三维稳态地温场全信息数值模拟  

Three-dimensional full information numerical simulation of steady geothermal field

作　　者：戴世坤[1,2] 田红军[1,2] 贾金荣 张莹[1,2] 朱德祥 赵文学 蒋凡 DAI ShiKun;TIAN HongJun;JIA JinRong;ZHANG Ying;ZHU DeXiang;ZHAO WenXue;JIANG Fan(Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring,Ministry of Education,Central South University,Changsha 410083,China;School of Geosciences and Info-Physics,Central South University,Changsha 410083,China;College of Marine Geosciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,长沙410083 [2]中南大学地球科学与信息物理学院,长沙410083 [3]中国海洋大学海洋地球科学学院,青岛266100

出　　处：《地球物理学报》2025年第3期988-1003,共16页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41574127);研究生自主探索创新项目(2023ZZTS0443)资助。

摘　　要：针对常规的数值模拟方法存在计算量大、边界条件近似和难以准确地模拟三维偏微分方程表征的物理信息等问题,本文提出了任意起伏地形下的一种高效、高精度的全信息数值模拟方法.该方法沿水平方向(-∞,+∞)进行二维全信息傅里叶变换,将三维偏微分方程转化为不同波数下的一维常微分方程进行求解,减少了计算量及存储需求,不同波数之间常微分方程相互独立,具有高度并行性.保留垂向为空间域并引入行波分解,消除了上下边界对模拟区域的影响,具有严格的上下边界条件,且每个垂向深度对应的水平网格任意,具有分辨率高,剖分灵活等特点.水平方向采用二维全信息傅里叶变换,获得异常场的正确波数谱信息,再对异常场所有的波数谱信息进行二维全信息逆变换,从而得到空间域的异常场.该方法在水平方向不存在截断效应,相对于标准FFT和Gauss-FFT,没有丢掉任何波数谱信息;每个单元利用一维形函数的高精度解和傅里叶变换的高效性,实现了高效、快速和准确地模拟三维偏微分方程描述的物理信息.本文设计棱柱体,对比数值解与解析解结果,验证了本文算法的正确性,分析异常场的波数谱分布特征,总结波数选取规律,同时对比本文算法与有限单元法、Gauss-FFT的计算精度与效率.设计高、低热导组合模型,进一步讨论边界条件的影响.最后设计任意起伏地形,说明本文算法对任意复杂地形下的适应性,为任意复杂条件大规模、高效、精细化反演成像、定量解释和人机相互解释奠定了基础.The conventional numerical simulation methods have some problems,such as large computation,approximate boundary conditions and difficulties in accurately simulating the physical information characterized by three-dimensional partial differential equations.Therefore,an efficient and highly accurate full information numerical simulation method is proposed for arbitrary undulating terrain in this paper.This method performs two-dimensional(2D)full information Fourier transform along the horizontal direction(-∞,+∞),transforming the three-dimensional(3D)partial differential equations into one-dimensional(1D)ordinary differential equations under different wavenumbers for solving,which reduces the calculation amount and storage requirements,and the ordinary differential equations between different wavenumbers are independent of each other and have high parallelism.Retaining the vertical direction as the spatial domain and introducing traveling wave decomposition eliminates the influence of the upper and lower boundaries on the simulation area.It has strict upper and lower boundary conditions,and the horizontal grid corresponding to each vertical depth is arbitrary,featuring high resolution and flexible discretization.The 2D full information Fourier transform is used in the horizontal direction to obtain the correct wavenumber spectral information of the anomalous field,and then the 2D full information inverse transform is applied to the wave number spectral information of the anomalous field,so as to obtain the anomalous field in the spatial domain.The method has no truncation effect in the horizontal direction,and does not lose any wave number spectral information compared to standard Fourier Transform(FFT)and Gauss-FFT;each unit utilizes the high-precision solution of the 1D shape function and the high efficiency of the Fourier transform,which realizes an efficient,fast,and accurate simulation of physical information described by 3D partial differential equations.In this paper,we design prismatic cylinders,compare

关 键 词：三维稳态地温场 全信息正反变换 波数谱信息 全信息数值模拟 任意起伏地形 

分 类 号：P314[天文地球—固体地球物理学]