Propagation of Disturbances in a Gutenberg-Bullen A' Spherical Earth Model: Travel Times and Amplitudes of S Waves

2013 ◽  
pp. 482-494 ◽  
Author(s):  
Mark Landisman ◽  
Yasuo Satô ◽  
Tatsuo Usami
Keyword(s):  
Earth Model ◽  
Travel Times ◽  
S Waves ◽  
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.

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

Stability of P an S velocities from Central California quarry blasts

1974 ◽  
Vol 64 (2) ◽  
pp. 343-353 ◽  
Author(s):  
T. V. McEvilly ◽  
L. R. Johnson
Keyword(s):  
Strike Slip ◽  
Travel Times ◽  
Mean Values ◽  
Central California ◽  
S Waves ◽  
Source Regions ◽  
Reading Errors ◽  
The Mean ◽  
Velocity Variations

abstract Travel times of crustal P and S waves from 70 quarry blasts in Central California between July 1961 and June 1973 have been measured for seven paths 46 to 168 km long passing in several cases within 10 km of hypocenters of moderate (ML 4.5 to 5.4) earthquakes. All P and S times and their ratios TS/TP lie within 2.3 per cent of the mean values and over 97 per cent of the TS/TP ratios lie within 1 per cent of the mean values. Variations can be explained by reading errors and uncertainties in source times and locations. There are no indications of velocity variations related to earthquake occurrences. Mean VP/VS ratios range from 1.73 to 1.84 for the various paths. The phenomenon of premonitory dilatancy accompanied by a 10 to 20 per cent reduction in VP or VP/VS cannot be reconciled with these observations unless the affected source regions have lateral dimensions less than about 5 km for these moderate strike-slip earthquakes.

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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