Revisiting the Phasor-Walkout method for detailed investigation of harmonic signals in time series

A well-known but rarely used powerful method to investigate the presence of harmonic signals in time series is the Phasor Walkout method (other names are: Graphical Fourier Transform, Summation Dial, Complex Demodulation). At a given test frequency the complex contributions (phasors) to the Fourier Transform of each sample in an equidistantly sampled series are added vectorially in the complex plane. The resulting pattern, the walkout, reveals information about the properties of the signal which is not easy to obtain by other methods. Synthetic examples are used to demonstrate the resolving power of the method. The following geophysical examples for the application of this method are shown: determination of the frequency of the breathing mode₀ S ₀ of the earth after a large earthquake; the study of superconducting gravimeter records after a large deep earthquake used in the core mode interpretation of a spectral peak, the study of the residualS ₃ (8 h period) signal in a tidal record and the bichromatic Rayleigh-waves from Mount Pinatubo on June 15, 1991.     

IDA和CDSN资料的长周期面波研究

１９８０年和１９９２年分别在昆明和北京白家疃台架设了ＩＤＡ观测仪器，１９８５年开始又陆续在北京，兰州，海拉尔等地布设和完善了ＣＤＳＮ数字化地震观测台网，为开展长周期面波研究提供了方便。本文结合国内外研究现状，论述了超长周期地震观测在地球自由振荡，震源物理面波理论地震图合成及非均匀地球介质结构研究中的应用。同时结合１９８９年５月６日发生在秘鲁的Ｍｓ７．０地震，介绍了利用简正振型资料开发地震矩张量反演     

Co-seismic Coulomb stress changes on the northern Tanlu fault zone caused by the Tohoku-Oki MW9.0 earthquake*

Based on the spherical earth dislocation theory and a fault slip model of the Tohoku-Oki M_W9.0 earthquake, the co-seismic Coulomb failure stress changes (ΔCFS) on the northern Tanlu fault zone at depths of 0–40 km are calculated. By comparing two sets of results from the spherical earth dislocation theory and the semi-infinite space one, the effect of earth curvature on the calculation results is analyzed quantitatively. First, we systematically summarize previous researches related to the northern Tanlu fault zone, divide the fault zone as detailed as possible, give the geometric parameters of each segment, and establish a segmented structural model of the northern Tanlu fault zone. Second, we calculate the Coulomb stress changes on the northern Tanlu fault zone by using the spherical earth dislocation theory. The result shows the Coulomb stress changes are no more than 0.003 MPa, which proves the great earthquake did not significantly change the stress state of the fault zone. Finally, we quantitatively analyze the disparities between the results of semi-infinite space dislocation theory and the spherical earth one. The average disparity between them is about 7.7% on the northern Tanlu fault zone and is 16.8% on the Fangzheng graben, the maximum disparity on this graben reaches up to 25.5%. It indicates that the effect of earth curvature can not be ignored. So it’s necessary to use the spherical earth dislocation theory instead of the semi-infinite space one to study the Coulomb stress change in the far field.     

Predicting strong motion parameters for the Chamoli earthquake of 28th March, 1999, Garhwal Himalaya, India, from simplified finite fault model

State of Uttaranchal in the northern part of India in the Garhwal Himalaya was hit by the Chamoli earthquake on 28th March, 1999 (GMT). This earthquake was recorded on a strong motion array installed in this region. The maximum peak ground acceleration of 353 cm/sec² was recorded at an accelerograph located at the Gopeshwar station at an approximate epicentral distance of 14 km. The simplified method of Midorikawa (1993) has been used to model finite fault responsible for causing the Chamoli earthquake. This method is based on the Empirical Green's Function (EGF) technique of Irikura (1986).Modifications in this method have been made to include layered earth model and transmission effects at each boundary by Joshi (2001). Rupture causing the Chamoli earthquake is placed in two structural models of the earth in this work: one is a homogeneous half space and other is the multi layered earth model. Comparison in terms of root mean square error (RMSE) is made between the simulated and actual strong motion parameters like peak acceleration and duration. It is seen that the introduction of multi layered earth system in this simplified technique is capable of significantly reducing the RMSE in observed and predicted strong motion parameters and defining the attenuation rate for peak ground acceleration of this earthquake.     

