利用海洋重力场变化分析洋底板块运动

洋底板块运动是地球动力学和全球变化研究的重要内容.本文根据质量迁移与地球外部重力场变化的对应关系,利用不同时期测高资料推算的1995—2019全球海洋重力场变化结果,反演分析全球洋底板块运动特征.研究表明,板块汇聚边界、板块内无震海岭、海山群、断裂带等区域重力异常变化显著,而在板块离散边界无明显变化趋势;西南印度洋中脊、大西洋中脊、中印度洋中脊等地区重力异常垂直梯度变化显著,且在西太平洋俯冲带、部分海岭区域也存在明显变化,其空间分布与地形基本吻合.海洋重力场变化整体上准确反映了全球洋底板块构造运动.相较于重力异常变化反演结果,重力垂直梯度的变化能够更为准确地反映洋底板块运动特征,特别是在洋中脊区域,扩张速率越小,垂直重力梯度变化越显著.此外,详细讨论了测高海洋重力场不确定因素对洋底板块运动分析结果的影响,海面坡度改正是主要因素之一.     

关于重力学反问题的几个判定准则─—在某些特定约束下的场源问题

从重力学反问题的基本理论出发,根据处理不适定问题的Tikhonov正则化原理,应用泛函分析概念,从理论上对如何将重力学反问题这一泛定的不适定问题在某些特定约束下转化成具有适定性的定解问题进行讨论．分别推演及刻画出重力场源密度在具有最小位能、最小L2模、最小H1,2模及最小“梯度模”等限定下的性质及表示式．对各种约束及对应的场源特性的数学、物理意义及合理性进行了分析．为重力学反问题研究提供理论判据．     

关于重力学反问题的几个判定准则─-在某些特定约束下的场源问题

从重力学反问题的基本理论出发,根据处理不适定问题的Tikhonov正则化原理,应用泛函分析概念,从理论上对如何将重力学反问题这一泛定的不适定问题在某些特定约束下转化成具有适定性的定解问题进行讨论．分别推演及刻画出重力场源密度在具有最小位能、最小L2模、最小H1,2模及最小“梯度模”等限定下的性质及表示式．对各种约束及对应的场源特性的数学、物理意义及合理性进行了分析．为重力学反问题研究提供理论判据．     

层状介质中断层位错引起的重力异常及其数值模拟

修正了文献［１］给出的两个公式和计算机程序中的个别错误，并根据文献［１］利用层状介质中的位错理论及其与相应重力变化的关系［２，５］，通过数值模拟方法研究了矩形位错面在不同尺度、倾向、埋深和位错的情况下有不同取向、量值的重力异常变化。此外，还对唐山地震、共和地震的重力资料作了几个测点的计算以探索地震物理前兆场空间和强度分布的复杂性。结果表明，断层错动引起的重力变化在空间、强度上的分布是十分复杂的。它是位错地表形变和地下层界面形变效应共同作用的产物，既可以是正异常，也可以是负异常。位错源的几何条件、埋深条件、位错方向和量值等对重力的空间、强度分布和范围有较强的影响。这就说明对于地震与重力异常的关系不能一概而论，要考虑一次地震特定条件的影响。本研究也为我们理解其它地震前兆物理场的复杂性提供了有益的启示     

THE FRACTAL DIMENSION OF GRAVITY DATA SETS AND ITS IMPLICATION FOR GRIDDING1

Gravity survey station locations are, in general, inhomogeneously distributed. This inevitably results in interpolation errors in the computation of a regular grid from the gravity data. The fractal dimension of the station distribution can be used to determine if an interpolated map is aliased at a specific wave-length and, moreover, it is often possible to determine an optimum gridding interval. Synthetic distributions of gravity station locations have been used for theoretical studies and it is found that for randomly distributed data there is a range of sizes for which the spatial data distribution has a fractal dimension of 2; that is, Euclidean. The minimum length scale at which the distribution ceases to be Euclidean is the optimum interpolation interval obeying Shannon's sampling theorem. For dimensions less than 2, the optimum interpolation interval is the shortest length at which the scaling regime is constant. In this case the gravity field cannot be interpolated without introducing some aliasing. As the fractal dimension characterizes the data distribution globally over the whole study area, the actual gridding interval, in some cases, will be smaller in order to represent short-wavelength features properly in the more densely sampled sub-areas, but this may generate spurious anomalies elsewhere. The proposed technique is applied to the station distribution of the Canadian national gravity data base and a series of sub-areas. A fractal dimension of 1.87 is maintained over a range of sizes from 15 km to over 1600 km. Although aliasing occurs, since the gravity field certainly contains much shorter wavelength anomalies, aliasing errors may be minimized by selecting the proper interpolation interval from the fractal analysis.     

