2D Seismic Finite Difference Numerical Simulation

To accurately model and study wave equations, numerical simulations are employed by discretizing the equations through finite difference methods. This approach involves implementing a computational grid where partial derivatives in the wave equation are approximated using finite difference schemes, such as central difference or staggered grid methods. The simulation typically utilizes explicit time-stepping algorithms like the leapfrog method to propagate wavefields through 2D media. Key implementation aspects include boundary condition handling (e.g., absorbing boundaries using PML) and stability criteria management through appropriate grid spacing and time steps. These simulations enable exploration of wave behavior in various scenarios, including propagation through heterogeneous media and interactions with geological structures. By analyzing simulation results through seismic snapshots and wavefield animations, researchers gain insights into complex wave phenomena, with applications spanning geophysics, civil engineering, and seismic hazard assessment. The core algorithm can be implemented using matrix operations and convolution techniques in programming languages like Python or MATLAB, with performance optimization through parallel computing approaches.