Применение криволинейных сеток для моделирования 2D волновых полей в неоднородных областях со сложной топографией

Abstract

The main practical interest of geophysics is the restoration of the structure of the medium. So one can understand whether there are hydrocarbon reservoirs at depth. Studying the structure of the medium by taking numerous samples and drilling wells is a very financially and time-consuming task. Therefore, the use of mathematical modeling seems to be a good alternative. If the calculations show a result similar to the initial data of the medium, then such algorithm for restoring the medium can be applied new regions. Verification of the algorithm should be carried out on real structures of the media, but real wave field data are not provided, since they are often the subject of trade secrets. In this case, the result of this work comes to the rescue. Numerical simulation is widely used in studying the processes of wave field propagation in various complex media. One way is to discrete the domain for which the simulation is being performed, and to construct a difference scheme for further numerical implementation. This work involves the construction of a mesh with curved quadrangles, which allows good agreement with the topography of the surface. A parallel algorithm of numerical modeling based on the numerical solution of a linear 2D system of elasticity theory written in displacements using a curvilinear mesh and an explicit difference scheme is proposed. The simulation results are presented. The calculations were carried out using the resources of the SSCC SB RAS.