潜艇重力梯度极值和深度的关系研究

研究潜艇重力梯度各分量的极值点坐标与潜艇到观测点垂直距离的关系。数值分析发现，除V_zz外，梯度张量其余分量均有多个极值点；V_xx和V_xz所有极值点的Y坐标、V_yy和V_zz中心极值点的Y坐标不随高度的变化而变化；V_yy、V_yz和V_zz所有极值点的X坐标、V_xx中心极值点的X坐标随高度的变化为非线性关系且变化较小；V_xx两侧极值点的X坐标、V_xz极值点的X坐标、V_xy极值点的X和Y坐标、V_yy两侧极值点的Y坐标和V_yz极值点的Y坐标随高度的变化为线性关系。根据极值点与潜艇的深度关系，验证了利用极值点坐标反演潜艇深度的可行性。

The Relationship between Extreme Values of Gravity Gradients and Depth of Submarine

This paper investigates the relationship between the extreme point coordinates of gravity gradients created by submarine and the vertical distance from the submarine to the observation point. Through statistical analysis, we find that, except for V_zz, the other gravity gradient components have multiple extreme points. Numerical results also show that the Y-coordinates of the extreme points of V_xx and V_xz, the central extreme points of V_yy and V_zz do not change with the changes of observation height. The X-coordinate of the central extreme point of V_xx and the extreme points of V_yy,V_yz and V_zz are all non-linear with observation height, but the correlations between X-coordinates of these values and the observation height are not strong. The X-coordinate of extreme points on both sides of Vxx, X-coordinate of extreme points of V_xz, coordinates of extreme points of V_xy,Y-coordinates of extreme points on both sides of V_yy and Y-coordinate of extreme points of V_yz are linear with the observation heights. Finally, based on the relationship between the extreme points and the depth of the submarine, the feasibility of using the extreme point coordinates to inverse the depth of the submarine is verified.