Numerical modeling of 3D DC resistivity method in the mixed space-wavenumber domain

Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptability and parallelism of the proposed algorithm.The findings show that the 3D numerical simulation method of DC resistivity method in a mixed space-wavenumber domain is highly efficient,precise,and parallel.

空间波数混合域地温场三维数值模拟方法研究

大规模精细、高效的地温场数值模拟在地热能开发利用中有重要作用。针对地下复杂模型地温场三维数值模拟计算量大、存储要求高这一问题,本文提出了一种空间波数混合域三维地温场数值模拟算法。该方法基于温度场的叠加原理,将地温场分解为背景温度场和异常温度场进行计算。背景场求解采用均匀层状模型;异常场求解时利用水平方向二维傅里叶变换,将异常场满足的三维偏微分方程转化为一系列不同波数之间相互独立的一维常微分方程,大大减少了计算量和存储量。常微分方程求解时单元剖分灵活、计算量小;算法充分利用了傅里叶变换的高效性、追赶法求解定带宽线性方程组的快速性,有效地提升了算法的计算效率。与COMSOL Multiphysics专业仿真有限元软件对比效率,在保证精度的前提下,采用相同的网格剖分,本文算法耗时与内存需求减少数量级倍数,且计算节点数越多,优势越明显。另外,文中设计多个模型研究了热导率大小、不同热流边界、区域构造形态和地形起伏等因素对地温场分布规律的影响,并以青海省共和盆地恰卜恰地区为例,基于地形高程数据和地热地质、地球物理勘查资料建立了三维地球物理模型,实现了该区域的地温场数值模拟。

起伏面磁场及其梯度张量快速三维正演方法（英文）

随着磁梯度张量测量技术迅速发展,为实现精细反演地下磁化率分布提供了数据保障。基于航空和陆地磁测数据的三维磁化率反演需要计算起伏面上的磁场,因此研究起伏面磁场及其梯度张量快速三维正演方法具有重要实际应用价值。针对任意磁化率分布、起伏面磁场及其梯度张量三维正演问题,本文提出了一种快速波数域三维正演方法,其关键环节包括:(1)结合棱柱体组合模型波数域表达式和Gauss-FFT算法,提出一种任意磁化分布情况下平面磁场及其梯度张量快速三维正演算法;(2)利用平面三维正演算法,计算多个高度平面磁场及其梯度张量,结合三次样条插值方法,实现起伏面磁场及其梯度张量三维正演。在此过程中,提出一种多个高度面情况下波数域加权系数快速计算方法,进一步提高了起伏面情况下三维正演的计算效率。通过设计不同模型算例,验证了新方法的计算精度和效率。