Determination of the Earth＇s free core nutation parameters by using tidal gravity data

The Earth＇s free core nutation （FCN） is a retrograde eigenrnode which is attributed to the interaction between the solid mantle and the liquid core of the rotational elliptical Earth. This mode appears as an eigenmode of nearly diurnal free wobble （NDFW） in a terrestrial reference frame with a period of about one day （XU et al, 2001）. Therefore, the NDFW will lead to an obvious resonance enhancement in the diurnal tidal gravity observations, especially those of the tidal waves with frequencies closed to its eigenfrequency such as P1, K1, ψ1 and Ф1. The FCN resonance parameters can be retrieved accurately by high-precision tidal gravity observations, especially those recorded with the superconducting gravimeters （SG）. The Global Geodynamics Project （GGP） organized by IUGG took it as an important content for determining the FCN resonance parameters by using gravity data. However, the results are affected by many factors such as station location, background noise, the selection of the tide-generating potential tables, ocean tide models, data processing techniques and so on. In our study, the FCN parameters will be retrieved by using the SG observations at Wuhan, and the effects of the choices of various tide-generating potential tables, oceanic models and weight functions on the estimation of the FCN parameters will be discussed in detail,     

The Application of the Acoustic Method to the Exploration of Urban Active Faults and a Comparison with the Artificial Earthquake, and Radar Methods

The depth of upper fault point is the key data for ascertaining the active age of a buried fault on a plain. The difference of depth obtained from same fault may be dozens to several hundred meters when using different geophysical methods. It can result in the absolutely opposite conclusions when judging fault activity. Because of a lack of an artificial earthquake source with wide band and high central-frequency, many kinds of methods have to be used together. The higher the frequency of the artificial earthquake wave, electromagnetic wave and sonic wave, the higher the resolution. However the attenuation is also very fast and the exploration depth is very shallow. The reverse is also true. The frequency of artificial seismic waves is in the tens of Hz. Its exploration depth is big and the resolution is poor. The frequency of radar electromagnetic waves is about a million Hz, indicating that the resolving power is better, but the exploration depth is very shallow. However, the acoustic frequency is thousands of Hz, its resolving power is better than that of the artificial earthquake method and the exploration depth is larger than that of the radar method. So it is suitable for extra-shallow exploration in the thick deposit strata of the Quaternary. The preliminary results detected using the high frequency acoustic method in extra-shallow layers indicates that previous inferences about some fault activity in the eastern part of the North China plain may need to be greatly corrected.     

Inversion of the Strain Accumulation State in Crustal Interior from Observations of Earth Tide Tilts

The strain accumulation state in crustal interior and its migration trend can be inverted from observational data of earth tide tilts.In China,large earthquakes frequently occur in the border area between Yunnan and Sichuan Provinces.Using the observational data for years from 7 stations in this area,γ(the amplitude factor of earth tide tilts)values that characterize the strain accumulation state in crustal interior have been inverted in this paper.It has been found out that,Ms>5 events in the area often occur when γreaches an anomaly value.Using the time-space collocational stereomodelling the migration trend of strain accumulation can be determined to make a prediction for the probable location of a forthcoming earthquake in the area.     

The application of the high-frequency electromagnetic sounding method in the exploration of underground thermal water

High-frequency electromagnetic sounding is an electromagnetic exploration method using the natural high-frequency electromagnetic field as a field source. It has higher resolution and greater depth penetration than the direct current method and is especially fit for geothermal energy exploration and low- and mid-level groundwater detection. We introduce a successful application of high-frequency electromagnetic sounding for evaluating geothermal water resources. The high frequency electromagnetic system （MT-USA with a frequency range from 10 KHz to 1 Hz） is first applied to sample field data from China. A remote reference station is used to assure sampled data quality. We then perform 2D inversion image processing with the electrical method data. The results basically indicate the spatial distribution of underground geothermal water and provide favorable clues to finding the sources of the subsurface geothermal water in this area.     

Check of Earth''''s free oscillations excited by Sumatra-Andaman Large Earthquake and discussions on the anisotropy of inner core

Sumatra-Andaman Large Earthquake on Dec. 26,2004 generated not only the Indian Ocean Tsunami but also the Earth's free oscillations (EFO). The signals of Earth's free oscillations were perfectly re-corded by the superconducting gravimeter C0-32 at Wuhan station in China. After the pre-treatment and spectral analysis on the observational data from Wuhan station,we obtained more than ninety EFO modes including 42 fundamental modes,2 radial modes and 49 harmonic modes. On the basis of the discussions on some observed harmonic modes and abnormal splitting phenomena,we considered that the real rigidity might be lower than the theoretical prediction of PREM model in the inner core and however the anisotropy of compressive wave was brightly higher than the present estimations in the inner core. This suggested that the anisotropy of the inner core could be much more complicated than our present understanding,and there might be some new geophysical phenomena in the formation process of the inner core.     

