Theories and applications of earthquake-induced gravity variation:Advances and perspectives

Earthquake-induced gravity variation refers to changes in the earth’s gravity field associated with seismic activities.In recent years,development in the theories has greatly promoted seismic deformation research,laying a solid theoretical foundation for the interpretation and application of seismological gravity monitoring.Traditional terrestrial gravity measurements continue to play a significant role in studies of interseismic,co-seismic,and post-seismic gravity field variations.For instance,superconducting gravimeter networks can detect co-seismic gravity change at the sub-micro Gal level.At the same time,the successful launch of satellite gravity missions(e.g.,the Gravity Recovery and Climate Experiment or GRACE)has also facilitated applied studies of the gravity variation associated with large earthquakes,and several remarkable breakthroughs have been achieved.The progress in gravity observation technologies(e.g.,GRACE and superconducting gravimetry)and advances in the theories have jointly promoted seismic deformation studies and raised many new research topics.For example,superconducting gravimetry has played an important role in analyses of episodic tremor,slow-slip events,and interseismic strain patterns;the monitoring of transient gravity signals and related theories have provided a new perspective on earthquake early warning systems;the mass transport detected by the GRACE satellites several months before an earthquake has brought new insights into earthquake prediction methods;the use of artificial intelligence to automatically identify tiny gravity change signals is a new approach to accurate and rapid determination of earthquake magnitude and location.Overall,many significant breakthroughs have been made in recent years,in terms of the theory,application,and observation measures.This article summarizes the progress,with the aim of providing a reference for seismologists and geodetic researchers studying the phenomenon of gravity variation,advances in related theories and applications,and future research directions in this discipline.

Gravity variation associated with Wenchuan earthquake in western Sichuan

Based on the data of mobile gravity observation from 1998 to 2008 in western Sichuan, spatial dynamic variation results of regional gravity field are obtained. The relationship between the gravity variation features and Wenchuan Ms8.0 earthquake is systematically analyzed. The results show： 1 ） Gravity variation is closely related to active fault tectonics, and gravity measurement can better reflect material migration following crustal tectonic activity near active fault. 2）The gravity field appeared a wider range regional gravity variation during Wenchuan earthquake occurrence. The dynamic patterns of gravity field demonstrates the evolution process of gravity field ： quasi - homogeneous state non - homogeneous state-earthquake occurrence.

Earthquake epicentroids in the Beijing- Tianjin-Tangshan-Zhangjiakou region inversed by gravity variation data

Gravity variation data observed in the process of seismogenesis and occurrences of earthquakes show that the location with the greatest gravity changes does not necessarily coincide with the epicenter. To explain this we defined the center of effective mass of stress volume as hypocentroid, and the vertical projection of which on the earths surface as epicentroid. Here we adopt three rotating models, including spheroid, ellipsoid and cylinder, to represent the region of an impending earthquake. Based on the models of gravity variations induced by uniform dilatancy, epicentroids associated with sixteen earthquakes with M>4.0 occurred in 1981~2000 in the Beijing-Tianjin-Tangshan-Zhangjiakou region are determined by means of a proposed least squares iterative inversion method. The results indicate that cylinder model is preferable to the other two, and epicentroids obtained by the cylinder model separate from the epicenters by a range of 0~40 km. Epicentroids are inevitably located within intact tectonic blocks, and usually cluster in groups; while the epicenters are generally located at the terminations of faults or at the intersections of faults. It seems that there exist earthquake-hatching areas in the block among faults. Earthquakes hatch in these areas, but occur around these areas, meanwhile the existence of faults may play an important role in controlling the processes.

Field source characteristic of gravity variation in Hexi region before Menyuan Ms6.4 earthquake based on the Euler deconvolution

This study adopted the Euler deconvolution method to conduct an inversion and interpretation of the depth and spatial distribution pattern of field source that lead to gravity variation. For this purpose, mobile gravity data from four periods in the Hexi region between 2011 and 2015 were obtained from an observation network. With a newly established theoretical model, we acquired the optimum inversion parameters and conducted calculation and analysis with the actual data. The results indicate that one is the appropriate value of the structure index for the inversion of the mobile gravity data. The inversion results of the actual data showed a comparable spatial distribution of the field source and a consistent structural trend with observations from the Qilian-Haiyuan Fault zone between 2011 and 2015. The distribution was in a blocking state at the epicenter of the Menyuan earthquake in 2016. Our quantitative study of the field source provides new insights into the inversion and interpretation of signals of mobile gravity variation.

