scholarly journals Magnetic anomalies caused by 2D polygonal structures with uniform arbitrary polarization: new insights from analytical/numerical comparison among available algorithm formulations

2020 ◽  
Author(s):  
Alessandro Ghirotto ◽  
Andrea Zunino ◽  
Egidio Armadillo ◽  
Klaus Mosegaard
Keyword(s):  
Magnetic Anomalies ◽  
Numerical Comparison ◽  
Arbitrary Polarization

MAGNETIC ANOMALIES DUE TO PRISM‐SHAPED BODIES WITH ARBITRARY POLARIZATION

Geophysics ◽  
1964 ◽  
Vol 29 (4) ◽  
pp. 517-531 ◽  
Author(s):  
B. K. Bhattacharyya
Keyword(s):  
Polarization Vector ◽  
Magnetic Anomalies ◽  
Field Vector ◽  
The Body ◽  
Simple Extension ◽  
Second Derivative ◽  
Positive Anomaly ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Dip Angle

A study is made of magnetic anomalies due to prism‐shaped bodies with arbitrary polarization. Expressions of the total field and its first and second derivatives are derived on the assumption of uniform magnetization through out the body. Formulas for all possible cases in connection with a rectangular prism with vertical sides can be obtained either directly from this paper or by simple extension of the formulas given here. Using the exact expressions given in this paper, the total field and its derivatives are evaluated conveniently and rapidly with the aid of a digital computer. The effect of the dip angle anti declination of the polarization vector on the size and shape of the magnetic anomaly is then studied for the case when the earth’s normal total field vector has a dip angle of 60° and declination of 0°. With an increase in the dip angle of the polarization vector, the negative anomaly occurring on the north of the causative body diminishes in magnitude, whereas the positive and second derivative anomalies increase to maximum values and then decrease. With an increase in declination, this latter trend is repeated with the positive anomaly but the negative and second‐derivative anomalies decrease systematically. Both the positive and second‐derivative anomalies become more and more symmetrical with respect to the prismatic body with increase in either the inclination or declination of the polarization vector.

A rapid method for three‐dimensional modeling of magnetic anomalies

Geophysics ◽  
1991 ◽  
Vol 56 (11) ◽  
pp. 1729-1737 ◽  
Author(s):  
D. Bhaskara Rao ◽  
N. Ramesh Babu
Keyword(s):  
Computing Time ◽  
Optimization Technique ◽  
Three Dimensional ◽  
Magnetic Anomalies ◽  
Total Field ◽  
Arbitrary Polarization ◽  
Three Dimensional Modeling ◽  
Prismatic Bodies ◽  
Forward Calculation ◽  
Approximate Equations

A computer program has been developed for three‐dimensional analysis of total field magnetic anomalies due to arbitrary polarization suitable for present‐day personal computers. A vertical sided prism with arbitrary polarization is used as a basic model. A nonlinear optimization technique based on Marquardt’s algorithm is used to estimate all parameters of the model. A combination of prisms is used to analyze more complex magnetic fields. Analytical methods are used to estimate the derivatives required in the simultaneous solutions of the normal equations. Methods have been developed to minimize the computing time in forward calculation as well as in inversion. Approximate equations have been derived for rapid calculation of magnetic anomalies and partial derivatives of anomalies of prismatic bodies, which are valid beyond short distances from the sources. The algorithm has been developed in such a way that the use of the exact and approximate equations may be efficiently monitored as a trade‐off between accuracy and speed. The method is applied to analyze a synthetic anomaly contour map and the total field aeromagnetic anomalies in the offshore region of Mahanadi basin, Orissa, India.

