Maximal Correlation Adjustment in Physical Geodesy

1993 ◽  
pp. 242-245
Author(s):  
Svetozar Petrović
Keyword(s):  
Physical Geodesy ◽  
Maximal Correlation

scholarly journals DETERMINATION AND MAPPING OF THE TERRESTRIAL GRAVITY ANOMALIES IN THE MOUNTAINOUS AREAS OF IRAQ

2021 ◽  
Vol 6 (24) ◽  
pp. 213-225
Author(s):  
Shazad Jamal Jalal ◽  
Tajul Ariffin Musa ◽  
Ami Hassan Md Din ◽  
Wan Anom Wan Aris
Keyword(s):  
Gravity Data ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Gravity Survey ◽  
Mountainous Areas ◽  
Entire Study ◽  
Terrestrial Gravity ◽  
The Past ◽  
Regional Gravity ◽  
Entire Study Area

Gravity data and computing gravity anomalies are regarded as vital for both geophysics and physical geodesy fields. The mountainous areas of Iraq are characterized by the lack of regional gravity data because gravity surveys are rarely performed in the past four decades due to the Iraq-Iran war and the internal unstable political situation of this particular region. In addition, the formal map of the available terrestrial gravity which was published by the French Database of Bureau Gravimetrique International (International Gravimetric Bureau-in English) (BGI), introduces Iraq and the study area as a remote area and in white color because of the unavailability of gravity data. However, a dense and local (not regional) gravity data is available which was conducted by geophysics researchers 13 years ago. Therefore, the regional gravity survey of 160 gravity points was performed by the authors at an average 11 km apart, which was covers the whole area of Sulaymaniyah Governorate (part of the mountainous areas of Iraq). In spite of Although the risk of mine fields within the study area, suitable safe routes as well as a helicopter was used for the gravity survey of several points on the top of mountains. The survey was conducted via Lacoste and Romberg geodetic gravimeter and GPS handheld. The objective of the study is to determine and map the gravity anomalies for the entire study area, the data of which would assist different geosciences applications.

Harmonic Correction for Residual Terrain Modelling (RTM) Technique in Physical Geodesy Applications

2021 ◽  
Author(s):  
Meng Yang ◽  
Xiao-Le Deng ◽  
Min Zhong
Keyword(s):  
Gravity Anomaly ◽  
Gravity Field ◽  
Physical Geodesy ◽  
Geoid Height ◽  
Gravity Field Modelling ◽  
Field Modelling ◽  
Condensation Method ◽  
Residual Terrain Modelling ◽  
Harmonic Correction ◽  
Terrain Modelling

<p>       In physical geodesy, the harmonic correction (HC), as one of the main problems when using residual terrain modelling (RTM), has become a research focus of high-frequency gravity field modelling. Over past decades, though various methods have been proposed to handle the HC issues for RTM technique, most of them focused on the HC for RTM gravity anomaly rather than other gravity functionals, such as RTM geoid height and gravity gradient. In practice, the HC for RTM geoid height was generally assumed to be negligible, but a quantification is yet studied. In this study, besides the highlighted HC for gravity anomaly in previous studies, the expressions of HC terms for RTM geoid height are provided in the framework of the classical condensation method under infinite Bouguer plate approximation. The errors involved by various assumption of the classical condensation method, e.g., mass inconsistency between infinite masses in the HC and limited masses in the RTM, and planar assumption of the Earth’s surface, are further studied. Based on the derived formulas, the quantification of HC for RTM geoid height when reference surface is expanded to degree and order of 2,159 is given. Our results showed the significance of HC for RTM geoid height, with values up to ~10 cm, in cm-level and mm-level geoid determination. With integration masses extending up to a sufficient distance, such as 1° from calculation point for the determination of RTM geoid height, the errors due to an infinite Bouguer plate approximation are neglectable small. The validation through comparison with terrestrial measurements proved that the HC terms provided in this study can improve the accuracy of RTM derived geoid height and are expected to be useful for applications of RTM technique in regional and global gravity field modelling.</p>

The rate of convergence of extremes of stationary normal sequences

1983 ◽  
Vol 15 (01) ◽  
pp. 54-80 ◽  
Author(s):  
Holger Rootzén
Keyword(s):  
Rate Of Convergence ◽  
Joint Distribution ◽  
Point Processes ◽  
Rates Of Convergence ◽  
Joint Distribution Function ◽  
Maximal Correlation ◽  
Standard Normal ◽  
Image Position ◽  
The Right ◽  
Right Order

