Extension of similarity measures in VSM: From orthogonal coordinate system to affine coordinate system

2014 ◽  
Author(s):  
Junyu Xuan ◽  
Jie Lu ◽  
Guangquan Zhang ◽  
Xiangfeng Luo
Keyword(s):  
Coordinate System ◽  
Similarity Measures ◽  
Orthogonal Coordinate System

Three‐component sonde orientation in a deviated well

Geophysics ◽  
1990 ◽  
Vol 55 (10) ◽  
pp. 1386-1388 ◽  
Author(s):  
M. Becquey ◽  
M. Dubesset
Keyword(s):  
Hydraulic Fracturing ◽  
Coordinate System ◽  
Vertical Plane ◽  
Vertical Axis ◽  
Horizontal Axis ◽  
Orthogonal Coordinate System ◽  
Coordinate Rotation ◽  
Orthogonal Components ◽  
Particle Velocities

In well seismics, when operating with a three‐component tool, particle velocities are measured in the sonde coordinate system but are often needed in other systems (e.g., source‐bound or geographic). When the well is vertical, a change from the three orthogonal components of the sonde to another orthogonal coordinate system can be performed through one rotation around the vertical axis and, if necessary, another one around a horizontal axis (Hardage, 1983). If the well is deviated, the change of coordinate system remains easy in the case when the source is located at the vertical of the sonde, or in the case when the source stands in the vertical plane defined by the local well axis. In the general case (offset VSPs or walkaways) or when looking for unknown sources (such as microseismic emissions induced by hydraulic fracturing), coordinate rotation may still be performed, provided that we first get back to a situation in which one of the axes is vertical.

scholarly journals Geometric characteristics of the deformation state of the shells with orthogonal coordinate system of the middle surfaces

2020 ◽  
Vol 16 (1) ◽  
pp. 38-44
Author(s):  
Vyacheslav N. Ivanov ◽  
Alisa A. Shmeleva
Keyword(s):  
Differential Geometry ◽  
Coordinate System ◽  
Thin Shell ◽  
Tensor Analysis ◽  
Vector Analysis ◽  
Thin Shells ◽  
Orthogonal Coordinate System ◽  
Deformation State ◽  
The Common ◽  
To Receive

The aim of this work is to receive the geometrical equations of strains of shells at the common orthogonal not conjugated coordinate system. At the most articles, textbooks and monographs on the theory and analysis of the thin shell there are considered the shells the coordinate system of which is given at the lines of main curvatures. Derivation of the geometric equations of the deformed state of the thin shells in the lines of main curvatures is given, specifically, at monographs of the theory of the thin shells of V.V. Novozhilov, K.F. Chernih, A.P. Filin and other Russian and foreign scientists. The standard methods of mathematic analyses, vector analysis and differential geometry are used to receive them. The method of tensor analysis is used for receiving the common equations of deformation of non orthogonal coordinate system of the middle shell surface of thin shell. The equations of deformation of the shells in common orthogonal coordinate system (not in the lines of main curvatures) are received on the base of this equation. Derivation of the geometric equations of deformations of thin shells in orthogonal not conjugated coordinate system on the base of differential geometry and vector analysis (without using of tensor analysis) is given at the article. This access may be used at textbooks as far as at most technical institutes the base of tensor analysis is not given.

Membrane Solution of Fiber-Reinforced Corrugated Shells of Revolution

1967 ◽  
Vol 1 (4) ◽  
pp. 382-388 ◽  
Author(s):  
Harold G. Franklin
Keyword(s):  
Coordinate System ◽  
Thin Shell ◽  
Middle Surface ◽  
Loading Conditions ◽  
Fiber Reinforced ◽  
Shells Of Revolution ◽  
Torsional Loading ◽  
Explicit Formulas ◽  
Orthogonal Coordinate System ◽  
Corrugated Shells

A membrane solution of fiber-reinforced corrugated shells of revolution under axial and torsional loading is determined from the equations of a thin shell whose middle surface is referred to an orthogonal coordinate system. Explicit formulas for the stress resultants are determined and the displacements are stated in terms of simple quadratures without specifying the shape of the profile of the shell. It is found that the displacements are coupled under both loading conditions except when the orientation of the fibers are at the two extremes.

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