A Hybrid Subdomain Chebyshev Spectral Method and Finite Difference Method for Viscoelastic Wave Modeling With Free Surface Using Improved Generalized Stiffness Reduction Method

Accurate numerical simulation of the viscoelastic wave equation is essential for studying anelastic seismic wave propagation and underpins both migration and full-waveform inversion techniques. Free surfaces introduce complex wave phenomena that must be properly represented in seismic modeling. We propose a hybrid scheme that combines a subdomain Chebyshev spectral method with finite-difference discretization in a curvilinear coordinate system. Local Chebyshev transforms and global spline interpolations enable the grid conforms exactly to the free surface and subsurface interfaces. Spatial derivatives are evaluated using Chebyshev points in the horizontal direction and finite-difference stencils in the vertical direction. The viscoelastic effect introduced by Generalized Maxwell Body can be calculated by recursive convolution method and the free surface boundary condition is realized by non-central finite difference scheme in the framework of the hybrid numerical method. For absorbing boundary, a Q-factor reduction scheme is improved to complement generalized stiffness reduction method of the viscoelastic media in the time domain. The proposed approach retains the high accuracy of spectral methods while permitting straightforward finite-difference treatment of the free-surface boundary condition. Numerical experiments on both homogeneous and heterogeneous models confirm the correctness and robustness of the proposed method.