The discontinuous-grid method can greatly reduce the storage requirement and computational cost in finite-difference modeling, especially for models with large velocity contrasts. However, this technique is mostly applied to time-domain methods. We have developed a discontinuous-grid finite-difference scheme for frequency-domain 2D scalar wave modeling. Special frequency-domain finite-difference stencils are designed in the fine-coarse grid transition zone. The coarse-to-fine-grid spacing ratio is restricted to [Formula: see text], where [Formula: see text] is a positive integer. Optimization equations are formulated to obtain expansion coefficients for irregular stencils in the transition zone. The proposed method works well when teamed with commonly used 9- and 25-point schemes. Compared with the conventional frequency-domain finite-difference method, the proposed discontinuous-grid method can largely reduce the size of the impedance matrix and number of nonzero elements. Numerical experiments demonstrated that the proposed discontinuous-grid scheme can significantly reduce memory and computational costs, while still yielding almost identical results compared with those from conventional uniform-grid simulations. When tested for a very long elapsed time, the frequency-domain discontinuous-grid method does not show instability problems as its time-domain counterpart usually does.
Optimally accurate second-order time-domain finite difference scheme for the elastic equation of motion: one-dimensional case