Approximate solutions of the surface mass loading of a spherical Earth model

1985 ◽  
Vol 29 (4) ◽  
pp. 326-338
Author(s):  
Antonín Zeman ◽  
Z. Martinů
Keyword(s):  
Approximate Solutions ◽  
Earth Model ◽  
Mass Loading ◽  
Surface Mass ◽  
Spherical Earth

scholarly journals Basis functions for the consistent and accurate representation of surface mass loading

2017 ◽  
Author(s):  
Peter Clarke ◽  
David Lavallee ◽  
Geoffrey Blewitt ◽  
Tonie van Dam
Keyword(s):  
Basis Functions ◽  
Mass Loading ◽  
Surface Mass ◽  
Accurate Representation

scholarly journals An Efficient Computation of Effective Ground Range Using an Oblate Earth Model

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Dalal A. Maturi ◽  
Malik Zaka Ullah ◽  
Shahid Ahmad ◽  
Fayyaz Ahmad
Keyword(s):  
Oblate Spheroid ◽  
Ballistic Missile ◽  
Earth Model ◽  
Arc Length ◽  
Efficient Computation ◽  
Explicit Formulas ◽  
Spherical Earth

An effcient method is presented to calculate the ground range of a ballistic missile trajectory on a nonrotating Earth. The spherical Earth model does not provide good approximation of distance between two locations on the surface of Earth. We used oblate spheroid Earth model because it provides better approximations. The effective ground range of a ballistic missile is an arc-length of a planner elliptic (or circle) curve which passes through the launch and target points on the surface of Earth model. A general formulation is presented to calculate the arc-length of an elliptic (or circle) curve which is the intersection of oblate Earth model and a plane. Explicit formulas are developed to calculate the coordinates of center of the ellipse as well as major and minor axes which are necessary ingredients for the calculation of effective ground range.

scholarly journals Analysis of the Potential Contributors to Common Mode Error in Chuandian Region of China

2020 ◽  
Vol 12 (5) ◽  
pp. 751
Author(s):  
Weijie Tan ◽  
Junping Chen ◽  
Danan Dong ◽  
Weijing Qu ◽  
Xueqing Xu
Keyword(s):  
Time Series ◽  
Soil Moisture ◽  
Principal Component ◽  
Mass Loading ◽  
Common Mode ◽  
Surface Mass ◽  
Common Mode Error ◽  
Comparison Results ◽  
Wide Range ◽  
Gps Time Series

Common mode error (CME) in Chuandian region of China is derived from 6-year continuous GPS time series and is identified by principal component analysis (PCA) method. It is revealed that the temporal behavior of the CME is not purely random, and contains unmodeled signals such as nonseasonal mass loadings. Its spatial distribution is quite uniform for all GPS sites in the region, and the first principal component, uniformly distributed in the region, has a spatial response of more than 70%. To further explore the potential contributors of CME, daily atmospheric mass loading and soil moisture mass loading effects are evaluated. Our results show that ~15% of CME can be explained by these daily surface mass loadings. The power spectral analysis is used to assess the CME. After removing atmospheric and soil moisture loadings from the CME, the power of the CME reduces in a wide range of frequencies. We also investigate the contribution of CME in GPS filtered residuals time series and it shows the Root Mean Squares (RMSs) of GPS time series are reduced by applying of the mass loading corrections in CME. These comparison results demonstrate that daily atmosphere pressure and the soil moisture mass loadings are a part of contributors to the CME in Chuandian region of China.

scholarly journals Geometric Spreading of Pn and Sn in a Spherical Earth Model

2007 ◽  
Vol 97 (6) ◽  
pp. 2053-2065 ◽  
Author(s):  
X. Yang ◽  
T. Lay ◽  
X.-B. Xie ◽  
M. S. Thorne
Keyword(s):  
Earth Model ◽  
Geometric Spreading ◽  
Spherical Earth

Transformation of the earthquake displacement field for spherical earth—Static case

1971 ◽  
Vol 61 (4) ◽  
pp. 861-874
Author(s):  
Hans R. Wason ◽  
Sarva Jit Singh
Keyword(s):  
Displacement Field ◽  
Spherical Surface ◽  
Homogeneous Medium ◽  
Addition Theorem ◽  
Polar Coordinate System ◽  
Earth Model ◽  
Static Case ◽  
Spherical Earth ◽  
Polar Coordinate ◽  
Internal Sources

abstract Explicit expressions for the static displacement field for a Volterra dislocation and a center of compression in an infinite homogeneous medium are obtained. Using an addition theorem, the field is transformed to a polar coordinate system with origin at the center of the Earth. Expressions for the discontinuity in the motion stress vector across the concentric spherical surface through the source are then obtained. These results can be used in studying the deformation of a multilayered spherical earth model induced by internal sources by the Thomson-Haskell matrix method which has so far been mostly applied to dynamic problems.

The bottom of the universe: Flat earth science in the Age of Encounter

2016 ◽  
Vol 55 (1) ◽  
pp. 61-85 ◽  
Author(s):  
James J Allegro
Keyword(s):  
Sixteenth Century ◽  
Earth Science ◽  
Earth Model ◽  
Early Christian ◽  
The Earth ◽  
Spherical Earth ◽  
Cast Doubt ◽  
European Thought ◽  
The Universe ◽  
Empirical Stance

This essay challenges the dominance of the spherical earth model in fifteenth- and early-sixteenth-century Western European thought. It examines parallel strains of Latin and vernacular writing that cast doubt on the existence of the southern hemisphere. Three factors shaped the alternate accounts of the earth as a plane and disk put forward by these sources: (1) the unsettling effects of maritime expansion on scientific thought; (2) the revival of interest in early Christian criticism of the spherical earth; and (3) a rigid empirical stance toward entities too large to observe in their entirety, including the earth. Criticism of the spherical earth model faded in the decades after Magellan’s crew returned from circuiting the earth in 1522.

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