We have developed a general method to obtain the equiripple and the least-squares finite-difference (FD) operator weights to compute arbitrary-order derivatives from arbitrary sample locations. The method is based on the complex-valued Remez exchange algorithm applied to three cost functions: the total error, the relative error, and the group-velocity error. We evaluate the method on three acoustic FD modeling examples. In the first example, we assess the accuracy obtained with the optimal coefficients when propagating acoustic waves through a medium. In the second example, we propagate a wave through an irregular grid. In the final example, we position a source and receiver at arbitrary locations in-between the modeling grid points. In the examples using regular grids, the equiripple solution to the relative cost function performs best. It obtains marginally (4%–10%) better results compared to the second-best option, the least-squares solution for the relative cost function. The least-squares solution for the relative error produced the only stable and accurate results also in the example of modeling on an irregular grid.
Finite difference operators from moving least squares interpolation
