Numerical methods of geodynamics in big data era: Review and outlook
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摘要: 随着大数据时代的到来，计算地球动力学数值计算方法体系更加完善. 本文系统地回顾了传统数值模拟方法在计算地球动力学领域的应用进展，包括：有限差分法、有限单元法、谱方法和谱元法；并对近年来一些新发展的算法和应用前景进行了综述，如：不连续Galerkin法、小波方法和格子玻尔兹曼方法等. 本综述有助于读者以整体视角了解地球动力学数值计算方法的发展脉络，并对大数据时代下研究适应日益丰富的数据和新算法提供有益参考.Abstract: With the advent of the era of big data, the framework of numerical method of computational geodynamics is perfected. In this paper, we review systematically the conventional numerical simulation methods in the field of computational geodynamics, included the finite-difference, finite-element, spectral method, and spectral element methods. In addition, some newly developed algorithms and their applications in recent years are reviewed, such as the discontinuous Galerkin methods, wavelet method, and lattice Boltzmann method. We hope that the review can give a holistic perspective to understand the development context of the numerical methods of geodynamics and provide a useful reference for studying and adapting to increasingly rich data and new algorithms in the era of big data.
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Key words:
- geodynamics /
- big data /
- numerical method
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图 1 有限元法模拟的Central Andes俯冲过程（修改自Salomon, 2018）.图中有限元法可以使用非规则网格，灵活设置计算模型，其中展示模型计算50000年之后的结果，分别是（a）位移（km）；（b）压力（MPa）；（c）热流（mW/m2）；（d）温度（K）
Figure 1. Central Andes subduction process simulated by finite element method (modified from Salomon, 2018). The finite element method can use irregular grid to flexibly set the calculation model, in which the results calculated by the model after 50000 years are shown, respectively: (a) displacement (km); (b) Pressure (MPa); (c) Heat flow (mW/m2); (d) Temperature (K)
图 2 DGM模拟声波—弹性波传播（修改自Hecht-Nielsen, 1992）
Figure 2. DGM simulates acoustic wave-elastic wave propagation (modified from Hecht-Nielsen, 1992)
图 3 小波方法表示的二维图像（Mallat, 1999）. （a）原始图像f(N)，分辨率N=256×256；（b）原始图像用正交小波分解的系数矩阵<f,Ψkj,n>，k=1,2,3,4，小波尺度因子为2j，大于阈值T的系数用黑点表示；（c）使用尺度因子最大的3组小波系数（N/16个）重建图像；（d）使用最大的N/16个系数重建图像
Figure 3. The wavelet method represents a two-dimensional image (Mallat, 1999). (a) Original image f(N), resolution N=256×256; (b) the original image using orthogonal wavelet decomposition coefficient matrix <f,Ψkj,n>, k = 1, 2, 3, 4, wavelet scale factor is 2j, is greater than the threshold value of T coefficient with black spots; (c) Three sets of wavelet coefficients (N/16) with the largest scale factor were used to reconstruct the image; (d) Reconstruct the image using the maximum N/16 coefficients
图 4 火星表面重力和地形的小波展示（修改自Kido and Yuen, 2003）.（a）原始重力；（b）原始地形；（c）不同尺度小波重建的重力；（d）不同尺度小波重建的地形. lw=8、16、32、64对应的尺度分别是424 km、212 km、106 km、53 km
Figure 4. A wavelet display for the gravity and topography of Mars (modified from Kido and Yuen, 2003). (a) Original gravity; (b) Original topography; (c) The gravity reconstruction by wavelets of different scales; (d) The topography reconstruction by wavelets of different scales. The corresponding scales of lw=8, 16, 32 and 64 are 424 km, 212 km, 106 km and 53 km respectively.
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