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     

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从１９９５年９月２０日山东苍山５．２级地震前源区及其附近不同小区应力场方向的动态变化入手，分析了主应力轴方位、仰角及其矛盾符号比等参量在５．２级地震前的异常变化及其时空演变特点，简析了可能成因，可为研究震前其它各类前兆异常提供背景依据     

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用通日月均值减去夜均值计算的月均值资料和Ｓｏｍｐｉ谱分析法分析了１４个台站的北向分量１年周期变化的振幅向相位，时段为１９８４－１９８８年。分析结果显示用Ｐ＾０ｎ（ｄｎｄ＝１，…，６）复合模式的估算的Ｃ值较合理。各台的Ｃ值比较一致。     

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本文通过对基岩水与孔隙水的比较分析，介绍了基岩水的分布、水动力学和水化学特征，指出了基岩水运动具有均位趋势、选择流动及汇流特性，得出了渗流理论不宜用于基岩水的结论。     

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