Detection of spheriodal free oscillation excited by Peru 8.2 <Emphasis Type="Italic">M</Emphasis><Subscript>s</Subscript> earthquake with five international superconducting gravimeter data

In this paper, authors obtain the spectral peaks of the earth free oscillation and check all normal modes from ₀S₀ to ₀S₄₈ accurately, with the Fourier analysis and the maximum entropy spectrum method dealing jointly with six groups of the observational residual data from five international superconducting gravimeter stations. By comparing the observational results in this paper with three former groups of observations or models, authors notice an extra discrepancy between two observational ₀S₂ modes excited separately by Peru earthquake and Alaska earthquake, which probably mirrors the anisotropy of the Earth’s inner core. The analysis on the splitting ₁S₂ mode shows that the asymmetric factor of rotationwise spectral splitting is possible to be different from that of anti-rotationwise spectral splitting.     

印度洋9.0级大地震激发的地球球型振荡和环型振荡

综合分析了中国数字地震台网（CDSN）改造后的5个长周期地震仪台站观测的3天的VHZ、VHE和VHN波形资料,利用功率谱密度估计方法,在没有对资料进行去固体潮处理的情况下,准确获得了2004年12月26日印度洋地震激发的0S3~0S78的基频球型振荡和部分谐频球型振荡和0T3~0T67的基频环型振荡,并与地球初步参考模型（PREM）的理论自由振荡周期进行了对比,发现实测振荡周期与PREM预测的振荡周期符合的很好.频率与PREM模型略微不一致的球型或环型振荡可以解释为地球介质的横向不均匀性和各向异性所致.因此地球自由振荡信息可用于揭示地球的三维不均匀结构信息或各向异性信息,并可能对区分地幔对流模式有所帮助.     

由中国CDSN台网检测到的汶川地震所激发的地球球型自由振荡

2008年5月12日汶川发生M8.0特大地震, 这次特大地震使得地球自身产生了整体的连续振动。 本文采用地震发生之后中国数字地震台网(CDSN)所记录到的5天地震波形, 对VHZ频段进行了功率谱密度分析。 由于CDSN台网的地震仪对低频信号具有压制特点, 所以没有对资料进行固体潮处理, 从而获得了大地震激发的73个(₀S₄～₀S₇₆)基频球型自由振荡和6个谐频球型自由振荡(₁S₂, ₃S₂, ₁S₄, ₁S₀, ₁S₇, ₄S₂), 并与PREM模型的理论自由振荡周期进行了对比, 结果表明观测振荡周期与PREM预测的振荡周期吻合很好。 所得结果可以进一步用来研究地震震源机制和地球内部结构, 并对大地震的震源破裂分布给出一定的约束。     

钻孔差应变仪观测的苏门答腊大地震激发的地球环型自由振荡

我们率先用钻孔应变仪观测资料研究了地球自由振荡. 泰安地震台有差应变和体应变两种钻孔应变观测仪器，都观测到2004年12月26日苏门答腊大地震激发的地球自由振荡. 体应变仪观测到地球的球型振荡，而差应变仪观测到地球的环型振荡. 两种观测还记录到环型振荡与球型振荡相互的耦合作用. 观测也记录到明显的一些振型的谱线分裂现象. 用直接观测到的高质量的环型振荡资料求解了0T8～0T19等主要振型的Q值. 根据两个方向的剪应变观测数据，求解了环型振荡的最大剪应变方向，发现这个方向是相当稳定的. 这种研究表明，高精度钻孔应变观测仪是一种理想的地壳形变观测仪器，可以为地球自由振荡研究提供更丰富的信息.     

