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摘要:
全球地磁感应测深能获得地幔转换带及下地幔上部的导电结构.但目前稀疏的地磁台站分布及部分台站的观测数据稳定性较差，影响了三维反演对地下电性结构的分辨力和反演可靠性.为此，区别于传统的L2-范数反演方法，本文提出并实现了基于L1-范数的地磁测深响应三维反演技术.在反演中，利用L1-范数度量数据预测误差，降低"飞点"数据的影响，将相关系数较小的C-响应估计也纳入反演数据中.三维正演模拟采用球坐标系下的交错网格有限差分法，反演采用有限内存拟牛顿法.文中利用指数概率密度分布函数构造非高斯噪声的合成数据，并采用棋盘模型对反演方法的可靠性进行了验证.之后，我们将本文提出的三维反演方法用于全球129个地磁观测台站的C-响应数据反演，结果表明在地幔转换带深部，中国东北地区为高导电异常，南欧和北非则均为高阻；夏威夷在900 km以下为高导；菲律宾海及以东地区在转换带表现为明显的高阻，这些结果与前人研究结果一致.由于采用了更多的台站数据，我们的反演结果还发现一些新的异常：南美洲南端，转换带表现为明显的高导；澳大利亚东南部，地幔转换带深部，也存在一个明显的高导异常，这些异常分布和地震层析成像的低速区一致.因此，L1-范数三维反演能够充分利用全球C-响应数据信息，提高地磁测深对地球深部电性结构的分辨能力，更好的研究全球地幔电性结构.
Abstract:Global geomagnetic depth sounding (GDS) permits to detect the electrical structure of mantle transition zone and the upper part of lower mantle. However, the resolution and reliability of 3-D GDS inversion are restricted by sparse distribution of observatories and rejection caused by records' poor stability. In this paper, a 3-D GDS inversion method based on L1-norm has been developed to solve the problem, which differs from the traditional L2-norm inversion. The algorithm uses L1-norm in the measure of data misfit when outliers occur in the data, so during inversion process we could take C-responses with low coherency into account at a certain observatory. The L-BFGS inversion method is used and the forward solver is based on a staggered-grid finite difference method in frequency domain for spherical geometry. Non-Gaussian noise of synthetic data are generated by using an exponential probability density function, then a checkerboard model inversion test is performed to ensure the valid of our method. This 3-D inversion method is applied to C-responses of 129 selected observatories around the world. Results show high conductivity beneath Northeast of China and high resistivity in lower mantle transition beneath South Europe and North Africa, while high conductivity also exists below 900 km in Hawaii and high resistivity is registered beneath Philippine Sea and the East. These features are coincident with previous studies. Due to more observatories are used, our results present more anomalies, such as the high conductivity in the mantle transition zone beneath southern South America, and the high conductivity in the lower part of mantle transition zone of southeastern Australia. These anomalies coincide with the low velocity areas derived from seismic tomography. This work demonstrates that the L1-norm inversion method can make full use of observatories' records and improve exploratory resolution of deep electrical distribution of the Earth, contributing to further study of the global mantle structure.
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Key words:
- Geomagnetic depth sounding /
- 3-D inversion /
- L-BFGS /
- L1-norm /
- C-response /
- Mantle structure
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图 1
国际地磁台站FUR(a、c)和LNP(b、d)的原始观测数据及处理得到的C-响应
Figure 1.
Observed data in time-series and estimated C-responses of FUR (a, c) and LNP (b, d)
图 3
理论上生成的指数随机噪声，这些噪声将被按照顺序叠加到下文的理论C-响应上产生具有“飞点”的合成数据
Figure 3.
The theoretical random noise data generated by exponential probability density function, and they will be added to the forward C-response in sequence to obtain the synthetic data with "outliers"
图 4
叠加指数噪声的合成数据L1-范数三维反演结果
Figure 4.
Inversion result of 3-D L1-norm of the synthetic data with exponential noise
图 5
叠加指数噪声的合成数据与L1-范数三维反演模型响应的交汇图
Figure 5.
Cross plots of inversion response obtained by L1-norm and synthetic data with exponential noise
图 6
反演数据拟合差(a)、模型粗糙度(b)、目标函数(c)和正则化因子(d)的迭代变化曲线
Figure 6.
Iterative curves of RMS (a), roughness of model (b), objective function (c) and regularization parameter (d)
图 7
全球C-响应数据L1-范数反演完成后各台站的数据拟合差分布
Figure 7.
The distribution of RMS in every observatory of the L1-norm inversion result of global C-responses
图 8
全球地磁台站L1-范数反演部分台站的数据拟合对比曲线
Figure 8.
Data fitting curves of global data′s L1-norm inversion in some stations
图 9
全球地幔转换带及下地幔上部电导率分布图
Figure 9.
Global electrical conductivity model in mantle transition zone and upper part of lower mantle
表 1
本文选取地磁台站的位置信息及平方相关系数(coh2)
Table 1.