Lidar study of the characteristics of gravity waves in the mesopause region at a southern low-latitude location

Using the technique developed by Gardner and Voelz [1987. Lidar studies of the nighttime sodium layer over Urbana, Illinois, 2. Gravity waves. Journal of Geophysical Research 92, 4673–4693] and a new method proposed by us, two groups of gravity wave parameters are extracted from 11 years sodium lidar measurements made at a southern low-latitude location. The wave occurrence frequencies, wave parameter distributions, and wave parameter relationships are given and compared with other lidar observations. The different lidar derived results can be attributed to different atmospheric parameters. The characteristics of these two groups of gravity waves are also compared, as well as that predicted by diffusive filtering theory, and we find the gravity wave relationships derived from our method are in better agreement with diffusive filtering theory predictions.     

于田M_s7.3地震震前重力扰动信号研究

2008年3月21日和2014年2月12日,新疆和田地区于田县先后发生两次M_s7.3地震.为分析两次地震前是否存在重力短临异常信号,应用Tsoft软件对原始数据进行理论固体潮改正和气压改正,并基于小波分解去除其低频趋势,有效提取了两次地震前国家连续重力观测网多台g-Phone重力仪的高频扰动信息.结果表明两次地震前都记录到高频扰动信号.2008年地震前牡丹江、沈阳台和漳州台三个台站记录到的高频扰动信号,主频分布在0.2~0.4 Hz.2014年地震前8个台站记录到两组不同频段的扰动信号.第一组信号集中在震前6天的东北台站,第二组扰动信号出现在震前3天的东南台站.两组扰动信号振幅呈现从北到南、从东到西逐步衰减的时空分布规律·同时期的气象资料显示局部强降雨与第二组扰动异常存在良好的相关性.对高频重力信号的时频分析结果表明震前第一组扰动信号存在异常频段0·13~0.18 Hz.应用扰动源扫描算法对2014年两组扰动信号进行空间定.位,结果显示第一组信号扰动源位置与于田震中相距约1935 km,不在于田地震的孕震区内;第二组信号扰动源来自海上.2008年和2014年于田地震第二组震前扰动信号与强降雨以及海浪影响相关.2014年第一组信号与于田地震的关系仍待进一步研究.     

Structure and State of Stress of the Chilean Subduction Zone from Terrestrial and Satellite-Derived Gravity and Gravity Gradient Data

It is well known that the quality of gravity modelling of the Earth’s lithosphere is heavily dependent on the limited number of available terrestrial gravity data. More recently, however, interest has grown within the geoscientific community to utilise the homogeneously measured satellite gravity and gravity gradient data for lithospheric scale modelling. Here, we present an interdisciplinary approach to determine the state of stress and rate of deformation in the Central Andean subduction system. We employed gravity data from terrestrial, satellite-based and combined sources using multiple methods to constrain stress, strain and gravitational potential energy (GPE). Well-constrained 3D density models, which were partly optimised using the combined regional gravity model IMOSAGA01C (Hosse et al. in Surv Geophys, 2014, this issue), were used as bases for the computation of stress anomalies on the top of the subducting oceanic Nazca plate and GPE relative to the base of the lithosphere. The geometries and physical parameters of the 3D density models were used for the computation of stresses and uplift rates in the dynamic modelling. The stress distributions, as derived from the static and dynamic modelling, reveal distinct positive anomalies of up to 80 MPa along the coastal Jurassic batholith belt. The anomalies correlate well with major seismicity in the shallow parts of the subduction system. Moreover, the pattern of stress distributions in the Andean convergent zone varies both along the north–south and west–east directions, suggesting that the continental fore-arc is highly segmented. Estimates of GPE show that the high Central Andes might be in a state of horizontal deviatoric tension. Models of gravity gradients from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellite mission were used to compute Bouguer-like gradient anomalies at 8 km above sea level. The analysis suggests that data from GOCE add significant value to the interpretation of lithospheric structures, given that the appropriate topographic correction is applied.     

