﻿ 基于量子漫步算法的地震震前异常挖掘
 计算机系统应用  2018, Vol. 27 Issue (10): 154-160 PDF

1. 福建师范大学 数学与信息学院, 福州 350117;
2. 福建农林大学 计算机与信息学院, 福州 350002

Anomaly Mining before Earthquake Based on Quantum Walk Algorithm
KONG Xiang-Zeng1, JIANG Xiao-Ying1, GUO Gong-De1, LI Nan2, LIN Ling1
1. College of Mathematics and Informatics, Fujian Normal University, Fuzhou 350117, China;
2. College of Computer and Information Science, Fujian Agriculture and Forestry University, Fuzhou 350002, China
Foundation item: Younth Project of National Natural Science Foundation of China (41601477); Guide Project of Fujian Provice (2015Y0054); Natural Science Foundation of Fujian Provice (2016J01280)
Abstract: There are some anomalies before the earthquake, especially the large earthquake. However, such abnormal information is too difficult to identify. Therefore, we cannot make full use of the abnormal information to predict the occurrence time of the earthquake in order to reduce the impact of the earthquake. To solve this problem, an anomaly mining method before earthquake based on the quantum walk algorithm is proposed to extract seismic Outgoing Long-wave Radiation (OLR) anomalies before the Wenchuan earthquake and the Lushan earthquake. Then, calculate the P value, anomaly value CD before and after the earthquake. Through statistical analysis method, the relationship between OLR anomalies and earthquake is explored. What is more, the algorithm is extended to the 8.0 magnitude and above earthquakes in the nearly last ten years. Through experiments, the effectiveness of the algorithm is verified. The experimental results show that the algorithm can effectively reflect the anomalies before and after the earthquake, and the larger the earthquake is, the more obvious anomaly is. Therefore, this algorithm is suitable for pre-earthquake anomaly excavation.
Key words: earthquake     quantum walk algorithm     OLR anomalies     anomaly mining

1 相关数据

2 研究方法

 $U = {U_S} \cdot ({I_P} \otimes {U_C})$ (1)

 图 1 离散量子漫步游走规则示意图

 $|{\psi _t}\rangle = {(U)^t}|{\psi _0}\rangle$ (2)

 $CD_n^{(\varepsilon )} = \frac{{\sum\limits_{k = 1}^{100} {\prod\limits_{i = 1}^n {(\varepsilon \hat p_{i,k}^{\varepsilon - 1})} } }}{{100}}$ (3)

 ${s_i} = s(Z,{z_i}) = \left\| {{z_i} - m} \right\|$ (4)

 ${\hat p_{i,k}}(Z \cup \{ {z_n}\} ,{\theta _n}) = \frac{{\# \{ j\left| {{s_j} > {s_i}} \right.\} + {\theta _{i,k}}\# \{ j\left| {{s_j} = {s_i}} \right.\} }}{i}$ (5)

 $C{D_n} \geqslant h$ (6)

3 结果与分析

(1)汶川地震和芦山地震对应的原始射出长波辐射OLR数据分别如图3(a)图4(a)所示. 量子漫步算法中, 窗口大小 $ws$ 取值为30–45的每个数, 然后求均值,以降低随机因素对结果造成的影响. 实验时, 根据文献[5], 将阈值 ${{h}}$ 设置为1000. 研究的数据时间周期为一年, 即从发生地震上一年的9月1日到第二年的9月1日. 黑色竖线表示地震发生时间.

 图 2 基于量子漫步算法的异常挖掘流程图

(2)为了进一步说明本文所提出的基于量子漫步算法的异常挖掘算法的可靠性和有效性, 现在扩展该算法的适用范围, 将该算法运用于分析2005年6月到2014年9月全球发生的16个8.0级及以上地震的异常数据. 受文章篇幅限制, 本文只展示其中部分地震的实验结果, 实验结果如图5~图10所示.

(3)为了说明P值和CD值在震前出现异常和地震发生之间的因果关系, 本文针对汶川和芦山地震分别设计了对比实验.

 图 3 汶川地震原始OLR数据、P值和异常值CD (2008-05-12)

 图 4 芦山地震原始OLR数据、P值和异常值CD (2013-04-20)

 图 5 秘鲁中部海岸附近地震异常值CD值(2007-08-15)

 图 6 印尼苏门答腊南部海中地震异常值CD值 (2007-09-12)

 图 7 智利比奥比奥省地震异常值CD值 (2010-02-27)

 图 8 日本本州东海岸附近海域地震异常值CD值 (2011-03-11)

 图 9 苏门答腊北部附近海域地震异常值CD值 (2012-04-11)

 图 10 智利北部沿海岸近海地震异常值CD值 (2014-04-02)

(4)为了说明本文提出的算法的优越性, 本文通过实验, 比较本文提出的基于量子漫步算法的异常挖掘算法与经典随机漫步算法提取地震异常特征的方法. 结果如下图所示. 其中, 实线曲线(图中左曲线)为100步量子漫步概率分布, 虚线曲线(图中右曲线)为随机漫步概率分布.

 图 11 量子漫步与经典随机漫步概率模型对比

4 结束语

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