Anomalous gravitational field of underwater vehicles and requirement analysis for the detection platform based on the dipole model
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摘要:
重力探潜是一种具有发展潜力的非声学探潜技术，目前仍处于理论探索阶段.本文推导了垂直偶极子模型的引力和引力梯度垂向分量的解析公式，分析了它们的空间分布特征.基于偶极子模型给出了一种潜航器异常重力场的仿真方法，并通过实例验证了方法的有效性，分析了潜航器重力异常和重力垂直梯度的空间变化，及其对重力探潜传感器精度和平台稳定性的需求.根据实例分析结果可以得到以下结论：（1）利用重力异常信号探测潜航器不具备可行性，但是基于重力梯度的重力探潜方法具有实用化价值，值得进一步研究；（2）本文建立的偶极子模型能够有效用于估计潜航器异常重力场的量级、探测平台的精度需求和可探测范围，为重力探潜研究提供了一个重要的理论分析工具.
Abstract:Gravitational detection for underwater vehicles (UV) is a potential non-acoustic detection technique, which is still at the stage of theoretical exploration at present. In this study, we derived analytic formula for the vertical components of gravity and gravity gradient of a vertical dipole, and analyzed characteristics of their spatial distribution. Based on the dipole model, a method to simulate anomalous gravitational field of UV was presented. An example was demonstrated to illustrate the effectiveness of the method and to analyze the spatial variation of gravity anomaly and gravity gradient of UV, as well as to estimate requirements for the accuracy of sensors and the stability of detection platform. The following conclusions can be drawn from the analysis results of the example. Gravity anomaly is not suitable to be used for the detection of UV. However, the detection technique based on gravity gradient is of practicable value and worthy to be studied further. The dipole model presented in this paper is a good tool for the theoretical study of gravitational detection of UV, which can be conveniently used to estimate the magnitude of the anomalous field derived from UV, accuracy requirements of detection platform and maximum detectable distance.
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图 3
不同α对应的重力异常(a)与重力垂直梯度(b)模最大值随高度的变化
Figure 3.
Modulus maximum of (a) gravity anomaly and (b) vertical gravity gradient varying with height for different α
图 4
潜艇重力异常绝对值的空间分布(α=1)
Figure 4.
Spatial distribution of absolute gravity anomaly derived from the submarine in case of α=1
图 5
潜艇垂直重力梯度绝对值的空间分布(α=1)
Figure 5.
Spatial distribution of absolute vertical gravity gradient derived from the submarine in case of α=1
图 6
(a) 重力异常和(b)重力垂直梯度绝对值在极角θ-斜距l平面内的等值线图
Figure 6.
Contour maps in (θ, l) plane of absolute value of (a) gravity anomaly and (b) vertical gravity gradient.
图 7
潜航器异常重力场量级的近似估值与精确值对比
Figure 7.
Comparison between approximate and exact magnitudes of the anomalous gravitational field induced by the underwater vehicle
表 1
重力异常和重力垂直梯度不同量级对应的最大高度
Table 1.
Maximum heights corresponding to different magnitudes of gravity anomaly and vertical gravity gradient
重力异常(m·s-2) 高度(m) 重力梯度(E) 高度*(m) 10-7 41 100 68/60 10-8 89 10-1 119/125 10-9 189 10-2 212/220 10-10 406 10-3 377/400 10-11 875 10-4 669/650 10-12 1884 10-5 1190/1220 注：*最后一列斜线后的值为张志强等(2019)的结果. 
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表 2
不同高度重力探测平台的精度需求
Table 2.
Accuracy requirement for the gravity detection platform
高度(m) 100 300 500 1000 1500 2000 重力异常(m·s-2) 6.69×10-9 2.48×10-10 5.35×10-11 6.69×10-12 1.98×10-12 8.36×10-13 重力仪精度(m·s-2) 10-9 10-10 10-11 10-12 10-12 10-13 平台稳定性(m) 2.17×10-3 8.03×10-5 1.73×10-5 2.17×10-6 6.42×10-7 2.71×10-7 重力梯度(E) 2.01×10-1 2.48×10-3 3.21×10-4 2.01×10-5 3.96×10-6 1.25×10-6 重力梯度仪精度(E) 10-1 10-3 10-4 10-5 10-6 10-6 平台稳定性(m) 1.38×102 1.71 2.21×10-1 1.38×10-2 2.73×10-3 8.65×10-4
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