Václav Petr

Potential field of a stationary electric current in a stratified medium with a three-dimensional perturbing body

SummaryThe potential of the electric field of a stationary current in a two-layered Earth is calculated by applying Greens formula in the case where a three-dimensional inhomogeneity of different conductivity is located in the basement of the layer. It is proved that the potential outside and inside the perturbing body can be calculated from the potential of an electric double-layer distributed on the surface of this body. An integral equation of the Fredholm type is derived for the surface density of the double-layer, together with some of its integral properties. A similar procedure can be applied to computing the magnetic anomalies of three-dimensional magnetized bodies, geothermal anomalies due to three-dimensional inhomogeneities of different heat conductivity, as well as to potential problems of theoretical electrical engineering.

Anomalous induction in the Carpathians

РезюмеОnuсывaюmся резульmamы uзученuя вaрuaчuŭеомaнumноо nоля зaреuсmрuровaнных о¶rt;новременно нa 9 nолевых сmaнцuях в¶rt;оль nрофuля ГСЗ No V, nересекaющео Кaрnamы. Деmaльно uзучaеmся зонa aномaльноŭ uн¶rt;укцuu нaрaнuце меж¶rt;у внещнuмu u ценmрaльнымu Кaрnamaмu. Посmроены векmоры uн¶rt;укцuu u aнaлuзuровaнa чaсmоmнaя хaрaкmерuсmuкa aномaльноо эффекma. По ¶rt;aнным нa оm¶rt;ельных сmaнцuях о¶rt;новременно зaреuсmрuровaнных возмущенuŭ осущесmвляеmся рaз¶rt;еленuе nоля нa внуmреннюю u внешнюю сосmaвляющuе. Оценuвaеmсялубuнa зaлеaнuя сосре¶rt;оmоченноо лuнеŭноо элекmрuческоо mокa, коmорыŭ являеmся о¶rt;нuм uз возможных uсmочнuков внуmреннео nоля. Элекmромaнumные хaрaкmерuсmuкu nоля соnосmaвлены с mеореmuческuмu aномaлuямu рaсчumaннымu ¶rt;ля некоmорых ¶rt;ву-мерно нео¶rt;норо¶rt;ныхеоэлекmрuческuх сmрукmур в¶rt;оль nрофuля чuсленным меmо¶rt;ом конечных рaзносmеŭ.

Electric and magnetic field of a stationary current in a stratified medium with a three-dimensional conductivity inhomogeneity

SummaryNew formulae have been derived for calculating the electric and magnetic field generated by an external source of a stationary electrical current in a stratified medium with a three-dimensional disturbing body in one of the layers. The potential of the anomalous current field is expressed in terms of the potential of a dipole layer, distributed over the surface of the disturbing body. The density of the dipole layer is calculated with the aid of the scalar Fredholm integral equation. The components of the magnetic field intensity are calculated from the superposition of the magnetic effects of elementary electric dipoles distributed over the surface of the disturbing body. The results of the numerical computation of the anomalous electric and magnetic field on the surface of the halfspace inside which a block of different electric conductivity is located, are given, the exciting field being homogeneous.

Magnetotellurisches feld in einem homogenen anisotropen medium

РезюмеРассматривается теория распространения плоских электромагнитнЫх волн в однородной анизотропной среде, где одна ось совпадает с направлением распространения электроманитной волны. БЫли вЫведенЫ вЫражения для главнЫх значений тензора проводимости и азимута одной главной составляющей тензора проводимости. Приводится также описание метода посредстввом которого приведеннЫе вЫше параметрЫ можно определить.

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in a two-layer earth

SummaryThe results of numerical computations of the electromagnetic field induced in a two-layer model of the Earth with a three-dimensional inhomogeneity (a block) in the subsurface layer are given. Several recommendations are given which have enabled the solution of a complicated system of integral equations and the computation of the field at the Earths surface in an effective way. The analysis of the obtained solution has proved that, in an anomalous electromagnetic field, the field of the horizontal electric dipole, oriented in the direction of the exciting field, is predominant. A number of practically usable diagrams and approximative formulae is given.

Electromagnetic induction of a three-dimensional conductivity inhomogeneity in the two-layered earth

SummaryThe calculation of the elements of Greens tensor function is presented for solving the problem of the electromagnetic induction by means of a vector integral equation. A two-layered Earth is considered as the medium, the surface layer including a three-dimensional conductivity inhomogeneity. Use is made of the boundary condition requiring the vertical component of the electric current to be zero at the Earths surface which partly simplifies the theoretical computation. Long-period asymptotics of the individual complicated functions, occurring in Greens tensor function as well as in the tensor function required to calculate the components of the anomalous magnetic field at the surface of the halfspace, were effected. With the aid of these asymptotics one can obtain estimates of the functions occurring in the theoretical analysis of the problem.

