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| Interpolation of potential-field data by Projection Onto Convex Sets algorithm with generalized exponential threshold and based on Discrete Cosine Transform |
AI Han-Bing( ), WANG Yan-Guo() |
| School of Geophysical and Measurement-Control Technology, East China University of Technology,Nanchang 330013, China |
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Abstract Data filling or interpolation is a fundamental and vital problem of potential-field data processing. Some data cannot be measured when some places are unable to reach, such as rivers, or cliffs. If we want to acquire the missing data for better subsequent processing, we need to interpolate or fill in the missing data. Hence, this article introduces the Discrete Cosine Transform (DCT) method into the Projection Onto Convex Sets (POCS) algorithm to tackle this problem, and a generalized exponential threshold attenuation method is also given. Finally, model tests and practical applications show that the POCS algorithm with generalized exponential threshold and based on DCT has the advantages of high accuracy, small filling or interpolating traces and the noise standard of the filled data are closer to real situation.
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Received: 04 January 2021
Published: 21 December 2021
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Corresponding Authors:
WANG Yan-Guo
E-mail: 1724178612@qq.com;wangyg8503@126.com
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The mechanism of POCS method[10]
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The flow-process diagram of POCS method to interpolate based on DCT
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| 模型编号 | 模型类型 | x方向范围/m | y方向范围/m | z方向范围/m | 密度/(g·cm-3) | | Model 1 | 圆柱体 | -200~200 | -190~-110 | 10~90 | 2 | | Model 2 | 棱柱体 | -50~50 | -50~50 | 20~400 | -2 | | Model 3 | 棱柱体 | -200~0 | 100~200 | 30~1000 | 2 | | Model 4 | 球体 | 100~200 | 100~200 | 10~110 | 2 |
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Model parameters
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Forward gravity anomaly with complete data and the target zone (pink part)
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Results of interpolation using conventional methods and the differences with the original data
a、b—interpolated result of Kriging and its residuo;c、d—interpolated result of radial basis function and its residuo;e、f—interpolated result of inverse distance to a power and its residuo;g、h—interpolated result of minimum curvature and its residuo
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| 处理方法 | 均方根误差/mGal | | 克里金法 | 0.123 | | 径向基函数法 | 0.113 | | 反距离加权法 | 0.285 | | 最小曲率法 | 0.217 |
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RMS errors of interpolating data using different conventional interpolation methods
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The relationship between the errors of interpolating data by using POCS with different threshold models and the total number of iterations
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Results of interpolation using POCS method with linear and exponential threshold and the difference with the original data (K=800)
a、b—interpolated result using linear threshold and its residuo;c、d—interpolated result using exponential threshold (Para=0.5) and its residuo;e、f—interpolated result using exponential threshold (Para=1) and its residuo;g、h—interpolated result using exponential threshold (Para=2) and its residuo
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Fig. 3
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Gravity anomaly and missing site after adding 30% random noise of Fig. 3
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Results of interpolating noise-corrupted data using conventional interpolation methods and the difference with the original noise-free data
a、b—interpolated result of Kriging and its residuo;c、d—interpolated result of radial basis function and its residuo;e、f—interpolated result of inverse distance to a power and its residuo;g、h—interpolated result of minimum curvature and its residuo
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| 插值方法 | 均方根误差/mGal | | 克里金法 | 0.191 | | 径向基函数法 | 0.185 | | 反距离加权法 | 0.315 | | 最小曲率法 | 0.280 |
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RMS errors of interpolating noise-corrupted data using different conventional interpolation methods
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The relationship between the errors of interpolation data using POCS with different threshold models for the noise-corrupted data and the total number of iterations
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Results of interpolation using POCS method with linear and exponential threshold model and the differences with the noise-free data
a、b—interpolated result using linear threshold and its residuo;c、d—interpolated result using exponential threshold (Para=0.5) and its residuo;e、f—interpolated result using exponential threshold (Para=1) and its residuo;g、h—interpolated result using exponential threshold (Para=2) and its residuo
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Bouguer gravity anomaly of Nenbei Farm in Heilongjiang Province and the target zone (pink part)
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Results of interpolation using conventional methods and the differences with the real data
a、b—interpolated result of Kriging and its residuo;c、d—interpolated result of radial basis function and its residuo;e、f—interpolated result of inverse distance to a power and its residuo;g、h—interpolated result of minimum curvature and its residuo
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| 处理方法名称 | 均方根误差/mGal | | 克里金法 | 0.105 | | 径向基函数法 | 0.091 | | 反距离加权法 | 0.298 | | 最小曲率法 | 0.105 |
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The errors of interpolation results using conventional methods for the read data
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The relationship between the errors of interpolating data using POCS with different threshold models and the total number of iterations
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Using exponential threshold-based POCS method to interpolate real field data
a—interpolated result (Para=0.5);b—the residuo (K=6500)
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