利用不同倾斜仪和应变仪检测地球自由振荡的对比与分析

中国地震局地壳形变观测台网布设有垂直摆倾斜仪、钻孔倾斜仪、洞体应变仪、分量式钻孔应变仪与体应变仪等地形变观测仪器。这些观测仪器均记录到了2011年日本M_W9.0大地震激发的自由振荡信号。本文分别利用单台数据和多台数据叠积,检测到_0S_3~_0S_(30)全部的球型自由振荡基频振型和_0T_3~_0T_(20)全部的环型自由振荡基频振型及部分谐频振型。此外,通过对这些检测结果的对比,分析了它们对不同自由振荡类型、不同频段的振型检测能力。分析发现垂直摆倾斜仪对球型自由振荡的检测结果最佳,且由于在低频段有较高的噪声干扰,钻孔倾斜仪无法检测到低阶的球型自由振荡。对于环型自由振荡的检测,分量式钻孔应变仪检测结果最佳。     

Constraining the focal mechanism of the Lushan earthquake with observations of the Earth’s free oscillations

The amplitudes of the Earth's free oscillations have a close relationship to earthquake focal mechanisms. Focal mechanisms of large earthquakes can be well analyzed and constrained with observations of long period free oscillations. Although the 2013 Lushan earthquake was only moderately sized, observable spherical normal modes were excited and clearly observed by a superconductive gravimeter and a broadband seismometer. We compare observed free oscillations with synthetic normal modes corresponding to four different focal mechanisms for the Lushan earthquake. The results show that source parameters can be analyzed and constrained by spherical normal modes in a 2.3–5 mHz frequency band. The scalar seismic moment M0 has a major influence on the amplitudes of free oscillations; additionally, the strike, dip, rake and depth of the hypocenter have minor influences. We found that the synthetic modes corresponding to the focal mechanism determined by the Global Centroid Moment Tensor show agreement to the observed modes, suggesting that earthquake magnitudes predicted in this way can readily reflect the total energy released by the earthquake. The scalar seismic moment obtained by far-field body wave inversion is significantly underestimated. Focal mechanism solutions can be improved by joint inversion of far- and near-field data.     

Penetration of the Earth’s free oscillations at 54 minute period into the atmosphere

It is known that the fundamental spheroidal mode ₀S₂ of the Earth free oscillation with a period of about 54 min forces atmospheric oscillations. We present a certain phase relationship for components of the ₀S₂ multiplet, which is based on synchronous collocated microbarograph and seismograph observations. This relationship is both the first observational manifestation of the Pekeris mode of global atmospheric oscillations with the 54 min period and a further proof of the Earths ₀S₂ mode penetrating into the atmosphere. We show that the linear non-dissipative model of steady forced oscillations in isothermal atmosphere at rest does not describe the penetration of the ₀S₂ mode into the atmosphere adequately.     

中国数字地震台网记录的昆仑山口西地震的球型自由振荡

利用中国数字地震台网 (CDSN)改造后的7个台站的VHZ波形资料, 采用功率谱密度估计方法, 利用中国数字地震台网地震仪对低频信号压制的特点, 在没有对资料去除固体潮影响的情况下, 提取了2001年11月14日昆仑山口西地震激发的₀S₄~₀S₇₆地球球型自由振荡, 并与地球初步参考模型(PREM)的理论自由振荡周期进行对比, 结果表明与PREM预测的球型自由振荡周期符合得很好。 该地震的地球自由振荡信息, 可用于地震震源机制研究和地球内部结构研究。     

The rotational and gravitational signature of the December 26, 2004 Sumatran earthquake

Besides generating seismic waves, which eventually dissipate, an earthquake also generates a static displacement field everywhere within the Earth. This global displacement field rearranges the Earth’s mass thereby causing the Earth’s rotation and gravitational field to change. The size of this change depends upon the magnitude, focal mechanism, and location of the earthquake. The Sumatran earthquake of December 26, 2004 is the largest earthquake to have occurred since the 1960 Chilean earthquake. Using a spherical, layered Earth model, the coseismic effect of the Sumatran earthquake upon the Earth’s length-of-day, polar motion, and low-degree harmonic coefficients of the gravitational field are computed. Using a model of the earthquake source that is composed of five subevents having a total moment-magnitude M _w of 9.3, it is found that this earthquake should have caused the length-of-day to decrease by 6.8 microseconds, the position of the Earth’s generalized figure axis to shift 2.32 milliarcseconds towards 127° E longitude, the Earth’s oblateness J ₂ to decrease by 2.37 × 10⁻¹¹ and the Earth’s pear-shapedness J ₃ to decrease by 0.63 × 10⁻¹¹. The predicted change in the length-of-day, position of the generalized figure axis, and J ₃ are probably not detectable by current measurement systems. But the predicted change in oblateness is perhaps detectable if other effects, such as those of the atmosphere, oceans, and continental water storage, can be adequately removed from the observations.     

