Caiwang Shi

and 3 more

A semi-analytical spectral element method (SASEM) is proposed to solve for the normal and leaky modes of elastic waves propagating in a planar waveguide with a half-space substrate. For the SH-wave modes, the transparent boundary condition is used to model the SH wavefields in the half-space substrate. To solve for the PSV-wave normal modes on the (+, +) Riemann sheet and leaky modes on the (+, −) Riemann sheet, the elastic wavefields in the finite-thickness layers are modeled using the displacements, whereas the wavefields in the half-space are modeled using the P- and S-wave potentials. In the substrate, the transparent boundary condition is used for the shear wavefields, whereas semi-infinite elements are introduced to treat the radiative boundary condition of the P wavefields. Then, a polynomial eigenvalue problem is derived, which can be transformed into a standard linear eigenvalue problem. Solving the eigenvalue problem, we can obtain the solutions of the normal and leaky modes. Several numerical tests were performed to verify the effectiveness of SASEM, as well as to demonstrate its high accuracy. Modal analyses of the oscillations of the solved modes demonstrate that the leaky modes differ from the normal modes because of the increasing wavefields in the half-space. Moreover, the guided-P modes are confirmed to be more dependent on the P-waves, whereas the normal and organ-pipe modes are primarily determined by the S-waves. Besides the crustal model composed of several homogeneous layers, SASEM is applied to a vertically inhomogeneous offshore model to demonstrate its applicability. The good agreement between the theoretical guided-P modes and the dispersion spectra not only shows the correctness of SASEM when analyzing waveguides composed of gradient layers but also indicates the potential for constraining the P-wave velocity using the guided-P modes.

Heng Zhang

and 4 more

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.

Zhengbo Li

and 11 more

Wenqiang Zhang

and 2 more