Abstract. 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 µGal 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 2 3 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.

The technique of the orthogonal projection of ionosphere electronic content variations for mapping total electron content (TEC) allows us to visualize ionospheric irregularities. For the reconstruction of global ionospheric characteristics, numerous global navigation satellite system (GNSS) receivers located in different regions of the Earth are used as sensors. We used dense GNSS networks in central Europe to detect and investigate a special type of plasma inhomogeneities, called travelling ionospheric disturbances (TID). Such use of GNSS sensors allows us to reconstruct the main TID parameters, such as spatial dimensions, velocities, and directions of their movement. The paper gives examples of the restoration of dynamic characteristics of ionospheric irregularities for quiet and disturbed geophysical conditions. Special attention is paid to the dynamics of ionospheric disturbances stimulated by the magnetic storms of two St. Patrick’s Days (17 March 2013 and 2015). Additional opportunities for the remote sensing of the ionosphere with the use of dense regional networks of GNSS receiving sensors have been noted too.

Abstract. 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 µGal 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 2 3 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.