scholarly journals A line integral approach for the computation of the potential harmonic coefficients of a constant density polyhedron

2020 ◽  
Vol 94 (3) ◽  
Author(s):  
Olivier Jamet ◽  
Dimitrios Tsoulis
Keyword(s):  
Integral Approach ◽  
Constant Density ◽  
Line Integral ◽  
Potential Harmonic

scholarly journals Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron

2009 ◽  
Vol 83 (10) ◽  
pp. 925-942 ◽  
Author(s):  
Dimitrios Tsoulis ◽  
Olivier Jamet ◽  
Jérôme Verdun ◽  
Nicolas Gonindard
Keyword(s):  
Constant Density ◽  
Recursive Algorithms ◽  
Potential Harmonic

The line integral approach to radarclinometry

1987 ◽  
Vol 38 (1) ◽  
pp. 59-95 ◽  
Author(s):  
Robert L. Wildey
Keyword(s):  
Integral Approach ◽  
Line Integral

A LINE‐INTEGRAL METHOD OF COMPUTING THE GRAVIMETRIC EFFECTS OF TWO‐DIMENSIONAL MASSES

Geophysics ◽  
1948 ◽  
Vol 13 (2) ◽  
pp. 215-225 ◽  
Author(s):  
M. King Hubbert
Keyword(s):  
Opposite Sign ◽  
Gravity Anomalies ◽  
Constant Density ◽  
Two Dimensional ◽  
Horizontal Scale ◽  
Special Equipment ◽  
Line Integral ◽  
Vertical Coordinate ◽  
Plane Normal ◽  
Polar Coordinate

Many computing schemes have been devised for determining the gravity anomalies produced by two‐dimensional masses. Most of these are based upon the evaluation of an areal integral and require specially constructed templates or tables. In the present paper it is shown that the gravity anomaly Δg at the origin of coordinates, produced by a two‐dimensional mass of constant density contrast Δρ, may be obtained quite simply by means of either of the line integrals [Formula: see text] where z is the vertical coordinate, and θ the polar coordinate expressed in radians of a point on the periphery of the mass in a plane normal to its axis and passing through the origin. The line integrals are evaluated around the periphery of the mass and are of opposite sign if taken in the same direction of traverse, or are of the same sign if taken in opposite directions. For use of these integrals no special equipment is required other than a simple template consisting of radial lines, θ=const., and horizontal lines, z=const., which can be constructed in a few minutes with protractor and scale. This can be constructed either for 1:1 or for an exaggerated vertical‐to‐horizontal scale.

Least-squares reverse time migration in the presence of density variations

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. S497-S509 ◽  
Author(s):  
Jizhong Yang ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Simulated Data ◽  
Integral Approach ◽  
Constant Density ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Density Assumption ◽  
Density Perturbations ◽  
Least Squares Migration

Least-squares migration (LSM) is commonly regarded as an amplitude-preserving or true amplitude migration algorithm that, compared with conventional migration, can provide migrated images with reduced migration artifacts, balanced amplitudes, and enhanced spatial resolution. Most applications of LSM are based on the constant-density assumption, which is not the case in the real earth. Consequently, the amplitude performance of LSM is not appropriate. To partially remedy this problem, we have developed a least-squares reverse time migration (LSRTM) scheme suitable for density variations in the acoustic approximation. An improved scattering-integral approach is adopted for implementation of LSRTM in the frequency domain. LSRTM images associated with velocity and density perturbations are simultaneously used to generate the simulated data, which better matches the recorded data in amplitudes. Summation of these two images provides a reflectivity model related to impedance perturbation that is in better accordance with the true one, than are the velocity and density images separately. Numerical examples based on a two-layer model and a small part of the Sigsbee2A model verify the effectiveness of our method.

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

Gandhian Method of Conflict Resolution: Perception of Educated Youths

2017 ◽  
Vol 1 (6) ◽  
pp. 1 ◽  
Author(s):  
Dr. P. K. Kar
Keyword(s):  
Conflict Resolution ◽  
Image Of God ◽  
Integral Approach ◽  
Human Beings ◽  
Life Itself ◽  
The Image Of God ◽  
Negative Concept

Gandhiji’s method of conflict resolution was based on truth and non-violence. Truth was for him the image of God. He did not believe in personal God. For Gandhi truth is God and God is truth. Life is a laboratory where experiments are carried on. That is why he named his autobiography “My Experiment with Truth”, without these experiments truth cannot be achieved. According to Gandhi, the sayings of a pure soul which possesses nonviolence, non-stealing, true speech, celibacy and non-possession is truth. The truth of Gandhiji was not confined to any country or community. In other words , his religion had no geographical limits. His patriotism was not different from the service of human beings but was its part and parcel(Mishra:102). Gandhiji developed an integral approach and perspective to the concept of life itself on the basis of experience and experiments. His ideas ,which came to be known to be his philosophy, were a part of his relentless search for truth(Iyer:270). The realization of this truth is possible only with the help of non-violence The negative concept of Ahimsa presupposes the absence of selfishness, jealousy and anger, but the positive conception of ahimsa demands the qualities of love ,liberalism, patience, resistance of injustice, and brutal force.

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