STATISTICAL PROPERTIES OF POTENTIAL FIELDS OVER A RANDOM MEDIUM

Geophysics ◽  
1967 ◽  
Vol 32 (1) ◽  
pp. 88-98 ◽  
Author(s):  
Prabakar S. Naidu
Keyword(s):  
Random Process ◽  
Autocorrelation Function ◽  
Potential Field ◽  
Random Potential ◽  
Mass Density ◽  
Random Medium ◽  
Statistical Properties ◽  
Potential Fields ◽  
Random Mass ◽  
The Relationship

Following a study of the statistical properties of a random potential field, which is often encountered as a background noise in observed geophysical potential fields, and particularly a study of conditions under which the random process is homogeneous and gaussian, an approximate analytical method has been developed to evaluate the correlation functions and the power spectrum of the random process when the mass density is locally uniform but varies randomly over an entire semi‐infinite space. The method is particularly convenient for it gives a unified approach to evaluating the statistical properties of gravity as well as magnetic fields. The relationship between the autocorrelation function of the random potential field and the random mass density is quite involved, but by assuming that the mass density in successive cells is completely uncorrelated the relationship can be simplified. It is a matter of considerable interest to estimate, from the autocorrelation function, the size of cell characteristic of the random medium which reflects the geological characteristics of the rocks.

SPECTRUM OF THE POTENTIAL FIELD DUE TO RANDOMLY DISTRIBUTED SOURCES

Geophysics ◽  
1968 ◽  
Vol 33 (2) ◽  
pp. 337-345 ◽  
Author(s):  
Prabakar Naidu
Keyword(s):  
Spectral Density ◽  
Random Field ◽  
Potential Field ◽  
Random Potential ◽  
Thin Sheet ◽  
Infinite Medium ◽  
Potential Fields ◽  
Density Functions ◽  
Spectral Density Functions ◽  
Different Levels

Covariance and spectral density functions of all three components of random potential fields are mutually related. The spectra of any one component on two different levels are related through an exponential function of the separation of the levels. If, starting from the earth’s surface, we continue the observed random field downward, we find that at a certain level the field becomes unstable. Such a limiting depth can be estimated from the spectrum of the observed field. The spectrum of the random field is related to the spectrum of random density or intensity of magnetization. The random sources are assumed to be confined to a thin sheet or a thick, infinite sheet, or to a semi‐infinite medium. In all these cases, a relation connecting the spectrum of the random density or the intensity of magnetization and the spectrum of the random field has been established.

scholarly journals Virtual Electric Dipole Field Applied to Autonomous Formation Flight Control of Unmanned Aerial Vehicles

Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4540
Author(s):  
Leszek Ambroziak ◽  
Maciej Ciężkowski
Keyword(s):  
Control System ◽  
Unmanned Aerial Vehicles ◽  
Flight Control ◽  
Electric Dipole ◽  
Potential Field ◽  
Control Algorithm ◽  
Formation Flight ◽  
Potential Fields ◽  
Dipole Potential ◽  
Aerial Vehicles

The following paper presents a method for the use of a virtual electric dipole potential field to control a leader-follower formation of autonomous Unmanned Aerial Vehicles (UAVs). The proposed control algorithm uses a virtual electric dipole potential field to determine the desired heading for a UAV follower. This method’s greatest advantage is the ability to rapidly change the potential field function depending on the position of the independent leader. Another advantage is that it ensures formation flight safety regardless of the positions of the initial leader or follower. Moreover, it is also possible to generate additional potential fields which guarantee obstacle and vehicle collision avoidance. The considered control system can easily be adapted to vehicles with different dynamics without the need to retune heading control channel gains and parameters. The paper closely describes and presents in detail the synthesis of the control algorithm based on vector fields obtained using scalar virtual electric dipole potential fields. The proposed control system was tested and its operation was verified through simulations. Generated potential fields as well as leader-follower flight parameters have been presented and thoroughly discussed within the paper. The obtained research results validate the effectiveness of this formation flight control method as well as prove that the described algorithm improves flight formation organization and helps ensure collision-free conditions.

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

On: “Reduction of magnetic and gravity data on an arbitrary surface acquired in a region of high topographic relief” by B. K. Bhattacharyya and K. C. Chan (GEOPHYSICS, December 1977, p. 1411–1430)

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1274-1275
Author(s):  
V. Courtillot ◽  
J. Ducruix ◽  
J. L. Le Mouël
Keyword(s):  
Potential Field ◽  
Gravity Data ◽  
Three Dimensional ◽  
Analytic Solutions ◽  
Helmholtz Equations ◽  
Data Points ◽  
The Subject ◽  
Christoffel Transformation ◽  
The Relationship ◽  
Topographic Relief

