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基于引力位理论结合均质长方体模型和密度-深度函数关系推导了变密度长方体模型正演重力异常表达式。利用高阶次的卫星重力场模型计算了汾渭盆地及周边地区由地壳密度分布不均引起的剩余布格重力异常,根据该剩余布格重力异常反演得到了该地区三维地壳密度分布。反演结果显示该区域地壳密度具有西北高、东南低且自西北向东南方向递减的特征,并和剩余布格重力异常分布形成良好的镜像关系;反演结果与Crust 1.0模型提供的结果较为吻合,证明了变密度长方体模型直接反演三维地壳密度分布是可行的。
Based on the gravitational potential theory and the homogeneous rectangular parallelepiped model and the density-depth relationship, the anomalous gravity anomalies expression of variable density cuboid model is deduced. The residual Bouguer gravity anomalies caused by the uneven distribution of crustal density in the Fenwei and surrounding areas were calculated by using the high order satellite gravity field model. Based on the residual Bouguer gravity anomaly inversion, the three-dimensional crustal density distribution in the area was obtained. The inversion results show that the crustal density in this region has the characteristics of high northwest, low southeast and decreasing from northwest to southeast, and forms a good mirror image of the residual Bouguer gravity anomaly distribution. The inversion results are in good agreement with the results provided by the Crust 1.0 model It is proved that it is feasible to directly invert the 3D crustal density distribution by the variable density cuboid model.