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

作　　者：张朝元[1,2] 

机构地区：[1]大理学院数学与计算机学院,大理671003 [2]清华大学数学科学系,北京100084

出　　处：《地球物理学进展》2014年第6期2592-2599,共8页Progress in Geophysics

基　　金：国家自然科学基金项目(41230210;41464004);Statoil company资助项目(4502502663);云南省教育厅科学研究基金重点项目(2013Z152)联合资助

摘　　要：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.

关 键 词：NAD算子 数值频散 高精度 地震波模拟 

分 类 号：P315[天文地球—地震学]