【作者】 刘元龙； 郑建昌； 武传真；

【Author】 Liu Yuanlong Zheng Jianchang Wu Chuanzhen (Institute of Geophysics,Chinese Academy of Sciences)

【机构】 中国科学院地球物理研究所；

【摘要】 以前常用日本坪井忠二(1958)提出、(1978)修改的三维sinx/x法计算三维密度界面。但此方法计算误差大,边缘损失大.为克服这些缺点,我们于1985—1987研究了这一新方法.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(最大误差在1—3%以内).用此公式导出正反演结合的反演三维密度界面的质面系数法.文中给出了宽度21与其埋深D之比为1.0、1.1及0.8的反演系数表.首先用合适的反演系数乘上相应的重力异常求出每块的面密度,再用面密度与体密度的关系及有关地震测深资料得出每个单元的近似厚度,再通过正演求出残差,由残差进行调整修改,一般调整二次即可得到满意结果.通过反演说明,本方法精度高.与日本坪井的sinx/x法比较计算说明,本方法比日本坪井方法精度高、收敛快、边缘损失小、计算速度快.实算说明,本方法结果与地震测深结果是一致的.这些结果表明,本方法的计算精度、速度、收敛快慢、边缘损失程度及适用性方面已达国际先进行列.同济大学出版的《东方地学论文集》将上述论文全部翻译成英文,向国内外介绍地学方面的优秀论文和进展.更多还原

【Abstract】 This paper presents a gravity formula of a rectangular mass plane.Comparing the gravity anomalies of this formula with the gravity anomalies of the rectangular parallelepiped (eq.11),it was obtained that when the ratio of the thicknessΔH 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 error is less than 1—3%).Therefore whenΔH/h is less than 0.4,we can use the simple gravity formula 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 and 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,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 sinx/x method,the results(Tab.4,Tab.5,and Fig.6) indicate that the present method achieve good effects,lesser errors,and faster convergence.更多还原