MATLAB Code Implementation for Seismic Modeling Forward Simulation

Seismic forward modeling is a crucial technique in geophysical exploration that predicts seismic wave propagation through subsurface media using numerical simulation methods. For geophysics students, mastering this technique enables deeper understanding of seismic wave propagation principles and inversion theory. In MATLAB, seismic forward modeling is typically implemented through numerical solutions of wave equations. Common forward modeling methods include Finite Difference Method (FDM) and Finite Element Method (FEM), with FDM being widely adopted due to its computational efficiency and straightforward implementation. The key implementation steps are: Medium Model Construction First, define subsurface velocity models which can represent homogeneous media, layered media, or complex structural models. By setting different velocity and density parameters, realistic geological conditions can be simulated using MATLAB matrix operations and mesh generation functions. Wave Equation Discretization Employ second-order or higher-order finite difference schemes to discretize the wave equation. Explicit difference schemes are commonly used for time discretization, while spatial discretization employs different difference operators based on accuracy requirements. The core implementation involves creating difference coefficient matrices and implementing time-stepping loops. Boundary Condition Handling To avoid boundary reflections interfering with simulation results, absorbing boundary conditions (such as Perfectly Matched Layer - PML) must be implemented to ensure gradual attenuation of seismic waves at boundaries. This requires adding damping terms to the boundary regions in the code. Source and Receiver Configuration Define source functions (e.g., Ricker wavelet) and receiver positions to simulate seismic excitation and signal acquisition processes. Wavefield propagation is computed through time iteration, with vibration data recorded at receiver points using array storage operations. Visualization and Validation Utilize MATLAB's plotting capabilities to display wavefield snapshots or synthetic seismic records. Compare results with theoretical solutions or commercial software outputs to validate program correctness, employing functions like imagesc, plot, and subplot for effective visualization. The program not only helps students understand wave theory but can also be extended to simulate complex models including anisotropic media and viscoelastic media, laying the foundation for subsequent inversion and interpretation workflows. Key MATLAB functions involved include matrix operations, convolution algorithms, and differential equation solvers.