内部膨胀源引起的粘弹地球的重力场变化及地面起伏──理论部分

GRAVITATIONAL VARIATION AND SURFICIAL UNDULATION OF VISCOELASTIC EARTH CAUSED BY INTERNAL DILATATION SOURCE

本文主要研究由内部膨胀源引起的粘弹介质地球的重力场变化及地面起伏．首先建立了适用于地球物理问题的关于一个粘弹性、自转、自引力、任意初始构形、任意模型参数分布及具有任意初始应力的地球之Ｂｅｔｔｉ互易定理在Ｌａｐｌａｃｅ变换参数域的表达形式；然后将这个理论用于讨论粘弹性、非自转、球形径向非均匀、自引力，初态为流体静力平衡的地球响应于内部膨胀源的重力场变化和地表起伏．

In this work we focus our attention on the gravitational variation and surficial undulation caused by internal dilatation source for a viscoelastic earth model. First we develop the Betti's reciprocal theorem which is applicable for a viscoelastic, self-rotating, self-gravitating earth with an arbitrary model parameters distribution,an arbitrary configuration and an arbitrary initial field,in the domain of Laplace transform parameters. Then we use this theory to investigate the gravitational variation and surficial undulation of a viscoelastic self-gravitating,spherical symmetric and hydrostatic earth responding to an internal dilatation source.