should be considered in seismic imaging and inversion. Seismic imaging in a vertical transversely isotropic (VTI) medium does not take into account the effects of the tilt angles, which can lead to degraded migrated images in areas with strong anisotropy. To correct such waveform distortion, reduce related image artifacts, and improve migration resolution, a tilted transversely isotropic (TTI) least-squares reverse time migration (LSRTM) method is presented. In the LSRTM, a pure qP-wave equation is used and solved with the finite-difference method. We have analyzed the stability condition for the pure qP-wave equation using the matrix method, which is used to ensure the stability of wave propagation in the TTI medium. Based on this wave equation, we derive a corresponding demigration (Born modeling) and adjoint migration operators to implement TTI LSRTM. Numerical tests on the synthetic data show the advantages of TTI LSRTM over VTI RTM and VTI LSRTM when the recorded data contain strong effects caused by large tilt angles. Our numerical experiments illustrate that the sensitivity of the adopted TTI LSRTM to the migration velocity errors is much higher than that to the anisotropic parameters (including epsilon, delta, and tilted angle parameters), and its sensitivity to the epsilon model and tilt angle is higher than that to the delta model.

This study derives a preconditioned stochastic conjugate gradient (CG) method that combines stochastic optimization with singular spectrum analysis (SSA) denoising to improve the efficiency and image quality of plane-wave least-squares reverse time migration (PLSRTM). This method reduces the computational costs of PLSRTM by applying a controlled group-sampling method to a sufficiently large number of plane-wave sections and accelerates the convergence using a hybrid of stochastic descent (SD) iteration and CG iteration. However, the group sampling also produces aliasing artifacts in the migration results. We use SSA denoising as a preconditioner to remove the artifacts. Moreover, we implement the preconditioning on the take-off angle-domain common-image gathers (CIGs) for better results. We conduct numerical tests using the Marmousi model and Sigsbee2A salt model and compare the results of this method with those of the SD method and the CG method. The results demonstrate that our method efficiently eliminates the artifacts and produces high-quality images and CIGs.

Seismic forward modeling in tilted transverse isotropic (TTI) media is crucial for the application of reverse time migration and full-waveform inversion. Modeling based on conventional coupled pseudoacoustic wave equations not only generates SV-wave artifacts, but it also suffers from instabilities in which the anisotropy parameter ε<δ. To address these issues, we have started with the exact vertical transversely isotropic phase velocity formula and developed novel pure qP- and qSV-wave governing equations in TTI media by using the optimal quadratic approximation. For the convenience of using finite-difference (FD) method to solve the new pure qP- and qSV-wave wave equations, we decompose the equations into a combination of a time-space-domain wave equation that can be solved by the FD method and a Poisson equation that can be solved by the pseudospectral method. We find that the high-frequency errors caused by the pseudospectral method and the usual truncation errors in FD schemes may be responsible for the instability of the numerical simulations. To stabilize the computation, we design a 2D low-pass filtering operator to eliminate severe high-frequency numerical noise. Several numerical examples demonstrate that modeling using the new pure qP-wave equations does not have qSV-wave artifacts interference and is stable for ε<δ. Our results indicate that our method can achieve highly accurate and stable modeling results even in extremely complex TTI media.

Gaussian-beam migration (GBM) is flexible and adaptable for imaging geologically complicated areas. It avoids some limitations, such as amplitude singularity in caustic zones and an inability to image multiple arrivals, of traditional ray-based migration approaches. Previous studies on GBM mainly focused on acoustic media. We have developed a 2D isotropic elastic GBM scheme for common-shot multicomponent records. Our method extrapolates P- and S-mode wavefields simultaneously using the Kirchhoff-Helmholtz integral solution of the isotropic elastodynamic equation. We separate the extrapolated wavefields into compressional and shear modes using the Helmholtz decomposition, and we then implement a modified dot-product imaging condition. This approach enables us to produce clear PP-images and avoid polarity reversal issues for PS-images. In addition, based on the theory of wavefield approximation in the effective vicinity of central rays, we derive a formula to compute the propagation angles of paraxial rays, which can be used to extract angle-domain common-image gathers.