The seismically active Andean and Central American margins: Can satellite gravity map lithospheric structures?

The spatial resolution and quality of geopotential models (EGM2008, EIGEN-5C, ITG-GRACE03s, and GOCO-01s) have been assessed as applied to lithospheric structure of the Andean and Central American subduction zones. For the validation, we compared the geopotential models with existing terrestrial gravity data and density models as constrained by seismic and geological data. The quality and resolution of the downward continued geopotential models in the Andes and Central America decrease with increasing topography and depend on the availability of terrestrial gravity data. High resolution of downward continued gravity data has been obtained over the Southern Andes where elevations are lower than 3000 m and sufficient terrestrial gravity data are available. The resolution decreases with an increase in elevation over the north Chilean Andes and Central America. The low resolution in Central America is mainly attributed to limited surface gravity data coverage of the region.To determine the minimum spatial dimension of a causative body that could be resolved using gravity gradient data, a synthetic gravity gradient response of a spherical anomalous mass has been computed at GOCE orbit height (254.9 km). It is shown that the minimum diameter of such a structure with density contrast of 240 kg m⁻³ should be at least ∼45 km to generate signal detectable at orbit height. The batholithic structure in Northern Chile, which is assumed to be associated with plate coupling and asperity generation, is about 60–120 km wide and could be traceable in GOCE data. Short wavelength anomalous structures are more pronounced in the components of the gravity gradient tensor and invariants than in the gravity field.As the ultimate objective of this study is to understand the state of stress along plate interface, the geometry of the density model, as constrained by combined gravity models and seismic data, has been used to develop dynamic model of the Andean margin. The results show that the stress regime in the fore-arc (high and low) tends to follow the trend of the earthquake distributions.     

TWO-DIMENSIONAL MASS DISTRIBUTIONS FROM GRAVITY ANOMALIES*

The oscillatory character of the solution obtained by Qureshi and Mula's method for the direct determination of two-dimensional mass distributions from gravity anomalies is examined.     

Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods

Liquid distributions in unsaturated porous media under different gravitational accelerations and corresponding macroscopic gaseous diffusion coefficients were investigated to enhance understanding of plant growth conditions in microgravity. We used a single-component, multiphase lattice Boltzmann code to simulate liquid configurations in two-dimensional porous media at varying water contents for different gravity conditions and measured gas diffusion through the media using a multicomponent lattice Boltzmann code. The relative diffusion coefficients (D rel) for simulations with and without gravity as functions of air-filled porosity were in good agreement with measured data and established models. We found significant differences in liquid configuration in porous media, leading to reductions in D rel of up to 25% under zero gravity. The study highlights potential applications of the lattice Boltzmann method for rapid and cost-effective evaluation of alternative plant growth media designs under variable gravity.     

The effect of the Baltic Sea level on gravity at the Metsähovi station

The loading effect of the Baltic Sea is immediately recognizable in the gravity record of the superconducting gravimeter T020 in Metsähovi, Finland, by simply inspecting residual gravity together with the tide gauge record at Helsinki 30 km away. The station is 10 km from the nearest bay of the Baltic Sea and 15 km from the open sea. Sea level variations in the Baltic are non-tidal and driven at short periods primarily by wind stress, at longer periods by water exchange through the Danish straits. Locally they can have a range of 2–3 m. Loading calculations show that a uniform layer of water covering the complete Baltic Sea increases the gravity in Metsähovi by 31 nm/s² per 1 m of water, and the vertical deformation is −11 mm. The observed gravity response to the local sea level is generally less, since the variations at short periods are far from uniform areally, the same water volume just being redistributed to different places. Regression of the whole gravity record (1994-2001) on local sea level gives 50–70% of the uniform layer response, as do loading calculations using actual water distributions derived from 11 tide gauges. However, both fits are dominated by some extreme values of short duration, and parts of the gravity record with long-period variations in sea level are close to the uniform layer response. The gravity observations can be used to test corrections for other co-located geodetic observations (GPS, satellite laser ranging) which are influenced by the load effect but not sensitive enough to discriminate between models.     

