Abstract

Wave propagation modeling in heterogeneous media requires numerical methods that can simultaneously handle complex geometries, artificial boundary reflections, and spatially varying resolution demands. In this study, we present a Discontinuous Galerkin (DG) forward modeling method for wave propagation with split-field absorbing boundary conditions and gradient-based adaptive meshes. The wave equation is formulated as a first-order hyperbolic system and discretized by the DG method, which preserves local conservation and is well suited for explicit Runge–Kutta time integration on unstructured meshes. To reduce spurious reflections from truncated computational boundaries, a split-field absorbing boundary treatment is introduced in the absorbing layer through directional damping terms, maintaining the first-order structure and local update form of the DG scheme. In addition, a physics-based mesh metric is constructed from the local velocity-gradient length scale, allowing the mesh to be automatically coarsened in smooth regions and refined near strong velocity contrasts, interfaces, and discontinuities. Numerical convergence tests show that the quadratic DG scheme achieves the expected third-order accuracy in the L2 norm. Quantitative PML evaluation gives a reflection coefficient of approximately 1.65 × 10−5, indicating effective suppression of artificial boundary reflections. For the three-dimensional Marmousi model, the proposed adaptive mesh reduces the number of tetrahedral elements from 158,492 to 88,681, decreases the CPU time from 241.4453 s to 139.1328 s, and reduces memory consumption from 3788.67 MB to 2109.55 MB compared with the uniform mesh. These results demonstrate that the proposed method can improve the balance between computational efficiency and solution accuracy while maintaining stable and physically interpretable wavefield modeling in heterogeneous media.

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