利用常熟地震台同场地形变仪记录检测对比地球自由振荡信号

利用常熟地震台同场地观测的洞体应变仪、体应变仪、水管倾斜仪、垂直摆倾斜仪记录数据,采用小波变换与功率谱密度估计方法,检测2011年3月11日日本9.0级大地震激发的地球自由振荡信号,其中检测到47个球型基频振型（₀S₃—₀S₄₉）、15个环型基频振型（₀T₅—0T₂₅）以及部分球型谐频振型,与地球初步参考模型（PREM）理论频率值基本符合,表明检测结果较好。对比结果显示：水管倾斜仪检测球型振荡振型能力最强,垂直摆倾斜仪检测环型振荡振型能力最强;体应变仪可检测到清晰的环型基频振型,且信噪比较高;倾斜仪对自由振荡信号的检测能力优于应变仪。     

利用连续重力观测约束2014智利Iquique地震的震源机制解

2014年4月1日,智利北部Iquique地区近海发生MW8.1地震,地震发生之后,国际上一些著名的地震科研机构和学者采用不同的数据和方法计算得到此次地震的震源机制解,但这些结果存在较大差异.地球长周期自由振荡的振幅主要依赖于地震矩的大小及地震断层的破裂方式,可以很好地约束地震震源机制.因此,本文根据2014年Iquique地震现有的6个不同震源机制解模拟计算了该地震激发的自由振荡信号,并与全国连续重力台网中16个弹簧重力仪的观测结果进行比对,基于1.5~5.3mHz的球型简正模分析和约束了Iquique地震的震源机制解.研究发现,基于美国地质调查局WPhase Moment Tensor Solution反演的震源机制解的自由振荡模拟值与实际观测符合最好,其相应的震级能较好反映Iquique地震释放的总能量,而利用海啸数据反演的标量地震矩偏小,联合远场和近场长周期观测数据反演可显著改善震源机制解.另外,还基于格尔木重力台站的模拟值与观测值定量分析了不同震源机制解参数对自由振荡振幅的影响.结果表明地震的标量地震矩M0对自由振荡振幅的影响最大,而断层走向、倾角、滑动方向角和震源深度对自由振荡的振幅影响相对较小.     

利用JCZ-1T地震计LP通道数据检测斐济M W 8.2深震激发的地球自由振荡

JCZ-1T地震计LP通道数据可有效应用于地球自由振荡信号探测。利用泰安基准地震台JCZ-1T地震计LP通道120小时数据记录,获得2018年8月19日斐济M_W 8.2深源地震激发的地球自由振荡,检测到基频球型振荡₀S₆-₀S₅₈几乎所有振型、球型振荡部分零级振型和高振型以及环形振荡部分基振型和高振型,与地球初步参考模型（PREM）的理论自由振荡周期进行对比,结果表明,振荡周期观测值与PREM理论值基本一致,二者微小差值应由地球介质的横向不均匀性和各向异性所致。     

Inversion of long-period body-wave data for the source process of the Gonghe, Qinghai, China earthquake

Long period body waves data recorded by the China Digital Seismograph Network (CDSN) are inverted for the seismic moment tensors of the April 26, 1990, Gonghe, QinghaiM _S=6.9 earthquake and itsM _S=5.0 after-shock occurred on May 7, 1990. In the inversion, the generalized reflection-transmission coefficient matrix method is used to generate Green’s function. From the inversion it is obtained that the rupture process of theM _S=5.0 aftershock is relatively simple, and that of the main shock is rather complex. There are at least two events during main shock rupture process with an interval about 35 seconds. The focal mechanisms of two events are roughly the same as that of the aftershock, all of them were mainly reverse dip-slipping faulting with minor left-lateral strike-slip motion. These results indicate that the Gonghe earthquake was the result of the farther extension of one NWW-SEE striking buried fault on the southern margin of Gonghe basin from shallower depth to deeper depth and from NW to SE under the action of a nearly horizontal NE direction compressive stress. Contribution No. 95A0111, Institute of Geophysics, SSB, China.     