Characteristics of satellite-gravity variations in the North-South Seismic Belt before the 2013 Lushan earthquake

To study the characteristics of gravity variations in and near the North-South Seismic Belt before the 2013 Lushan earthquake,we used the geopotential-field models based on monthly data of the RI.~5 GRACE satellite to calculate the gravity changes. Here we present the patterns of annually cumulative variation, differentiatial variation and secular trend, as well as the continuous time-series at 4 characteristic sites during 2004 -2012. The result shows that the anomalous positive-to-negative transition zone, in which the epicenter of the 2008 Wenchuan earthquake was located, did not show any new gravity change before the Lushan earthquake, though located in the same zone.

Discrete Wavelet Multi-scale Decomposition of the Temporal Gravity Variations in North China

On the basis of the absolute and relative gravity observations in North China,spatial dynamic variation of regional gravity fields is obtained. A multi-scale decomposition technique is used to separate anomalies at different depths,and give some explanation to gravity variation at different time space scales. Gravity variation trends in North China are improved. Based on this result and the analysis of wavelet power spectrum,the images of the depth of wavelet approximation and detail are obtained. The results obtained are of scientific significance for the deep understanding of potential seismic risk in North China from gravity variations in different time space scales.

Gravity variation before the Akto Ms6.7 earthquake, Xinjiang

The relationship between gravity variation and the Akto Ms6.7 earthquake on November 11, 2016, was studied by use of mobile gravity observation data from the China continental structural environmental monitoring network. The result revealed that before the Akto earthquake, a high positive gravity variation was observed in the Pamir tectonic knots region （within a maximum magnitude of approximately ＋80 microgal）, which was consistent with the existing knowledge of gravity abnormality and the locations of strong earthquakes. In view of the recent strong seismic activities in the Pamir tectonic knots region, as well as the strong upward crust movement and compressive strain, it is believed that gravity change in the Pamir tectonic knots region reflects the recent strong seismic activities and crust movement.

Modeling the Dynamic Gravity Variations of Northeastern Margin of Qinghai-Xizang (Tibet) Plateau by Using Bicubic Spline Interpolation Function

In this paper, the spatial-temporal gravity variation patterns of the northeastern margin of Qinghal-Xizang （Tibet） Plateau in 1992 - 2001 are modeled using bicubic spline interpolation functions and the relations of gravity change with seismicity and tectonic movement are discussed preliminarily. The results show as follows： ① Regional gravitational field changes regularly and the gravity abnormity zone or gravity concentration zone appears in the earthquake preparation process; ②In the significant time period, the gravity variation shows different features in the northwest, southeast and northeast parts of the surveyed region respectively, with Lanzhou as its boundary;③The gravity variation distribution is basically identical to the strike of tectonic fault zone of the region, and the contour of gravity variation is closely related to the fault distribution.

Analyses on gravity variation before and after the Lijiang earthquake based on a finite rectangular dislocation model

The methods were discussed to calculate the gravity variation due to crustal deformation based on a model of dis-location on a finite rectangular plane. Taking the Lijiang MS=7.0 earthquake as an example the calculating princi-ple of fault parameters were determined, and the results were given. Of particular interests were the characteristics of the gravity variations in different dislocation types. With comparison between the calculated results and the practical measurements, it was found that the model could to some extent account for the observations. But it failed to give explanations to the more far spatial gravity variation.

Variation of gravity before the Alxa Zuoqi M5.8 earthquake

In this study, a classic survey adjustment computation method was used for data obtained in the Inner Mongolia and Ningxia gravimetric networks between September 2013 and April 2015 so as to investigate the variation of gravity before the Alxa Zuoqi M5.8 earthquake. The relationship between gravity variation and the Alxa Zuoqi M5.8 earthquake was analyzed. The results showed that： （1） the severe variation in gravity field at the test sites before the Alxa Zuoqi M5.8 earthquake, as well as the subsequent accelerated rising, might be an earthquake precursor; （2） the Alxa Zuoqi M5.8 earthquake occurred at the turning point where the high-gravity gradient zone changed from the NE direction to NW.

