Observation of free oscillations after the 2010 Chile and 2011 Japan earthquakes by superconducting gravimeter in Kutch,Gujarat,India

In this paper,we present observations of free oscillations of the Earth after major earthquakes in Chile(February 27,2010,Mw8.8)and Japan(March 11,2011,Mw9.1)using data from the dual-sphere superconducting gravimeter(SG-055),installed at Badargadh(23°0.47 N,70°0.62 E),Kutch,Gujarat,India in March 2009.To see the noise characteristics,we calculated the power spectral density of the gravity time series of 5 quiet days in the frequency band 0.05-20 mHz using the new low noise model(NLNM)as a reference.We compared the noise level of the Badargadh site to other SG sites around the world.This shows that the Badargadh SG is in a low noise state.We find that the noise increases at frequencies below 1 mHz.Such a characteristic is also observed in Djougou(Afrique,Benin)and Strasbourg(France).Using theoretical tides for Gujarat,we estimated a scale factor of about-814 nm/s~2/V for Gravl(lowersphere)and about-775 nm/s~2/V for Grav2(upper-sphere).We corrected the influence of atmospheric pressure from the one-second gravity data before switching to the frequency domain.We extracted a total of 53 Earth’s Free Oscillations(EFO)modes during the earthquake in Japan and about 47 EFO modes during the earthquake in Chile.We are able to extract the lowest0S2spheroidal mode(0.30945 mHz or54 min)and0S0radial mode(0.81439 mHz or 20 min).The longer time series shows individual0S2singlets and0S3(0.46855 mHz)singlets due to the Coriolis splitting effect.We cross-referenced the frequencies of these modes using the PREM model and previous global observations.The correlation coefficient between the observed and the PREM model for these two events are 0.999 for Japan earthquake and 0.993 for Chile earthquake.This validates the quality of the data useful for low-frequency studies in seismology.We also calculated the relative deviations of our observed fundamental modes with previously determined observed and theoretical values.We found that the relative deviations of our observed free oscillations do not exceed 0.5%,indicating good correlations.

Detection and interpretation of the Earth's free oscillations excited by the great Sumatra-Andaman earthquake with GGP station data

The mode serials of the Earth’s free oscillation provide some important information on the Earth’s deep structure and superconducting gravimeters （SG） can investigate the phenomena of the Earth’s free oscillations with high accuracy. The great Sumatra-Andaman earthquake fully excited the Earth’s free oscillations and these signals were perfectly recorded by five superconducting gravimeters in the globe. After the pre-treatment and spectral analysis on the SG observation data, we obtained the experimented mode serials of the Earth’s free oscillations consisting of 147 modes with GGP station data. These observed modes were themselves some new important data for the study of the Earth’s deep structure. On the basis of the discussions on some checked inner-core-sensitive modes, we distinguished three layers from the inner core, and the boundary of the upper layer was compatible with the formerly known transition zone in the inner core based on seismic body waves and supported that there were the hemispherical variation and very lower shear velocity zone in the lower inner core.

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 su- perconductive 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 M~ has a major influence on the amplitudes of free oscillations; additionally, the strike, dip, rake and depth of the hypocenter have mi- nor 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 inver- sion is significantly underestimated. Focal mechanism solutions can be improved by joint inversion of far- and near-field data.

Earth's Free Toroidal Oscillations Observed by the JCZ-1 Seismometer

We firstly detected the Earth's free toroidal oscillations excited by three large earthquakes in Japan,2011,Chile,2010 and Indonesia,2005 from the observed data of the JCZ-1 seismometer at Wuhan Seismic Station. The eigenperiods of basic modes (0T2 - 0T67 ) and first modes (1T2 ～ 1T50 ) were detected,and their error ratios were less than 0. 5% by comparing the observed eigenvalues with the theoretical eigenvalues in PREM. We supplemented some modes- 0T11,0T15 , 0T19 , 1T4 , 1T5 and 1T14 ,which were not mentioned in PREM,and also observed the spectral line multi-peak phenomenon from 0T2, 0T6 , 0T7 and 0T8 . These results show that the JCZ-1 seismometer is able to precisely observe the Earth's long period toroidal free oscillations.

