A Refined Least Squares Collocation Method Based on Multiquadric Function

XIE Xilin; XU Caijun; WEN Yangmao; ZHOU Lixuan

doi:10.13203/j.whugis20150664

Volume 43 Issue 4

Apr. 2018

Turn off MathJax

Article Contents

Abstract

References

Geomatics and Information Science of Wuhan University > 2018 > 43(4): 592-598. > DOI: 10.13203/j.whugis20150664

XIE Xilin, XU Caijun, WEN Yangmao, ZHOU Lixuan. A Refined Least Squares Collocation Method Based on Multiquadric Function[J]. Geomatics and Information Science of Wuhan University, 2018, 43(4): 592-598. DOI: 10.13203/j.whugis20150664

Citation:

PDF (5260 KB)

A Refined Least Squares Collocation Method Based on Multiquadric Function

XIE Xilin^1,,
XU Caijun^{1, 2, 3},
WEN Yangmao^{1, 2, 3, ,},
ZHOU Lixuan¹

1.
School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China
2.
Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan 430079, China
3.
Collaborative Innovation Center of Geospatial Technology, Wuhan University, Wuhan 430079, China

Funds:

The National High-Tech Research and Development Program of China (863 Program) 2013AA122501-3

the Special Earthquake Industry Research Project 201308009

the National Natural Science Foundation of China 41431069

the National Natural Science Foundation of China 41574002

the National Natural Science Foundation of China 41721003

the National Natural Science Foundation of China 41774011

More Information

Author Bio:
XIE Xilin, master, specializes in the theories and methods of Geophysical Geodesy.xlxie@whu.edu.cn
Corresponding author:
WEN Yangmao, PhD, associate professor.E-mail:ymwen@sgg.whu.edu.cn
Received Date: March 05, 2016
Published Date: April 04, 2018

Graphical Abstract

Abstract

Abstract

Trend removal is the most common approach in conventional least squares collocation (LSC) to deal with nonstationarity. Due to the inaccuracy of the trend model, conventional LSC can barely eliminate the drift component of the data that results in estimation bias of the local covariance function and error of the interpolation values. Here we present a refined LSC method to estimate the drift component of the field and compensate the residualfrom LSC. The refined method employs the mulitiquadric function to approach the drift and the collocation to estimate signals. We apply the refined method to a synthetic data set and coseismic displacement data from the 2009 L'Aquila, Italy earthquake, and compare the results of refined method with conventional methods. The statistical results of residuals indicate that the refined method can achieve a more accurate result than conventional methods and is affected less by the observation distribution.
- multiquadric function,
- least squares collocation,
- spatial interpolation,
- ill-condition

FullText(HTML)

References (27)

