求解声波方程的高精度NAD方法及其波场模拟  

A high accuracy NAD method for solving acoustic equation and its wave-field simulations

作　　者：张朝元[1] 

机构地区：[1]大理学院数学与计算机学院,云南大理671003

出　　处：《云南大学学报（自然科学版）》2015年第1期9-16,共8页Journal of Yunnan University(Natural Sciences Edition)

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

摘　　要：通过引入高阶精度的近似解析离散算子,给出了一种求解声波方程的八阶NAD方法.数值误差分析和计算效率结果显示,与四阶LWC方法和八阶LWC方法相比,八阶NAD方法具有高数值精度、高计算效率和低存储量.应用NAD方法模拟地震波在复杂非均匀3层介质和Marmousi模型中的传播,数值结果表明该方法能有效压制数值频散,具有较强的地震波模拟适用能力.We first present the eighth-order NAD method for solving the acoustic equation by introducing the nearly analytic discrete operator with high-order accuracy.Then the analysis of numerical errors and results of computational efficiency show the eighth-order NAD method has high numerical accuracy, high computational ef- ficiency and low computing storage, compared against the fourth-order Lax-Wendroff correction （LWC） scheme and the eighth-order LWC scheme.At last,we apply the eighth-order NAD method to model the seismic wave- field propagating in complex heterogeneous three-layer medium and Marmousi model.The numerical results illus- trate that the new method can effectively suppress numerical dispersion.And the eighth-order NAD method has strong application of seismic wave simulation.

关 键 词：近似解析离散化算子 高精度 数值频散 数值误差 波场模拟 

分 类 号：P631[天文地球—地质矿产勘探] O241[天文地球—地质学]