###### Abstract  
The staggered grid finite difference method has emerged as one of the most commonly used approaches in finite difference methodologies due to its high computational accuracy and stability. Inevitably, discretizing over time and space domains in finite difference methods leads to numerical artifacts. This paper introduces a novel approach that combines the widely used Taylor series expansion with the least squares method to effectively suppress numerical dispersion. We have derived the coefficients for the staggered grid finite difference method by integrating Taylor series expansions with the least squares method. To validate the effectiveness of our approach, we conducted analyses on accuracy, dispersion, and stability, alongside simple and complex numerical examples. The results indicate that our method not only inherits the capabilities of the original Taylor series and least squares methods in suppressing numerical dispersion across small and medium wavenumber ranges but also surpasses the original methods. Moreover, it demonstrates robust dispersion suppression capabilities at high wavenumber ranges. Taylor expansion; least square; acoustic wave; staggered grid finite difference Article An Integrated Taylor Expansion and Least Squares Approach to Enhanced Acoustic Wave Staggered Grid Finite Difference Modeling  
202414100761  
-wavenumber points in the time-space domain. [PERSON] and [PERSON]. [12] proposed an effective modeling strategy based on the element FDM to simulate three-dimensional time domain acoustic wave propagation, which can handle changes in P-wave velocity and media density while maintaining high computational efficiency. [PERSON] et al. [13] introduced an efficient scheme for acoustic propagation using implicit FD operators, which utilizes fewer points to estimate derivatives, thereby reducing computational costs by almost half. However, these methods simplify calculations by approximating the time and spatial derivatives at the central point using differential equations across multiple grid points, inevitably leading to issues of temporal and spatial numerical dispersion. The selection of the differential scheme significantly impacts numerical dispersion. Unlike regular grid methods, the staggered grid method [14; 15; 16; 17; 18; 19; 20], which separates velocity and stress components across different grids, better adapts to the underground medium's geometrical and physical characteristics. Consequently, staggered grid finite difference (SGFD) methods achieve higher modeling precision and stability, making them preferred for enhancing the accuracy of acoustic wavefield simulations. Given that acoustic wave propagation spans both time and space, numerous studies have been conducted to improve the accuracy and stability of SGFD computational results. Notable among these are the Taylor series expansion method (TEM) [21; 22; 23; 24; 25] and the least squares method (LSM) [8; 26; 27; 28; 29; 30]. TEM, which is a straightforward numerical method, approximates the target function as a simple linear polynomial when applied to the acoustic wave equation, facilitating the derivation of high-precision FD coefficients. Given its high accuracy under zero wavenumber conditions, TEM is primarily suited to small wavenumber ranges in forward modeling [28]. LSM, which is more complex than TEM, is a widely used optimization technique that minimizes the objective function to identify FD coefficients in which the squared error is minimal, with derivatives set to zero at the first order. In SGFD simulations of acoustic waves, LSM can adjust forward modeling results to align more closely with actual data, thereby enhancing simulation accuracy. As a global optimization method, LSM is apt for large wavenumber ranges in forward modeling [28; 30]. Due to TEM's high accuracy in the small wavenumber range, some researchers have combined it with other methods to compensate for the limited numerical simulation precision of original techniques in this range. For instance, [PERSON] et al.