朱姣,
邱长凯,
蔡晶,
吉林大学地球探测科学与技术学院, 长春 130026
基金项目: 国家重点研发计划（2017YFC0601900，2016YFC0303100），国家自然科学基金重点项目（41530320）及面上项目（41774125），中国科学院先导专项（XDA14020102），吉林大学高层次科技创新团队建设项目资金资助（JLUSTIRT）和中央高校基本科研业务费专项资金资助
详细信息
作者简介: 殷长春, 男, 1965年生, 教授, 国家"****"特聘专家, 主要从事电磁勘探理论, 航空和海洋电磁方面的研究.E-mail:yinchangchun@jlu.edu.cn
通讯作者: 蔡晶, 女, 1958年生, 高级工程师, 主要从事电磁勘探, 航空电磁数据处理和正反演方面的研究.E-mail:caijing1936@126.com
中图分类号: P631收稿日期:2016-10-09
修回日期:2018-04-18
上线日期:2018-06-05
Spatially constrained inversion for airborne EM data using quasi-3D models
YIN ChangChun,ZHU Jiao,
QIU ChangKai,
CAI Jing,
College of GeoExploration Science and Technology, Jilin University, Changchun 130026, China
More Information
Corresponding author: CAI Jing,E-mail:caijing1936@126.com
MSC: P631--> Received Date: 09 October 2016
Revised Date: 18 April 2018
Available Online: 05 June 2018
摘要
摘要:为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题，通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外，同时还考虑了垂直测线方向测点在空间上的相互约束.为此，首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案，然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵，并使用L-BFGS算法使目标函数最小化，获得最优拟三维模型空间反演解.基于理论模型和实测数据反演，对单点反演与两种空间约束反演方案的有效性进行比较，证明本文空间约束反演算法对于噪声的压制效果好，反演的界面连续光滑，同时内存需求和反演时间少，是一种快速有效的反演策略.
关键词: 航空电磁/
时间域/
拟三维/
空间约束反演/
L-BFGS算法
Abstract:One-dimensional (1D) models play a important role in inversion of geophysical airborne EM (AEM) data. They are based on single sites, which means that for each survey site one has to assume a starting model and then run the inversion. Due to the non-linear problem in airborne EM, such inversion can easily be trapped in local minima, resulting in discontinuity in the inverted section along the profile. This situation can become more serious when the data are noisy, which lead to frequent abrupt changes and oscillations in the inverted resistivity section. To solve this problem, we consider the traditional lateral constraints on adjacent points along a survey as well as spatial constraints in the direction of perpendicular to the survey line. By incorporating known geo-electrical information, e.g. from other geophysical surveys or borehole data, we can also extend the convergence information of inversion from a single site to those in the whole profile. In this way, we can improve the inversion for the whole survey data. This method becomes especially useful when the underground layering is conspicuous, such as in sedimentary areas.
In this paper, we enforce the constraints in two perpendicular directions by adding a constraint term in the objective functional. The constraints are built by the weighted differences of parameters between neighboring stations both along and normal to the survey line. For the inversion process, we use the quasi-Newton algorithm of L-BFGS, in which the inverse Hessian matrix is calculated iteratively from an initial positive-definite matrix (usually unit matrix). We use the Wolfe conditions to determine the length for model parameter updates.
For the numerical experiments, we take two models for the spatially constrained inversion(SCI)both on synthetic data and survey data:a fixed-depth model and a variable-depth model. For comparison purpose, we first run the single-station inversion and then we invert the same dataset with two models of the SCI. We also run the constraints with different weights in different directions to investigate the role of the weights in the inversion.
The comparison of inversion results from different methods shows that the inversion with spatial constraints can greatly improve the continuity of the inverted resistivity section, especially when both the resistivity and layer thickness are allowed to vary. This proves the validity of our SCI method for airborne EM data inversion.
Key words:Airborne EM/
Time-domain/
Quasi three-dimensional/
Spatially constrained inversion (SCI)/
L-BFGS algorithm
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