On the Ultra Long Propagation of Felt Ground Motion Due to the <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> 8.3 Deep-Focus Sea-of-Okhotsk Earthquake of May 24, 2013

This study uses macroseismic data and wave equations to solve the problem of ultra long propagation of felt ground motion (over 9000 km from the epicenter) due to the Sea-of-Okhotsk earthquake. We show that the principal mechanism of this phenomenon could be excitation of a previously unknown standing radial wave as a mode of the Earth’s free oscillations, ₀S₀, due to the superposition of an incident and a reflected spherical P wave in the epicentral area of the Sea-of-Okhotsk earthquake. The standing wave generates slowly attenuating P waves that travel over the earth’s surface that act as carrying waves; when superposed on these, direct body waves acquire the ability to travel over great distances. We show previously unknown parameters of the radial mode ₀S₀ for the initial phase of earth deformation due to the large deep-focus earthquake. We used data on the Sea-of-Okhotsk and Bolivian earthquakes to show that large deep-focus earthquakes can excite free oscillations of the Earth that are not only recorded by instrumental means, but are also felt by people, with the amplification of the macroseismic effect being directly related to the phenomenon of resonance for multistory buildings.     

Changes in earthquake energy class as a factor affecting the parameters of the recurrence relation: The Baikal region

The numerical modeling of actually observed events contained in the Baikal earthquake catalog allowed the production of synthetic catalogs. These catalogs reflect real situations that can give rise to heterogeneities in earthquake catalogs acquired by seismological monitoring. For each of the resulting 65 catalogs we calculated the slope γ and seismic activity (so-called in Russian; it is the seismicity rate or the constant term in the frequency-size relation) A ₁₀ in the recurrence relation. We also investigated the effects of changes in estimates of earthquake energy class on the parameters of the recurrence relation. It was shown that the slope γ is not very sensitive, but that the seismic activity A ₁₀ is sensitive, to changes in earthquake energy class and can be used to test an earthquake catalog for heterogeneity. Formulas were derived to relate the parameters of recurrence relations and the scaling factors of two energy scales, which can yield recurrence parameters for one of the scales, provided we know the ratio of the respective scaling factors and the recurrence parameters based on the other scale.     

Application of rock creep experiment in calculating the viscoelastic parameters of earth medium

The viscosity of earth medium can explain many geophysical phenomena. The uplifting velocity of Ti- betan Plateau may be caused by extrusion of the low viscosity channel in middle and lower crust[1]. The post-deformation after earthquake also relates to the rheology of earth medium[2]. The aftershock sequence is considered a process of strain release after stress dropped[3]. There are two kinds of models in the study of rheological character of crustal medium, elastoplas- only when the forced…     

An analysis of anomalous weather and climate around the M S=6.2 earthquake of Zhangbei region

Through analysis we found that some mesoscale anomalous regions (10¹–10² km) of meteorological parameters such as the special drought areas, unusual warm areas, the largest snowfall center, low pressure area together with the epicenter area of M _S=6.2 Zhangbei earthquake on January 10, 1998 are located at the same area, i.e. there appears the “Five areas corresponding” phenomenon. Meanwhile, three times of low pressure evolution are generated and develop in the earthquake area in five days after the occurrence of the earthquake. The abnormal variation of the lower limit of frozen soil layer shows indirectly that unusual warm in earthquake areas are related to the upward thermal conduction from the deeper layer of earth surface.     

甘肃张掖MS5.0地震前山丹地电异常探讨

2019年9月16日在甘肃省张掖市甘州区发生M_S5.0地震,震前山丹地电阻率和地电场观测资料出现了较为明显的短临异常,震中距63 km。本文对该异常进行分析总结,排除周围观测环境,观测系统,自然环境,磁暴等因素外,认为该异常是较为可信的地震前兆异常。地电阻率观测资料异常形态NS测道表现为转折快速上升-缓慢下降,EW测道为转折缓慢上升,N45°W测道为缓慢下降-转折缓慢上升。地电场观测资料异常形态长极距NS道、长极距N45°E道、短极距NS道表现为转折同步缓慢上升,长极距EW道和短极距EW道转折同步缓慢下降,短极距N45°E道异常不明显。地震在异常持续过程中出现转折变化或上升(下降)速率发生改变时发生。     

Analysis of Paleoseismic Events of Dahuzhuang Trench at the Xiadian Fault

The Xiadian Fault is a very important concealed active fault in the Beijing Plain. It is the seismogenic fault of the Sanhe-Pinggu M_S8.0 earthquake in 1679. The ancient earthquake sequence in the long historical period is of great significance to understand accurately the activity characteristics of the fault and effectively reduce the earthquake disaster risk in Beijing. We have re-interpreted the Dahuzhuang trench, and identified three layers of buried paleosol, six collapsed wedges and one sand liquefaction event. Further, through the comparison with the landmark strata and paleo-earthquake events revealed by other trenches on the fault, an ancient earthquake sequence with a long historical period of the Xiadian Fault was established:since the 31ka, the Xiadian Fault has 11 occurrences of earthquake events (including the 1679 earthquake), and the average recurrence interval is about 2.8ka. The paleo-seismic sequence also shows that there is an ancient earthquake cluster period from 25ka to 15ka, and there are 5 strong earthquakes in the cluster period. The average recurrence interval is about 2.0ka, which reflects the phase difference of the Xiadian Fault activity.     

