Overset grids approach for topography modeling in elastic-wave modeling using the grid-characteristic method

Abstract

While modeling seismic wave propagation, it is important to take into account nontrivial topography, as this topography causes multiple complex phenomena, such as diffraction at rough surfaces, complex propagation of Rayleigh waves, and side effects caused by wave interference. The primary goal of this research is to construct a method that implements the free surface on topography, utilizing an overset curved grid for characterization, while keeping the main grid structured rectangular. For a combination of the regular and curve-linear grid, the workability of the grid characteristics method using overset grids (also known as the Chimera grid approach) is analyzed. One of the benefits of this approach is computational complexity reduction, caused by the fact that simulation in a regular, homogeneous physical area using a sparse regular rectangle grid is simpler. The simplification of the mesh building mechanism (one grid is regular, and the other can be automatically built using surface data) is a side effect. Despite its simplicity, the method we propose allows us to increase the digitalization of fractured regions and minimize the Courant number. This paper contains various comparisons of modeling results produced by the proposed method-based solver, and results produced by the well-known solver specfem2d, as well as previous modeling results for the same problems. The drawback of the method is that an interpolation error can worsen an overall model accuracy and reduce the computational schema order. Some countermeasures against it are described. For this paper, only two-dimensional models are analyzed. However, the method we propose can be applied to the three-dimensional problems with minimal adaptation required.

Application of a Modification of the Grid-Characteristic Method using Overset Grids for Explicit Interface Description to Modelling the Relief of the Ocean Shelf

“…The choice of this method is due to its good accuracy and low resource consumption. Earlier in [6] it was shown how this method can be used to describe a free surface of a complex shape, and in this paper it is used to describe the interface of media.…”

“…For each of the overset grids, several nodes closest to the boundary of the layers along all axes are called ghost nodes (phantom nodes). The values in these nodes are not used to calculate new values in the nodes of the main grid, but on the contrary, the values in them are overwritten by the values from the main grid [6]. The number of phantom node layers used is determined based on the difference scheme used, in our case it is equal to two, since a five-point difference scheme is used.…”

Direct seismic modeling: day surface topography and shallow subsurface anisotropy

“…Для расчета волновых полей в упругих средах с резким изменением упругих параметров может быть использован сеточно-характеристический метод [7,8]. С ним был объединен метод наложенных сеток, позволяющий корректно описывать криволинейные границы [9]. В настоящем исследовании используется другой подход.…”