Advances in numerical modeling of metallogenic dynamics: A review of theories, methods and technologies
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摘要:
成矿动力学数值模拟以数学、物理及化学的基本规律为原理，结合实际地质资料，建立定量表征成矿过程的数学模型(数学-物理方程)，再利用有限元或有限差分等方法通过计算机的高效计算进行求解，模拟成矿作用动力学过程及其成矿响应，揭示成矿规律并指导找矿。它集合了地质、数学、物理、化学及计算机等多个学科的研究理论与方法，具有鲜明的多学科交叉融合的特点。近年来，在计算科学与数学地质理论与方法快速发展的推动下，成矿动力学数值模拟研究取得了重要研究进展。为此，归纳和梳理了成矿动力学数值模拟的基本理论与方法，对比了目前4种常用的(成矿)数值模拟软件的特点，结合当前开展这方面研究所取得的进展，介绍了近10年来成矿动力学数值模拟的发展与应用现状。得出以下主要结论与认识：①多场耦合成矿动力学数值模拟是当前能够重现大尺度复杂成矿过程的唯一可行方法，随着高性能计算技术与非线性动力学理论的快速发展与日趋完善，它已成为现代数学地球科学的研究热点和发展方向之一，是揭示成矿机制及获取矿产勘查信息的重要手段，具有很大的发展潜力；②成矿动力学数值模拟目前仍存在模拟参量不确定、多场过程耦合不完全等局限性，是其未来的发展重点，当前已有很多研究致力于破解这方面的难题；③在大数据驱动科学研究的新范式下，成矿动力学数值模拟与机器学习方法相结合，可以有效地反演成矿作用过程并进行矿产定量预测，是成矿动力学数值模拟方法在矿床成因与矿产勘查领域应用研究的重要突破口。理清了成矿动力学数值模拟的基本方法与关键难题，明确了成矿动力学数值模拟对促进矿床成因与勘查研究的重要作用，阐述了成矿动力学数值模拟发展的前缘方向，为成矿动力学计算模拟研究提供了基础指导。
Abstract:Based on geological surveys and experimental data, numerical modeling of metallogenic dynamics (NMMD) establishes a mathematical model (mathematical-physical equation) that quantitatively characterizes metallogenic processes using the basic laws of mathematics, physics and chemistry. Then, using the finite element or finite difference method, the model is built through efficient computer calculation, simulating the metallogenic dynamic process and its metallogenic response, revealing metallogenic law and guiding prospecting. NMMD integrates theories and methods of geology, mathematics, physics, chemistry, computers and other disciplines and has distinct characteristics of interdisciplinary integration. In recent years, driven by the rapid development of computational science and mathematical geology, important progress has been made in NMMD. This paper summarizes the basic theories and methods of NMMD, compares the characteristics of four metallogenic numerical simulation software programs, and introduces the development and application status of NMMD with progress of the author′s team in the past decade. The main conclusions and understandings are as follows: ①Multi-field coupled metallogenic dynamics numerical simulation is the only feasible method to reproduce the large-scale complex metallogenic process. With the rapid development and improvement of high-performance computing technology and nonlinear dynamics theory, it becomes one of the research hotspots and development directions of modern mathematical geoscience. It is important to reveal the metallogenic mechanism and obtain mineral exploration information, which has great potential for development; ②At present, there are some limitations in NMMD, such as uncertain simulation parameters and incomplete coupling of multifield processes, which will be the focus of its future development. Numerous studies have been devoted to solving these problems; ③Under a new paradigm of scientific research driven by big data, a combination of NMMD and machine learning can effectively invert the metallogenic process and quantitatively predict mineral resources. This method is an important breakthrough in the application of NMMD in deposit genesis and mineral exploration. This paper clarifies the basic methods and key problems of NMMD in promoting the study of deposit genesis and exploration, and expounds the frontier direction of NMMD, which provides basic guidance for the study of computational modeling of metallogenic dynamics.