三种变换在强震记录分析方面的研究

在简要地介绍比较了傅立叶变换、小波变换、希尔伯特-黄变换理论的基础上,针对集集地震大量强震记录进行各种变换分析比较,以探求希尔伯特-黄变换在强震记录分析中应用的前景.通过对集集地震60条不同震中距和场地的强震纪录,分别作傅立叶频谱、希尔伯特-黄边际谱和能量密度谱分析,列表归纳对比显示希尔伯特-黄变换在强震记录处理中基本表现出和其他变换相同的趋势,并有其新特点,能体现出强地震动的瞬时特性,是对现有强震数据处理方法重要的补充.     

PI Forecast for the Sichuan-Yunnan Region: Retrospective Test after the May 12, 2008, Wenchuan Earthquake

The May 12, 2008, Wenchuan M _S 8.0/M _w 7.9 earthquake occurred in the middle part of the north–south seismic zone in central west China, being one of the greatest thrust events on land in recent years. To explore whether there were some indications of the increase of strong earthquake probabilities before the Wenchuan earthquake, we conducted a retrospective forecast test applying the Pattern Informatics (PI) algorithm to the earthquakes in the Sichuan-Yunnan region since 1992. A regional earthquake catalogue complete to M _L 3.0 from 01/01/1977 to 15/06/2008 was used. A 15-year long ‘sliding time window’ was used in the PI calculation, with ‘anomaly training time window’ and ‘forecast time window’ both set to 5 years. With a forecast target magnitude of M _S 5.5, the ROC test shows that the PI forecast outperforms not only random guess but also the simple number-counting approach based on the clustering hypothesis of earthquakes (the RI forecast). ‘Hotspots’ can be seen in the region of the northern Longmenshan fault which is responsible for the Wenchuan earthquake. However, when considering bigger grid size and higher cutoff magnitude, such ‘hotspots’ disappear and there is very little indication of an impending great earthquake.     

丽江7.0级地震过程的重力变化与小波分析

利用小波分析方法对云南西部地区的多期重力观测资料进行了计算,并将 计算前后的重力结果进行了对比分析,同时讨论了不同阶的小波分解结果的物理意 义及其与地震之间的对应关系．由对应于地壳浅层物质状态变化的一阶小波分解所 得结果显示,在地震前的１９９２～１９９３、１９９３～１９９４、１９９４～１９９５年等多期重力变化中 震源附近都有一定的异常,特别是１９９５～１９９６年的同震变化更加明显。而反映地球 深层物质状态变化的重力二、三阶小波的分解结果虽然对地震过程有一定的响应,但 不是特别明显,这与丽江７．０级地震发生在浅层（深约１０ ｋｍ）是一致的。     

Probabilistic assessment of earthquake recurrence in the January 26, 2001 earthquake region of Gujrat, India

Kutch region of Gujrat is one of the most seismic prone regions of India. Recently, it has been rocked by a large earthquake (M _w = 7.7) on January 26, 2001. The probabilities of occurrence of large earthquake (M≥6.0 and M≥5.0) in a specified interval of time for different elapsed times have been estimated on the basis of observed time-intervals between the large earthquakes (M≥6.0 and M≥5.0) using three probabilistic models, namely, Weibull, Gamma and Lognormal. The earthquakes of magnitude ≥5.0 covering about 180 years have been used for this analysis. However, the method of maximum likelihood estimation (MLE) has been applied for computation of earthquake hazard parameters. The mean interval of occurrence of earthquakes and standard deviation are estimated as 20.18 and 8.40 years for M≥5.0 and 36.32 and 12.49 years, for M≥6.0, respectively, for this region. For the earthquakes M≥5.0, the estimated cumulative probability reaches 0.8 after about 27 years for Lognormal and Gamma models and about 28 years for Weibull model while it reaches 0.9 after about 32 years for all the models. However, for the earthquakes M≥6.0, the estimated cumulative probability reaches 0.8 after about 47 years for all the models while it reaches 0.9 after about 53, 54 and 55 years for Weibull, Gamma and Lognormal model, respectively. The conditional probability also reaches about 0.8 to 0.9 for the time period of 28 to 40 years and 50 to 60 years for M≥5.0 and M≥6.0, respectively, for all the models. The probability of occurrence of an earthquake is very high between 28 to 42 years for the magnitudes ≥5.0 and between 47 to 55 years for the magnitudes ≥6.0, respectively, past from the last earthquake (2001).     

