An Explicit Finite Difference Method Based on the Mixed Domain Function Approximation and Adaptive Spatial Operator Length Scheme

In this abstract, we propose a new explicit finite difference method with high accuracy and efficiency. Starting from acoustic wave equation with constant velocity and density, we derive the new FD method with spatial arbitrary even-order accuracy based on the mixed wavenumber-space (k-space) domain function approximation, and derive the FD coefficients by minimizing the approximation error in a least-square (LS) sense. The new method has an exact temporal derivatives discretization in homogeneous media and also owns a higher temporal accuracy in the heterogeneous media by compensating the temporal dispersion with a second order k-space operator. Meanwhile, a new variable spatial operator length scheme is proposed and adopted to further reduce the computational cost of the FD coefficients calculation and the time marching wavefield extrapolation. We test the new proposed FD method with variable spatial operator length scheme in the 2D homogeneous model and the modified Sigsbee2 model. The numerical results demonstrate the efficiency and flexibility of the new method with variable-length spatial operators.