On some properties in the emergence and evolution of the oscillations of the Earth after earthquakes

The records from wideband seismic stations are analyzed for studying the oscillations of the Earth that emerged after the earthquakes in Sumatra on December 26, 2004 (M = 9.2), Chile on February 27, 2010 (M = 8.8), and after the Tohoku megaearthquake on March 11, 2011 (M = 9.0). Attention is focused on the band with a period of 20.46 min, which includes the free radial mode ₀S₀. It is established that the emergence of oscillations in the frequency interval corresponding to the free oscillations of the Earth is delayed by a lag, which increases with increasing period. Pulsations of the 20.46-min band, which appear in the interval from 5 to 7 days after the earthquake and have a period of 127–129 min, are revealed. The patterns of the amplitude attenuation of the 20.46-min band are different at stations located in zones with different tectonic activity. These features manifest themselves in the search through different stations and through different earthquakes.     

Re-examination of the earth's free oxcillations excited by the Kamchatka earthquake of November 4, 1952

Benioff's suggestion that the 58-min period sinusoidal oscillation found on a Pasadena strain seismogram after the Kamchatka earthquake of November 4, 1952 may represent the earth's gravest normal mode is re-examined in terms of a slow large-scale post-seismic deformation. The mechanism and the seismic moment of the main shock of the Kamchatka earthquake are determined by using the amplitude and the initial phase of G₂ and R₂ recorded at Pasadena and R₆ recorded at Palisades. By constraining the dip angle and the strike of the fault at 30° (towards NW) and N34°E, respectively, on the basis of the geometry of the Benioff zone, the slip angle is determined as 110° which represents 74% thrust and 26% right-lateral faulting. The direction of the slip angle agrees with the slip direction of the Pacific plate. A seismic moment of 3.5 · 10²⁹ dyn cm is obtained. If a fault area of 650 · 200 km² is assumed, an average dislocation of 5 m is obtained. Spectral analyses of the Pasadena strain records show that the 58-min sinusoidal oscillation in fact consists of a spectral peak near 54 min which is very close to the ₀S₂ mode and other high-frequency peaks which can be correlated to the earth's normal modes. The records from two independent recording galvanometers correlate with each other very well, indicating that the recorded oscillation represents a real strain and not instrumental noise. The phase relation between the NS and EW components is consistent with the strain field associated with ₀S₂ mode. Although these results provide positive evidence for a slow post-seismic deformation, the cause of the abrupt termination of the oscillation and the excitation mechanism remain unresolved.     

2016年12月25日智利M7.6地震球型自由振荡检测

智利M7.6的地震激发了地球自由振荡,利用中国数字台网(CDSN)的10个台站记录到7 d的VHZ波形数据,采用功率谱密度估计方法,在没有滤波的情况下,提取了2016年12月25日智利地震激发的地球球型自由振荡基频振型_0S_4～_0S₅₃和一系列的谐频振型,并与PREM模型的理论自由振荡频率峰值进行对比,发现2.5～4.5×10¹³Hz的频率值与PREM模型预测的球型自由振荡周期符合得很好,说明本次地震确实激发了全球范围内的自由振荡,而4.5～6×10¹³ Hz的频率值稍微有偏离,这是由于地壳的横向不均匀所致,可以用来研究地球内部的构造。     

Temporal vP/vS variation characteristics in different zones of China’s Capital Circle area before and after Wen’an earthquake

On July 4, 2006, an earthquake of MS5.1 took place in Wen’an, Hebei Province, just at the south center of China’s Capital Circle area digital seismograph network. It is the strongest event recorded ever since the network went into operation in 2002. We processed the vast amounts of phase data yielded by the 107 digital seismic stations between 2002~2007 using Wadati method. In order to improve the precision and stability of shear and compressional wave velocities (vP/vS) calculation, we impose a number of restrictions on the computation environment and condition, e.g., the earthquakes are densely concentrated, selected stations are limited in range, the number of stations in- volved in the computation is larger than 5 and linear fitting features high precision and small error. Under these restrictions, the study shows that vP/vS in and around Wen’an and Tangshan underwent a normal-low-normal proc- ess one year before Wen’an earthquake, vP/vS became obviously low and the low ratio lasted for about one year, meanwhile, little variation of vP/vS was seen in Xingtai, northwest of Beijing, southwest of Beijing, Beijing-Tianjin and Beijing; after the quake, the vP/vS returned normal in Wen’an and Tangshan. Error and stability analysis of the calculated result for vP/vS shows it is convincible that anomaly appeared in and around Wen’an and Tangshan be- fore Wen’an earthquake.     

