Antonín Zeman

Seismotectonic model of the upper part of the Earth's crust of Czechoslovakia

РезюмеКорреляцuя месm вознuкновенuя землеmрясенuŭ нa mеррumорuu Чехословaкuu u ее окресmносmu с ¶rt;aннымu nо неоmекmонuке,геоморфологuu, современным ¶rt;вuженuям земноŭ коры, космuческоŭ съемке nоверхносmu Землu uгеофuзuческuм nолям nозволuлa вы¶rt;елumь основные сmрукmырные блокu в верхнеŭ чaсmu земноŭ коры. Нa зонaх меж¶rt;у эmuмu блокaмu нaблю¶rt;aеmся возрaсmaнuе ¶rt;олговременных ¶rt;вuженuŭ, особенно в неоu¶rt;ном nерuо¶rt;е. Поэmому nре¶rt;лaгaемaя сеŭсмоmекmонuческaя мо¶rt;ель верхнеŭ чaсmu земноŭ коры основaнa нa современных знaнuяхгео¶rt;uнaмuческuх nроцессов, nроuсхо¶rt;ящuх нa uзучaемоŭ mеррumорuu, u нa uх связu с nо¶rt;вuжнымu зонaмu.SummaryA correlation of the earthquake occurrence on the territory of Czechoslovakia and in its close neighbourhood with the data on the neotectonic and geomorphological development of the respective area, the recent movements of the Earths crust, the courses of photolineations and on the geophysical fields enabled the fundamental structural blocks in the upper part of the Earths crust to be singled out. The contact zones established between the above blocks exhibit increased long-term movement tendencies particularly in the Neoid period. A seismotectonic model of the upper part of the Earths crust of Czechoslovakia, compiled with the use of the data mentioned above, is described.

Definition of the normal gravity field including the constant part of tides

РезюмеПре¶rt;сmaвляеmся о¶rt;нa aльmернamuвa решенuя ¶rt;uскуmuровaнноŭ nроблемы uсключенuя влuянuя внешнuх мaсс, вызывaющuх nосmоянную чaсmь nрuлuвного nоля, uз возмущaющего nоmенцuaлa. Решенuе основaно нa новом оnре¶rt;еленuu нормaльного nоля сuлы mяжесmu, коmорое эmу чaсmь nрuлuвного nоля в себе зaключaеm. Докaзывaеmся, чmо в кaчесmве uсmочнuкa эmого nоля можно учumывamь мaссы ¶rt;вух окружносmеŭ в nлоскосmu земного эквamорa, рa¶rt;uусы коmорых nрuблuзumельно рaвны сре¶rt;нuм рaссmоянuям Луны u Солнцa оm Землu. Преж¶rt;е всего выве¶rt;ено новое нормaльное nоле сuлы mяжесmu в сферuческом nрuблuженuu, коmорое nозволяеm nросmо ¶rt;окaзamь, чmо знaченuе нормaльного nоmенцuaлa сuлы mяжесmu нa референцноŭ nоверхносmu не меняеmся u чmо uзмененuе оnре¶rt;еленuя высоm незнaчumельное. О¶rt;uнaковым сnособом (см. [1]) выве¶rt;ено нормaльное nоле сuлы mяжесmu ¶rt;ля уровенного эллunсоu¶rt;a.SummaryOne alternative of solving the problem of eliminating the effect of external masses, generating the constant part of the tidal field, from the perturbing potential is presented. The solution is founded on a new definition of the normal gravity field which contains this part of the tidal field. It is proved that two material circles in the plane of the Earths equator, whose radii are approximately equal to the mean distances of the Moon and Sun from the Earth, can be considered as the source of this field. The new normal gravity field is first derived in the spherical approximation, which enables one to prove simply that the value of the normal gravity potential on the reference surface does not change, and that the change in the definition of the heights is insignificant. The normal gravity field for the equipotential ellipsoid is derived in the same way according to [1].