References

[1]	Moritz H. Least Squares Collocation[J].Reviews of Geophysics and Space Physics, 1978(16):421-430 doi: 10.1029/RG016i003p00421/full
[2]	吴啸龙, 杨志强, 党永超.基于球面最小二乘配置的福建省地壳水平形变研究[J].武汉大学学报·信息科学版, 2015, 40(3):401-405 http://ch.whu.edu.cn/CN/abstract/abstract3218.shtml Wu Xiaolong, Yang Zhiqiang, Dang Yongchao. Study on Horizontal Crustal Deformation in Fujian Province Using Spherical Least Square Collocation[J].Geomatics and Information Science of Wuhan University, 2015, 40(3):401-405 http://ch.whu.edu.cn/CN/abstract/abstract3218.shtml
[3]	陶本藻, 姚宜斌.基于多面核函数配置型模型的参数估计[J].武汉大学学报·信息科学版, 2003, 28(5):547-550 http://ch.whu.edu.cn/CN/abstract/abstract4778.shtml Tao Benzao, Yao Yibin. Parameter Estimation Based on Multi-quadric Collocation Model[J]. Geo-matics and Information Science of Wuhan University, 2003, 28(5):547-550 http://ch.whu.edu.cn/CN/abstract/abstract4778.shtml
[4]	Kahle H G, Cocard M, Peter Y, et al. The GPS Strain Field in the Aegean Sea and Western Anatolia[J].Geophysical Research Letters, 1999, 26(16):2513-2516 doi: 10.1029/1999GL900403
[5]	Kahle H G, Cocard M, Peter Y, et al. GPS-Derived Strain Rate Field Within the Boundary Zones of the Eurasian, African, and Arabian Plates[J].Journal of Geophysical Research, 2000, 105(B10):23353-23370 doi: 10.1029/2000JB900238
[6]	Moritz H. Advanced Physical Geodesy[M]. Tunbridge Wells:Abacus, 1980
[7]	Lambeck K. The Perth Basin:A Possible Framework for its Formation and Evolution[J].Exploration Geophysics, 1987, 18(1-2):124-128 doi: 10.1071/EG987124
[8]	柴洪洲, 崔岳, 明锋.最小二乘配置方法确定中国大陆主要块体运动模型[J].测绘学报, 2009, 38(1):61-65 https://www.wenkuxiazai.com/doc/e81c2c748e9951e79b892774.html Chai Hongzhou, Cui Yue, Ming Feng. The Determination of Chinese Mainland Crustal Movement Model Using Least-Squares Collocation[J].ActaGeodaetica et Cartographica Sinica, 2009, 38(1):61-65 https://www.wenkuxiazai.com/doc/e81c2c748e9951e79b892774.html
[9]	陈光保, 陈永奇, 何秀凤.基于改进最小二乘配置的地壳垂直形变分析[J].大地测量与地球动力学, 2010, 30(4):128-132 http://www.cnki.com.cn/Article/CJFDTotal-CHTB201301008.htm Chen Guangbao, Chen Yongqi, He Xiufeng. Analysis of Vertical Crust Deformation by Using Improved Least Square Collocation[J].Journal of Geodesy and Geodynamics, 2010, 30(4):128-132 http://www.cnki.com.cn/Article/CJFDTotal-CHTB201301008.htm
[10]	Armstrong M. Basic Linear Geostatistics[M]. Berlin:Springer, 1998
[11]	Tscherning C C. Geoid Determination by 3D Least-Squares Collocation[M]//Sanso F, Sideris M G. Geoid Determination; Theory and Methods, Lecture Notes in Earth System Sciences 110. Berlin Heidelberg:Springer-Verlag, 2013:311-329
[12]	Goad C C, Tscherning C C, Chin M M. Gravity Empirical Covariance Values for the Continental United States[J]. Journal of Geophysical Research, 1984, 89(B9):7962-7968 doi: 10.1029/JB089iB09p07962
[13]	Stopar B, Kuhar A T M, Turk G. GPS-Derived Geoid Using Artificial Neural Network and Least Squares Collocation[J]. Survey Review, 2006, 38(300):513-524 doi: 10.1179/sre.2006.38.300.513
[14]	Cressie N. Statistics for Spatial Data[M]. New York:Wiley Inc., 1993
[15]	Hardy R L. Multiquadric Equations of Topography and Other Irregular Surfaces[J]. Journal of Geophysical Research, 1971, 76(8):1905-1915 doi: 10.1029/JB076i008p01905
[16]	Hardy R L. Research Results in the Application of Multiquadric Equations to Surveying and Mapping Problems[J]. Surveying and Mapping, 1975, 35:321-332 https://trid.trb.org/view/66619
[17]	Franke R. Scattered Data Interpolation-Tests of Some Methods[J]. Mathematics of Computation, 1982, 38(157):181-200 http://www.ams.org/journals/mcom/1982-38-157/S0025-5718-1982-0637296-4/home.html
[18]	Kansa E J. Multiquadrics-A Scattered Data Approximation Scheme with Applications to Computational Fluid-Dynamics-I Surface Approximations and Partial Derivative Estimates[J]. Computers & Mathematics with Applications, 1990, 19(8-9):127-145 https://www.sciencedirect.com/science/article/pii/089812219090270T
[19]	武艳强, 江在森, 杨国华, 等.利用多面函数整体求解GPS应变场的方法及应用[J].武汉大学学报·信息科学版, 2009, 34(9):1085-1089 http://ch.whu.edu.cn/CN/abstract/abstract1372.shtml Wu Yanqiang, Jiang Zaisen, Yang Guohua, et al. Application and Method of GPS Strain Calculating in Whole Mode Using Multi-surface Function[J].Geomatics and Information Science of Wuhan University, 2009, 34(9):1085-1089 http://ch.whu.edu.cn/CN/abstract/abstract1372.shtml
[20]	刘经南, 施闯, 姚宜斌, 等.多面函数拟合法及其在建立中国地壳平面运动速度场模型中的应用研究[J].武汉大学学报·信息科学版, 2001, 26(6):500-508 http://ch.whu.edu.cn/CN/abstract/abstract5221.shtml Liu Jingnan, Shi Chuang, Yao Yibin, et al. Hardy Function Interpolation and its Applications to the Establishment of Crustal Movement Speed Field[J].Geomatics and Information Science of Wuhan University, 2001, 26(6):500-508 http://ch.whu.edu.cn/CN/abstract/abstract5221.shtml
[21]	陈家军, 郭乔羽, 王红旗, 等.应用协同-泛克立格法估计地下水水位[J].水利学报, 2000, 31(7):7-13 https://www.wenkuxiazai.com/doc/ac9a6ec0360cba1aa911da05.html Chen Jiajun, Guo Qiaoyu, Wang Hongqi, et al. The Application of Co-universal Kriging Method for Estimation of Groundwater Table[J]. Journal of Hydraulic Engineering, 2000, 31(7):7-13 https://www.wenkuxiazai.com/doc/ac9a6ec0360cba1aa911da05.html
[22]	Okada Y. Surface Deformation due to Shear and tensile Faults in a Half-Space[J].International Journal of Rock Mechanics and Mining Sciences &Geomechanics Abstracts, 1985, 23(4):1135-1154 http://bssa.geoscienceworld.org/content/75/4/1135.short
[23]	温扬茂, 何平, 许才军, 等.联合Envisat和ALOS卫星影像确定L'Aquila地震震源机制[J].地球物理学报, 2012, 55(1):53-65 Wen Yangmao, He Ping, Xu Caijun, et al. Source Parameters of the 2009 L'Aquila Earthquake, Italy from Envisat and ALOS Satellite SAR Images[J]. Chinese Journal of Geophysics, 2012, 55(1):53-65
[24]	Cheloni D, D'Agostino N, D'Anastasio E, et al. Coseismic and Initial Post-Seismic Slip of the 2009 Mw 6.3 L'Aquila Earthquake, Italy, from GPS Measurements[J].Geophysical Journal International, 2010, 181(3):1539-1546 doi: 10.1111/j.1365-246X.2010.04584.x
[25]	黄谟涛, 欧阳永忠, 翟国君, 等.融合多源重力数据的Tikhonov正则化配置法[J].海洋测绘, 2013, 33(3):6-12 http://d.wanfangdata.com.cn/Periodical_hych201303002.aspx Huang Motao, Ouyang Yongzhong, Zhai Guojun, et al. Tikhonov Regularization Collocation for Multi-source Gravity Data Fusion Processing[J]. Hydrographic Surveying and Charting, 2013, 33(3):6-12 http://d.wanfangdata.com.cn/Periodical_hych201303002.aspx
[26]	Tikhonov A N, Arsenin V Y. Solutions of Ill-posed Problems[M]. New York:Wiley Inc., 1977
[27]	Hansen P C. Analysis of Discrete Ill-posed Problems by Means of the L-curve[J]. Siam Review, 1992, 34(4):561-580 doi: 10.1137/1034115

