Numerical simulation of seismic waves in 2D using the finite element method - Troya Yunga, Ariel Santiago (2024)
In Geology, obtaining subsurface models leads to a better understanding of it. Generally, these surveys are carried out through geophysical methods; the most widely used is seismic surveys. One of the techniques to find subsurface velocity models through seismic methods is the Full-Wave Inversion (FWI). To use this method is necessary to solve the elastic wave equation numerically. The most common method used has been finite differences. However, this method leads to errors for long simulation periods in time due to error accumulation. On the other hand, this method does not include the boundary conditions in the elastic equation solution. To avoid these issues, it is proposed to solve numerically the elastic wave equation using the finite element method. To have a better approach, it is solved the case in 1D and implemented it in Python to compare both methods. The 2D case is solved explicitly for the time building the mass and stiffness matrices, and establishing clearly how the method works, which is Finite Elements for the space and Finite Differences for the time. Afterward, it is written a script in Python to build the matrices. It is hoped that this method could be used to improve the simulation of seismic waves as part of a larger research project of FWI.