地球内核平动振荡的地震激发

本文利用球对称、非自转、弹性和各向同性地球模型(SNREI)理论模拟计算了地球内核平动振荡的地震激发.以2004年12月26日苏门答腊大地震为例,讨论震源机制解(标量地震矩、走向、倾角、滑动角和深度)对内核平动振荡振幅激发的影响;基于全球21个Mw8.0级以上的大地震,分别计算10个数据资料较好的超导重力台站理论上可以接收到的内核平动振荡信号的频率域振幅.结果表明标量地震矩对内核平动振荡振幅的影响最大,走向、倾角、滑动角和深度对内核平动振荡振幅也有一定影响,但是影响相对较小;不同区域获得的由大地震引起的内核平动振荡信号的幅度存在显著差异,此结果为频率域多台站加权迭积提供了计算基础.另外,只有武汉台站接收到的2011年日本Tohoku Mw9.1地震激发的内核平动振荡的振幅值达到了地球表面高精度、高灵敏度的超导重力仪检测水平,振幅值为0.0103nm·s-2.结果说明地震激发的内核平动振荡的信号极其微弱,信号几乎淹没在背景噪声中,必须利用多台站迭积法才有可能将信号提取出来.     

Spheroidal Oscillations in the Earth Excited by the Wenchuan Earthquake

Based on the digital observational data from pendulum tilt-meters and water tube tilt-meters, the spheroidal free oscillations of the Earth, excited by the M_S8.0 Wenchuan earthquake of May 12, 2008, were obtained using the method of power spectral density estimation without any calculation to erase solid tides. The result matches well with the PREM results. Compared to the theoretical free oscillation from the PREM model, all relative errors are concentrated on 0.1% except for _0S_7, whose relative error is greater than 0.3%. This research provides a new method to determine the spheroidal modes of Earth's free oscillations from observations of the pendulum tilt-meter and water tube tilt-meter, which may be useful in the future study of the Earth's free oscillations.     

From 3-Hz P Waves to 0 S 2: No Evidence of A Slow Component to the Source of the 2011 Tohoku Earthquake

In the hours following the 2011 Honshu event, and as part of tsunami warning procedures at the Laboratoire de Géophysique in Papeete, Tahiti, the seismic source of the event was analyzed using a number of real-time procedures. The ultra-long period mantle magnitude algorithm suggests a static moment of 4.1 × 10²⁹ dyn cm, not significantly different from the National Earthquake Information Center (NEIC) value obtained by W-phase inversion. The slowness parameter, $\Uptheta = -5.65, $ is slightly deficient, but characteristic of other large subduction events such as Nias (2005) or Peru (2001); it remains significantly larger than for slow earthquakes such as Sumatra (2004) or Mentawai (2010). Similarly, the duration of high-frequency (2–4 Hz) P waves in relation to seismic moment or estimated energy, fails to document any slowness in the seismic source. These results were confirmed in the ensuing weeks by the analysis of the lowest-frequency spheroidal modes of the Earth. A dataset of 117 fits for eight modes (including the gravest one, ₀ S ₂, and the breathing mode, ₀ S ₀) yields a remarkably flat spectrum, with an average moment of 3.5 × 10²⁹ dyn cm (*/1.07). This behavior of the Tohoku earthquake explains the generally successful real-time modeling of its teleseismic tsunami, based on available seismic source scaling laws. On the other hand, it confirms the dichotomy, among mega-quakes (M ₀ > 10²⁹ dyn cm) between regular events (Nias, 2005; Chile, 2010; Sendai, 2011) and slow ones (Chile, 1960; Alaska, 1964; Sumatra, 2004; and probably Rat Island, 1965), whose origin remains unexplained.