宁波台矿泉井水温异常与萨尔瓦多8.0级地震的关系

2001年1月9日起开始宁波台矿泉井井水温度出现异常，通过检查、分析后认为很可能与萨尔瓦多8.0级地震有关系。从日均值图上看，异常在震前6天开始出现，至震前1天达到最大，表现为打破正常的波动规律，呈负异常；从整点测值图看，主要是震前36小时出现负阶跃。分析认为出现的水温异常可能是一种地震前的长周期波通过上地幔或软流层传播而至，间接地影响地下流体发生微小的温度变化。     

基于Sentinel-1A数据反演漾濞MS6.4地震的同震形变场及断层几何参数

2021年5月21日晚21时48分,云南省大理州漾濞县(震中:25.67°N,99.87°E)发生M_S6.4地震,震源深度8 km。为快速获得此次地震同震形变场及断层几何参数,研究该次地震的发震构造等,文章基于震前、震后的sentinel-1A卫星升降轨SAR数据进行二轨法差分雷达干涉测量(DInSAR),并基于Okada弹性半空间位错模型反演断层几何参数。研究结果如下:(1)此次地震造成的同震形变场长约19 km,宽约20 km;(2)升轨雷达视线向最大形变约为8.2 cm,降轨雷达视线向最大形变约为8.7 cm;(3)地震断层走向为313.7°,倾角为87°,滑动角为175°,为右旋走滑型断层,最大滑动量为0.79 m,反演得出的地震矩为1.48×10~(18) N·m,矩震级为M_W6.1。在川滇块体向南挤出的构造背景下,块体西边界的维西—乔后断裂、红河断裂发生右旋走滑,本次地震便是维西—乔后断裂南段分支断裂右旋走滑活动的体现。     

深井宽频钻孔应变地震仪与高频地震学——地震预测观测技术的发展方向,实现地震预报的希望

40年地震预报实践表明，测震学方法提供了当前地震预报工作最大部分的地震预测信息.发展“深井宽频钻孔应变地震仪”可将惯性摆地震仪的观测频宽提高数十倍，地动位移的放大倍率提高数十到数千倍.这种安装在数百米深基岩地层中与地层牢固连结的仪器既可以接收周期长达数万秒的固体潮波，也能以数亿倍的地动位移放大倍率接收地层微破裂发出的高频极微震和“地声”.深井宽频钻孔应变地震仪这种“超级地震仪”将为地震预报工作提供更多的预报信息而大步推进地震预测工作向前发展.     

2004年印尼苏门答腊MW9.0地震前地震活动增强现象及其与地球自转的关系

选取2004年12月26日印尼苏门答腊M_W9.0地震的余震分布空间范围为研究区域,该区域位于缅甸小板块中部,纬度范围为2°N~15°N.根据USGS地震目录,研究了2004年印尼苏门答腊M_W9.0地震前地震频次的时空变化,并分析了地震活动与地球自转的关系.结果显示:1)在余震区域范围内,地震频次自2000年开始出现了明显的上升趋势变化,反映了地震活动的增强过程,临近地震发生前,地震频次有一定幅度的回落;2)通过地震频次空间扫描,发现震前在震中附近区域地震活动增强显著;3)在1990~2004年的15年中,单位时间内发生的地震数在地球自转季节性变化减速时段与加速时段之比值r_da在震前出现明显的上升过程:1998年~2002年r_da缓慢上升,2002年底r_da快速上升达最高值,之后,r_da呈现下降趋势,直至苏门答腊M_W9.0地震发生;4)2000年1月~2004年11月间,在纬度1°N~7°N的空间范围内的震中附近地区, 5.5级以上地震都发生在地球自转季节性变化减速时段内;5)地震活动累积年频次相对于其长期平均值的变化量ΔN与地球自转"十年起伏"变化关系表现为地球自转减速时ΔN上升,地震活动增强,加速时ΔN下降,地震活动减弱.这些现象并非偶然,可能预示着地球自转减速与苏门答腊M_W9.0地震之间存在着某种联系,这些结果对地震孕育过程的认识和地震预测研究具有一定的价值.     

Elimination of effects of earthquake in monitoring crustal movement

Monitoring crustal movements is important in understanding the earth surface and in developing theories about plate tectonics. Plate tectonics describes earth crust which consists of a number of plates moving relative to one another. Global plate models suggest that plate movements are constant due to the fact that relative movements of plates were represented by averaged plate motion. However, if an earthquake occurs, the uniform movement of related plates does not follow the regular trend. In analysis by Kalman Filter, the effects of an earthquake occured within crustal movement monitoring period by geodetic method have been eliminated by a proposed approach, Fading Memory Filter. The proposed method was tested using a real/simulated data. The results of the test showed that the effect of a strong earthquake (M_w = 7.1) which had occurred in the Gulf of Eilat/Aqaba was eliminated. Consequently, the proposed method is capable of removing or eliminating a suddan effect in monitoring crustal movements in the analysis by using the Kalman Filter.