Simulation of acoustic wavefields in heterogeneous media: A robust method for automatic suppression of numerical dispersion
Simulation of acoustic wavefields in heterogeneous media: A robust method for automatic suppression of numerical dispersion
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DOI：
10.1190/1.3428483
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发表时间：
2010-06
期刊：
影响因子：
3.3
通讯作者：
Dinghui Yang;Guojie Song;Biaolong Hua;H. Calandra
中科院分区：
文献类型：
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作者：
Dinghui Yang;Guojie Song;Biaolong Hua;H. Calandra
数值色散限制了数值模拟方法在大规模计算中求解声波方程的应用。近年来发展了用于抑制数值色散的近解析离散方法nadm及其改进版本。该方法对之前的两种方法进行了改进，并进一步提高了抑制二维非均匀介质中声波传播的数值色散的能力，该方法利用声波位移、粒子速度及其梯度，通过截断泰勒展开和高阶插值近似方法重构声波场。对于所提出的方法，我们研究了它的实现，并将其与高阶Lax-Wendroff校正LWC方案、原始的近解析离散方法NADM及其改进版本在数值色散、计算成本和计算机存储要求方面进行了比较。分析了该算法在一维和二维情况下给出的数值色散关系，并对二维情况下的精确解进行了数值计算。数值结果表明，改进后的方法在很大的空间网格增量下不会产生明显的数值色散。当声波方程离散化时，当每个波长使用的样本太少时，或者当模型具有较大的速度对比度时，它可以模拟高频波传播，并自动抑制数值色散。与高阶LWC方法不同，我们目前的方法可以节省大量的计算空间和内存需求，因为可以使用非常大的网格增量。改进后的方法可用于大尺度波场的模拟。
Numerical dispersion limits the application of numerical simulation methods for solving the acoustic wave equation in largescalecomputation.ThenearlyanalyticdiscretemethodNADM and its improved version for suppressing numerical dispersion weredevelopedrecently.Thisnewmethodisarefinementoftwo previousmethodsandfurtherincreasestheabilityofsuppressing numerical dispersion for modeling acoustic wave propagation in 2D heterogeneous media, which uses acoustic wave displacement, particle velocity, and their gradients to restructure the acoustic wavefield via the truncated Taylor expansion and the high-order interpolation approximate method. For the method proposed,weinvestigateitsimplementationandcompareitwith the higher-order Lax-Wendroff correction LWC scheme, the original nearly analytic discrete method NADM and its improved version with regard to numerical dispersion, computational costs, and computer storage requirements. The numerical dispersionrelationsprovidedbytherefinedalgorithmfor1Dand 2D cases are analyzed, as well as the numerical results obtained bythismethodagainsttheexactsolutionforthe2Dacousticcase. Numerical results show that the refined method gives no visible numericaldispersionforverylargespatialgridincrements.Itcan simulatehigh-frequencywavepropagationforagivengridinterval and automatically suppress the numerical dispersion when the acoustic wave equation is discretized, when too few samples per wavelength are used, or when models have large velocity contrasts. Unlike the high-order LWC methods, our present methodcansavesubstantialcomputationalcostsandmemoryrequirements because very large grid increments can be used. The refined method can be used for the simulation of large-scale wavefields.