虚拟波场降速条件下电性源瞬变电磁垂直磁场分量的波场反变换方法  

Inverse wavefield transform of vertical magnetic signal of galvanic source TEM when slowing down pseudo-wavefield velocity

作　　者：范克睿 王刚[1,2] 鲁凯亮 郑新 李貅 孙兴邦[5] FAN KeRui;WANG Gang;LU KaiLiang;ZHENG Xin;LI Xiu;SUN XingBang(Shandong Provincial Key Laboratory of Civil Engineering Disaster Prevention and Mitigation,Shandong University of Science and Technology,Qingdao 266590,China;College of Civil Engineering and Architecture,Shandong University of Science and Technology,Qingdao 266590,China;College of Geology Engineering and Geomatics,Chang'an University,Xi'an 710054,China;Integrated Geophysical Simulation Lab of Chang'an University(Key Laboratory of Chinese Geophysical Society),Xi'an 710054,China;Geotechnical and Structural Engineering Research Center,Shandong University,Jinan 250061,China)

机构地区：[1]山东省土木工程防灾减灾重点实验室,山东科技大学,青岛266590 [2]山东科技大学土木工程与建筑学院,青岛266590 [3]长安大学地质工程与测绘学院,西安710054 [4]长安大学地球物理场多参数综合模拟实验室(中国地球物理学会重点实验室),西安710054 [5]山东大学岩土与结构工程研究中心,济南250061

出　　处：《地球物理学报》2023年第4期1743-1757,共15页Chinese Journal of Geophysics

基　　金：山东省自然科学基金项目(ZR2022QE242);山东省土木工程防灾减灾重点实验室开放基金项目(CDPM2021KF11)联合资助。

摘　　要：通过波场反变换从瞬变电磁信号中提取虚拟波场是定位电性界面和刻画地下导电目标形态的有效手段.波场反变换过程中,降低虚拟波场速度有利于改善虚拟波场对电性界面的分辨能力.然而,波场变换核函数随时间、虚拟时间以及虚拟波场速度变化的动态范围极大,且随虚拟波场降速而进一步扩大,造成波场反变换问题高度不适定,制约了虚拟波场提取的精度和效果.对此,在虚拟波场降速的条件下,本文以核函数在无穷区间上积分的解析解为准绳,通过最优化与数据拟合得到了经验公式,确定了波场反变换所需的最优积分区间;在适应采集时间与虚拟波场速度的同时,最大限度缩短了积分区间长度,降低了核函数变化的动态范围,压制了波场反变换方程的病态程度.此外,通过引入精细积分方法求解波场反变换方程,提高了波场反变换方程的求解精度.为验证方法的有效性与可靠性,对正演模拟的电性源瞬变电磁垂直磁场分量及其时间导数分量进行了波场反变换;结果回代后的拟合数据与正演数据的相对误差小于5%.在所提取的虚拟波场记录中观察到了合理的运动学特征,如实反映了低阻目标层深度、厚度和二次场观测时间范围的变化.在计算条件相同的前提下,通过降低虚拟波场速度,改善了波场反变换的精度和效果.降速后提取的虚拟波场记录对低阻层上下界面的刻画更为清晰.在对实测数据的处理中,本文的虚拟波场降速、积分区间最优化和精细积分求解方法得到了合理可信的虚拟波场提取结果,为进一步利用虚拟波场开展低阻目标体成像提供了数据保障.Extracting the Pseudo-wavefield by inverse wavefield transform from the Transient Electromagnetic Method(TEM)signal is an effective way to provide structural information of the subsurface conductive objects.Slowing down the velocity of the pseudo-wavefield can improve the resolution of the pseudo-wavefield to the subsurface interface between different conductivity.However,the accuracy and effect of pseudo-wavefield extraction is limited by the highly ill-posed inverse wavefield transform,resulting from the extremely large dynamic range of its kernel function.The variation of time,pseudo-time and the pseudo-wavefield's velocity can all affect the dynamic range of the kernel function,which is extended in the process of slowing down the pseudo-wavefield velocity,the result of which is the poor accuracy and fewer"wave-like"traces.We provide an inverse wavefield transform method for the vertical magnetic components of galvanic source TEM data when slowing down the velocity of the pseudo-wavefield.In this paper,the optimal numerical integration interval required for the inverse wavefield transform was determined by taking the analytical solution of the kernel function integral over the infinite interval as the criterion and the empirical formula obtained by optimization and data fitting;while adapting to the arbitrary time range and virtual wavefield velocity,the length of the numerical integration interval is minimized,the dynamic range of the kernel function change is reduced,and the pathological degree of the wavefield inverse transform equation is suppressed.In addition,the accuracy of solving the wavefield inverse transformation equation is improved by introducing the precise integration method to solve the wavefield inverse transformation equation.To verify the validity and reliability of the method,the wavefield inverse transform is performed on the electric source transient electromagnetic vertical magnetic field components and their time derivative components from the forward simulation.The relative error betw

关 键 词：瞬变电磁 波场变换 降速 电性源 垂直磁场 

分 类 号：P631[天文地球—地质矿产勘探]