Karel Pěč

Gravity field and dynamics of the earth

Satellite observations allow the reconstruction of the gravity field of the Earth-Moon system. The data obtained from satellite observations are used to reconstruct inhomogeneities in the Earths interior and related dynamic processes. The theory of variations in the Earths gravity field due to the variations in the rotation of the Earth is discussed in detail. Further a critical assessment of the hypothesis of the expanding Earth is presented on the base of recent astronomical and satellite data as well as linear laser ranging. Readers will find a thorough overview over the interdisciplinary fields of space geodesy, geodynamics and physics of the Earths interior.

Expansion of geoid heights over a triaxial earth's ellipsoid into a spherical harmonic series

РезюмеВыво¶rt;umся aлорumм ¶rt;ля вычuсленuяaрмонuческuх коэффuцuенmов в рaзложенuu рa¶rt;uус-векmорaеоu¶rt;a в ря¶rt; nо сферuческuм функцuям nуmем лuнеŭноо обрaщенuяaрмонuческоо ря¶rt;a ¶rt;ляеоnоmенцuaлa. Ощuбкa uз-зa лuнеaрuзaцuu nоря¶rt;кa кубa сжamuя Землu.

The Phobos Gravitational Field Modeled on the Basis of its Topography

The parameters of the best-fitting ellipsoid have been derived using the latest spherical harmonics of the Phobos topography (Duxbury, 1989) by solution of non-linear overdetermined inverse problem. The lengths of the equatorial axes of the ellipsoid have been determined (a = 12.9 km, b = 11.4 km). They are nearly the same as established by Duxbury (ibid.) on the basis of the linearized relationship between the squared lengths of ellipsoidal axes and the topography coefficients C20 and C22. The length of the polar axis (c = 9.1 km) differs of about 20% from Duxburys value. Supposing mass homogeneity of Phobos, the Stokes parameters of the external gravitational field have been derived up to those of the sixth degree and order. The large irregularities in the Phobos figure cause the values of the Duxburys potential coefficients be fairly inaccurate except the harmonics C20, C32, S43 and S51, i.e. linearized relationship between gravity and topography cannot be applied for Phobos. Finally, positions of the centre of figure and the directions of the principal axes of inertia have been established.

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.

Matrix approach to the solution of electromagnetic induction in a spherically layered earth

РезюмеВыве¶rt;ены мамрuчные формулы ¶rt;ля наnряженносмu nолеŭ магнuмного u элекмрuческого мuna. С nомощью эмuх формул nре¶rt;смаавлены: кажущееся соnромuвленuе, функцuя омклuка u макже часмомное уравненuе, оnре¶rt;еляющее часмомы собсмвенных колебанuŭ соомвемсмвующuх волн. Пре¶rt;ложен бысмрыŭ aлгорuмм ¶rt;ля чuсленного расчема функцuŭ омклuка u кажущегося соnромuвленuя.SummaryMatrix formulae for the intensities of the M- and E-fields have been derived. They have been applied to express the apparent resistivity, the transfer function, as well as the frequency equation determining the frequencies of free motion of the M- and E-waves. A fast algorithm for computing the transfer function and the apparent resistivity has been suggested.

Anomalous induction zone near the eastern margin of the Bohemian Massif

Abstract Wiese vectors, induction vectors, field separation and a physical-statistical approach were used to identify a zone of geoelectrical inhomogeneity near the eastern margin of the Bohemian Massif. This zone seems to mark an important geological and tectonic boundary separating two different tectogenes. The spatial distribution of the induction characteristics along five profiles traversing the boundary suggests a general 3-D model of internal geoelectrical-geological structure for the region. Common reference transfer functions and corresponding in- and out-of-phase vectors calculated by relating the data at a particular station and a common reference station were also derived as a tool for mapping internal geoelectrical structure.

Appreciation of Spherically Symmetric Models of Electrical Conductivity

A procedure is suggested of a more effective and faster computation of the impedance, the transfer function and amplitudes of the induced field in a spherically symmetric model of the electrical conductivity. The existing induction data have been supplemented by about 80 new values derived from the analysis of daily means. The fit of the existing 1-D models of the electrical conductivity of the mantle to the set of induction data is investigated. The characteristic equation for the free electromagnetic oscillations of a radially inhomogeneous Earth is derived and its possible importance in solving the inverse problem of electric conductivity is pointed out.

Principal moments of inertia, secular love number and origin of Phobos

Abstract A dynamic model of Phobos has been treated: its boundary surface is an equipotential surface specified by the 2nd zonal and the 2nd sectorial Stokes parameters plus the constant term in the tidal potential due to Mars; the body is homogeneous. Principal moments of inertia, libration coefficients, the 2nd degree Stokes parameters, and the secular Love Number k s of the model have been estimated numerically. Numerical value of k s supports the hypothesis that Phobos was formed out of primordial matter by accretion in orbit under the synchronous zone.

Single- and inter-station transfer functions for non-synchronous geomagnetic arrays — I. Theory of methods used in data analysis

РезюмеИзлaгaеmся mеорuя многомерного когеренmного aнaлuзa(сnекmрaльнŭ nо¶rt;хо¶rt;) в nрuмененuu к рaсчеmaм о¶rt;но-u меж-сmaнцuонных nере¶rt;amочных функцuŭ u сооmвеmсmвующuх векmорных хaрaкmерuсmuк uн¶rt;укцuu nо зanuсaм вaрuaцuŭ сосmaвляющuх мaгнumного nоля Землu. Прuво¶rt;umся maкже меmо¶rt; оценкu aнaлогuчных хaрaкmерuсmuк uн¶rt;укцuu nуmем рaсчеma в временноŭ облaсmu uмnульсного оmклuкa сuсmемы. Оnuсывaюmся aлгорumмы nрогрaмм реaлuзующuх рaсчеmы u хaрaкmерuзуюmся выве¶rt;енные nосле рaсчеma naрaмеmры.SummaryThe theory of the multivariate coherence analysis(spectral domain approach) is developed for calculating single- and inter-station transfer functions and corresponding vector induction characteristics from time variations of the geomagnetic field components. An alternative approach of calculating similar induction characteristics using a time domain algorithm is shown.

Models of electric conductivity in the upper mantle

SummaryThe accessible data of the apparent resistivity ϱT(√T) were collected and supplemented by the spectral analysis of daily means of geomagnetic components observed at world geomagnetic observatories. The data were least-squares fitted; four models of the resistivity in the upper mantle which agree with the experimental data were obtained by solving the inverse problem using Marquardts gradient-expansion algorithm.