In their paper, Bhattacharryya and Chan address the problem of reduction of magnetic and gravity data on an arbitrary surface acquired in a region of high topographic relief. In their work, the authors are kind enough to mention our contribution to the solution of the problem of finding the sources responsible for an observed magnetic or gravity anomaly, using the general formalism of inverse problems (Courtillot et al, 1974). Unfortunately, however, the authors seem to be unaware of our other publications which are far more relevant to their subject. Courtillot et al (1973) solved the problem of continuation of a potential field measured on an uneven profile, using the Backus and Gilbert approach. Another reference relevant to this problem (solved by Bhattacharryya and Chan on p. 1424) is Parker and Klitgord (1972), who used the Schwartz‐Christoffel transformation. The work was extended to the case of three‐dimensional potential fields measured on an uneven surface by Ducruix et al (1974). Indeed, the development of our paper is strikingly similar to that of Bhattacharryya and Chan, although the method is quite different. In our paper, we give many illustrations of both theoretical and real cases, in which our method is seen to perform very well. We leave it to the reader to compare the results provided by both methods and to compare the methods themselves. In a third paper (Le Mouël et al, 1975), we generalized the method and showed how one could obtain excellent approximate analytic solutions of the Dirichlet and Neumann problems in the two‐dimensional case for a contour with any arbitrary shape. Finally, let us take the opportunity of this discussion to mention a review of the subject which appears in French in Courtillot (1977) and in English, much expanded, in Courtillot et al (1978). In this last paper, which should be of interest in solving a variety of geophysical problems, we show how our method allows one to continue a potential field measured on an entirely arbitrary set of data points in any number of dimensions for the various coordinate systems in which the Laplace and Helmholtz equations are separable. We also establish the relationship between our method and a generalization of the theory of generalized inverse matrices. One other relevant reference on that subject is Parker (1977). In the case of spherical coordinates, an application can be the continuation of satellite data, a problem studied by Bhattacharryya (1977).

scholarly journals Potential Field Cellular Automata Model for Pedestrian Evacuation in a Domain with a Ramp

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Xiao-Xia Jian ◽  
Xiaoning Zhang
Keyword(s):  
Cellular Automata ◽  
Potential Field ◽  
Empty Space ◽  
Domino Effect ◽  
Cellular Automata Model ◽  
Pedestrian Evacuation ◽  
Crowd Density ◽  
Proposed Model ◽  
The Cost ◽  
The Relationship

We propose a potential field cellular automata model with a pushing force field to simulate the pedestrian evacuation in a domain with a ramp. We construct a cost potential depending on the ramp angle and introduce a function to evaluate the pushing force, which is related to the cost and the desired direction of pedestrian. With increase of crowd density, there is no empty space for pedestrian moving forward; pedestrian will purposefully push another pedestrian on her or his desired location to arrive the destination quickly. We analyse the relationship between the slope of ramp and the pushing force and investigate the changing of injured situations with the changing of the slope of ramp. When the number of pedestrians and the ramp angle arrive at certain critical points, the Domino effect will be simulated by this proposed model.

DEXP: A fast method to determine the depth and the structural index of potential fields sources

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. I1-I11 ◽  
Author(s):  
Maurizio Fedi
Keyword(s):  
Potential Field ◽  
Extreme Points ◽  
Power Laws ◽  
Potential Fields ◽  
Newtonian Potential ◽  
Specific Power ◽  
Scaling Exponent ◽  
Fast Method ◽  
Structural Index ◽  
Derivatives Of

We show that potential fields enjoy valuable properties when they are scaled by specific power laws of the altitude. We describe the theory for the gravity field, the magnetic field, and their derivatives of any order and propose a method, called here Depth from Extreme Points (DEXP), to interpret any potential field. The DEXP method allows estimates of source depths, density, and structural index from the extreme points of a 3D field scaled according to specific power laws of the altitude. Depths to sources are obtained from the position of the extreme points of the scaled field, and the excess mass (or dipole moment) is obtained from the scaled field values. Although the scaling laws are theoretically derived for sources such as poles, dipoles, lines of poles, and lines of dipoles, we give also criteria to estimate the correct scaling law directly from the data. The scaling exponent of such laws is shown to be related to the structural index involved in Euler Deconvolution theory. The method is fast and stable because it takes advantage of the regular behavior of potential field data versus the altitude [Formula: see text]. As a result of stability, the DEXP method may be applied to anomalies with rather low SNRs. Also stable are DEXP applications to vertical and horizontal derivatives of a Newtonian potential of various orders in which we use theoretically determined scaling functions for each order of a derivative. This helps to reduce mutual interference effects and to obtain meaningful representations of the distribution of sources versus depth, with no prefiltering. The DEXP method does not require that magnetic anomalies to be reduced to the pole, and meaningful results are obtained by processing its analytical signal. Application to different cases of either synthetic or real data shows its applicability to any type of potential field investigation, including geological, petroleum, mining, archeological, and environmental studies.

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