基于NAD算法的声波方程时间四阶差分解法  

Acoustic Wave Equation Time Fourth-order Difference Solution Based on NAD Algorithm

作　　者：田雪丰[1] Tian Xuefeng(Geophysical Prospecting Research Institute, CNACG, Zhuozhou, Hebei 072750)

机构地区：[1]中国煤炭地质总局地球物理勘探研究院,河北涿州072750

出　　处：《中国煤炭地质》2019年第2期60-65,71,共7页Coal Geology of China

基　　金：国家自然科学基金(41674118);国家重点研发计划(2018YFC1405900);国家科技重大专项(2016ZX05027-002)联合资助

摘　　要：波动方程数值模拟是研究地震波传播机理的重要工具,有限差分求解波动方程是当前地震波数值模拟的主要方法之一。当地下介质中的地震波速度较低或地震波高频成分丰富时,常规有限差分技术常常产生严重的数值频散误差,这种误差会降低数值模拟的精度,影响对地震波传播机理的分析。为压制地震波数值模拟时产生的数值频散误差,提高波场模拟精度,提出了基于NAD算子的时间四阶精度波动方程差分格式。根据对应的差分格式,分析了该差分格式的数值频散关系。与常规四阶精度差分算法的频散曲线相比,基于NAD时间四阶精度差分方法不但能够实现时间频散的有效压制,同时其基于更多网格点的位移分量和位移梯度分量空间微分求解方法还能够实现空间频散的有效压制。另外在相同模型条件下,基于NAD算法的声波方程时间四阶差分解法可采用大网格对模拟空间进行差分离散,减少网格数,提高计算效率。The wave equation numerical simulation is a major tool in seismic wave travel mechanism analysis. The finite difference solution for wave equation is one of principal methods in seismic wave numerical simulation at present. When seismic wave velocity is rather low or high frequency components abundant in underground medium, conventional finite difference techniques can often produce serious numerical frequency dispersion errors. This kind of errors will lower down numerical simulation precision and impact seismic wave travel mechanism analysis. To suppress dispersion errors in seismic wave numerical simulation, improve wave field simulation precision, a time fourth-order precision wave equation difference scheme based on NAD operator has been put forward. Based on corresponding difference scheme, analyzed the numerical dispersion relationship of the scheme. Compared with conventional fourth-order precision difference algorithm dispersion curves, to based on NAD algorithm not only can realize effective suppression of time dispersion, meanwhile, its displacement and displacement gradient components spatial differential solution method based on more mesh points can also realize spatial dispersion effective suppression. In addition, under the same model condition, based on NAD algorithm acoustic wave equation time forth-order difference solution can use bigger mesh to carry out difference dispersion on simulated space, reduce mesh number and improve computational efficiency.

关 键 词：声波方程 有限差分 数值模拟 数值频散 近似解析离散算法 

分 类 号：P631[天文地球—地质矿产勘探]