Let {ξ; t = 1, 2, …} be a stationary normal sequence with zero means, unit variances, and covariances let be independent and standard normal, and write . In this paper we find bounds on which are roughly of the order where ρ is the maximal correlation, ρ =sup {0, r 1 , r 2, …}. It is further shown that, at least for m-dependent sequences, the bounds are of the right order and, in a simple example, the errors are evaluated numerically. Bounds of the same order on the rate of convergence of the point processes of exceedances of one or several levels are obtained using a ‘representation' approach (which seems to be of rather wide applicability). As corollaries we obtain rates of convergence of several functionals of the point processes, including the joint distribution function of the k largest values amongst ξ1, …, ξn.

scholarly journals Estimating Visual Field Mean Deviation using Optical Coherence Tomographic Nerve Fiber Layer Measurements in Glaucoma Patients

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Ou Tan ◽  
David S. Greenfield ◽  
Brian A. Francis ◽  
Rohit Varma ◽  
Joel S. Schuman ◽  
...  
Keyword(s):  
Visual Field ◽  
Nerve Fiber ◽  
Weighted Averaging ◽  
Mean Deviation ◽  
Optical Coherence ◽  
Fiber Layer ◽  
Nerve Fiber Layer ◽  
Maximal Correlation ◽  
Advanced Stages ◽  
Higher Sensitivity

AbstractTo construct an optical coherence tomography (OCT) nerve fiber layer (NFL) parameter that has maximal correlation and agreement with visual field (VF) mean deviation (MD). The NFL_MD parameter in dB scale was calculated from the peripapillary NFL thickness profile nonlinear transformation and VF area-weighted averaging. From the Advanced Imaging for Glaucoma study, 245 normal, 420 pre-perimetric glaucoma (PPG), and 289 perimetric glaucoma (PG) eyes were selected. NFL_MD had significantly higher correlation (Pearson R: 0.68 vs 0.55, p < 0.001) with VF_MD than the overall NFL thickness. NFL_MD also had significantly higher sensitivity in detecting PPG (0.14 vs 0.08) and PG (0.60 vs 0.43) at the 99% specificity level. NFL_MD had better reproducibility than VF_MD (0.35 vs 0.69 dB, p < 0.001). The differences between NFL_MD and VF_MD were −0.34 ± 1.71 dB, −0.01 ± 2.08 dB and 3.54 ± 3.18 dB and 7.17 ± 2.68 dB for PPG, early PG, moderate PG, and severe PG subgroups, respectively. In summary, OCT-based NFL_MD has better correlation with VF_MD and greater diagnostic sensitivity than the average NFL thickness. It has better reproducibility than VF_MD, which may be advantageous in detecting progression. It agrees well with VF_MD in early glaucoma but underestimates damage in moderate~advanced stages.

Empirical Determination of the Gravity Anomaly Covariance Function in Mountainous Areas

1980 ◽  
Vol 34 (3) ◽  
pp. 251-264 ◽  
Author(s):  
Gerard Lachapelle ◽  
K. P. Schwarz
Keyword(s):  
Gravity Anomaly ◽  
Covariance Function ◽  
Physical Geodesy ◽  
Gravity Anomalies ◽  
Mountainous Areas ◽  
The North ◽  
Regression Parameters ◽  
Free Air ◽  
Vening Meinesz ◽  
Free Air Gravity

An evaluation of the empirical gravity anomaly covariance function using over 95 000 surface gravity anomalies in the North American Western Cordillera was carried out. A regression analysis of the data exhibits a strong and quasi-linear correlation of free air gravity anomalies with heights. This height correlation is removed from the free air anomalies prior to the numerical evaluation of the gravity anomaly covariance function. This covariance function agrees well with that evaluated previously by the authors for the remainder of Canada. A possible use for such a covariance function of ‘height independent’ gravity anomalies in mountainous areas is described. First, the height independent gravity anomaly at a point of known height is evaluated by least squares prediction using neighboring measured height independent gravity anomalies. Secondly, the part caused by the height correlation is calculated using linear regression parameters estimated previously and added to the predicted height independent gravity anomaly to obtain a predicted standard free air anomaly. This technique can be used to densify the coverage of free air anomalies for subsequent use in integral formulas of physical geodesy, e.g., those of Stokes and Vening Meinesz. This method requires that point topographic heights be given on a grid.

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