Polyhedral approximations in physical geodesy

1996 ◽  
Vol 70 (11) ◽  
pp. 755-767 ◽  
Author(s):  
M. Ivan
Keyword(s):  
Physical Geodesy ◽  
Polyhedral Approximations

scholarly journals Polyhedral approximations of the semidefinite cone and their application

2021 ◽  
Author(s):  
Yuzhu Wang ◽  
Akihiro Tanaka ◽  
Akiko Yoshise
Keyword(s):  
Initial Approximation ◽  
Semidefinite Relaxation ◽  
Stable Set ◽  
Cutting Plane Methods ◽  
Diagonally Dominant Matrices ◽  
Maximum Stable Set ◽  
Simple Expansion ◽  
Diagonally Dominant ◽  
Polyhedral Approximations ◽  
Semidefinite Cone

AbstractWe develop techniques to construct a series of sparse polyhedral approximations of the semidefinite cone. Motivated by the semidefinite (SD) bases proposed by Tanaka and Yoshise (Ann Oper Res 265:155–182, 2018), we propose a simple expansion of SD bases so as to keep the sparsity of the matrices composing it. We prove that the polyhedral approximation using our expanded SD bases contains the set of all diagonally dominant matrices and is contained in the set of all scaled diagonally dominant matrices. We also prove that the set of all scaled diagonally dominant matrices can be expressed using an infinite number of expanded SD bases. We use our approximations as the initial approximation in cutting plane methods for solving a semidefinite relaxation of the maximum stable set problem. It is found that the proposed methods with expanded SD bases are significantly more efficient than methods using other existing approximations or solving semidefinite relaxation problems directly.

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>

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