复杂形体重力异常高阶导数的正演计算
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摘要
本文利用截面为任意边数的二度多边形来逼近不规则形状的地质体，并运用差商原理正演其水平、垂直导数，特别是高阶导数。理论计算和实测资料的计算结果表明，该方法具有较高的精度。将截面为水平圆柱体的垂向四次寻数理论正演值与用边数为100的多边形逼近的差商法计算结果对比，其相对误差仅为0．2％。利用此法计算了高阳地区重力布格异常的四次导数，显示出4个局部小异常，与地震剖面上的4个潜山位置相对应。
Irregular-shaped geologic body can be approximated to a 2-D polygon that hasoptional sides. Then,horizontal and vertical derivatives (particularly the high-orderderivatives )of its gravity anomaly can be forward computed by applying differencequotlent principle. Theoretical and real data results show that our method bringsquite good accuracy. For example, theoretical forward reoult of verticalof0urthderivative of gravity anomaly resulting from a horizontal circular cylinder was com-pared with the difference quotient method result that was obtained by approximat-ing 100-side polygon to cross section of the circular cylinder,which only found theerror of 0.2%. This method was used to estimate the fourth derivative of gravityanomaly in Gaoyang area. Thus,four local anomalous bodies were displayed,whichcorrespond to four buried hills in seismic section.
Irregular-shaped geologic body can be approximated to a 2-D polygon that hasoptional sides. Then,horizontal and vertical derivatives (particularly the high-orderderivatives )of its gravity anomaly can be forward computed by applying differencequotlent principle. Theoretical and real data results show that our method bringsquite good accuracy. For example, theoretical forward reoult of verticalof0urthderivative of gravity anomaly resulting from a horizontal circular cylinder was com-pared with the difference quotient method result that was obtained by approximat-ing 100-side polygon to cross section of the circular cylinder,which only found theerror of 0.2%. This method was used to estimate the fourth derivative of gravityanomaly in Gaoyang area. Thus,four local anomalous bodies were displayed,whichcorrespond to four buried hills in seismic section.
引文
1Murthy I V R and Rao DB.Gravity anomalies of two-dimensional bodies of irregular cross-section withdensity contrast varying with depth.Geophysics,1979,44(9):1525～1530
2王家林等编著.石油重磁解释,石油工业出版社,1991
2王家林等编著.石油重磁解释,石油工业出版社,1991
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