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.

Detection of Earth's free oscillation excited by the Japan Mw9.0 Earthquake using different tiltmeter and strainmeter

The observatory network of the Crustal Deformation China Seismological Bureau was equipped with vertical pendulum tiltmeter,borehole tiltmeter,tunnel extension meters,multi-component borehole strainmeter,body strainmeter and other tilt and strain observation instruments.All of these instruments have recorded the Earth’s free oscillation excited by the Japan Mw9.0 Earthquake.By analyzing those observations,all of the spheroidal oscillation modes(0S3-0S30)and toroidal oscillation modes(0T3-0T20)excited by the Japan Mw9.0 Earthquake were detected in this paper.In addition,comparing the different observation results which obtained by those instruments,we revealed their capacity to observe different kinds of oscillation and different frequency band modes,and analyzed report the reason.We found that the body strainmeter and the vertical pendulum tiltmeter have better observing results for spheroidal oscillation.Because of high noise in low frequency band,the borehole tiltmeter cannot observe the low-order spheroidal oscillation.In terms of observing the toroidal oscillation,the multi-component borehole strainmeter got a best result.The vertical pendulum tiltmeter observes a few toroidal oscillation modes,and the tunnel extension meters can only observe some low-order modes.

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori(MAP)algorithm for channel estimation and data detection in the presence of Phase Noise(PHN)in iterative Orthogonal Frequency Division Multiplexing(OFDM)receivers used for high speed and high spectral efficient wireless communication systems.The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm.The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution.The frequency-domain estimation of Channel Transfer Function(CTF)in frequency selective fading makes the method simpler,compared with the estimation of Channel Impulse Response(CIR)in the time domain.Two different time-varying PHN models,produced by Free Running Oscillator(FRO)and Phase-Locked Loop(PLL)oscillator,are presented and compared for performance difference with proposed OFDM receiver.Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound(CRLB),and the simulation results for joint MAP data detection are compared with“NO PHN"performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.

Detecting the Earthquake Excited Spheroidal Free Oscillation of the Earth by Use of Observational Data at Huzhou Seismic Station

By using the digital observations of the pendulum tiltmeter, water tube tiltmeter,extensometer and volumetric strainmeter at Huzhou station and with the power spectrum density estimation method,we acquired the_0S_5-_0S_50 fundamental sphere free oscillations caused by the Japan earthquake on March 11,2011,then compared it with the PREM model. The relative errors are mostly bigger than 1.2‰. The extensometer and volume strainmeter can clearly detect _0S_2,_0S_3and_0S_4,which are closely related to the deep structure and earth's interior.

Zero-Magnetic-Field Oscillation of Spin Transfer Nano-Oscillator with a Second-Order-Perpendicular-Anisotropy Free Layer

The zero-magnetic-field oscillation behavior of spin torque nano-oscillator （STNO） with a perpendicularly mag- netized free layer with second-order uniaxial anisotropy is studied theoretically based on the Landau-Lifshitz- Cilbert-Slonczewski equation. It is demonstrated numerically that the second-order uniaxial anisotropy plays a significant role in the occurrence of a zero-magnetic-field steady-state precession, which can be understood in terms of the energy balance between the energy accumulation due to the spin torque and the energy dissipation due to the Gilbert damping. In particular, a relatively large zero-magnetic-field-oscillation current region, in which the corresponding microwave frequency is increased while the threshold current still maintains an almost constant value, can be obtained by modulating the second-order uniaxial anisotropy of the free layer. These results suggest a tunable zero-magnetic-field STNO, and it may be a promising configuration for STNO＇s applications in future wireless communications.

