The spacetime gravitational field of a deformable body

The high-resolution analysis of orbit perturbations of terrestrial artificial satellites has documented that the eigengravitation of a massive body like the Earth changes in time, namely with periodic and aperiodic constituents. For the space-time variation of the gravitational field the action of internal and external volume as well as surface forces on a deformable massive body are responsible. Free of any assumption on the symmetry of the constitution of the deformable body we review the incremental spatial (“Eulerian”) and material (“Lagrangean”) gravitational field equations, in particular the source terms (two constituents: the divergence of the displacement field as well as the projection of the displacement field onto the gradient of the reference mass density function) and the `jump conditions' at the boundary surface of the body as well as at internal interfaces both in linear approximation. A spherical harmonic expansion in terms of multipoles of the incremental Eulerian gravitational potential is presented. Three types of spherical multipoles are identified, namely the dilatation multipoles, the transport displacement multipoles and those multipoles which are generated by mass condensation onto the boundary reference surface or internal interfaces. The degree-one term has been identified as non-zero, thus as a “dipole moment” being responsible for the varying position of the deformable body's mass centre. Finally, for those deformable bodies which enjoy a spherically symmetric constitution, emphasis is on the functional relation between Green functions, namely between Fourier-/ Laplace-transformed volume versus surface Love-Shida functions (h(r),l(r) versus h ^′(r),l ^′(r)) and Love functions k(r) versus k ^′(r). The functional relation is numerically tested for an active tidal force/potential and an active loading force/potential, proving an excellent agreement with experimental results. Received: December 1995 / Accepted: 1 February 1997     

中国重力异常的小波变换与多尺度分析

阐述了小波变换及多尺度分析方法的原理，利用二维小波多尺度分析方法对中国布格重力异常进行了分解，并从其中划分出有意义的剩余异常．模型结果证明方法有效．由于本文方法可以将重力异常分解成各种几何尺度意义下的不同成分，这为重力解释和研究地壳的结构提供更多更新的依据．     

重力场中的完整坐标与非完整坐标

阐明重力场中完整坐标系、非完整坐标系及其之间的转换关系以及完整坐标系的存在对大地测量的意义．指出水准测量中的理论闭合差是由于它所参照的局部笛卡尔坐标系是一个非完整坐标系导致的，并给出了计算理论闭合差的严密公式．     

分层重力图像方法及其应用

分层重力图像方法是依据三维地震波速的层析成像结果，通过速度与密度相关关系，转换得到分层的密度结构模型，计算并给出各分层在地表的重力异常分布图像．以中国大陆为例，给出其不同深度的7个分层的重力异常图像和不同分层叠加的综合（或总合）重力异常分布图像．经过与实测的中国布格重力异常资料对比分析，结果表明两者的重力场特征相当一致；分层重力图像的结果能较好地反映地下不同深度的物质分布．     

青藏高原及其邻区岩石层三维密度结构

搜集了青藏高原及其邻近区域的S波速度三维层析成像结果和2万多个实测重力点资料，将重力资料进行各种改正并网格化为30′×30′的布格重力异常．首先采用密度差与S波速度差之间的经验关系式，建立青藏地区岩石层密度的初始模型，再利用布格重力异常进行阻尼最小二乘法反演，得到青藏地区岩石层三维密度分布结果．反演结果表明：（1）青藏高原岩石层密度分布不仅在纵向上不均匀，而且在横向存在明显的不均匀．在深度10－70km范围内，高原整体呈低密度特性，在50－70km深度范围内低密度特征更加突出，与周缘地区存在0，1g／cm³的密度差．而在90－110km深度范围内，高原岩石层地幔显示密度高．（2）岩层密度分布与大地构造有明显相关的分区性，显示出青藏块体、巴颜喀拉块体、塔里木块体和印度块体．     

Study on the Gravity Field and Deep-Seated Crustal Structure at the North Margin of the Qinghai-Tibet Plateau

1.I~ductionThenorthernmarginoftheQinghai-TibetplateauincludestheAltllnMis.,theQilianMis.,KunlunMis.,theQaidambasinandthesouthernTarimbasin.ThisareaistCctonicallycharacterizedbyintensiveCenozoicdeformationwithcomplicateddeformationalmechedsm(Molnaretal.,1987;Zheng,1991;Culetal.,1994;Ding,1995andXuetal.,1996).Thedeformationalmechanismsincludethrust-napping,strike-slipping,extensionandblockrotation,aswellassimultaneousupliftingandtypicalbasin-rangetectonics(CulandXu,1996).IntermsofCenozoi…     

GPS在1:20万区域重力测量中的应用

介绍了利用GPS开展1：20万石棉幅区域重力测量的情况，对正确掌握GPS的工作方法作了研究，并总结了应用该项技术的成功经验和遗留问题。     

The onset of Pleistocene glaciation in the Barents Sea: implications for glacial isostatic adjustment

In this paper the effect of a delayed onset of glaciation in the Barents Sea on glacial isostatic adjustment is investigated. The model calculations solve the sea-level equation governing the total mass redistributions associated with the last glaciation cycle on a spherically symmetric, linear, Maxwell viscoelastic earth for two different scenarios for the growth phase of the Barents Sea ice sheet. In the first ice model a linear growing history is used for the Barents Sea ice sheet, which closely relates its development to the build-up of other major Late Pleistocene ice sheets. In the second ice model the accumulation of the Barents Sea ice sheet is restricted to the last 6 ka prior to the last glacial maximum.
The calculations predict relative sea levels, present-day radial velocities, and gravity anomalies for the area formerly covered by the Weichselian ice sheet. The results show that observed relative sea levels in the Barents Sea are appropriate for distinguishing between the different glaciation histories. In particular, present-day observables such as the free-air gravity anomaly over the Barents Sea, and the present-day radial velocities are sensitive to changes in the glaciation history on this scale.
A palaeobathymetry derived from relative sea-level predictions before the last glacial maximum based on the second ice model essentially agrees with a palaeobathymetry derived by Lambeck (1995). The additional emerged areas provide centres for the build-up of an ice sheet and thus support the theory of Hald, Danielsen & Lorentzen (1990) and Mangerud et al. (1992) that the Barents Sea was an essentially marine environment shortly before the last glacial maximum.     

Yucatán karst features and the size of Chicxulub crater

The buried Chicxulub impact structure is marked by a dramatic ring of sinkholes (called cenotes if containing water), and adjacent less prominent partial rings, which have been shown to coincide with maxima in horizontal gravity gradients and a topographic depression. These observations, along with the discreteness and spacing of the features, suggest a formation mechanism involving faulting in the outer slump zone of the crater, which would thus have a diameter of approximately 180 km.
An opposing view, based primarily on the interpretation of gravity data, is that (he crater is much larger than the cenote ring implies. Given the association of the known cenote ring with faults, we here examine northern Yucatan for similar rings in gravity, surface features and elevation, which we might expect to be associated with outer concentric faults in the case of a larger, possibly multiring, structure.
No such outer rings have been found, although definite patterns are seen in the distribution of karst features outside the crater rim. We explain these patterns as resulting mainly from deformation related to the block fault zone that parallels tbe shelf edge of eastern Yucatan.