Distribution of vertical crustal movement rates in the Tohoku district, Japan, predicted by least-squares collocation

1997 ◽  
Vol 71 (7) ◽  
pp. 432-442 ◽  
Author(s):  
G. S. El-Fiky ◽  
Teruyuki Kato ◽  
Yoichiro Fujii
Keyword(s):  
Least Squares ◽  
Crustal Movement ◽  
Least Squares Collocation ◽  
Vertical Crustal Movement ◽  
Movement Rates

scholarly journals Adaptive Least-Squares Collocation Algorithm Considering Distance Scale Factor for GPS Crustal Velocity Field Fitting and Estimation

2019 ◽  
Vol 11 (22) ◽  
pp. 2692 ◽  
Author(s):  
Wei Qu ◽  
Hailu Chen ◽  
Shichuan Liang ◽  
Qin Zhang ◽  
Lihua Zhao ◽  
...  
Keyword(s):  
Least Squares ◽  
Covariance Function ◽  
High Reliability ◽  
Scale Factor ◽  
Distance Scale ◽  
Crustal Movement ◽  
Least Squares Collocation ◽  
Crustal Velocity ◽  
Regional Tectonic ◽  
Gps Observations

High-precision, high-reliability, and high-density GPS crustal velocity are extremely important requirements for geodynamic analysis. The least-squares collocation algorithm (LSC) has unique advantages over crustal movement models to overcome observation errors in GPS data and the sparseness and poor geometric distribution in GPS observations. However, traditional LSC algorithms often encounter negative covariance statistics, and thus, calculating statistical Gaussian covariance function based on the selected distance interval leads to inaccurate estimation of the correlation between the random signals. An unreliable Gaussian statistical covariance function also leads to inconsistency in observation noise and signal variance. In this study, we present an improved LSC algorithm that takes into account the combination of distance scale factor and adaptive adjustment to overcome these problems. The rationality and practicability of the new algorithm was verified by using GPS observations. Results show that the new algorithm introduces the distance scale factor, which effectively weakens the influence of systematic errors by improving the function model. The new algorithm can better reflect the characteristics of GPS crustal movement, which can provide valuable basic data for use in the analysis of regional tectonic dynamics using GPS observations.

Further Analysis of Vertical Crustal Movement Observations in the Lac St. Jean Area, Quebec

1972 ◽  
Vol 9 (9) ◽  
pp. 1139-1147 ◽  
Author(s):  
Petr Vaníček ◽  
Angus C. Hamilton
Keyword(s):  
Systematic Error ◽  
Confidence Limit ◽  
Statistical Tests ◽  
Crustal Movement ◽  
Quebec City ◽  
Confidence Limits ◽  
Downward Movement ◽  
Vertical Crustal Movement ◽  
Movement Rates ◽  
The North

Further statistical tests have been made on levelling data in the Lac St. Jean area of Québec. These tests confirm that relative to Québec City there is downward movement focussed about Stoneham at the rate of 45.7 cm per century with a 95% confidence limit of ± 14.5 cm per century, and that there is uplift to the north and west with rates and 95% confidence limits of 58.8 ± 12.5 cm per century at St. Félicien and 83.5 ± 22.8 cm per century at Senneterre.A test for correlation between elevation differences and movement rates showed no significant effect; this is interpreted as evidence there was no appreciable systematic error in the levelling. From these analyses the possibility that the results might be explained in terms of errors, either random or systematic, can be rejected without any reservations.

scholarly journals The least-squares collocation method in the mechanics of deformable solids

2021 ◽  
Vol 1715 ◽  
pp. 012029
Author(s):  
Sergey Golushko ◽  
Vasily Shapeev ◽  
Vasily Belyaev ◽  
Luka Bryndin ◽  
Artem Boltaev ◽  
...  
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Least Squares Collocation ◽  
Deformable Solids ◽  
Mechanics Of Deformable Solids

scholarly journals On the uncertainty of height anomaly differences predicted by least-squares collocation

2020 ◽  
Vol 10 (1) ◽  
pp. 53-61
Author(s):  
E. Mysen
Keyword(s):  
Least Squares ◽  
Spatial Separation ◽  
Height Anomaly ◽  
Surface Model ◽  
Least Squares Collocation ◽  
Normal Heights ◽  
Gravimetric Quasigeoid ◽  
The Difference ◽  
Grid Interpolation ◽  
Gps Observations

AbstractA network of pointwise available height anomalies, derived from levelling and GPS observations, can be densified by adjusting a gravimetric quasigeoid using least-squares collocation. The resulting type of Corrector Surface Model (CSM) is applied by Norwegian surveyors to convert ellipsoidal heights to normal heights expressed in the official height system NN2000. In this work, the uncertainty related to the use of a CSM to predict differences in height anomaly was sought. As previously, the application of variograms to determine the local statistical properties of the adopted collocation model led to predictions that were consistent with their computed uncertainties. For the purpose of predicting height anomaly differences, the effect of collocation was seen to be moderate in general for the small spatial separations considered (< 10 km). However, the relative impact of collocation could be appreciable, and increasing with distance, near the network. At last, it was argued that conservative uncertainties of height anomaly differences may be obtained by rescaling output of a grid interpolation by \sqrt \Delta, where Δ is the spatial separation of the two locations for which the difference is sought.

Application of Fitting Estimation Method in GPS Height Fitting

2013 ◽  
Vol 694-697 ◽  
pp. 2545-2549 ◽  
Author(s):  
Qian Wen Cheng ◽  
Lu Ben Zhang ◽  
Hong Hua Chen
Keyword(s):  
Least Squares ◽  
Estimation Method ◽  
Least Square ◽  
Least Squares Collocation ◽  
Normal Height ◽  
Geodetic Height ◽  
The Given ◽  
Surveying And Mapping

The key point researched by many scholars in the field of surveying and mapping is how to use the given geodetic height H measured by GPS to obtain the normal height. Although many commonly-used fitting methods have solved many problems, they all value the pending parameters as the nonrandom variables. Figuring out the best valuations, according to the traditional least square principle, only considers its trend or randomness, which is theoretically incomprehensive and have limitations in practice. Therefore, a method is needed not only considers its trend but also takes randomness into account. This method is called the least squares collocation.

scholarly journals Polar motion from ILS observations with least-squares collocation

1988 ◽  
Vol 128 ◽  
pp. 215-220
Author(s):  
R. Verbeiren
Keyword(s):  
Least Squares ◽  
Observational Data ◽  
Polar Motion ◽  
Parameter Determination ◽  
Large Set ◽  
Powerful Method ◽  
Least Squares Collocation ◽  
Computational Step

Least-squares collocation is a powerful method for combining interpolation, filtering and parameter determination in one single computational step. We show that the method is applicable to the computation of polar motion values from a very large set of basic observational data. In this study, we use the ILS observations from 1900 to 1978.

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