The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 2 1/2‐ Dimensional Environment*

Eskola, L.; Hongisto, H.

doi:10.1111/j.1365-2478.1981.tb00404.x

Cited by 12 publications

(6 citation statements)

References 2 publications

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“…The mathematical formulations by Eskola and Hongisto (1981) for solving the resistivity problems is in its present form valid only for an electrically isotropic model. For an anisotropic model, however, modifications must be made in the formulae of the primary field ((31a) and (33)) and the Green's function ( (2) and (30)).…”

Section: Eskola**mentioning

confidence: 99%

Addendum to “The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 21/2‐dimensional Environment” by L. Eskola and H. Hongisto*

Eskola

1984

Geophysical Prospecting

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Section: Eskola**mentioning

confidence: 99%

Addendum to “The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 21/2‐dimensional Environment” by L. Eskola and H. Hongisto*

Eskola

1984

Geophysical Prospecting

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“…K ' is Green's function of the mirror sub-area corresponding to the singular sub-area (k = i ) and derived from (9) and (33). The integrated Green's functions (33) can be obtained after some manipulations from Eskola (1979) and Eskola and Hongisto (1981). Note that the kernel of integral equations (17)-(20) (in shape) is Green's function of the potential of the double source for the half-space.…”

Section: (7)mentioning

confidence: 99%

Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind*

Eloranta¹

1986

Geophysical Prospecting

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ELORANTA, E.H. 1986, Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind, Geophysical Prospecting 34,856-872.An integral equation method is described for solving the potential problem of a stationary electric current in a medium that is linear, isotropic and piecewise homogeneous in terms of electrical conductivity. The integral equations are Fredholm's equations of the 'second kind ' developed for the potential of the electric field. In this method the discontinuitysurfaces of electrical conductivity are divided into 'sub-areas' that are so small that the value of their potential can be regarded as constant.The equations are applied to 3-D galvanic modeling. In the numerical examples the convergence is examined. The results are also compared with solutions derived with other integral equations. Examples are given of anomalies of apparent resistivity and mise-i-lamasse methods, assuming finite conductivity contrast. We show that the numerical solutions converge more rapidly than compared to solutions published earlier for the electric field. This results from the fact that the potential (as a function of the location coordinate) behaves more regularly than the electric field. The equations are applicable to all cases where conductivity contrast is finite.

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“…Such a configuration having a 3-D wavefield in a 2-D medium is sometimes called the '2.5-D problem' (e.g. Eskola & Hongisto 1981). Fortunately, the structures in geophysically interesting regions can sometimes be approximated by models in which the heterogeneity patterns are 2-D. Also, most seismic experiments, such as refraction surveys, have been arranged to retrieve 2-D structures under the array of receivers.…”

Section: Introductionmentioning

confidence: 99%

2.5-Dmodelling of elastic waves using the pseudospectral method

Furumura

Takenaka

1996

Geophysical Journal International

103

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The pseudospectral code bamps is used to evolve axisymmetric gravitational waves. We consider a one-parameter family of Brill wave initial data, taking the seed function and strength parameter of Holz et. al. A careful comparison is made to earlier work. Our results are mostly in agreement with the literature, but we do find that some amplitudes reported elsewhere as subcritical evolve to form apparent horizons. Related to this point we find that by altering the slicing condition, the position of the peak of the Kretschmann scalar in these supercritical data can be controlled so that it appears away from the symmetry axis before the method fails, demonstrating that such behavior is at least partially a coordinate effect. We are able to tune the strength parameter to an interval of range 1 − A/A 10 −6 around the onset of apparent horizon formation. In this regime we find that large spikes appear in the Kretschmann scalar on the symmetry axis but away from the origin. From the supercritical side disjoint apparent horizons form around these spikes. On the subcritical side, down to this range, evidence of power-law scaling of the Kretschmann scalar is not conclusive, but the data can be fitted as a power-law with periodic wiggle.

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The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 2 1/2‐ Dimensional Environment*

Cited by 12 publications

References 2 publications

Addendum to “The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 21/2‐dimensional Environment” by L. Eskola and H. Hongisto*

Addendum to “The Solution of the Stationary Electric Field Strength and Potential of a Point Current Source in a 21/2‐dimensional Environment” by L. Eskola and H. Hongisto*

Potential Field of a Stationary Electric Current Using Fredholm's Integral Equations of the Second Kind*

2.5-Dmodelling of elastic waves using the pseudospectral method

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