Optimizing staggered-grid finite-difference method based on the least-squares combination of the square window function

Abstract

The staggered-grid finite-difference method (SGFDM) has been extensively employed in numerical modeling, seismic imaging, and waveform inversion because of its high efficiency, accuracy, and practicality. Numerical modeling accuracy is crucial for imaging and inversion. Truncating the spatial convolution sequence of the pseudospectral method by window functions can derive the finite-difference method. However, truncation error is inevitable; it can create illusions in numerical modeling, leading to misjudgments. To reduce the truncation error and improve numerical modeling accuracy, enhancing the performance of the truncated window function is imperative. In this study, a new optimal window function was investigated based on the least-squares combination of square windows. Then, the new optimized window function was used to truncate the spatial convolution sequence of the pseudospectral method and obtain an optimized SGFDM. Dispersion analysis showed that the optimized SGFDM has wider spectrum coverage than the conventional SGFDM at the same order. In addition, at low orders, the error range of the new optimized SGFDM could be strictly controlled within 1‱, whereas, at high orders, while ensuring accuracy, the spectrum coverage significantly improved. Finally, numerical modeling for elastic waves demonstrated that the optimized SGFDM could superiorly suppress numerical dispersion and improve calculation efficiency.