MEASUREMENT OF TELLURIC “RELATIVE ELLIPSE AREA” BY MEANS OF “VECTOGRAMS”

Geophysics ◽  
1968 ◽  
Vol 33 (1) ◽  
pp. 127-131 ◽  
Author(s):  
S. H. Yungul
Keyword(s):  
Electrical Properties ◽  
Coordinate System ◽  
Correlation Coefficients ◽  
Base Station ◽  
Real Numbers ◽  
Field Station ◽  
Orthogonal Coordinate System ◽  
Orthogonal Components ◽  
The Subject ◽  
Ellipse Area

The subject of this note is a method of acquisition and reduction of data in connection with what is commonly known as the “telluric method,” which primarily deals with the parameter known as “relative ellipse area.” Let us suppose that at an instant t the orthogonal components of the telluric (electric) field at a point B, called Base Station, are [Formula: see text] and [Formula: see text]. At the same instant, the components at another point F, called Field Station, measured in another orthogonal coordinate system, are [Formula: see text] and [Formula: see text]. It is assumed that these components are related to each other as follows: [Formula: see text] (1) where a, b, c, and d are real numbers, called the “correlation coefficients,” which depend only on the directions of the measuring axes and on the electrical properties of the subsurface. It follows that the Jacobian of the transformation from the x‐y system to the u‐v system, [Formula: see text] depends only on the electrical properties of the subsurface; it is called the relative ellipse area at F with respect to B. For information concerning the validity of equation (1), and the geologic meaning of J, the reader may refer to a book by Berdichevskii (1960).

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 A Method of Implementing a 4 × 4 Correlation Matrix for Evaluating the Uplink Channel Properties of MIMO Over-the-Air Apparatus

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6184
Author(s):  
Kazuhiro Honda
Keyword(s):  
Correlation Matrix ◽  
Channel Model ◽  
Multiple Input Multiple Output ◽  
Correlation Coefficients ◽  
Base Station ◽  
Theoretical Formula ◽  
Secondary Wave ◽  
Two Dimensional ◽  
Mimo Antenna ◽  
Channel Properties

This paper presents a method of implementing a 4 × 4 correlation matrix for evaluating the uplink channel properties of multiple-input multiple-output (MIMO) antennas using an over-the-air measurement system. First, the implementation model used to determine the correlation coefficients between the signals received at the base station (BS) antennas via the uplink channel is described. Then, a methodology is introduced to achieve a 4 × 4 correlation matrix for a BS MIMO antenna based on Jakes’ model by setting the initial phases of the secondary wave sources in the two-dimensional channel model. The performance of the uplink channel for a four-element MIMO terminal array antenna is evaluated using a two-dimensional bidirectional fading emulator. The results show that the measured correlation coefficients between the signals received via the uplink channel at the BS antennas using the proposed method are in good agreement with the BS correlation characteristics calculated using Monte Carlo simulation and the theoretical formula, thereby confirming the effectiveness of the proposed method.

scholarly journals Navigation by Dead Reckoning and Local Cues

1993 ◽  
Vol 46 (3) ◽  
pp. 364-370 ◽  
Author(s):  
A. S. Etienne ◽  
V. Séguinot
Keyword(s):  
Coordinate System ◽  
Dead Reckoning ◽  
Cognitive Map ◽  
Familiar Environment ◽  
The Subject ◽  
Absolute Coordinate System ◽  
Actual Location ◽  
Local Cues

According to comprehensive theories of navigation, animals navigate by using two complementary strategies: (1) dead reckoning informs the subject in a continuous manner on its actual location with respect to an Earthbound or absolute coordinate system; while (2) long-term associations between particular landmarks and specific locations allow the animal to find its way within a familiar environment. If the subject structures familiar space as a system of interconnected places – the so-called ‘cognitive map’ – it may know through dead reckoning where it is located on its map and relate its route-based expectations to the actually perceived scenario of local cues.

scholarly journals A Nonuniform Bound to an Independent Test in High Dimensional Data Analysis via Stein’s Method

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Nahathai Rerkruthairat
Keyword(s):  
Normal Approximation ◽  
Correlation Coefficients ◽  
Random Variable ◽  
Stein’S Method ◽  
High Dimensional ◽  
Stein's Method ◽  
Real Numbers ◽  
Complete Independence ◽  
Independent Test ◽  
Sample Correlation

The Berry-Esseen bound for the random variable based on the sum of squared sample correlation coefficients and used to test the complete independence in high diemensions is shown by Stein’s method. Although the Berry-Esseen bound can be applied to all real numbers in R, a nonuniform bound at a real number z usually provides a sharper bound if z is fixed. In this paper, we present the first version of a nonuniform bound on a normal approximation for this random variable with an optimal rate of 1/0.5+|z|·O1/m by using Stein’s method.

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