典型断层模型的重力全梯度张量特征研究

Study on Characteristics of the Full Gravity Gradient Tensors of the Typical Fault Models

摘要: 以高斯定理为出发点，将计算梯度张量的体积分变成包围该积分域的全表面积分，利用格林公式把对每个面的积分变成对每条边的线积分之和，实现了对5个具有不同断层倾角的三维断层模型的梯度张量数值计算，得到其梯度张量平面分布图。断层模型的Vzz分量能够直接反映断层上下盘的轮廓，并且异常的符号直接反映场源体剩余密度的盈亏；Vxx和Vyy分量以密集的等值线带反映出断层上下盘在南北向和东西向的边缘；而Vzx和Vzy则以极值的形式反映出上下盘的边缘位置，且Vzx分量以极小值的形式揭示出断层面的位置；Vxy分量以极值圈闭的特征揭示上下盘的各个角点位置。对三维断层模型梯度张量分布特征的研究为从重力学方面对断裂构造的识别提供了理论依据。

Abstract: The gravity gradient tensors of five three-dimensional fault models with different dip angle were calculated and got their plane distribution map by applying the divergence theorem, which changed the volume integral into surface integral, then changed into line integral by using Green’s theorem. The characteristics of gravity gradient tensors of five fault models show that the Vzz component can directly reflect the shapes of the fault footwall, and its abnormal symbols directly reflect the profit or loss of the residual density. Vxx and Vyy components with dense isoline zone reflect the edge of fault footwall in north-south or east-west direction. While Vzx and Vzy reflect the edge of the lower plate in the form of extremum, and Vzx component reveals a fault surface in the form of minimum. Vxy component reflects the cornor of the footwall in the form of extremal. The research on the gradient tensor distribution characteristics of three dimensional fault models could provide a theory basis for finding fault tectonic.