Location details and squared coherencies (coh2) of observatories used in this paper
Code GMlon GMlat Coh2 AAA 152.937 34.315 0.449 ABG 146.402 10.268 0.034 AIA 5.575 -55.174 0.401 AMS 144.635 -46.32 0.384 API 262.697 -15.328 0.268 AQU 94.645 42.39 0.751 ARS 140.047 49.199 0.457 ASH 135.294 31.065 0.555 ASP 208.237 -32.794 0.647 BDV 97.724 48.751 0.791 BEL 105.266 50.237 0.735 BFE 98.546 55.43 0.478 BFO 91.911 49.025 0.765 BGY 112.655 28.271 0.471 BJI 187.094 29.994 0.56 BMT 187.108 30.254 0.718 BOU 320.783 48.33 0.34 BOX 123.612 53.446 0.253 BSL 339.909 39.942 0.6 CBI 211.725 18.584 0.441 CDP 176.108 20.891 0.494 CLF 85.796 49.796 0.713 CNB 226.954 -42.604 0.755 CNH 194.888 34.086 0.569 COI 71.957 44.093 0.252 CTA 221.017 -27.905 0.694 CTS 94.28 46.235 0.633 DAL 331.621 42.055 0.49 DLR 327.465 38.208 0.522 DOU 88.998 51.384 0.736 EBR 81.332 43.281 0.622 ELT 112.086 26.275 0.544 ESA 209.524 30.58 0.503 ESK 83.617 57.776 0.281 EYR 253.798 -47.064 0.585 FRD 353.503 48.291 0.318 FRN 305.442 43.465 0.638 FUR 94.727 48.351 0.76 GCK 102.533 43.28 0.73 GLM 168.291 26.501 0.691 GNA 188.932 -41.806 0.436 GUI 60.606 33.71 0.676 GWC 351.917 65.329 0.257 GZH 184.913 12.998 0.369 HAD 80.076 53.865 0.667 HBK 94.727 -27.156 0.249 HER 84.367 -34.03 0.496 HLP 104.704 53.23 0.569 HON 269.87 21.66 0.457 HRB 101.232 46.861 0.767 HTY 208.882 24.319 0.563 IRT 177.125 42.048 0.509 ISK 109.267 38.403 0.554 IZN 109.737 37.743 0.715 JAI 150.034 18.237 0.492 KAK 208.847 27.492 0.64 KDU 205.679 -21.87 0.563 KGD 150.643 41.223 0.212 KIV 113.541 47.581 0.653 KNY 200.843 22.013 0.567 KNZ 208.753 26.502 0.526 KOU 19.731 14.772 0.246 KSH 151.646 30.732 0.726 KZN 131.711 49.804 0.334 LMM 99.575 -28.043 0.453 LNP 192.219 15.111 0.186 LRM 186.547 -32.296 0.396 LVV 107.22 47.871 0.54 LZH 176.319 25.976 0.632 MAB 90.153 51.384 0.731 MBO 57.511 20.034 0.261 MCQ 244.161 -59.985 0.05 MIZ 209.406 30.442 0.667 MMB 211.368 35.472 0.706 MNK 112.912 51.619 0.42 MOS 121.675 51.075 0.474 MZL 187.77 39.577 0.742 NCK 99.742 46.884 0.742 NEW 304.93 54.798 0.149 NGK 97.729 51.861 0.725 NGP 152.489 12.17 0.125 NVS 159.933 45.473 0.409 ODE 112.692 43.673 0.802 PAF 133.194 -56.88 0.029 PAG 105.09 40.639 0.831 PBQ 351.968 65.34 0.276 PET 221.589 45.891 0.517 PHU 178.103 10.901 0.237 PMG 220.559 -17.197 0.392 PPT 285.189 -15.146 0.347 PST 11.587 -41.816 0.727 QIX 180.052 24.464 0.613 QSB 113.655 30.289 0.695 RSV 99.404 55.509 0.424 SBL 14.508 53.805 0.54 SFS 73.491 40.207 0.433 SGE 28.938 -45.68 0.47 SHL 164.966 15.804 0.359 SHU 257.03 54.327 0.367 SIL 165.812 15.126 0.379 SJG 6.167 28.199 0.212 SPT 75.95 42.746 0.817 SSH 191.967 21.204 0.452 SSO 205.28 24.507 0.299 STJ 24.029 57.031 0.169 SUA 107.716 42.394 0.738 SVD 142.204 49.217 0.428 SZT 60.827 33.838 0.383 TAM 81.97 24.605 0.637 TAN 116.101 -23.655 0.293 TDC 53.771 -31.475 0.644 TEN 60.826 33.836 0.363 TFS 123.993 36.956 0.732 THJ 175.065 13.906 0.492 THY 100.597 45.971 0.815 TKT 146.219 33.133 0.534 TOO 223.129 -45.281 0.392 TRW 5.64 -33.187 0.612 TSU 86.137 -18.819 0.337 TUC 316.271 39.803 0.627 UJJ 149.637 14.519 0.278 UPS 106.336 58.505 0.203 VAL 74.53 55.756 0.552 VIC 297.82 54.098 0.199 VLA 200.882 34.314 0.497 WHN 185.899 20.452 0.48 WIK 99.602 47.564 0.766 WNG 95.08 54.09 0.6 YAK 196.394 52.367 0.05 注：表中各列分别为台站的代码、地磁经度、地磁纬度和平方相关系数；当平方相关系数小于0.5时，表中以灰色背景标出.
Note：Including the code, location (longitude and latitude, both in geomagnetic coordinate) and the coh2 of every station. The marked gray zone indicates the squared coherency less than 0.5.
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No. layer ρ/Ωm Thickness/km 1 158 100 2 100 150 3 15.8 160 4 10.0 110 5 3.1 150 6 1.0 230 7 1.0 300 8 1.0 400 9 1.0 400 10 0.5 400 11 0.1 490 12 地核 3481
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