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Key words:
- metallogenic dynamic /
- numerical simulation method /
- software technology /
- application
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图 2 成矿动力学多场(过程)耦合数值模拟的概念模型(据文献[4]修改)
Figure 2. A conceptual model for multi field (process) coupled numerical simulation of metallogenic dynamics
图 3 成矿动力学数值模拟的基本步骤
Figure 3. Basic steps of the numerical simulation of metallogenic dynamics
图 4 有限元法的基本原理图
a.单元划分示意图；b.单元剖分；c.剖分单元细化；d.单元精细化；e.确定单元节点；f.单元节点分析；g.求解节点位移
Figure 4. Basic schematic diagram of the finite element method
图 6 边界元法的基本原理图
a.离散的内边界单元；b.单元划分示意图；c.离散的外边界单元；en为面的外法线方向的单位向量；边界L离散为N个单元；i为单元号
Figure 6. Basic schematic diagram of the boundary element method
图 7 德兴斑岩铜矿床斑岩体倾伏角(α)变化对成矿控制作用的力-热-流三场耦合数值模拟结果[95]
a.等效应力等值面图；b.体积应变等值面图；c.断裂面达西速度图；d.温度切面图
Figure 7. Results of numerical simulation of the force-heat-flow of the controlling effect of porphyry dip angle (α) on mineralization in the Dexing porphyry copper deposit
图 8 基于成矿条件数值模拟的粤北凡口铅锌矿床成矿预测[63]
a.构造应力场模拟应力等值线图；b.成矿预测图
Figure 8. Metallogenic prediction of the Fankou lead-zinc deposit in northern Guangdong Province based on numerical simulation of metallogenic conditions
表 1 3种数值模拟求解方法的原理及特点
Table 1. Principles and characteristics of three numerical simulation solutions
求解方法 基本原理 优点 缺点 有限单元法 将连续的求解域离散为有限个单元，把连续域中的无限自由度问题转变成离散域中的有限自由度问题 可以模拟各种复杂的几何形状结构；求解方法系统化、标准化，能够广泛应用；可求解非线性问题并进行多场耦合分析[44] 处理复杂问题较耗费计算资源；对无限求解域没有较好的处理方法[45-46] 有限差分法 将有限个由离散点构成的网格来代替连续的定解区域，用有限差分方程组来近似地代替原微分方程和定解条件 计算方法简便灵活，在计算机上易于实现，通用性强；能利用结构网格的拓扑优势扩大模板，构造出高精度格式[10, 47] 仅适用规则区域及边界条件，求解线性、均质问题；前、后处理工作量较大[48] 边界元法 不在连续体域内划分单元，只在定义域的边界上划分单元，再通过满足控制方程的函数去逼近边界条件 单元数量相对较少，数据准备简单；降低了计算复杂度；更适合处理开放空间内的物理问题[49-51] 不适合处理复杂边界条件的问题；不规则区域处理繁琐 
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表 2 FLAC2D/3D、ANSYS、ABAQUS与COMSOL Multiphysics在成矿动力学数值模拟中的应用实例及特点分析
Table 2. Application examples and characteristic analysis of FLAC2D/3D, ANSYS, ABAQUS and COMSOL Multiphysics in the numerical simulation of metallogenic dynamics
软件名称 简介 优点 缺点 应用实例 FLAC2D/3D 主要以岩石力学为基础，能够较好地模拟岩石变形和流体流动，分析变形、渗流、热传导等耦合作用 采用动态分析方法，“显示解”方案，求解过程占用内存小，运算时间短，效率较高。利于求解复杂、规模较大的问题 前处理能力较弱，构建复杂地质模型难度较大，使用其他软件构建时需要转化。缺少化学反应模拟的相关模块 文献[10, 48, 58-62] ANSYS 全面地覆盖了流体流动分析、热分析和结构应力分析等多场耦合分析 前处理功能强大，建模比较便捷，同时具备多数CAD软件接口；具备多种物理场优化功能，配合多场耦合分析；具有强大的结构静力分析功能 求解非线性问题的能力有限；化学反应模拟的功能较弱 文献[63-67] ABAQUS 集中于结构力学及相关领域的研究，同时具备热传导及流体运移的多场耦合分析 强大的非线性分析能力，可以解决其他软件不收敛的非线性问题；采用CAD方式建模和可视化视窗系统，有很好的人机交互体验 流体动力学模拟的能力较弱，缺少化学反应模拟的相关模块；多场耦合分析能力相对较弱 文献[68-72] COMSOL Multiphysics 拥有大量的预定义动力学模型，范围涵盖流体流动、热传导、结构力学、化学反应以及多场耦合模拟 完全开放的架构，用户可以根据需要轻松自由地定义所需要的专业偏微分方程；内嵌了丰富的CAD建模工具，同时支持第三方CAD导入功能；具有丰富的后处理功能 对复杂的非线性问题的求解的能力相对不足，容易出现不收敛问题 文献[44, 46, 73-77]
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