基于NAD算子和FCT技术改进的Runge-Kutta方法及其波场模拟  

Improved Runge-Kutta method and its wave-field simulation based on NAD operator and FCT technique

作　　者：张朝元 

机构地区：[1]大理大学数学与计算机学院,大理671003

出　　处：《地球物理学进展》2016年第3期1274-1280,共7页Progress in Geophysics

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

摘　　要：地震波正演数值模拟中所产生的数值频散严重地影响波场模拟的精度和分辨率.基于声波方程,以8阶精度的近似解析离散算子来校正差分算子对空间偏导数进行离散,以三阶Runge-Kutta方法对时间导数进行离散,并结合通量校正传输技术以抑制数值频散,从而建立基于NAD算子和TCF技术改进的Runge-Kutta方法.波场模拟结果表明,该方法在抑制数值频散上明显优越于传统的高阶有限差分方法.同时,该方法对模拟地震波在复杂介质中的传播有着很强的适应能力.The numerical dispersion, existing in the forward numerical simulation of seismic wave,interferes with the wave-field modeling seriously and decreases the precision of simulation greatly.Based on the acoustic wave equation,an improved Runge-Kutta method is proposed by combining NAD operator and FCT technique. The new method uses an eighth-order accurate nearly analytic discrete operator to discretize the high-order spatial derivatives for correcting finite-difference operator,employs a thirdorder Runge-Kutta method discretize the temporal derivatives,and uses the flux-corrected transport technique to eliminate the numerical dispersion. The results of wave-field simulations show that this method is obviously superior to traditional high-order finitedifference methods in eliminating the numerical dispersion. At the same time,this method has a strong adaptability for simulating seismic wave propagation in complex media.

关 键 词：RUNGE-KUTTA方法 近似解析离散化算子 通量校正传输技术 数值频散 波场模拟 

分 类 号：P631[天文地球—地质矿产勘探]