An optimized time-space-domain finite difference method with piecewise constant interpolation coefficients for scalar wave propagation

In this paper, we construct an optimized time-space-domain finite difference scheme with piecewise constant interpolation coefficients for a three-dimensional scalar wave equation to further accelerate the time-space-domain method. The scheme adopts piecewise constant interpolation coefficients by approximating the wave equation for several consecutive velocity intervals, and switches between the groups of coefficients by conditional branching when programming. In this way, it avoids the time consumption caused by loading the optimal coefficients consecutively in accordance with different wave velocities in heterogeneous media. To obtain effective coefficients, we minimize the high order norm of time-space-domain misfit to approach the constraint effect of the maximum norm. The Newton algorithm is applied to keep the optimizing problem solvable and avoid the slow convergence of evolutionary methods. We explore the stability criterion, numerical dispersion of this scheme and apply it to homogeneous, multilayer and complex models. Theoretical analyses and numerical experiments demonstrate that this scheme achieves almost the same ability to suppress the numerical dispersion as the former time-space-domain method and reduces the computational time cost significantly, providing a powerful tool for seismic modelling and high-resolution imaging.