A Multi-Parameter Regularization Method in Downward Continuation for Airborne Gravity Data
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摘要: 为了克服航空重力向下延拓解算的病态性影响，介绍了一种多参数正则化方法，以均方误差最小为目标函数，设计了选取正则化参数的迭代算法，并比较了基于L曲线法、广义交叉核实(generalized cross-validation，GCV)方法选取正则化参数的Tikhonov正则化方法，同时给出了均方误差意义下多参数正则化解优于最小二乘估计的条件。基于EGM2008地球重力场模型进行了仿真试验，计算结果表明，多参数正则化方法能够保证向下延拓结果的可靠性和稳定性，并优于现有的Tikhonov正则化方法，验证了多参数方法在航空重力向下延拓中的可行性。
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关键词:
- 航空重力 /
- 向下延拓 /
- Tikhonov正则化 /
- 多参数正则化
Abstract: To overcome the ill-posed problem of downward continuation for airborne gravity data, the paper proposes an alternative multi-parameter regularization method. The algorithm for selecting the regularization is proposed based on the minimization of mean squares error (MSE).In addition, the comparative analysis of the L-curve and generalized eross-validation(GCV) method of selecting the Tikhonov regularization parameter is conducted. Under of MSE, the condition that the multi-parameter regularization method is superior to the least-squares is given. By making using of the EGM2008 earth gravity model, the simulation experiment is performed. The numerical results show that the multi-parameter regularization method can guarantee the reliability and stability of downward continuation. And the multi-parameter regularization method shows the better performance than the general Tikhonov regularization method so that the feasibility of multiparameter regularization method in downward continuation for airborne gravity data is demonstrated.-
Keywords:
- airborne gravity /
- downward continuation /
- Tikhonov regularization /
- multi-parameter
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图 2 3 mGal误差条件下航空重力向下延拓值与地面参考重力值的差值绝对值(区域1)
Figure 2. Absolute Difference of Down‐Continue Results and Reference Value with 3 mGal Random Error (First Area)
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图 3 5 mGal误差条件下航空重力向下延拓值与地面参考重力值的差值绝对值(区域1)
Figure 3. Absolute Difference of Down‐Continue Results and Reference Value with 5 mGal Random Error (First Area)
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图 4 3 mGal误差条件下航空重力向下延拓值与地面参考重力值的差值绝对值(区域2)
Figure 4. Absolute Difference of Down‐Continue Results and Reference Value with 3 mGal Random Error (Second Area)
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图 5 5 mGal误差条件下航空重力向下延拓值与地面参考重力值的差值绝对值(区域2)
Figure 5. Absolute Difference of Down‐Continue Results and Reference Value with 5 mGal Random Error (Second Area)
表 1 各种方案大地水准面重力异常与参考值之间距离绝对值的统计结果(区域1) /mGal
Table 1 Statistical Results of Computing Geoid Gravity Gravity Anomaly and Reference Value for Each Scheme(First Area) /mGal
误差 方案 最大值 最小值 平均值 RMS 3 1 520.3 0.2 109.2 134.7 2 29.1 0.0 6.7 8.5 3 27.8 0.0 6.4 8.1 4 18.3 0.0 4.2 5.3 5 1 804.3 0.8 194.5 245.9 2 43.8 0.0 8.2 10.4 3 36.0 0.0 6.9 8.7 4 23.0 0.0 5.3 6.8 
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表 2 各种方案大地水准面重力异常与参考值之间距离绝对值的统计结果(区域2)/mGal
Table 2 Statistical Results of Computing Geoid Gravity Gravity Anomaly and Reference Value for Each Scheme(Second Area) /mGal
误差 方案 最大值 最小值 平均值 RMS 3 1 866.8 0.5 164.6 209.9 2 11.9 0.0 2.5 3.1 3 9.9 0.0 2.2 2.7 4 5.6 0.0 1.2 1.6 5 1 1 027.1 0.7 259.0 327.0 2 16.1 0.0 3.3 4.2 3 11.7 0.0 2.7 3.3 4 3.3 0.0 1.9 2.4
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