基于全局光滑约束的地磁测深<i>C</i>-响应估计

doi:10.6038/cjg2019M0199

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摘要地磁测深C-响应，包含着地球内部结构的导电信息，因此获得高质量的C-响应估计对于揭示地球内部准确的电性结构至关重要，为此本文提出一种计算地磁测深C-响应的新思路.不同于以往单个频点估计办法，新方法基于相邻频率C-响应连续光滑的特性同时估计所有频率的C-响应.首先，根据求取C-响应的Z/H方法，由观测的H_r和H_θ构造估计C-响应的线性方程组；为了增强方程组求解的稳定性，克服噪声影响，要求估计的C-响应满足光滑性条件，从而将无约束的C-响应估计转化为阻尼最小二乘理论的C-响应估计优化问题.合成数据和实际台站数据的测试结果表明，光滑约束优化技术能比传统的逐频求取方法得到更加合理和连续的响应曲线；虽然正则化参数的选择对C-响应估计的结果有明显影响，但通过L-曲线和V-曲线确定的最优正则化参数可以在保证数据真实性的前提下获得最佳的C-响应估计.基于全局光滑约束获得的C-响应为提高反演结果的可靠性奠定基础，为利用更多台站的C-响应获得高分辨力的地球深部电性结构提供了技术支持.

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关键词 ：地磁测深, C-响应, 正则化反演, 约束优化, 地球内部

Abstract：C-responses of geomagnetic depth sounding (GDS) contain effective information on the internal structure of the earth, so the accurate C-responses estimation is very important for revealing the accurate electrical structure in the earth. To this end, a new method to estimate the C-responses of GDS is proposed in this paper. Different from the previous single frequency estimation methods, this approach simultaneously estimates the C-responses of all frequencies based on the continuous smoothing characteristic of the adjacent frequency. First, the linear equations are constructed from the observed H_r and H_θ based on the Z/H method. In order to enhance the stability of the equations and overcome the influence of noise, the estimated C-responses are required to satisfy the smoothness condition, and the unconstrained C-responses estimation is transformed into an optimization problem of the damped least squares theory. The tests of synthetic data and real observational data indicate that the smooth constrained technology can obtain more reasonable and continuous curves than the traditional methods. Although the regularization parameter has an important influence on the estimation, the optimal regularization parameter determined by L-curve and V-curve methods can obtain the best C-responses while ensuring the authenticity of the data. The C-responses obtained by this method lay the foundation for improving the reliability of the inversion results, and provide technical support for the high-resolution electrical structure of the earth's interior by using C-responses of more observatories.

Key words： Geomagnetic depth sounding C-responses Regularized inversion Constrained optimization Earth's interior

收稿日期: 2018-05-09

PACS:	P631
	P318

基金资助:国家重大科研仪器专项（2011YQ05006010），安徽省国土资源科技项目（2016-K-19）联合资助.

通讯作者: 翁爱华,男,1968年生,教授,主要从事电磁法勘探方法技术、正反演理论研究.E-mail:wengah@jlu.edu.cn E-mail: wengah@jlu.edu.cn

作者简介: 张艳辉,男,1991年生,在读博士,主要从事地球电磁法及电磁勘探正反演理论研究.E-mail:zhangyh15@mails.jlu.edu.cn

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http://www.geophy.cn//CN/10.6038/cjg2019M0199 或 http://www.geophy.cn//CN/Y2019/V62/I5/1898

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