[1]	DU Yan, NING Lize, XIE Mowen, BAI Yunfei, LI Heng, JIA Beining. A Prediction Model of Landslide Displacement in Reservoir Area Considering Time Lag Effect[J]. Geomatics and Information Science of Wuhan University, 2024, 49(8): 1347-1355. DOI: 10.13203/j.whugis20220133
[2]	XIAO Ruya, HE Xiufeng. Deformation Monitoring of Reservoirs and Dams Using Time-Series InSAR[J]. Geomatics and Information Science of Wuhan University, 2019, 44(9): 1334-1341. DOI: 10.13203/j.whugis20170327
[3]	ZHANG Yan, LV Pinji, LIU Jia. Impact of the Yangtze River Three Gorges Reservoir on Fault Activity[J]. Geomatics and Information Science of Wuhan University, 2017, 42(10): 1497-1500. DOI: 10.13203/j.whugis20140983
[4]	HUANG Shengxiang, LUO Li. Stability Analysis and Results of the Landslide MonitoringDatum in the Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2014, 39(3): 367-372. DOI: 10.13203/j.whugis20120019
[5]	WU Xueling, REN Fu, NIU Ruiqing. Spatial Intelligent Prediction of Landslide Hazard Based on Multi-source Data in Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2013, 38(8): 963-968.
[6]	HU Teng, DU Ruilin, ZHANG Zhenhua, WU Yue. Simulation and Mechanism Analysis on Crustal Vertically Deformation in Three Gorges Reservoir Area Under the Condition of Reservoir Impoundment[J]. Geomatics and Information Science of Wuhan University, 2010, 35(1): 33-36.
[7]	WU Tao, YAN Huiwu, TANG Guigang. Prediction on Time Series Analysis of Water Quality in Yangtze Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2006, 31(6): 500-502.
[8]	DU Ruilin, QIAO Xuejun, YANG Shaomin, WANG Qi. Results of the Crustal Deformation by GPS Survey and Horizontal Strain Rate Fields in the Three Gorges Area[J]. Geomatics and Information Science of Wuhan University, 2004, 29(9): 768-771.
[9]	SHI Dong, CHEN Jun, ZHU Qing. Oil-Gas Reservoir Evaluation Based on GIS[J]. Geomatics and Information Science of Wuhan University, 2004, 29(7): 592-596.
[10]	JIANG Fuzhen. Role of Gravimetry in Monitoring the Crustal Deformation of Three Gorges Reservoir Area[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6): 679-682.

