Seismic Wavefield Forward Modeling in Dual-Phase Media Using High-Order Finite Difference Algorithms

Seismic wavefield forward modeling in dual-phase media is a critical component in seismic exploration and geological modeling, enabling researchers to understand wave propagation characteristics in complex subsurface structures. High-order finite difference algorithms have become widely adopted for this simulation due to their high computational accuracy and excellent stability.

### Core Methodology

Dual-Phase Media Modeling Dual-phase media consist of solid skeletal frames and pore fluids, requiring simultaneous consideration of solid-fluid coupling interactions during wave propagation. The Biot theory is typically employed to describe the dynamic behavior, involving multiple variables including solid-phase displacements and fluid pressures. In code implementation, this requires defining separate material property matrices for solid and fluid components, with coupling terms handled through cross-variable dependencies.

High-Order Finite Difference Discretization Spatial derivatives in the wave equation are approximated using high-order difference schemes (such as 8th or 10th order) to minimize numerical dispersion and enhance simulation accuracy. Temporal discretization employs second or fourth-order staggered-grid difference schemes to ensure numerical stability during time iteration. Code implementation typically involves creating difference coefficient arrays and applying them through convolution operations across spatial grids.

Boundary Condition Handling To suppress artificial boundary reflections, Perfectly Matched Layer (PML) absorbing boundary conditions are implemented by gradually attenuating wavefield energy at domain boundaries. Internal interfaces (such as lithological boundaries) require explicit treatment through parameter smoothing or interface condition enforcement. Programming implementation involves creating damping profiles for PML regions and developing interface detection algorithms for material transitions.

Parallel Optimization and Implementation In MATLAB environments, computational efficiency can be enhanced through vectorized matrix operations, though large-scale models necessitate parallel computing approaches (using parfor loops or GPU acceleration). Memory management becomes crucial, particularly for 3D simulations where grid storage demands significant resources. Code optimization strategies include memory pre-allocation, data chunking for large domains, and efficient sparse matrix storage for material property matrices.

### Extended Considerations

Multi-physics Coupling: Additional coupling with thermal or chemical fields can be incorporated to simulate more complex geological processes through extended governing equations. Data-Driven Optimization: Integration with machine learning methods enables training surrogate models using simulation data to accelerate inversion processes, potentially implemented through neural network interfaces with the finite difference core.

This methodology provides high-fidelity forward modeling data for subsequent inversion and interpretation workflows, making it suitable for applications in petroleum exploration, groundwater resource assessment, and other subsurface characterization scenarios.