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

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.

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.

scholarly journals Universal dispersion tables 1. Love waves across oceans and continents on a spherical earth

1964 ◽  
Vol 54 (2) ◽  
pp. 681-726
Author(s):  
Don L. Anderson
Keyword(s):  
Wave Dispersion ◽  
Love Waves ◽  
Earth Model ◽  
Powerful Method ◽  
Surface Wave Dispersion ◽  
Period Range ◽  
The Earth ◽  
Data Application ◽  
Dispersion Data ◽  
Spherical Earth

ABSTRACT The variational approach to surface wave dispersion problems has been largely replaced by the powerful method of Haskell which is exact and particularly convenient for use on digital computers. This paper shows how the two methods may be combined to yield dispersion curves which can be used to interpret data from any layered structure. A set of graphs and tables is presented which can be used to calculate the dispersion of Love waves in the period range of 4 to 1000 seconds over any spherical earth model. In addition, it is possible to determine by inspection which portion of the earth is contributing to a set of observed dispersion data thereby facilitating the design of an appropriate earth model. These tables can be used to determine how much freedom can be taken with proposed models without violating dispersion data. Application to the inverse problem is immediate.

Static deformation of a spherical earth model by internal dislocations

1969 ◽  
Vol 59 (2) ◽  
pp. 813-853
Author(s):  
Ari Ben-Menahem ◽  
Sarva Jit Singh ◽  
Faïza Solomon
Keyword(s):  
Poisson Ratio ◽  
Epicentral Distance ◽  
Source Parameters ◽  
Nodal Line ◽  
Earth Model ◽  
Lower Hemisphere ◽  
Surface Displacements ◽  
Spherical Earth ◽  
Global Deformation ◽  
Deformation Patterns

abstract A localized displacement dislocation is placed inside a homogeneous non-gravitating elastic sphere. The ensuing deformation is obtained in the form of rapidly converging series for arbitrary values of the Poisson ratio and the source parameters. Surface displacements and strains are computed for various sources for an average earth model. The numerical results are mapped on tangential planes and displayed in several forms. It is found that in the range 30° < θ < 120° the elongation strains fall off with the epicentral distance like Δ−α where 114 < α < 6, provided one proceeds along an arc which does not intersect a nodal line. In the lower hemisphere (90° < θ < 180°) relative to the source, seismic events such as the Chilean earthquake of May, 1960, should produce strains of the order of 10−9, which are on the threshold of detectability of modern extensometers, tiltmeters and rotationmeters. The range in which the half-space approximation is valid is determined. It is demonstrated that global deformation patterns of major earthquakes can serve as a useful diagnostic tool for recovering the source's spatial characteristics.

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