Cited By

Cited by

Periodical cited type(6)

1.	李惠民，彭紫薇，李相如. 气候变化下干旱对大别山区植被的影响研究. 治淮. 2024(12): 44-46 .
2.	谢萍，张双喜，金涛勇，韦瑜，蔡剑锋，许晨. 武汉市GRACE水储量变化与气象干旱关联趋势分析. 排灌机械工程学报. 2023(06): 624-629 .
3.	胡艳茹，梁丽娇，何立平，许文锋，刘正学，兰波. 三峡水库蓄水前后库区及周边区域降水变化及其影响因素. 地理研究. 2023(07): 1921-1940 .
4.	肖家豪，张双喜，韦瑜，蔡剑锋，洪敏. 基于GPS垂向位移测定云南地区陆地水储量及其对累积降雨的响应机制. 测绘通报. 2022(01): 61-65 .
5.	咬登魁，段功豪. 基于季节性SARIMA模型的武汉市长序列降雨量趋势分析与预测. 地下水. 2022(02): 166-168 .
6.	谢萍，张双喜，周吕，李庆隆，肖家豪，蔡剑锋. 武汉市中心城区地表形变与洪涝灾害防治新策略. 武汉大学学报(信息科学版). 2021(07): 1015-1024 .

Other cited types(7)

Get Citation

PDF

XML

Article views (1815) PDF downloads (366) Cited by(13)

A Refined Least Squares Collocation Method Based on Multiquadric Function

Abstract

References

Related Articles

Cited by

Periodical cited type(6)

Other cited types(7)

Catalog

Related

A Refined Least Squares Collocation Method Based on Multiquadric Function

Abstract

References

Related Articles

Cited by

Periodical cited type(6)

Other cited types(7)

Catalog

Related

Export File

Citation

Format

Content