﻿ 基于循环神经网络的重力异常数据推估研究
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 大地测量与地球动力学  2021, Vol. 41 Issue (3): 234-237  DOI: 10.14075/j.jgg.2021.03.003

### 引用本文

SHE Yawen, FU Guangyu. Estimation of Gravity Anomaly Data Based on Recurrent Neural Network[J]. Journal of Geodesy and Geodynamics, 2021, 41(3): 234-237.

### Foundation support

National Key Research and Development Program of China, No.2018YFC1503503, 2018YFC1503704; National Natural Science Foundation of China, No.41874003; Special Fund for Basic Scientific Research of Institute of Earthquake Forecasting, CEA, No.2020IEF0502, 2020IEF0708.

### Corresponding author

FU Guangyu, PhD, researcher, majors in seismic dislocation deformation and gravity, E-mail: fugy@ief.ac.cn.

### 第一作者简介

SHE Yawen, PhD, majors in gravity observation and interpretation, E-mail: sheyawen@outlook.com.

### 文章历史

1. 南京大学地球科学与工程学院，南京市仙林大道163号，210023;
2. 中国地震局地震预测研究所地震预测重点实验室，北京市复兴路63号，100036

1 自由空气重力异常数据

 图 1 鄂尔多斯西南缘自由空气重力异常场 Fig. 1 Free-air gravity anomaly field in the southwestern margin of Ordos
2 长短期记忆循环神经网络 2.1 循环神经网络

 图 2 循环神经网络结构 Fig. 2 Structure of recurrent neural network
 $\boldsymbol{O}_{i}=g\left(\boldsymbol{V} \boldsymbol{S}_{i}\right)$ (1)
 $\boldsymbol{S}_{i}=f\left(\boldsymbol{U} \boldsymbol{I}_{i}+\boldsymbol{W} \boldsymbol{S}_{i-1}\right)$ (2)

 $\begin{array}{c} \boldsymbol{O}_{i}=g\left(\boldsymbol{V} f\left(\boldsymbol{U} \boldsymbol{I}_{i}+\boldsymbol{W} f\left(\boldsymbol{U} \boldsymbol{I}_{i-1}+\boldsymbol{W} f\left(\boldsymbol{U} \boldsymbol{I}_{i-2}+\right.\right.\right.\right. \\ \left.\left.\left.\boldsymbol{W} f\left(\boldsymbol{U}\boldsymbol{I}_{i-3}+\boldsymbol{\cdots}\right)\right)\right)\right) \end{array}$ (3)

2.2 长短期记忆神经元

LSTM将RNN中Si替换为2个输出值进行处理，即神经元的当前状态值Ci和输出值hiCi可保存序列数据的长期状态，通过遗忘门(Fi)、输入门(Ii)和输出门(Oi)进行控制。图 3为LSTM神经元结构图，其中各变量之间的数学关系见式(4)：

 图 3 长短期记忆神经网络结构 Fig. 3 Structure of long short-term memory
 $\begin{array}{l} \boldsymbol{I} \boldsymbol{n}_{i}=\tanh \left(\boldsymbol{W}_{x I n} \boldsymbol{I}_{i}+\boldsymbol{W}_{h I n} \boldsymbol{h}_{i-1}+b_{i}\right) \\ \boldsymbol{J}_{i}=\operatorname{sigm}\left(\boldsymbol{W}_{x j} \boldsymbol{I}_{i}+\boldsymbol{W}_{h j} \boldsymbol{h}_{i-1}+b_{j}\right) \\ \boldsymbol{F}_{i}=\operatorname{sigm}\left(\boldsymbol{W}_{x f} \boldsymbol{I}_{i}+\boldsymbol{W}_{h f} \boldsymbol{h}_{i-1}+b_{f}\right) \\ \boldsymbol{O}_{i}=\tanh \left(\boldsymbol{W}_{x o} \boldsymbol{I}_{i}+\boldsymbol{W}_{h o} \boldsymbol{h}_{i-1}+b_{o}\right) \\ \boldsymbol{C}_{i}=\boldsymbol{C}_{i-1} \odot \boldsymbol{F}_{i}+\boldsymbol{I}_{i} \odot \boldsymbol{J}_{i} \\ \boldsymbol{h}_{i}=\tanh \left(\boldsymbol{C}_{i}\right) \odot \boldsymbol{O}_{i} \end{array}$ (4)

3 不同推估方法对比分析

 图 4 基于观测数据的不同推估方法对比 Fig. 4 Comparison of different estimated methods based on observation data

 图 5 基于不同推估方法的鄂尔多斯西南缘自由空气重力异常场 Fig. 5 Free-air gravity anomaly field in the southwestern margin of Ordos based on different estimation methods
4 结语

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Estimation of Gravity Anomaly Data Based on Recurrent Neural Network
SHE Yawen1,2     FU Guangyu2
1. School of Earth Sciences and Engineering, Nanjing University, 163 Xianlin Road, Nanjing 210023, China;
2. Key Laboratory of Earthquake Forecasting, Institute of Earthquake Forecasting, CEA, 63 Fuxing Road, Beijing 100036, China
Abstract: We adopt the gravity observation data of the southwestern margin of Ordos to train the long short-term memory recurrent neural network (LSTM). The results show that LSTM can obtain good estimation results based on limited data. Through comparing and analyzing the estimated results of LSTM and ordinary Kriging method based on free-air gravity anomaly data, we find that the estimation ability of neural network is better than ordinary Kriging method, but Kriging method performs better in terms of computing efficiency. Using the free-air gravity anomaly data to estimate the entire area, we show that LSTM method is significantly better than Kriging method. Adding elevation data as a constraint can effectively improve the accuracy of free-air gravity anomaly field estimated by LSTM method.
Key words: long short-term memory recurrent neural network; free-air gravity anomaly; Kriging method