Anomaly of geomagnetic variations in the southeastern margin of the Bohemian Massif

РезюмеПре¶rt;лагaюмся резульмамы обрабомкu магнuмоварuaцuонных nолевых uзмеренuŭ nо мрем nрофuлям, nересекающuм ю—в кромку Чещского массuва. По оченкам векморов uн¶rt;укцuu (векморов Вuзе), nо расчuманным uз nере¶rt;амочных функцuŭ комnлексным векморам uн¶rt;укцuu (векморам Шмукера), nо резулвмамам раз¶rt;еленuя nоля варuaцuŭ на внещнюю u внумреннюю часмu u nо резульмамам aналuза ¶rt;анных фuзuко-смамuсмuческuм мемо¶rt;ом была обнаружена зонагеоэлекмрuческоŭ нео¶rt;норо¶rt;носмu совna¶rt;ающая в раŭоне nрофuлеŭ с Мораво-Сuлезuŭскоŭ зоноŭ. По ¶rt;анным aналuза uсмочнuк внумреннего aномального nоля залегaем наглубuне nоря¶rt;ка 20–25 км.SummaryMagnetic variations were recorded along three profiles crossing the southeastern margin of the Bohemian Massif. The data were processed in order to get induction vectors (Wiesevectors) and in-phase and out-of-phase induction vectors (Schmucker-vectors). Several events of field variations were separated into external and internal parts. The same events were also treated by a physical-statistical approach. Taking into account these results, we were able to delineate a zone of electrical inhomogeneity. It is in close relation to the Moravo-Silesian lineament. The depth of the internal anomalous field source was estimated at 20 to 25 km.

Spectral theory of electromagnetic induction in a radially and laterally inhomogeneous earth

РезюмеУрaвненuя в чaсmных nроuзво¶rt;ных ¶rt;ля элекmромaгнumноŭ uн¶rt;укцuu в Землu mрехмерно нео¶rt;норо¶rt;ноŭ nо nрово¶rt;uмосmu nереве¶rt;ены в сuсmему обыкновенных ¶rt;uфференцuaльных урaвненuŭ вmорого nоря¶rt;кa ¶rt;ля сnекmрaльных коэффuцuенmов nоля.SummaryThe partial differential equations of electromagnetic induction in a 3-D Earth of inhomogeneous conductivity are reduced to a system of ordinary differential equations of the 2nd order for the spectral coefficients of the field.

Stresses and displacements due to a stationary point source of heat in an elastic halfspace

РезюмеДaеmся крamкuŭ выво¶rt; формул ¶rt;ля mермоуnругuх нanряженnuŭ u смещенuŭ, вызывaемых сmaцuонaрным mочечным uсmочнuком mеnлa в уnругом nолуnросmрaнсmве. Нa основaнuu вычuсленuŭ nокaзaно, чmо вознuкaющuе нanряженuя являюmся нanряженuямu рaсmягuвaющего muna u вызывaюm зaмеmные возмущенuя nоля лumосmamuческuх нanряженuŭ вб лuзu nоверхносmu nолуnросmрaнсmвa. Анaлuзuруюсmя некоmорыегео¶rt;uнaмuческuе сле¶rt;сmвuя воз¶rt;еŭсmвuя maкuх нanряженuŭ, в чaсmносmu: a) вз¶rt;уmuе лumосферы в эnuценmрaльноŭ облaсmu uсmочнuкa mеnлa; б) возможносmь вознuкновенuя конuческuх nоверхносmеŭ рaзломa u uх ролu nрu вознuкновенuu кaнaлов nронuкновенuя мaгмы к nоверхносmu Землu; в) обрaзовaнuе рaсmягuвaющuх нanряженuŭ в облaсmяхгеоmермuческuх aномaлuŭ, коmорые могуm nроявляmься в вu¶rt;е nовыщенноŭ сеŭсмuческоŭ aкmuвносmu верхнеŭ лumосферы в эmuх облaсmях.

Induction vector estimates in the Bohemian Massif and in the transition zone to the Carpathians

РезюмеПрuво¶rt;яmся резульmamы оценок векmоров uн¶rt;укцuu nо новым nолевым сmaнцuям в Чещском мaссuве u в nерехо¶rt;ноŭ зоне к Кaрnamaм. Целью рaбоmы являеmся рaзщuренuе uмеющеося у рaзлuчных aвmоров мaссuвa ¶rt;aнных, коmорыŭ можеm uсnользовamься ¶rt;ля uссле¶rt;овaнuя реuонaльных aномaлuŭ элекmроnрово¶rt;носmu в Евроnе.