On the GPS-based ionospheric perturbation after the Tohoku earthquake of March 11, 2011

Based on the data from the GPS receiving networks in Japan and America which have a high time resolution (2 min), two-dimensional (2D) distributions of the variations in the ionospheric total electron content (TEC) are constructed both close to and far from of the epicenter of the submarine earthquake of March 11, 2011 in Japan. Above the epicenter, a diverging multi-period disturbance appears after the main shock due to the acoustic gravity waves. Far from the epicenter, the wave trains associated with the tsunamigenic atmospheric internal gravity waves are revealed. These atmospheric waves significantly advance the arrival of the tsunami signal initially on the Hawaiian islands and then on the western coast of North America. The presence of the tsunami precursor in the form of atmospheric gravity waves is supported by the numerical calculations and by the analysis of the dispersion relation for the waves in the atmosphere. The detected ionospheric responses close and far from the epicenter can be used in the early tsunami warning systems.     

Parameterization of gravity wave momentum deposition based on nonlinear wave interactions: basic formulation and sensitivity tests

We present a practical method for parameterization of gravity wave drag based on the Medvedev and Klaassen (1995. Journal of Geophysical Research 100, 25,841–25,853) theory of gravity wave spectral evolution and saturation. The only tuning necessary for the scheme involves assumptions about the nature of the source spectrum of subgrid-scale gravity waves, i.e. the wavenumbers, launch heights and amplitudes of the spectral components. In this paper we employ a column model with representative distributions of mean wind and temperature to examine the sensitivity of the parameterized wave drag to the source spectra. For the range of anticipated variability of source spectra in the troposphere the scheme produces plausible results consistent with observations and with theoretical estimates. Computationally, the scheme is as efficient as a multiple-wave Lindzen scheme, and suitable for use in general circulation models (GCMs) of the atmosphere.     

四川中西部地区地壳结构与重力均衡

汶川M_S8.0地震的“孕育”、发生和发展是深部物质分异、调整和运移的产物.为此,在四川中西部地区（松潘—甘孜,龙门山断裂系和四川盆地）应用重力布格异常场资料并通过两条典型剖面的地壳厚度(Moho界面深度）分布与依据Airy均衡理论给出的理论均衡地壳厚度做对比分析,探讨四川盆地、龙门山造山带、邛崃山等川西地域的地壳均衡状态,得到龙门山及其以西地带的深部地壳结构.龙门山造山带恰处于很不均衡的状态,即与其西北和东南部相比差异明显,故地壳处于不稳定状态.为探讨该区重力场均衡与强烈地震活动之间的关系,还必须进行新一轮的高精度观测,以对该区深部精细结构、重力场效应和均衡补偿深入研究.此外,本文研究结果有益于震后确定城镇布局和为不同类型建筑物重建选址提供深部要素.     

Optimal Design of a Gravity Survey Network and its Application to Delineate the Jabera-Damoh Structure in the Vindhyan Basin,Central India

Fractal dimension analysis was carried out for optimal designing of 2-D gravity survey network and to determine an optimum range of gridding interval to generate least aliased Bouguer anomaly maps. As a test case, this method has been successfully applied to the Jabera-Damoh region of the Vindhyan Basin, which is considered as a potential hydrocarbon bearing area. In particular, we aim to delineate accurately the lateral extent of a possible hydrocarbon bearing structure. To achieve this aim, fractal dimension of survey network was computed using 2-D distributions of observation points in the planning phase of the survey so that the optimum station spacing for gravity survey can be obtained. A range of optimum gridding interval for the gravity data set was suggested using the box-counting method of fractal dimension determination. Bouguer anomaly maps of the region are prepared utilizing the optimum gridding interval. For the first time, these anomaly maps clearly outline the gravity evidence of an anomalous rifted structure, which is bounded by parallel faults on either side. This structure is interpreted as a favorable basin for the occurrence of hydrocarbons. Another finding of this study has been the delineation of an apparently small ridge-like structure running east-west, dividing this basin in two parts. A subsurface geological model along a profile across the Jabera structure has also been presented.     