Detection of spheriodal free oscillation excited by Peru 8.2 M_s 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.     

Application of ensemble kalman filter to geophysical parameters retrieval in remote sensing:A case study of kernel-driven BRDF model inversion

Remote sensing can provide multi-spatial resolution, multi-temporal resolution multi-spectral band and multi-angular data for the observation of land surface. At present, one of research focuses is how to make the best of these data to retrieve geophysical parameters in conjunction with their a priori knowledge and simul-taneously consider the influence of data uncertainties on inversion results[1-5]. The essence of remote sensing lies in inversion. It is difficult to precisely retrieve parame…     

A numerical study on matching relationships of gravity waves in nonlinear interactions

Applying a fully nonlinear numerical scheme with second-order temporal and spatial precision,nonlinear interactions of gravity waves are simulated and the matching relationships of the wavelengths and frequencies of the interacting waves are discussed.In resonant interactions,the wavelengths of the excited wave are in good agreement with the values derived from sum or difference resonant conditions,and the frequencies of the three waves also satisfy the matching condition.Since the interacting waves obey the resonant conditions,resonant interactions have a reversible feature that for a resonant wave triad,any two waves are selected to be the initial perturbations,and the third wave can then be excited through sum or difference resonant interaction.The numerical results for nonresonant triads show that in nonresonant interactions,the wave vectors tend to approximately match in a single direction,generally in the horizontal direction.The frequency of the excited wave is close to the matching value,and the degree of mismatching of frequencies may depend on the combined effect of both the wavenumber and frequency mismatches that should benefit energy exchange to the greatest extent.The matching and mismatching relationships in nonresonant interactions differ from the results of weak interaction theory that the wave vectors are required to satisfy the resonant matching condition but the frequencies are permitted to mismatch and oscillate with amplitude of half the mismatching frequency.Nonresonant excitation has an irreversible characteristic,which is different from what is found for the resonant interaction.For specified initial primary and secondary waves,it is difficult to predict the values of the mismatching wavenumber and frequency for the excited wave owing to the complexity.     

The inversion of density structure by graphic processing unit （GPU） and identification of igneous rocks in Xisha area

Organic reefs, the targets of deep-water petroleum exploration, developed widely in Xisha area. However, there are concealed igneous rocks undersea, to which organic rocks have nearly equal wave impedance. So the igneous rocks have become interference for future exploration by having similar seismic reflection characteristics. Yet, the density and magnetism of organic reefs are very different from igneous rocks. It has obvious advantages to identify organic reefs and igneous rocks by gravity and magnetic data. At first, frequency decomposition was applied to the free-air gravity anomaly in Xisha area to obtain the 2D subdivision of the gravity anomaly and magnetic anomaly in the vertical direction. Thus, the distribution of igneous rocks in the horizontal direction can be acquired according to high-frequency field, low-frequency field, and its physical properties. Then, 3D forward modeling of gravitational field was carried out to establish the density model of this area by reference to physical properties of rocks based on former researches. Furthermore, 3D inversion of gravity anomaly by genetic algorithm method of the graphic processing unit(GPU) parallel processing in Xisha target area was applied, and 3D density structure of this area was obtained. By this way, we can confine the igneous rocks to the certain depth according to the density of the igneous rocks. The frequency decomposition and 3D inversion of gravity anomaly by genetic algorithm method of the GPU parallel processing proved to be a useful method for recognizing igneous rocks to its 3D geological position. So organic reefs and igneous rocks can be identified, which provide a prescient information for further exploration.     

Recovery of the gravity field from GOCE data by using the invariants of gradient tensor

The gravity field models GUCAS_EGM and GUCAS_EGM_DL are established from GOCE data (GOCE Level 2 Products from Nov. 1 to Dec. 31, 2009) based on the method of the invariants of the gravity gradient tensor, where GUCAS_EGM is derived after GOCE gravity gradient data are filtered with FIR, and GUCAS_EGM_DL is computed with an additional Durbin-Levison arithmetic apart from FIR. Since this method, different from current programs dealing with GOCE data, is introduced for the first time, some new problems are required to be discussed in advance; for example, how to filter GOCE gravity gradient data, how to compute the invariants of the gradient tensor, and how to deal with the pole gap and so on. In addition, by comparing our models with ones recommended by ESA, it can be seen that the variations of GUCAS_EGM and the models recommended by ESA to EGM08 are almost equivalent, and the variation of GUCAS_EGM_DL to EGM08 is obviously less than ones of the recommended models.     