The MING proposal at SHINE:megahertz cavity enhanced X‑ray generation

The cavity-based X-ray free-electron laser(XFEL)has promise in producing fully coherent pulses with a bandwidth of a few meV and very stable intensity,whereas the currently existing self-amplified spontaneous emission(SASE)XFEL is capable of generating ultra-short pulses with chaotic spectra.In general,a cavity-based XFEL can provide a spectral brightness three orders of magnitude higher than that of the SASE mode,thereby opening a new door for cutting-edge scientific research.With the development of superconducting MHz repetition-rate XFEL facilities such as FLASH,European-XFEL,LCLS-II,and SHINE,practical cavity-based XFEL operations are becoming increasingly achievable.In this study,megahertz cavity enhanced X-ray generation(MING)is proposed based on China’s first hard XFEL facility-SHINE,which we refer to as MING@SHINE.

Investigation on the Natural Modes of A Semi-Closed Floating Tank

Vessels with semi-closed tanks(i.e.,well docks)are widely applied in the military operation and maritime engineer-ing.The water is bound by the semi-closed floating tank and forced by both the incident waves and ship’s motions.The free surface oscillations inside the flooded well dock is thus distinctive and very complicated.So far,the natural modes of semi-closed floating tanks have not yet been studied.This paper investigates the characteristics of natural modes of a floating semi-closed tank by combining a mode-resolving model based on mild-slope equations and a hydrodynamic model based on computational fluid dynamics.Results show that the first three natural periods(i.e.,74,23.6,and 14 s)of the tank fall into the band of swell and infragravity waves and they could be triggered under certain circumstance.Multi-period free surface oscillations are observed inside the tank,including the longest natural period(i.e.,74 s),though the incident waves are monochromatic.A possible generation mechanism for the long-period mode is explained on the basis of liquid sloshing and harbor oscillations.Moreover,a long-period component with a period close to the natural mode of well dock is observed in the ship motions,which is generated by the interaction between the waves and ship.

Evaluation of the seismic moment of the April 20,2013 Lushan earthquake

The April 20, 2013 Lushan earthquake which occurred in Sichuan, China had only moderate thrust. However, the computed seismic moments （M0） for the Lushan earthquake calculated by several institutions differ significantly from 0.4 × 1019 to 1.69 ×019 Nm, up to four times difference. We evaluate ten computed Mos by using normal mode observations from superconducting gravimeters in China's Mainland. We compute synthetic normal modes on the basis of moment tensor solutions and fit them to the observed normal modes. Comparison of our results indicates that Mo is the main cause for some large differences between observations and synthetics. We sug- gest that a moment magnitude of Mw6.6, corresponding to a Mo of 0.97-1.08 × 1019 Nm, characterizes the size and strength of the seismic source of the Lushan earthquake.

Process Analysis of In-situ Strain during the M_s8.0 Wenchuan Earthquake—Data from the Stress Monitoring Station at Shandan

There were huge life and property losses during the Ms8.0 Wenchuan earthquake on May 12, 2008. Strain fluctuation curves were completely recorded at stress observatory stations in the Qinghai-Tibet plateau and its surroundings in the process of the earthquake. This paper introduces the geological background of the Wenchuan earthquake and the profile of in-situ stress monitoring stations. In particular, data of 174 earthquakes （Ms4.0-Ms8.5） were processed and analyzed with various methods, which were recorded at the Shandan station from August 2007 to December 2008. The results were compared with other seismic data, and further analyses were done for the recoded strain seismic waves, co-seismic strain stepovers, pre-earthquake strain valleys, Earth＇s free oscillations before and after the earthquake and their physical implications. During the Wenchuan earthquake, the strainmeter recorded a huge extensional strain of 70 seconds, which shows that the Wenchuan earthquake is a rupture process predominated by thrusting. Significant precursory strain anomalies were detected 48 hours, 30 hours, 8 hours and 37 minutes before the earthquake. The anomalies are very high and their forms are very similar to that of the main shock. Similar anomalies can also be found in strain curves of other shocks greater than Ms7.0, indicating that such anomalies are prevalent before a great earthquake. In this paper, it is shown that medium aftershocks （Ms5.5- 6.0） can also cause Earth＇s free oscillations. Study of free oscillations is of great significance to understand the internal structure of the Earth and focal mechanisms of earthquakes and to recognize slow shocks, thus providing a scientific basis for the prevention and treatment of geological disasters and the prediction of future earthquakes.

