地面大功率瞬变电磁三维快速正反演方法及应用

瞬变电磁法（Transient Electromagnetic Method，TEM）因易实施、信噪比高、探测深度大以及高效性，已经在深部矿产勘查、工程勘探等领域广泛应用。

目前，瞬变电磁数据反演以一维和二维为主，或使用简单的三维块状建模来粗略拟合三维TEM的响应，但实际勘探中地电结构较为复杂，简单的数据处理方式很难解释复杂的模型，因此实现三维真实地质模型解释已经成为未来发展趋势。然而，由于计算效率低、内存消耗大等问题限制了三维正反演的发展。本文基于观测分解理论，在时间域提出多尺度并行时间步进概念实现任意波形模拟，并利用观测分解框架，将空间与时间尺度相互匹配，发射源依据时间道剖分成不同数目的偶极子，将全局问题分解为大量互不相关的电磁（Electromagnetic，EM）子问题，实现三维快速正演。最终利用高斯牛顿法开展带地形的三维反演研究，利用“热启动”模式，结合理论和实际地质模型实现三维精准且高效反演。

在正反演理论方面，基于交错网格的有限体积和一阶后退欧拉研究了TEM三维正演空间域与时间域离散，利用“算子”思想给出了散度、旋度以及梯度算子的矩阵形式，并研究了任意复杂形式的回线源和接地长导线源的初始场计算方式，实现复杂形式激励源的三维正演；在此基础上，利用高斯牛顿法推导三维反演控制法方程，使用不精确的预条件共轭梯度算法求解法方程，最终形成一套稳定、高效、高精度且能计算复杂地形的时间域电磁法三维反演框架。

本文提出多尺度并行时间步进概念实现时间域电磁法三维任意波形响应求解。该方法利用阶跃波形响应在时间上的错位相减获得类冲激响应，与波形卷积获得带波形的电磁场响应；在时间通道上采用多尺度并行时间步进方式，利用层状模型研究了每个时间道对应的特征步长，计算每个时间道响应时仅需要求解一次大型稀疏矩阵；利用不同的层状模型研究了一种定量评价脉冲类波形、梯形波on-time部分的有效脉宽方式，能够保证off-time响应精度的同时，极大减少了on-time波形采样的数目；模拟不同复杂程度的三维模型，与传统的三维算法相比，多尺度并行时间步进算法模拟任一时间道响应时使用同一特征步长仅需要一次矩阵分解，各时间道独立计算互不依赖，在满足计算精度的同时显著提升计算效率。

本文基于观测分解数值框架提出三维空间离散与时间尺度匹配概念，将大的全局问题快速分解为大量互不相关的子EM问题。首先，TEM数据的每个时间通道通过时间步长独立求解，其特征时间步长与TEM感应的尺度相匹配，因此后期时间通道的数据不需要早期时间的解。第二，大型发射源被分成许多偶极子源，每个偶极子源可以在偶极子源-接收点的局部网格上单独求解，将全局问题分解为许多更小的子问题，这些子问题相互独立并行加速求解。第三，开发新型去中心化高性能并行计算模式：扫描模式与计算模式。扫描模式用于监听全局的“开始”和“结束”指令；计算模式开启子问题的计算，每个计算节点之间互不通讯，在执行过程中，根据每个节点的计算能力动态调整子问题的数目，能够很好解决传统大规模并行时计算机产生的稳定性不足、负载均衡以及可扩展性不足等问题，提升大量局部子EM问题并行计算效率。模拟多种三维经典模型，通过与传统方法的结果比较，此方法数值精度得到验证。最后，利用加拿大Tli Kwi Cho真实地电模型进行测试，在负载均衡的情况下有多达31200核同时运行，数值实验中观察到近乎线性的加速比，表明了此方法具有极佳的可扩展性。

高斯牛顿法反演属于局部最优化算法，反演时受初始模型的影响大。为了验证初始模型对于三维反演的重要性，本文首先选取简单地质模型反演，发现选取的初始模型均能够成功拟合数据，正确显示地质体信息，但选取接近于真实地质体地电参数信息的初始模型会显著提升三维反演的计算效率；其次选取复杂的地电结构三维反演，结果表明选取好的初始模型不仅仅能够提升计算效率更能精确反映地质目标体信息。之后，本文通过对中国广东省石嘴多金属矿区的大回线TEM数据进行预研究，利用多尺度并行时间步进和去中心化的观测分解理论算法实现三维快速建模，发现当激励源穿过一个导电性能截然不同的接触点且环绕一个良导体时，导电区域外的接收点可以观察到负的瞬变或符号反转现象，岩样电阻率数据证明此区域具有强烈的横向不均匀性，三维模型解释更为合理。然而，以均匀半空间作为初始和参考模型三维反演未能收敛，表明大回线TEM数据的三维反演更容易出现稳定性问题。利用快速正演建模过程中建立的概念性块状模型作为初始和参考模型来实现“热启动”反演，成功地捕捉到了两个地层之间垂直接触带的关键结构，获得了与已知地质和地球物理信息一致的三维导电性模型，并通过可控源音频大地电磁法（Controlled-Source Audio-frequency Magnetotelluric，CSAMT）电阻率截面所验证；最后，研究广东省英德市竹子坑矿区接地长导线源的TEM实测数据，结合钻孔资料信息，成功证明了三维快速正演建模和“热启动”反演方法在高分辨率深部矿产勘探中的需求和能力。

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