Acoustic Wave Equation Wavefield Simulation

Acoustic wave equation wavefield simulation serves as a crucial tool for studying wave propagation characteristics, widely applied in fields such as seismic exploration and acoustic imaging. MATLAB-based simulation programs solve the acoustic wave equation using numerical methods to visually demonstrate the dynamic evolution of wavefields.

The core implementation typically involves the following components:

Mathematical Model Construction The second-order acoustic wave equation is employed as the governing equation, describing the evolution of pressure fields across space and time. The velocity term in the equation reflects variations in medium properties, serving as a key parameter for simulating complex geological structures. In code implementation, this involves defining velocity models through matrix operations and handling spatial derivatives using differential operators.

Numerical Discretization Methods Finite difference method is used for spatiotemporal discretization: Spatial derivatives are approximated using central difference schemes, with second-order or higher-order formats balancing accuracy and computational cost Time advancement typically employs explicit difference schemes (such as leapfrog method), requiring compliance with CFL stability conditions. Code implementation involves creating difference coefficient matrices and implementing time-stepping loops with stability checks.

Boundary Treatment Techniques To eliminate artificial boundary reflections, absorbing boundary conditions (like PML) or special difference schemes are introduced, causing wavefields to gradually attenuate in boundary regions. Implementation requires adding damping layers and modifying difference schemes near boundaries through conditional statements.

Visualization Presentation Achieved through MATLAB's graphical capabilities: Time slice displays show wavefront propagation processes Color mapping represents wavefield intensity distribution Dynamic video generation captures complete wavefield evolution records. Key functions include pcolor for 2D visualization, quiver for vector fields, and videoWriter for animation creation.

Special attention must be paid to numerical dispersion control and computational efficiency optimization in program development. For large-scale simulations, parallel computing or GPU acceleration techniques can be employed. This simulation approach provides low-cost research means for theoretical verification and practical applications (such as acoustic device design and subsurface structure inversion).