Validity and reliability of three methods of stiffness assessment

Background：Stiffness is commonly assessed in relation to injury and athletic performance.The purpose of this research was to compare the validity and reliability of 3 in vivo methods of stiffness assessment using 1 cohort of participants.Methods：To determine inter-day reliability,15 female netballers were assessed for stiffness twice within 1 week using unilateral hopping（vertical stiffness）,free oscillations of the calf,and myometry of various muscles of the triceps surae.To establish convergent construct validity,stiffness was compared to static and dynamic strength measurements.Results：Test–retest stiffness results revealed that vertical stiffness produced moderate to high reliability results and myometry presented moderate to very high reliability.In contrast,the free oscillation technique displayed low to moderate reliability.Vertical stiffness demonstrated a significa t correlation with rate of force development during a squat jump,whilst myometer stiffness measurements from 3 sites in the lower limb revealed significan correlations with isometric rate of force development.Further,significan negative correlations were evident between the eccentric utilisation ratio and various myometer stiffness results.No relationships were established between the free oscillation technique and any of the performance measurements.Conclusion：These results suggest that vertical stiffness and myometry are valid and reliable methods for assessing stiffness.

THE EFFECT OF LONGITUDINAL OSCILLATIONS ON FREE CONVECTION FROM A VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

In this paper oscillatory 2-D natural convection from a vertical isothermal wall embedded in a po- rous medium, and originating from the oscillation of longitudinal fluid flow, has been investigated both analytically and numerically. Two asymptotic solutions, valid for large and small values of dimensionless frequency γ respectively, are obtained in the closed form. In the range where the asymptotic solutions break down, numerical results to the governing equations are obtained by local similarity meth- od. Both numerical and analytical results show that pulsatory components of the flow and heat transfer depend only on the parameter γ, and the effect of longitudinal oscillation is to decrease the magnitude or' pulsatory Nusselt number with a phase lag between 0 and 90 deg. A correlation for pulsatory heat trans- fer rates is proposed in the whole range of γ within 3% accuracy compared with the numerical results.

Significant intervals of energy transforms in bubbles freely oscillating in liquids

A wall motion of a bubble freely oscillating in a liquid is studied from the point of view of energy conversions at different instants. It is shown that the time of the bubble oscillation can be divided into two distinct intervals. In the first long interval （here called PK and KP intervals） the prevailing energy conversion is between the potential energy of the bubble and the kinetic energy of the liquid. In the second short interval （here called KI and IK intervals） the kinetic energy of the liquid is transformed into the internal energy of the gas/vapor in the bubble interior and into some other forms of energy. By observing the bubble wall motion in the PK and KP intervals, it is shown that only the value of the maximum bubble radius in the corresponding oscillation can be determined. However, only the knowledge of the maximum bubble radii is insufficient for formulation of a correct theoretical model. Unfortunately this fact is often not noticed in the literature.

Aerodynamic design,analysis,and validation techniques for the Tianwen-1 entry module

