Efficient and accurate traveltime calculations of seismic waves have important applications in tomography, prestack migration, earthquake location, etc. Anisotropy significantly affects the traveltimes of seismic wave. For high-resolution imaging and inversion, it is necessary to consider anisotropy in the traveltime calculations. The fast sweeping method (FSM) does not need to track and store the minimum traveltime point of wavefront, which has important applications in computing the anisotropic first-arrival traveltime. The conventional method that solves a transformed traveltime quartic equation combined with FSM is suitable for general anisotropic media. However, this method involves finding the intervals of roots and solving the quartic equations using bisection algorithm at each iteration, leading to high computational cost and instability for the 3D problems. In our previous work, for the vertical transversely isotropic (VTI) case, we developed an FSM to compute the qP-wave first-arrival traveltimes by analytically solving the simplified quadratic slowness equation in a specific triangular-pyramid stencil. This method greatly improves the computational efficiency. However, for the qP and qSV waves, analytically solving the slowness equation cannot be extended to tilted transversely isotropic (TTI) media. To address this problem, we introduced the Newton method in the triangular-pyramid local solver to quickly solve the TTI slowness equation. For the qSH wave, its slowness equation is quadratic and simple to solve. The proposed method provides an efficient procedure for the traveltime calculations of qP, qSV, and qSH waves in 3D general TTI media. Numerical examples have verified the efficiency and accuracy of the proposed method.

Recently, many studies have demonstrated the use of teleseismic P wave coda autocorrelation for imaging lithosphere structures. However, the reliability of the extracted reflections remains uncertain and a means of evaluation is lacking. In this paper, we propose a velocity analysis method that conveniently solves this problem in place of a synthetic experiment. This method considers the average velocity used for the horizontal slowness correction as an unknown quantity, and then uses the continuously varying average velocity for the horizontal slowness correction. Finally, this method obtains a stacked result that varies with the average velocity and the vertical two-way travel time to produce a va−t0 diagram. This method is similar to the velocity analysis method used in exploration geophysics. In this diagram, reliable reflections correspond to focused energy clusters, while noise lacks this feature. Therefore, this method helps determine which reflections are reliable, while also finding the appropriate parameters for data processing. Synthetic data tests were performed to demonstrate the validity of this method, as well as a test of field data for station BOSA, which illustrates the successful application of the method in the case of a sharp and flat Moho discontinuity. Finally, we applied the method to the NCISP-6 dense array, and observed obvious energy clusters representing reflections from the Moho discontinuity in the results of most stations. The depth and shape of the Moho discontinuity determined by this test is consistent with receiver function results, which verifies the robustness of this method in relatively complex applications.

Traditional finite difference method for electromagnetic simulation is based on staggered grid, whilst researches on collocated grid are few. We present a high-order collocated-grid finite-difference method for modelling electromagnetic waves with a topographic ground surface by solving 2D time-domain Maxwell equations in curvilinear coordinates. The proposed method, incorporating curvilinear coordinates, collocated grids and MacCormack finite-difference scheme techniques, can describe the geometry of the irregular interface better and avoid the numerical scattering caused by the staircase approximation in the conventional finite-difference method for electromagnetic wavefield modelling. The first-order 2D Maxwell equations on curvilinear grids are solved by an optimized MacCormack finite-difference scheme, first presented by Hixon (1997). As the collocated grids are implemented, in which the electric and magnetic fields are discretized at the same grids, the interfacial boundary conditions need to be considered. Therefore, a novel effective interface method is presented to handle the conditions. The proposed method is verified by a series of ground penetrating radar application models, such as homogeneous space, multilayered media and buried cavity models, by comparing synthetic waveforms with independent reference solutions, such as the analytical solution, the generalized reflection/transmission method and an open-source program gprMax. Comparisons show that the proposed method does well in handling multiple reflections and curved interfaces.