Regional gravity field model constructed by the least squares collocation
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摘要:
基于非均匀分布的陆地重力观测数据，重构局部重力场模型是区域重力资料处理与解释的重要环节。本文对比了多种局部重力场建模方法，并以EGM2008模型提供的自由空气重力异常模型重采样数据进行测试，综合比较了不同噪声条件下不同建模方法的实际效果。结果表明：在不同噪声水平下，优选出适合重力位场问题的协方差函数后，最小二乘配置法的建模效果优于其它方法。
Abstract:Based on the non-uniform distribution of terrestrial gravity observation data, the reconstruction of local gravity field model is a key to the processing and interpretation of regional gravity data. In this paper, a variety of local gravity field modeling methods are compared, and the resampling data of the free air gravity anomaly model provided by the EGM2008 model are tested, and the actual effects of different modeling methods under different noise conditions are compared. The results show that the least squares collocation method is better than other ones in modeling when the covariance function suitable for gravity potential field problem is optimized at different noise levels.
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Keywords:
- least-squares collocation /
- local gravity field /
- noise /
- covariance function /
- gravity model
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图 1 华北地区自由重力异常场
图中地震事件为中国地震台网中心记录的2012年5月至2019年1月期间的MS≥4.0地震
Figure 1. Free gravity anomaly field in North China
The figure shows the MS≥4.0 events recorded by the China Earthquake Networks Center from May 2012 to January 2019
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图 2 不同插值法网格化结果对比
（a） 仿真重力异常场；（b） 反距离加权法插值结果；（c） 最小曲率法插值结果；（d） 最小二乘配置法插值结果
Figure 2. Comparison of meshing results of different interpolation methods
（a） Simulated gravity anomaly field；（b） Inverse distance weighting interpolation results；（c） Minimum curvature interpolation results；（d） Least squares collocation interpolation results
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图 3 不同插值法残差影像图
（a） 最小二乘配置法；（b） 最小曲率法；（c） 反距离加权法
Figure 3. Images of residuals for different interpolation methods
（a） Least squares collocation method；（b） Minimum curvature method；（c） Inverse distance weighting method
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图 4 不同插值法不同水平噪声对应的残差标准差
Figure 4. Residual standard deviation corresponding to different levels of noise for three interpolation methods
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图 5 采用T-R协方差函数所得的最小二乘配置参数拟合结果
（a） 协方差函数拟合结果图；（b） 参数A对协方差函数的影响；（c） 参数r′对协方差函数的影响；（d） 参数n对协方差函数的影响
Figure 5. Least-squares collocation parameter fitted by T-R covariance function
（a） Result by fitting covariance function；（b） The effect of parameter A on the covariance function；（c） The effect of parameter r′ on the covariance function；（d） The effect of parameter n on the covariance function
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图 6 基于不同插值法的重力场模型对比
（a） 自由空气重力异常场；（b） 最小曲率法插值结果；（c） 反距离加权法插值结果；（d） 最小二乘配置法插值结果
Figure 6. Comparison of gravity field models bassed on different interpolation method
（a） Free air gravity anomaly field；（b） Interpolation result of minimum curvature method；（c） Interpolation result of inverse distance weighting method；（d） Interpolation result of least square collocation method
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图 7 不同插值方法的残差影像图
（a） 最小二乘配置法；（b） 最小曲率法；（c） 反距离加权法
Figure 7. Images of residuals of different interpolation methods
（a） Least square collocation method；（b） Minimum curvature method；（c） Inverse distance weighting method
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