Tri-frequency spectrum method and results for resolving the parameters of Earth's liquid core free nutation

The parameters of Earth free core nutation (FCN) are two relatively significant geophysical parameters. Sasao et al. (1980) and Wahr and Bergen (1986) provided the theoretical estimation values of FCN parameters. Gwinn, Herring and Shapiro (1987) first obtained the observational values of FCN parameters by very long base Interference (VLBI) at Cambridge University. In the same year, Neuberg and Zürn in former West Germany and Hinderer in France began to retrieve FCN parameters by the observation of gravity tides and introduced the stacking method. The other scholars who researched into the same geophysical problems by applying the data of gravity tides basically followed the stacking method. The results they reached were similar to the observational result of FCN parameters given by Neuberg et al. in 1987. But the observational results of FCN parameters gained from gravity tides were not identical with those from VLBI, mainly because of the large difference of quality of FCN. So there was not an affirmative observational result of FCN parameters since then. In this paper, The authors firstly introduce the tri-frequency spectrum method with clearly geometrical and geophysical meaning for the resolution of FCN parameters, and the observational results of FCN parameters obtained from tide data at three superconducting gravity stations were accordant with those from VLBI, which will be relatively important to arriving at a certain observational result of FCN parameters.     

Tri-frequency spectrum method and results for resolving the parameters of Earth’s liquid core free nutation

The parameters of Earth free core nutation (FCN) are two relatively significant geophysical parameters. Sasao et al. (1980) and Wahr and Bergen (1986) provided the theoretical estimation values of FCN parameters. Gwinn, Herring and Shapiro (1987) first obtained the observational values of FCN parameters by very long base Interference (VLBI) at Cambridge University. In the same year, Neuberg and Zürn in former West Germany and Hinderer in France began to retrieve FCN parameters by the observation of gravity tides and introduced the stacking method. The other scholars who researched into the same geophysical problems by applying the data of gravity tides basically followed the stacking method. The results they reached were similar to the observational result of FCN parameters given by Neuberg et al. in 1987. But the observational results of FCN parameters gained from gravity tides were not identical with those from VLBI, mainly because of the large difference of quality of FCN. So there was not an affirmative observational result of FCN parameters since then. In this paper, The authors firstly introduce the tri-frequency spectrum method with clearly geometrical and geophysical meaning for the resolution of FCN parameters, and the observational results of FCN parameters obtained from tide data at three superconducting gravity stations were accordant with those from VLBI, which will be relatively important to arriving at a certain observational result of FCN parameters.     

武汉台重力潮汐长期观测结果

采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s^-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型.     

Free core nutation period inferred from the gravity measurements at Józefosław

The Free Core Nutation (FCN) is an important eigenmode which affects both Earth rotation and body tide. The FCN parameters, the resonance period and the quality factor are important for understanding the dynamics of the Earth at nearly diurnal periods. Those parameters are usually estimated either from the Very Long Baseline Interferometry (VLBI) observations of nutation, or from the tidal gravity measurements. In this paper we investigate the determination of the FCN parameters from gravity records covering a period of more than three years, collected with the use of a LaCoste&Romberg Earth Tide no. 26 gravimeter, located at Józefos?aw observatory near Warsaw. From the resonant enhancements of gravimetric factors and phases of diurnal tidal gravity waves, we could infer the FCN period to be equal to 430 sidereal days. This result is in very good agreement with previous gravimetric and VLBI nutation results, confirming the discrepancy in the dynamic flattening of the outer liquid core from its theoretical value based on the hydrostatic equilibrium assumption. The estimated FCN quality factor (Q ≈ 1300) is considerably smaller than the VLBI nutation result, which confirms that the local gravity measurements are more sensitive than VLBI global analyses to site-dependent phenomena (such as atmospheric and indirect ocean tidal effects). We also investigated the importance of gravimetric corrections in the FCN analysis, including numerical tests and simulations. This allowed us to estimate the uncertainty of FCN parameters due to improper or incomplete set of environmental corrections. We took also into account the impact of gravimetric factor errors and tidal wave selection on estimated FCN parameters. We demonstrated that despite relatively noisy measurements due to unfavorable gravimeter location, we were able to obtain very good results in case when proper correction and tidal wave selection were applied.     

