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IMPÉDANCES ET MATRICES CARACTÉRISTIQUES EN PROSPECTION ÉLECTROMAGNÉTIQUE*

 

作者: J. LOEB,  

 

期刊: Geophysical Prospecting  (WILEY Available online 1959)
卷期: Volume 7, issue 1  

页码: 77-90

 

ISSN:0016-8025

 

年代: 1959

 

DOI:10.1111/j.1365-2478.1959.tb01455.x

 

出版商: Blackwell Publishing Ltd

 

数据来源: WILEY

 

摘要:

AbstractAn analogy is established between the propagation of an electromagnetic field in a horizontally stratified conductive medium and that of currents in a linear electric network. This analogy will allow us to know in which case measurements executed at the surface of the ground can provide information about the properties of deeper layers. The situation is the same as when one tries, by means of impedance measurements at the input terminals, to know the properties of electric lines or lumped networks.A symmetrical linear network establishes between:VoltagesV1andV2(respectively at input and output terminals)CurrentsI1andI2(respectively at input and output terminals), the relationshipis called the “phase constant” andZthe characteristic impedance The tableis called “characteristic matrix”If one then takes the horizontal components of an electromagnetic field, one can compare the voltageVwith the horizontal electric fieldE(in voltsm‐1) and the currentIwith the horizontal magnetic fieldH(in Ampm−1)For plane waves in vacuum, one gets (Schelkunoff)Z=C(velocity of light)A layer whose thickness isDhas a phase constant⌈= 2 πD/λ (λ= wavelength)For plane waves in a conductive, non magnetic medium whose conductivity is δ, one getsFor the system of waves created by a point‐source one expresses the solution, since it is classical, as a sum or integral of differentmodes. For each of these modes, one can still write a bilinear relationship similar to (1), and calculateZand ⌈.A generalization of this result is given.Boundary conditions that exist at the surfaces of separation are met by writing the continuity ofEandH. This condition exactly corresponds to the fact that there oneVand oneIat the junctions of various sections of lines, or networks.The characteristic matrix of a cascade of networks‐or here that of a horizontally stratified ground– is the product of the matrixes of each network. If, in addition, one knows the end impedance–here the conductivity λnof the last layer, supposed to be infinite–one can compute the input impedanceReof the whole system. In electromagnetic prospecting, it isRethat conditions the observable field.Inversely, if measurements were infinitely accurate, the. knowledge of the surface field would give all the thicknessesDand conductivities δ of intermediate layers, in the same way that impedance measurements at the input terminals of a cable would allow to locate any failure. The imperfection of measurements causes the elements located too far away (from the point of view of wave a

 

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