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摘要: 在激光干涉绝对重力仪的研制中，每次测量落体都要自由下落7~20 cm的距离，在此过程中地表重力垂直梯度引入的误差最高可达60×10-8 m/s2。因此，需要计算出每次测量值对应的测量高度，即在该位置时，落体运动的距离内重力垂直梯度对绝对重力测量值的综合误差为零。基于对落体下落运动方程的分析，提出一了种新的绝对重力仪测量高度的计算方法。对比发现，当起始计算时间较小并接近于0（小于0.015 s）时，该算法与已有的算法结果具有较好的一致性，最大偏差不大于3 mm，梯度归算误差不大于1×10-8 m/s2（μGal）。在仪器自主研发的过程中，当起始计算时间较长（大于0.015 s）时，该算法可以更合理地计算绝对重力测量值对应的测量高度。Abstract: In the design of laser interference absolute gravimeters, the falling-body for each measurement needs to freely fall about 7-20 cm along the vertical direction, corresponding to a gradient error up to 60 μGal. So the measurement-height must be computed where the combined effect of the gravity gradient is equal to zero. This paper bases on the analysis for the equation of the falling-body movement and proposes a new algorithm to calculate the measurement-height of the absolute gravimeter. From the comparison with other algorithms we could find:(1) if the beginning time of the trajectory is close to zero(less than 0.015 s), the measurement height of the absolute gravimeters using our algorithm coincides to the other algorithms, with the maximum deviation less than 3 mm and the gradient error less than 1 μGal; (2) during the process of independent research and development, if the beginning time of the trajectory is more than zero(0.015 s or even longer), the measurement height calculated by our algorithm is more reasonable.
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图 2 不同起始时间和固定下落高度下的4种算法计算仪器高度
Figure 2. Measurement Heights of the 4 Algorithms for Different Beginning Time With Fixed Drop Height
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图 3 起始时间为0.01 s时不同下落高度的4种算法计算结果
Figure 3. Measurement Heights of the 4 Algorithms for Different Drop Height While the Beginning Time is 0.01 s
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图 4 起始时间为0.05 s时不同下落高度的4种算法计算结果
Figure 4. Measurement Heights of the 4 Algorithms for Different Drop Height While the Beginning Time is 0.05 s
表 1 4种算法得到的仪器测量高度(g0=9.8 m/s2, Hi=0.8 m)
Table 1 Measurement Heights of the Four Algorithms(g0=9.8 m/s2, Hi=0.8 m)
算法 相关参数 测量高度Hr/m Zumberge t2=0.128 s 0.773 2 Niebauer t2=0.128 s 0.771 3 Timmen A=56.0，B=102.4
C=61.2，D=14.0
E=1.0，F=112.0
G=168.0，H=67.2
I=5.6，t1=0.0 s
t2=0.128 s0.771 3 本文算法 t1=0 s
t2=0.128 s0.773 2 
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