Correction due to finite speed of light in absolute gravimeters

Correction due to finite speed of light is among the most inconsistent ones in absolute gravimetry. Formulas reported by different authors yield corrections scattered up to 8 $\mu$Gal with no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect, however, in implementing the models we additionally introduce two scales of time associated with moving and resting reflectors, derive a set of rules to switch between the scales, and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulas for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for $\frac23$ of the total correction due to finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models

ВАРИАЦИИ СИЛЫ ТЯЖЕСТИ И СОВРЕМЕННАЯ ГЕОДИНАМИКА ЮГОЗАПАДНОЙ ЧАСТИ БАЙКАЛЬСКОГО РЕГИОНА

Modern methods for determination of gravity values make it possible to obtain measurements with the accuracy up to 10–9 from g0 of the normal value (up to 1 microgal = 10 m/sec2). While all the systematic and periodic effects are excluded, a question is raised about stability of the gravity field of the Earth over time. Changes of the altitude (the Earth’s radius) with time can be estimated with an accuracy of 0.1 mm by modern space geodetic techniques, such as VLBI method. Our experiments for evaluation of stability of the gravity values over the past decades are based on the data obtained by Russian and foreign observatories using absolute ballistic laser gravimeters. The results put a limit of 10–10 per year to changes of the Earth’s radius. These estimations can be useful for testing hypotheses in tectonics.Measurements of non-tidal variations of gravity (Δg), which were obtained from 1992 to 2012 at the Talaya seismic station (located in the south-western part of the Baikal region), are interpreted together with GPS observation data. At the Talaya seismic station, the linear component of gravity variations corresponds to changes in the elevation of this site. The correlation coefficient is close to the normal value of the vertical gradient of gravity. At this site, coseismic gravity variations at the time of the Kultuk earthquake (27 August 2008, Mw=6.3) were caused by a combined effect of the change of the site’s elevation and deformation of the crust. Our estimations of the coseismic effects are consistent with results obtained by modeling based on the available seismic data.Современные методы определения значения силы тяжести позволяют проводить измерения с точностью до 10–9 от g0 нормального значения (до 1 микрогала = 10 нм/с2). При этом исключаются все систематические и периодические эффекты и возникает вопрос о стабильности поля силы тяжести Земли во времени. Оценить изменения высоты (радиуса Земли) во времени с точностью до 0.1 мм позволяют современные методы космической геодезии (VLBI метод). Экспериментальные оценки стабильности значения силы тяжести за последние десятилетия сделаны по материалам отечественных и зарубежных обсерваторий, использующих абсолютные лазерные баллистические гравиметры. Полученные результаты ограничивают изменение радиуса Земли значением 10–10 в год. Эти оценки можно использовать для тестирования тектонических гипотез.Результаты измерений неприливных вариаций ускорения силы тяжести Δg, проведенных в 1992–2012 гг. на сейсмостанции «Талая» (юго-западная часть Байкальского региона), интерпретируются совместно с данными GPS-наблюдений. Линейная составляющая вариации силы тяжести на станции Талая соответствует изменениям высоты пункта. Коэффициент корреляции близок к нормальному значению вертикального градиента силы тяжести. Косейсмические вариации силы тяжести на этом пункте в эпоху Култукского землетрясения (27.08.2008 г., Мw=6.3) вызваны комплексным эффектом изменения высоты пункта и деформации земной коры. Оценки косейсмических эффектов соответствуют результатам моделирования на основе сейсмологических данных

GRAVITY VARIATIONS AND RECENT GEODYNAMICS OF THE SOUTH-WESTERN PART OF THE BAIKAL REGION

Modern methods for determination of gravity values make it possible to obtain measurements with the accuracy up to 10–9 from g0 of the normal value (up to 1 microgal = 10 m/sec2). While all the systematic and periodic effects are excluded, a question is raised about stability of the gravity field of the Earth over time. Changes of the altitude (the Earth’s radius) with time can be estimated with an accuracy of 0.1 mm by modern space geodetic techniques, such as VLBI method. Our experiments for evaluation of stability of the gravity values over the past decades are based on the data obtained by Russian and foreign observatories using absolute ballistic laser gravimeters. The results put a limit of 10–10 per year to changes of the Earth’s radius. These estimations can be useful for testing hypotheses in tectonics.Measurements of non-tidal variations of gravity (Δg), which were obtained from 1992 to 2012 at the Talaya seismic station (located in the south-western part of the Baikal region), are interpreted together with GPS observation data. At the Talaya seismic station, the linear component of gravity variations corresponds to changes in the elevation of this site. The correlation coefficient is close to the normal value of the vertical gradient of gravity. At this site, coseismic gravity variations at the time of the Kultuk earthquake (27 August 2008, Mw=6.3) were caused by a combined effect of the change of the site’s elevation and deformation of the crust. Our estimations of the coseismic effects are consistent with results obtained by modeling based on the available seismic data