Exploring the Boundaries of the Number–Temporal Order Association

2015 ◽  
Vol 62 (3) ◽  
pp. 198-205 ◽  
Author(s):  
Dana Ganor-Stern
Keyword(s):  
Embodied Cognition ◽  
Mental Representation ◽  
Temporal Order ◽  
Past Research ◽  
Numerical Comparison ◽  
Negative Number ◽  
Comparison Task ◽  
Negative Numbers ◽  
The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

2002 ◽  
Vol 7 (1) ◽  
pp. 31-42
Author(s):  
J. Šaltytė ◽  
K. Dučinskas
Keyword(s):  
Spatial Correlation ◽  
Random Fields ◽  
Data Augmentation ◽  
Gaussian Random Fields ◽  
Classification Rule ◽  
Numerical Comparison ◽  
First Order ◽  
Bayesian Risk ◽  
Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

Numerical Comparison of Drag Coefficient between Nacelle Lip-Skin with and without Bias Acoustic Liner

2016 ◽  
Vol 10 (6) ◽  
pp. 390 ◽  
Author(s):  
Qummare Azam ◽  
Mohd Azmi Ismail ◽  
Nurul Musfirah Mazlan ◽  
Musavir Bashir
Keyword(s):  
Drag Coefficient ◽  
Numerical Comparison ◽  
Acoustic Liner

Large magnetic anomalies over Russia revealed by balloon data

2004 ◽  
Vol 6 (6) ◽  
pp. 457-460
Author(s):  
K. A. Nazarova ◽  
T. Sabaka ◽  
Yu. Tsvetkov ◽  
J. Heirtzler
Keyword(s):  
Magnetic Anomalies

scholarly journals A Dynamic Distance Measure of Picture Fuzzy Sets and Its Application

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 436
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Distance Measure ◽  
Distance Measures ◽  
Numerical Comparison ◽  
Mathematical Tool ◽  
Practical Applications ◽  
Fuzzy Point ◽  
Point Operator ◽  
The Difference ◽  
Picture Fuzzy Sets

Picture fuzzy sets, which are the extension of intuitionistic fuzzy sets, can deal with inconsistent information better in practical applications. A distance measure is an important mathematical tool to calculate the difference degree between picture fuzzy sets. Although some distance measures of picture fuzzy sets have been constructed, there are some unreasonable and counterintuitive cases. The main reason is that the existing distance measures do not or seldom consider the refusal degree of picture fuzzy sets. In order to solve these unreasonable and counterintuitive cases, in this paper, we propose a dynamic distance measure of picture fuzzy sets based on a picture fuzzy point operator. Through a numerical comparison and multi-criteria decision-making problems, we show that the proposed distance measure is reasonable and effective.

scholarly journals From the Vector to Scalar Perturbations Addition in the Stark Broadening Theory of Spectral Lines

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 176
Author(s):  
Valery Astapenko ◽  
Andrei Letunov ◽  
Valery Lisitsa
Keyword(s):  
Spectral Line ◽  
Stark Effect ◽  
Coulomb Field ◽  
Spectral Lines ◽  
Alternative Methods ◽  
Scalar Perturbation ◽  
Numerical Comparison ◽  
Line Shapes ◽  
Stark Effects ◽  
The Impact

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. The analytical solution of the problem is unachievable with famous Chandrasekhar–Von-Neumann results up to the present time. The alternative methods are connected with modeling of a real ion Coulomb field dynamics by approximate models. One of the most accurate theories of ions dynamics effect on line shapes in plasmas is the Frequency Fluctuation Model (FFM) tested by the comparison with plasma microfield numerical simulations. The goal of the present paper is to make a detailed comparison of the FFM results with analytical ones for the linear and quadratic Stark effects in different limiting cases. The main problem is connected with perturbation additions laws known to be vector for small particle velocities (static line shapes) and scalar for large velocities (the impact limit). The general solutions for line shapes known in the frame of scalar perturbation additions are used to test the FFM procedure. The difference between “scalar” and “vector” models is demonstrated both for linear and quadratic Stark effects. It is shown that correct transition from static to impact limits for linear Stark-effect needs in account of the dependence of electric field jumping frequency in FFM on the field strengths. However, the constant jumping frequency is quite satisfactory for description of the quadratic Stark-effect. The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented.

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