Secular changes of the geoid in the Fennoscandian land uplift region

РезюмеПре¶rt;сmaвлены ¶rt;вa вaрuaнma меmо¶rt;a оnре¶rt;еленuя вековых uзмененuŭгеоu¶rt;a в облaсmu nо¶rt;ъемa Фенноскaн¶rt;uu. Обa uсхо¶rt;яm uзгunоmезы uзосamuческоŭ комnенсaцuu Эрu-Хеŭскaненa. Первыŭ вaрuaнm — обычное uнmегрuровaнuе Сmоксa uзмененuŭ aномaлuŭ в свобо¶rt;ном воз¶rt;ухе в ¶rt;aнноŭ облaсmu. Был выве¶rt;ен вmороŭ вaрuaнm, основaнныŭ нa вычuсленuuгрaвumaцuонного nоmенцuaлa nоверхносmного слоя nо¶rt;ъемa, u рaвного слоя нaглубuне комnенсaцuu. Зamем вычuсленные uзмененuя формыгеоu¶rt;a срaвнuвaюmся с резульmamaмu Бьерхaммaрa nогеофuзuческоŭ uнmерnреmaцuu рaзложенuя nоmенцuaлa сuлы mяжесmu Землu (регuонaльноŭ ¶rt;еnрессuuгеоu¶rt;a в облaсmu Скaн¶rt;uнaвuu). Регрессuонныŭ aнaлuз укaзывaеm нa сuльную взauмосвязъ обеuх велuчuн (r=0,88). Оценuвaеmся время, необхо¶rt;uмое ¶rt;ля вырaвнuвaнuя обнaруженноŭ ¶rt;еnрессuuгеоu¶rt;a. Выве¶rt;ено сооmнощенuе ¶rt;ля уmочненuя uзмеренных знaченuŭ nо¶rt;ъемов Скaн¶rt;uнaвuu, включaющее уnругую реaкцuю Землu нa uзмененuегрaвumaцuонного nоmенцuaлa u возмущенuя, выmекaющuе uз векового уменьщенuяглубuны северноŭ чaсmu Бaлmuŭского моря.SummaryTwo alternative methods are presented of determining the secular changes of the geoid in the Fennoscandian uplift region. Both are based on the Airy-Heiskanen hypothesis of isostatic compensation. The first alternative is the usual Stokes integration of changes of free-air anomalies in the given region. Another alternative was derived, which is based on calculating the gravitational potential of the surface uplift layer and of the same layer at the depth of compensation. The calculated changes of the shape of the geoid were then compared with the results of Bjerhammars geophysical interpretation of the expansion of the Earths gravity potential (regional depression of the geoid in the Fennoscandian uplift region). Regression analysis indicates a strong correlation between the two quantities (r=0.88). The time required to level this depression of the geoid is estimated. A relation was derived for improving the accuracy of the observed values of Fennoscandian uplifts, which takes into account the elastic reaction of the Earths body to the change of gravitational potential and perturbations, caused by the secular decrease of the depth of the northern part of the Baltic Sea.

Tilts due to the free nutation of the Earth's axis in the results of geodetic observations

SummarySimple expressions for the deformation of equipotential surfaces and changes of the deflections of the vertical are derived at points of the Earths surface, which are due to the variations of the rotational component of the gravity potential under free nutation of the Earths axis of rotation (pole wandering). The results of the solution of this problem given in[1] are discussed. The values of the tilts and the changes of geoid heights for extreme deviations of the poles are considered from the point of view of the effect on measuring tilts and on levelling. An elastically deformable Earth is assumed. It is concluded that reductions with respect to the mean Earths pole are not realistic at the present degree of accuracy of levelling. The necessity to reduce long-term tilt observations, or the possibility of determining the time variations of the rotational axis from the analysis of these observations is pointed out.

Study of the Influence of the Indirect Effect of Ocean Tides and of the Direct Deformation Effect of the Atmosphere on the Results of GPS Observations

The geodynamic interpretation of the results of GPS observations among the permanently operating stations which establish the frame for defining and conserving the coordinate system and simultaneously for describing the fundamental tendencies of dynamics in the area represented by them, should be deprived of the effects of geodynamic phenomena, which can be either periodic or short-term (even non-periodic) so that secular changes may be found. Some of these influences are included in scientific processing software, others have to be modelled later. The purpose of this project is to determine the influences of the indirect effect of ocean tides and the direct deformational effect of the atmosphere on the results of GPS observations, performed at stations Pecný (Czech Republic), Wettzell (FRG) and Graz (Austria), and also for the GPS stations of the Central Europe Regional Geodynamic Project (CERGOP) in the region of Central and East Europe. On the basis of analyses and results it is possible to claim that at the present accuracy of GPS observations the influence of ocean loading and atmospheric pressure effects for geodynamic campaigns in the region of the Czech Republic is negligible. For campaigns in larger regions (i.e. Central Europe) atmospheric corrections will have to be applied to height differences. These corrections, however, due to their periodicity have negligible influence on secular changes.

The constant part of the tidal field in the theory of heights

SummaryThe problem of the constant part of the tidal field is still topical in view of the recommendations of IAG[1, 2] to eliminate the tidal effect of external masses from all geodetic measurements under preservation of the effect of the time-constant tidal deformation of the Earth. The paper discusses the consequences of accepting this recommendation for normal heights, and suggests a solution based on the new definition of the normal gravity field[3].

On the gravitation absorption hypothesis

РезюмеПре¶rt;лaгaеmся aнaлuзuровamь ¶rt;aнные uзмеренuŭ сверхnрово¶rt;нымuгрaвuмеmрaмu maкже с mочкu зренuя nроверкuгunоmезы nог¶rt;лaщенuягрaвumaцuu. Нa основе mеореmuческuх ¶rt;aнных зa mрехлеmнuŭ nерuо¶rt; был вычuслен сnекmр nре¶rt;nолaгaемого эффекma экрaнuровaнuягрaвumaцuонного воз¶rt;еŭсmвuя Солнцa земным mелом нa велuчuну ускоренuя сuлы mяжесmu ¶rt;ля nрuлuвноŭ сmaнцuu Брюссель (Рuс. 2a–е).SummaryIt is recommended that the data from measurements with supraconducting gravity meters be also analysed with regard to verifying the gravitation absorption hypothesis. Based on theoretical data from a3-year period, the spectrum of the assumed effect of shielding the gravitational influence of the Sun by the Earths body on the value of the acceleration of gravity has been calculated for the tidal station Brussels (Figs 2a–e).

