基于NAD算子的高精度低数值频散地震波模拟方法

A seismic field modeling method with high accuracy and low numerical dispersion based on the NAD operator

基于二维声波方程,使用四阶截断的泰勒展开式离散时间偏导数,利用八阶精度的近似解析离散算子离散空间高阶偏导数,发展了一种八阶ONAD方法.通过数值误差、计算效率和复杂介质波场模拟等考察研究,结果均显示该方法在压制数值频散、计算效率和波场模拟精度等方面明显优越于四阶LAX-Wendroff Corrected(LWC)方法和八阶LWC方法.因此,八阶ONAD方法是一种有望在地震波模拟得到应用的十分有效的数值模拟方法.

The eighth-order ONAD method is developed for solving the 2-D acoustic wave equation.The new method uses the fourth-order truncated Taylor expansion to discretize partial derivative of time,and employs the eighth-order nearly analytic discrete operator discretize high-order partial derivatives of space.Through studying the numerical error,computational efficiency and complex medium wave-field simulations,those results show that this method is obviously superior to the fourth-order LAX-Wendroff Corrected（LWC）method and the eighth-order LWC method in suppressing the numerical dispersion,computational efficiency and simulation precision of wave-fields.Therefore,the eighth-order ONAD method is a very effective method of numerical simulation and can be applied in the seismic wave simulation.