The clear differences between the atmosphere of Mars and the Earth coupled with the lack of a domestic research basis were significant challenges for the aerodynamic prediction and verification of Tianwen-1.In addition,the Mars entry,descent,and landing(EDL)mission led to specific requirements for the accuracy of the aerodynamic deceleration performance,stability,aerothermal heating,and various complex aerodynamic coupling problems of the entry module.This study analyzes the key and difficult aerodynamic and aerothermodynamic problems related to the Mars EDL process.Then,the study process and results of the design and optimization of the entry module configuration are presented along with the calculations and experiments used to obtain the aerodynamic and aerothermodynamic characteristics in the Martian atmosphere.In addition,the simulation and verification of the low-frequency free oscillation characteristics under a large separation flow are described,and some special aerodynamic coupling problems such as the aeroelastic buffeting response of the trim tab are discussed.Finally,the atmospheric parameters and aerodynamic characteristics obtained from the flight data of the Tianwen-1 entry module are compared with the design data.The data obtained from the aerodynamic design,analysis,and verification of the Tianwen-1 entry module all meet the engineering requirements.In particular,the flight data results for the atmospheric parameters,trim angles of attack,and trim axial forces are within the envelopes of the prediction deviation zones.

Effect of cavity length detuning on the output characteristics for the middle infrared FEL oscillator of FELiChEM

FELiChEM is an infrared free electron laser（FEL） facility currently under construction, which consists of two oscillators generating middle-infrared and far-infrared laser covering the spectral range of 2.5–200 μm. In this paper, we numerically study the output characteristics of the middle-infrared oscillator with accurate cavity length detuning. Emphasis is put on the temporal structure of the micropulse and the corresponding spectral bandwidth.Taking the radiation wavelengths of 50 μm and 5 μm as examples, we show that the output pulse duration can be tuned in the range of 1–6 ps with corresponding bandwidth of 13%–0.2% by adjusting the cavity length detuning.In addition, a special discussion on the comb structure is presented, and it is indicated that the comb structure may arise in the output optical pulse when the normalized slippage length is much smaller than unity. This work has reference value for the operation of FELiChEM and other FEL oscillators.

Coupled hydroelastic vibrations of an elliptical cylindrical tank with an elastic bottom

An exact three-dimensional analysis based on the linear potential theory and the elaborated method of eigenfunction expansion in elliptic coordinates are presented to study the free coupled elasto-hyrodynamic characteristics of an upright non-deformable cylindrical container of elliptical planform with a flexible bottom plate, filled to an arbitrary depth with an inviscid incompressible liquid. Extensive numerical data are presented in an orderly fashion for the first few symmetric/anti-symmetric coupled hydroelastic natural frequencies as a function of fluid depth parameter for two plate aspect ratios. Also, selected hydrodynamic and structural deformation modes shapes are presented in graphical form. The effects of liquid level, bottom plate elasticity, and cross sectional aspect ratio on the sloshing frequencies and hydrodynamic pressure modes are examined. The validity of the results is examined through computations using a commercial finite element package as well as by comparison with the data available in literature.

Observations of the Singlets of Higher-Degree Modes Based on the OSE

In this study,we selected 18 SG（superconducting gravimeter）records from 15 GGP stations with 99 vertical and 69 horizontal components of IRIS broad-band seismograms during 2004 Sumatra Earthquake to detect the splitting of higher-degree Earth’s free oscillations modes（0S4,0S7〈sub〉0S10,2S4,1S5,2S5,1S6）and 12 inner-core sensitive modes（25S2,27S2,6S3,9S3,13S3,15S3,11S4,18S4,8S5,11S5,23S5,16S6）by using OSE（optimal sequence estimation）method which only considers self-coupling.Results indicate that OSE can completely isolate singlets of high-degree modes in time-domain,effectively resolve the coupled multiplets independently,and reduce the possibility of mode mixing and end effect,showing that OSE could improve some signals’signal-to-noise ratio.Comparing the results of SG records with seismic data sets suggests that the number of SG records is inadequate to detect all singlets of higher modes.Hence we mainly selected plentiful seismograms of IRIS to observe the multiplets of higher modes.We estimate frequencies of the singlets using AR method and evaluate the measurement error using bootstrap method.Besides,we compared the observations with the predictions of PREM-tidal model.This study demonstrates that OSE is effective in isolating singlets of Earth’s free oscillations with higher modes.The experimental results may provide constraints to the construction of 3D Earth model.