Approximate solutions of the surface mass loading of a spherical Earth model

РезюмеПросmое nрямолuнеŭное uзобрaженuе слaaемых nрuблuзumельноо nлоскосmново решенuя mочечноŭ вещесmвенноŭ нaрузкu nоверхносmu Землu в nо¶rt;хо¶rt;ящеŭ сuсmеме коор¶rt;uнam ве¶rt;еm к выбору maкоŭ крuвоŭ вmороŭ сmеnенu, коmорaя нauлучшuм обрaзом nо¶rt;хо¶rt;um к сферuческому решенuю ¶rt;ля ¶rt;aнноŭ мо¶rt;елu Землu. Новое nрuблuзumельное решенuе, коmорое можно nо aнaлоuu к nлоскосmному решенuю нaзвamь naрaболuческuм решенuем, nозволяеm uсnользовamь nросmые вво¶rt;ные ¶rt;aнные nлоскосmноо решенuя ¶rt;aже ¶rt;ля сущесmвенно большuх уловых рaссmоянuŭ. Срaвненuе с сферuческuм решенuем осущесmвлено вычuсленuем влuянuŭ волны М2 морскuх nрuлuвов. Резульmamы вычuсленuŭ ¶rt; ля nрuлuвноŭ сmaнцuu Брюссель ¶rt;окaзывaюm у¶rt;овлеmворumельное солaсuе обоuх решенuŭ ¶rt;aже ¶rt;лялобaльных зa¶rt;aч.SummarySimple linear representation of the components of an approximate plane solution of point mass loading of the Earths surface in a conveniently chosen coordinate system leads to selection of a 2nd-degree curve which is the best fit of the spherical solution for the given Earth model. The new approximate solution, which, analogously to the plane solution, can be called a parabolic solution, enables the simple input parameters of the plane solution to be used also for substantially larger angular distances. The comparison with the spherical solution is carried out by computing the effects of the M2-wave of ocean tides. The results of the computations for the tidal station Brussels prove the two solutions to be in sufficient agreement for global problems as well.

Lamé's elastic constants determined from the results of geodetic measurements

РезюмеМеmо¶rt; оnре¶rt;еленuя элaсmuчных консmaнm Лaмэ μ u λ, основaнныŭ нa ¶rt;aнных о рaсnре¶rt;еленuu во¶rt;ных мaсс uскусmвенноо во¶rt;охрaнuлuщa u нa резульmamaх нuвелuрных uзмеренuŭ, uсnолненных вблuзu во¶rt;ных мaсс в nерuо¶rt; nере¶rt; нanолненuем во¶rt;охрaнuлuщa u nосле ео нanолненuя. Рещенuе uсхо¶rt;um uз nре¶rt;nоложенuя, чmо nрuблuзumельно ¶rt;еŭсmвumельнa nрямaя nроnорцuонaльносmь меж¶rt;у велuчuноŭ uзмененuŭ nревыщенuя mочек, выявленных uз рaзнuц резульmamов нuвелuровaнuя, u nоmенцuaлом сuлы nрumяженuя во¶rt;ных мaсс в эmuх mочкaх. О¶rt;овременно nре¶rt;nолоaеmся, чmо выявленные uзмененuя nревыщенuŭ зaвuсяm оm элaсmuчных консmaнm сре¶rt;ы (консmaнmы Лaмэ μ u λ). Эmоm меmо¶rt; был nрuменен в облaсmu во¶rt;охрaнuлuщa Кaрuбa нa реке Зaмбезu, a резульmuрующuе велuчuны μ=(0,69±0,03)×1011 Рa сооmвеmсmвуюm велuчuнaм мо¶rt;елu Булленa ¶rt;лялубuн оm 100 ¶rt;о 200 км.

Estimate of the effect of changes of atmospheric pressure on the results of levelling

РезюмеОбрaзовaнuя amмосферных ¶rt;aвленuŭ зaмещaюmсяеомеmрuческu более nросmымu мо¶rt;елямu u выво¶rt;umся влuянuе uх мaсс нa уровенные nоверхносmu в месmaх,¶rt;е реuсmрuруеmся нaклон. О¶rt;новременно оnре¶rt;еляюmся знaченuя нaклонов, вызывaемых уnруuмu ¶rt;еформaцuямu земноŭ nоверхносmu. Друuмu косвеннымu влuянuямu nренебреaеmся. Для слычaя мо¶rt;елu вычuслены обе ¶rt;еформaцuu u nосле¶rt;нuмu вызвaнныŭ общuŭ нaклон. Выве¶rt;енные сооmнощенuя ¶rt;ля нaклонa nрuменяюmся к нuвелuрным нaблю¶rt;енuям.