On the resolving power of the VLF method

Bezvoda, Václav; Segeth, Karel

doi:10.1007/bf00877041

Cited by 1 publication

(5 citation statements)

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“…We are interested in the two most important VLF parameters in the E-polarization on the surface of the Earth (z = 0), namely the apparent resistivity, pa, and tan 8, where 8 is the inclination of the major axis of the polarization ellipse of the magnetic field vector (Smith and Ward 1974, Kaikkonen 1979, Bezvoda and Segeth 1982a, 1982b. We are interested in the two most important VLF parameters in the E-polarization on the surface of the Earth (z = 0), namely the apparent resistivity, pa, and tan 8, where 8 is the inclination of the major axis of the polarization ellipse of the magnetic field vector (Smith and Ward 1974, Kaikkonen 1979, Bezvoda and Segeth 1982a, 1982b.…”

Section: A Test Example For the V L F Methodsmentioning

confidence: 99%

“…We calculate the field of two or three vertical, relatively conductive, thin dykes placed in a less conductive half-space. We are interested in the two most important VLF parameters in the E-polarization on the surface of the Earth (z = 0), namely the apparent resistivity, pa, and tan 8, where 8 is the inclination of the major axis of the polarization ellipse of the magnetic field vector (Smith and Ward 1974, Kaikkonen 1979, Bezvoda and Segeth 1982a, 1982b. The determination of these parameters follows the described computation of the field U and includes also numerical differentiation.…”

Section: A Test Example For the V L F Methodsmentioning

confidence: 99%

“…Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case. Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case.…”

Section: Formulation O F T H E Problemmentioning

confidence: 99%

“…The mathematical model of the quasi-static approximation of the field of the harmonic electromagnetic plane wave is represented by the Helmholtz equation with a complex piecewise constant coefficient of the absolute term on a rectangle (see, e.g., Kaikkonen 1979, Bezvoda andSegeth 1982a). In this case, the coefficient of the absolute term in the Helmholtz equation is expressed with the help of the function ~( y , z ) = 6 and the solution sought is the only non-zero component of a suitably chosen vector of the field.…”

Section: Formulation O F T H E Problemmentioning

confidence: 99%

“…Further we put u(0) = 1. Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case.…”

Section: Formulation O F T H E Problemmentioning

confidence: 99%

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An Application of Fast Algorithms to Numerical Electromagnetic Modeling*

Bezvoda

Segeth

1987

Geophysical Prospecting

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Numerical electromagnetic modeling by the finite‐difference or finite‐element methods leads to a large sparse system of linear algebraic equations. Fast direct methods, requiring an order of at most q log q arithmetic operations to solve a system of q equations, cannot easily be applied to such a system. This paper describes the iterative application of a fast method, namely cyclic reduction, to the numerical solution of the Helmholtz equation with a piecewise constant imaginary coefficient of the absolute term in a plane domain. By means of numerical tests the advantages and limitations of the method compared with classical direct methods are discussed. The iterative application of the cyclic reduction method is very efficient if one can exploit a known solution of a similar (e.g., simpler) problem as the initial approximation. This makes cyclic reduction a powerful tool in solving the inverse problem by trial‐and‐error.

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Section: A Test Example For the V L F Methodsmentioning

confidence: 99%

Section: A Test Example For the V L F Methodsmentioning

confidence: 99%

Section: Formulation O F T H E Problemmentioning

confidence: 99%

Section: Formulation O F T H E Problemmentioning

confidence: 99%

“…Further we put u(0) = 1. Equation (5), with these conditions, can be solved easily (e.g., Cagniard 1953, Praus 1976, Bezvoda and Segeth 1982a, 1985, also in the n-layer case.…”

Section: Formulation O F T H E Problemmentioning

confidence: 99%

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