Temporal variation of gravity field prior to the Ludian Ms6.5 and Kangding Ms6.3 earthquakes

Using mobile gravity data from the central area of Sichuan and Yunnan Provinces, the relationship between gravity variation and earthquakes was studied based on the Ludian Ms6.5 earthquake that occurred on August 3rd, 2014, and the Kangding Ms6.3 earthquake that occurred on November 22 nd, 2014; the mechanism of gravity variation was also explored. The results are as follows：（1） Prior to both earthquakes, gravity variation exhibited similar characteristics as those observed before both the Tangshan and Wenchuan earthquakes, in which typical precursor anomalies were positive gravity variation near the epicenter and the occurrence of a high-gravity-gradient zone across the epicenter prior to the earthquake.（2） A relatively accurate prediction of the occurrence locations of the two earthquakes was made by the Gravity Network Center of China（GNCC） based on these precursor anomalies. In the gravity study report on the 2014 earthquake trends submitted at the end of 2013, the Daofu-Shimian section at the junction of the Xianshuihe and Longmenshan fault zones was noted as an earthquake-risk region with a predicted magnitude of 6.5, which covered the epicenter of the Kangding Ms6.3 earthquake. In another report on earthquake trends in southwestern China submitted in mid-2014, the Lianfeng, Zhaotong fault zone was also classified as an earthquake-risk region with a magnitude of 6.0, and the central area of this region basically overlapped with the epicenter of the Ludian Ms6.5 earthquake.（3） The gravity variation characteristics are reasonably consistent with crustal movements, and deep material migration is likely the primary cause of gravity variation.

Temporal variation of gravity-field in North China before and after the 2011 Japan Mw9. 0 earthquake

By using absolute and relative-gravity data recorded by the gravity network in North China, we obtained some large-scale and high-spatial-resolution images of gravity variation in this area for the first time. By analyzing these images, we found that the gravity in Liaodong peninsula area showed an obvious increase of 80 × 10^-8ms^-2 during about one- and-half year before the 2011 Japan Mwg. 0 earthquake, and a rapid decrease after the earthquake. This gravity variation is similar to that observed previously for the 1976 Tangshan 1147.8 earthquake.

Spatial and temporal variation of gravity field in the capital region

The high accurate gravity measurement have been carried out many years in the capital region. The main characteristics of the change of gravity field during the latest eight years (1981 - 1988) in the region are presented inthis paper. The more gravitational variation appeared in the southern and south-eastern part, the maximum variation come to 10-6 ms-2. In the northern part, for instance: Chengde City, and Wan-clan County - westTaihang mountain area which are in the westside of the network, were relative stable. The noticeable areas ofgravitational variation were in Tianjin-Baxian-Renqiu which correspon d with the crustal vertical deformation.The main cause of that is related to pump ground water and petroleum.

Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment（GRACE） mission can significantly improve our knowledge of the temporal variability of the Earth＇s gravity field.We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements.The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution.The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics（IGG） temporal gravity field models.IGG temporal gravity field models were compared with GRACE Release05（RL05） products in following aspects：（i） the trend of the mass anomaly in China and its nearby regions within 2005-2010; （ii） the root mean squares of the global mass anomaly during 2005-2010; （iii） time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010.The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects（i）-（iii）.Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG,17.1 ± 1.3 cm for the Centre for Space Research（CSR）,16.4 ± 0.9 cm for the GeoForschungsZentrum（GFZ） and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory（JPL） in terms of equivalent water height（EWH）,respectively.The root mean squares of the mean mass anomaly in Sahara were 1.2 cm,0.9 cm,0.9 cm and 1.2 cm for temporal gravity field models of IGG,CSR,GFZ and JPL,respectively.Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR,GFZ and JPL.

Stream Function Wave Derived by Unified Variational Principle of Water Gravity Wave

Based on the linear wave, solitary wave and fifth order stokes wave derived by use of the Unified Variational Principle of Water Gravity Wave (UVPWGW), this paper derives stream function wave theory by using UVPWGW. This paper will handle the Kinematic Free Surface Boundary Condition (KFSBC) and Dynamic Free Surface Boundary Condition (DFSBC) directly and give the optimum solution, instead of the conditions Sigma(Q(av) - Q(i))(2) = min, and the related equations of stational condition. When the wave height H, period T and water depth D are given, the original stream function wave will be determined, and can not be adjusted if it does not agree with the real case; in the present method, the adjustment can be done by adding several constraint conditions, for example, the wave profile can be adjusted according to the condition of accurate peak position. The examples given in this paper show that for the original stream function wave, the DFSBC can be fairly well satisfied, but the KFSBC can not; however, the stream function wave derived by UVPWGW is better than the original one in the sense of minimum error squares in the aspect of the level at which KFSBC and DFSBC are satisfied.

