三度体（物性随深度变化模型）位场波谱的正演计算

本文将均质的任意二维、三维物体位场的波谱解析表达式的研究成果推广到变密度、变磁化强度的更一般的情形。对密度差随深度呈指数函数衰减或线性变化的模型,获得了任意倾斜多边形质量面、斜平行六面体以及一般的多面体等形体的重力谱的解析表达式。它们的结构与均质体相应表达式一样简单,易于计算。以上结果表明,在很一般的条件下,位场波谱具有指数函数和的形式。

THE COMPUTATION OF SPECTRUM OF POTENTIAL FIELD DUE TO 3-D ARBITRARY BODIES WITH PHYSICAL PARAMETERS VARYING WITH DEPTH

The analytical expressions of spectra of gravity on the plane Z0 = 0 due to arbitrary homogeneous bodies are extended in this paper to the case where density contrast varies with depth ξ. The expression of a polyhedron whose density contrast p varies as an exponential density-depth function is given bywhere n,- is the outward normal to Si, the ith-polygon of its surface, βi is the strike of Si, αij is the direction of the jth-edge of Si, Zij is a vector with components （xij, yij, zij）, the coodinates of the jth-apex of Si,ρij is the density contrast of the apex, andSimpler expressions have been obtained for a sloping straight line segment, a polygon or a parallel hexahedron.The spectrum expression due to bodies with linearly varying density contrast can be approximated by the above expressions.It has already been evident4] that the Poisson Formula can be applied to the case where remains a constant vector in spite of the variation of magnetization J with space, so one may reasonably conclude that the above conclusions might be extended to obtain the spectrum expressions of magnetic anomalies due to arbitrary bodies with magnetization varying in value with depth.