利用重力资料反演三维密度界面的质面系数法

文中给出一深度为h的水平矩形质面在地面产生的重力公式,对比了此公式算出的重力异常与三维长方体公式算出的重力异常,得出:当三维地质体的厚度与其埋深之比小于0.2-0.4时,二者的重力效应几乎相等,它们之间最大偏差在1-3％以内。用给出的重力公式进一步导出了重力反演三维密度界面的质面系数法。用理想模式检验,结果表明,本文给出的方法收敛快,反演误差较小,计算效果较好。最后用一实例,验证了方法的适用性。

INVERSION OF THE THREE DIMENSIONAL DENSITY DISCONTINUITY BY USE OF A METHOD OF "COMPRESSED MASS PLANE COEFFICIENT" BASED ON THE GRAVITY DATA

This paper presents a gravity formula of a rectangular mass plane （eq. 1-2）. Comparing-the gravity anomalies of this formula with the gravity anomalies of the rectangular parallelepiped （eq. 11）, obtained that when the ratio of the thickness AH and the buried depth h of three dimensional geological body is less than 0.2-0.4, the gravity effect of rectangle mass plane is nearly equal to the gravity effect of rectangular parallelepiped （their maximum relatively erroris less than 1-3%）. Therefore when △H/h is less than 0.4, we can use the simple gravityformula of rectangle mass plane instead of three dimensional geological body to compute the gravity anomalies. Based on this formula, this paper presents a method called "Compressed mass plane coefficient" to invert the 3-D discontinuity. The inverse coefficients of 21 （width）/D （depth） =1.0,1.1, 0.8 are given in Tab. 1, Tab. 3, Tab. 8 respectively. At first, the gravity data is inversed, using the inverse coefficients to get the surface density of each element of the rectangular mass plane. Then from the relation between surface density and mass density of each element （eq. 9）, the thickness of each three dimensional element can be calculated and the approximate thickness of the interface tentatively obtained. Further improvements of the estimate-thickness of the density interface can be made by direct gravity computation of the model thus obtained and repeated adjustments of the results in order to minimize the difference between computed and observed gravity anomalies. In that way, it may be possible to get the better depths of the density discontinuity.To test this method of gravity inversion, the hypothetic model and an observed profile are introduced here as examples （Fig. 5, Tab. 7）. In comparing with three dimensional sin x/x method, the results （Tab. 4, Tab. 5, and Fig. 6） indicate that the present method achieve good effects, lesser errors, and faster convergence.