Consideration of the Daily Variation of Gravity on the Manifestation of Gravitational Shielding

The result of mathematical and physical analysis of the daily change in gravity is presented. The subject of consideration was the manifestation of semi-daily factors in diurnal variations of gravity. The assumption is investigated, according to which the cause of the half-day factors is the gravitational shielding of the planet Earth. Gravitational shielding is considered as a function of the size and thickness of celestial bodies and growing with distance from their poles. It is concluded that the planet Earth has the property of partial gravitational shielding, and the Moon does not have enough thickness to exhibit a tangible gravitational shielding. The obtained mathematical results correspond to the existing experimental data. It is suggested that gravitational shielding is the cause of the precession of the perihelion of Mercury and the peculiarities of the manifestation of tidal processes. It is assumed that gravitational shielding is one of the main reasons for the presence of hidden substances in the Universe. It is concluded that the physical picture with mutual shielding of interaction elements corresponds to the classical ideas of Fatio and Lesage. This approach is proposed as an alternative point of view to the existing theory on the description of tidal processes. It is shown that the existing basic approach to the description of tidal forces is unsatisfactory: the factors underlying the existing approaches have values 10 times less than those observed and cannot be considered as the reason for the manifestation of half-day manifestations in the daily change in gravity. The work is a continuation of the implementation by the author of P. Dirac’s ideas about accounting for the size of microparticles in physical theory.

Seasonal gravity changes estimated from GRACE data

Since 2002, the GRACE program has provided a large amount of high-precision data, which can be used to detect temporal gravity variations related to global mass re-distribution inside the fluid envelop of the surface of the Earth. In order to make use of the GRACE data to investigate earthquake-related gravity changes in China, we first studied the degree variances of the monthly GRACE gravity field models, and then applied decorrelation and Gaussian smoothing method to obtain seasonal gravity changes in China. By deducting the multi-year mean seasonal variations from the seasonal maos,we found some earthouake-related gravity anomalies.

Terrestrial water storage variation in Hebei plain area of China,based on ground surface gravimetry

Variation of terrestrial water storage in the Hebei plain area from March 2010 to June 2014 was studied using ground gravimetry combined with vertical displacement data from the Global Navigation Satellite System.Results show that observed gravity variation in this area increased continuously,basically reflecting a trend toward land subsidence.With the effect of this subsidence removed,a dominantnegative change in gravity variation was evident,reflecting an average rate of decrease in terrestrial water in this area of 0.10±0.053 m/y,and this is equivalent to a volume of 81.5±43.2×108 m^(3)and is consistent with the spatial distribution of groundwater change from measured hydrologic data.These results can be an essential reference and supplement for the study of terrestrial water variation in the Hebei plain area,and indicate that ground surface gravimetry can be used as an important mean for studying changes in terrestrial water.

The inverse study of crustal damage state with gravity data in frequency domain

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Gravity and GPS Measurements at South-West Part of Baikal Rift

Measurements of non-tidal variations of gravity （Ag）, which were obtained from 1992 to 2012 at the Talaya seismic station （located in the south-western part of the Baikal region）, are interpreted together with GPS （Global Position System） observation data, which were obtained from 2000 to 2013 at the same station. An absolute gravimeter was used for gravity observation. The strongest precision requirements concern tidal gravity prediction. It is the reason why we investigated tidal effect by LCR （LaCoste ＆ Romberg） gravimeter from 1996 to 1997 at the same station. We use tested tidal model for correction of gravity change. The linear component of gravity variations corresponds to changes in the elevation of the site. The correlation coefficient is close to the normal value of the vertical gradient of gravity. At this site, coseismic gravity variations at the time of the Kultuk earthquake （August 27, 2008, Mw = 6.5） were caused by a combined effect of the change of the site＇s elevation and deformation of the crust. Our estimations of the coseismic effects are consistent with results obtained by modeling based on the available seismic data.