Temporal variations in free core nutation period

Based on the nearly diurnal resonance in the tidal gravity observations,the temporal variations in period of the Earth's free core nutation (FCN) are investigated by using the tidal gravity observations of 18-year duration recorded continu-ously with a superconducting gravimeter (SG) at Brussels. The effects of the global oceanic tide loading and local barometric pressure on the SG observations have been removed by using eleven high-precision global digital models of oceanic tides and barometric pressure me...     

Time Variations In Gravity And Inferences On The Earth's Structure And Dynamics

This paper reviews how the study of the surface gravity changes is able to provide useful information on the Earth's structure and global dynamics. The spectral range which is observable with superconducting gravimeters is broad and goes from the seismic frequency band to periods longer than one year. We first investigate the seismic and sub-seismic bands with a special attention paid to the gravity detection of core modes in the liquid core and to the Slichter mode of translation of the solid inner core. In the tidal bands, we show how accurate measurements allow us to infer constraints on various phenomena such as mantle (an-)elasticity, as well as ocean and atmospheric loading. The observation of the Free Core Nutation resonance in the diurnal frequency band is reviewed and indirectly suggests an increase in the ellipticity of the core-mantle boundary with respect to its hydrostatic value. A similar resonance is also theoretically predicted in the diurnal band for the rotation of the solid inner core (Free Inner Core Nutation) but we show that its detection is much more difficult because of the small amplitude and lack of a nearby tidal frequency. Oceanic and atmospheric loading mechanisms induce gravity changes over a wide spectral range and we present some recent progress in this field. Finally, because superconducting gravimeters have high calibration stability and small long-term instrumental drift, they can easily measure longperiod gravity variations due to polar motion and hydrogeology.     

Investigation of the time variability of diurnal tides and resonant FCN period

The time variability of diurnal tides was investigated by analyzing gravity observations from global superconducting gravimeter (SG) stations with running time intervals. Through least-square and Bayesian approaches, FCN resonance parameters were estimated for each data section after obtaining the tidal parameters of mainly diurnal tidal waves. The correlation of the time variation in diurnal tidal waves and FCN period was discussed. For comparison, a similar method was used to analyze VLBI observations to study the time variability of nutation terms and FCN period. The variation trend of the FCN period totally depends on the Ψ1 wave in tidal gravity and on the retrograde annual term in nutation. We observed a similar variation trend in the FCN periods obtained from different SG stations worldwide and VLBI observations. The relation between diurnal tides and LOD variations is discussed and the possible mechanisms of the decadal variation in FCN periods were discussed.     

On the Mechanism of the Secular Tidal Acceleration of the Solid Inner Core and the Viscosity of the Liquid Core

As is known, the secular deceleration of the Earth's diurnal rotation is explained mainly by the tidal friction in the ocean. Below we consider this mechanism in some detail, taking into account also elastic deformations of the mantle under the action of ocean loading and the interaction between the tide-generating body, ocean tidal wave, liquid outer core, and solid inner core. It is shown that elastic displacements of the core-mantle boundary under the action of ocean loading are of about the same amplitude and phase as the elastic loading displacements of the Earth's outer surface. As a result, side by side with the mechanism of secular deceleration of diurnal rotation of the mantle, there are also (1) the opposite mechanism of secular acceleration of diurnal rotation of the outer liquid core and of the solid inner core and (2) the mechanism of excitation of differential rotation in the liquid core. Taking these effects into account, we compare theoretical and modern observed data on the eastward drift of the solid inner core. It is shown that the best agreement may be obtained if the turbulent viscosity of the liquid core is about 2 × 10 ³ Poise     

北京地区最新重力潮汐结果及其在检测液核共振效应中的应用

利用中国计量科学研究院北京昌平基地iGrav-012超导重力仪最新观测资料,对其作仔细地预处理,根据调和分析方法精密测定了重力潮汐参数,基于负荷理论与卷积积分技术获得了包含HAM11a,DTU10,EOT11a在内的14个全球海潮模型的重力海潮负荷效应,利用近周日频段内潮波振幅因子的共振效应求解了自由核章动(FCN)的本征参数.调和分析结果表明,重力潮汐的观测精度非常高,标准差达到1.184nm·s-2.基于加汉宁窗的快速傅里叶变换方法获得地震频段的地震噪声等级(SNM)为0.206,说明该台站是低背景噪声的.周日主波O1和K1经海潮模型作负荷效应改正的平均有效性分别为83%和85%;使用13个高精度海潮模型进行迭积计算获得的FCN本征周期为430.0(427.8,432.3)恒星日,品质因子Q值为-5137.