The determination of the regional part of the vertical gradient anomaly by a geodetic method

Summary The significance of the vertical gradients of gravity is great in geophysics and also in geodesy. In geophysics the observed vertical gradients can give valuable information about mass distributions close to the surface of the earth and in geodesy they may be used in determining the shape of the equipotential surfaces. The observed vertical gradients are very sensitive to masses close to the surface of the earth and they change very rapidly. Therefore, they should not be used for purposes such as the reduction of the observed gravity to the sea level. The normal vertical gradients are not the best either for this purpose because they are much too uniform on the surface of the earth. The best values for practical purposes are probably the regional vertical gradients.This paper presents a method to determine the regional vertical gradient anomalies in large areas from geodetic observations which, added to the normal part, will give the regional vertical gradients.     

Mean Free-Air Gravity Anomalies in the Mountains

Mean free-air gravity anomalies are often needed in geodesy for gravity field modelling. Two possible ways of compiling the mean free-air gravity anomalies are discussed. One way is via simple Bouguer gravity anomalies and the second and more time consuming way is via refined Bouguer gravity anomalies. In flat areas the differences between using any of the two ways should not be significant. In the mountains however, every effect introducing a high dependency, such as e.g. terrain effect, can negatively affect the interpolation process. In fact, a numerical experiment conducted in one part of Rocky Mountains revealed large and systematic differences. The effect of these differences on the geoid model is more then two meters in the test area. Our investigation shows that this bias is caused by the location of gravity measurement points, chosen mostly on hill-tops. At such points, the terrain correction to gravity is systematically larger than the mean value of the correction. Therefore, it is not possible to prevent the mean free-air gravity anomalies obtained from simple Bouguer gravity anomalies from having a systematic bias. One can see this bias as a result of the aliasing effect because the simple Bouguer gravity anomalies in the mountains contain a higher frequency signal (terrain effect) that is, according to sampling theorem, impossible to reconstruct by sparse measured gravity data, see e.g. (Goos et al., 2003). Therefore, the more rigorous way of computing the mean free-air gravity anomalies is via refined Bouguer gravity anomalies.     

Two-phase flow properties of a horizontal fracture: The effect of aperture distribution

A systematic numerical method has been presented to investigate the constitutive relationships between two-phase flow properties of horizontal fractures and aperture distributions. Based on fractal geometry, single rough-walled fractures are generated numerically by modified successive random addition (SRA) method and then aperture distributions with truncated Gaussian distribution are formed by shear displacement between lower and upper surfaces. (The truncated Gaussian distribution is used to describe aperture evolution under different normal stresses.) According to the assumption of two-dimensional porous media and local parallel plate model, invasion percolation approach is employed to model the two-phase flow displacement (imbibition) in generated horizontal fractures, in which capillary forces are dominant over viscous and gravity forces. For truncated Gaussian distributions, constitutive relationships from numerical simulation are compared to closed-form relationships and a good agreement is obtained. The simulation results indicate strong phase interference with the sum of two phase relative permeability values being less than one in the intermediate saturations. It is found that fracture properties related to residual saturations depend on spatial correlation of aperture distributions. Based on the simulation results, we proposed an empirical relationship between the fracture residual-saturation-rated parameters and the corresponding aperture distributions.     

双重约束条件下的连续重力观测非线性漂移改正方法分析

连续重力观测去除固体潮后所得重力残差结果,除了受仪器故障、自然因素、人为因素以及供电系统干扰外,弹簧重力仪的长期漂移也成为重力变化的重要影响因素,故漂移改正不可忽略。本文以高台地震台近5年的连续重力观测资料为数据基础,采用多阶多项式拟合法,并以驰豫分析结果和流动重力场结果为约束,研究弹簧重力仪的非线性漂移特征及其漂移改正的合理性。研究结果表明：高台重力仪的线性和非线性漂移特征明显,严重影响了其他微弱重力信号的提取,而驰豫分析处理结果和流动重力场成为有效地辅助约束手段,在其双重制约下进行非线性漂移改正,使所得重力非潮汐结果更为准确可靠,为地震预测预报提供较为准确的参考依据。