Obtaining the most accurate and reliable gravimetric data has always been and remains the main task of gravimetry. The purpose of the authors’ long-term research and this work in particular is to determine interference in gravimetric data caused by various external influences and to find ways to take them into account or eliminate them. The proposed method of iteratively taking pressure and tidal correction into account made it possible to increase the accuracy of single gravimetric readings to ±2 µGal. The main instruments for many years of research were relative automated gravimeters of the CG Autograv series from Scintrex; the main results obtained in this work are shown based on their example. In CG-5 and CG-6 gravimeters, the instrumental accuracy is 1.0 and 0.1 µGal, respectively. However, it cannot be said that a single reading will give the gravity increment with the specified accuracy. Relative gravimeters, in addition to the desired value, also record the device response to inertial influence, changes in meteorological factors, and its own hardware errors, which cannot be eliminated without additional information. Under the conditions of the Zapolskoye geophysical observatory in the Vladimir region, continuous gravimetric, seismic, and meteorological measurements were carried out for 8.5 months. The obtained data made it possible to analyze the possibility of partially taking the influence of the atmospheric pressure and determining the correct delta factors for 20 groups of waves with periods of 48 days or less into account. The minimum duration of the gravimetric series to obtain delta factors of waves with periods from 0.02 to 3.38 cycles per day was also estimated at 6 months.

The results of the first high-precision airborne gravimetric route survey, which was conducted in 2023 along a transverse profile of Lake Baikal at a flight altitude of 5300 m, are presented. The use of an airborne gravimetric complex based on the AN-26BRL aircraft–laboratory is described. Directly over the lake, the largest negative measured anomaly of the gravity field was –180.8 mGal and the horizontal gradient of the field measurement was up to 9 and 5 mGal/km for the western and eastern shores of Lake Baikal, respectively. The internal convergence of anomaly values along the route profile for a complex of three gravimeters was 0.74 mGal. The estimations of the resolution and reliability of most topical current global models of the Earth’s gravity field (UGM-SGG-2, EGM2008, XGM2019, and Sandwell and Smith v32) based on satellite data are assessed for the Baikal rift basin. It is shown that the mean square deviations of the field along the entire profile between the values calculated from satellite models with a number of spherical harmonic coefficients of ≥2190 and the airborne gravimetric observations are 9.5‒17.9 mGal, whereas the maximum deviations at individual points of the route are 40–80 mGal. The comparison with data on the marine gravimetric survey on a scale of 1 : 500 000 is carried out using airborne profile data. Due to the highly detailed data along the airborne gravimetry profile, it is established that the factual value of the main negative anomaly on the air profile is higher than that accepted for the analysis and complex interpretation of geophysical data in the area of Lake Baikal.

This study estimates the impact level of storm microseisms on long-term gravimetric measurements. Gravimetric measurements were conducted at the Zapolskoe, Obninsk, and Murmansk sites using CG-5 Autograv relative gravity meters. Seismic measurements were carried out concurrently with gravimetric measurements at Zapolskoe. The analysis of these measurements demonstrates the feasibility of utilizing seismic data as control information to estimate the high-frequency noise component of gravimetric data. Based on the additional seismic information from the services of the Incorporated Research Institutions for Seismology, the correspondence between the attenuation of the noise component in gravimetric measurements and the data from the modeled sensitive element of the gravimeter, which utilizes seismic series as an input, is identified. The first characterization of the storm-induced background noise of gravimetric measurements at the Murmansk site is obtained. Furthermore, the possibility of predicting measurement errors based on meteorological forecasts is refined, which can aid in the planning of gravimetric work.

With the increase in accuracy and resolution of modern global models of the Earth’s gravity field, more opportunities have appeared to use them in solving the regional gravimetric problems. At the same time, the estimates of existing models depending on the region and geomorphology, as well as methods for predicting the reliability of data in models, taking into account the scale and nature of the problem being solved, become more important. The article is devoted to new estimates of modern models of the gravity field in various regions of the World Ocean and over various geomorphological structures. The estimates were obtained by comparing the data of the most relevant models of the gravity field with the data of high–precision marine areal and route surveys carried out in all major areas of the World Ocean. Based on the results, the model field is promising and it is possible to estimate the spatial distribution of model field errors in the World Ocean. A method for efficient preliminary zoning of a model field in the ocean is proposed. The features of the development of the Earth’s gravity field models are considered, taking into account their actual accuracy and resolution, as well as the issue of general reliability of modern model data in the high-latitude Arctic.

This work is aimed at estimating the long-term continuing measurements of the acceleration of gravity at the Ledovo fundamental gravity station and first order stations of the gravimetric network of the Russian Federation. The observations are carried out by absolute gravimeters beginning from the mid-1970s to the present time. It is shown that the observed value of the acceleration of gravity at the Ledovo station has a tendency to decrease during last 45 years; according to our estimates, the value decreased by 32 µGal. The measurements carried out at first order gravity stations in Russia after renewal of network maintenance are compared with measurements carried out in the 1980s.

This chapter focuses on models of the Earth’s gravity field, estimation of their accuracy, and use in applied problems. Various accuracy estimation approaches, including those based on the use of a priori and a posteriori estimates are presented. Gravimetric coverage of the Earth areas is considered. Quality monitoring of relative gravity measurements at sea with account for the global models is discussed. Using a large amount of survey data, EGM2008 is compared with marine gravity measurements by calculating the residuals. The widespread map-aided navigation method is addressed. The stochastic filtering algorithms for map-aided navigation within the Bayesian approach are reviewed and compared. Efficiency of the Earth’s gravity field data use for navigation purposes is discussed.

This chapter provides a historical overview of gravimetric surveys in the Arctic. Findings from modern airborne gravimetric surveys in the Arctic carried out by Russian and international companies are analyzed. Marine and airborne gravimetric surveys using the Chekan gravimeters in hard-to-reach areas of the Earth, such as the Geographic North Pole, the Greenland shelf, coastal seas of the Antarctic, and the Himalayas are addressed. Polar versions of the GT-2A gravimeter with the necessary modifications of equipment and software for all-latitude applications are covered. Application of multi-antenna GNSS receivers in these areas is analyzed, and the method of transition to quasi-geodetic coordinates is described.

Marine gravimetry aims to obtain accurate and reliable data on gravity field anomalies in water areas. Modern gravimetric systems such as Chekan-AM feature high accuracy due to the novel circuit and design solutions in the conditions specified in the technical description. The article discusses the influence of ambient temperature and humidity on the accuracy of the Chekan-AM gravimeter. These meteorological factors matter both during short measurement periods, within individual survey lines, and long periods, during expeditions far away from the reference points. For 18 months, the authors of the article have been carrying out laboratory tests of the gravimeter with simultaneous registration of meteorological parameters. Based on the observation results, the correlation dependences of the zero-point drift of the gravimeter sensitive element on seasonal temperature and humidity variations were calculated. Marine expeditions data were also studied, with analysis of the temperature impact over a short time period during the marine gravimetric survey. Based on the results of the experiments it was shown that meteorological monitoring should be performed in the course of gravimetric surveys, including those onboard research vessels. An additional thermal noise becomes noticeable in the survey conducted in an area with low variations in the gravity field, and it should be considered when analyzing and evaluating the results.

Transient processes in gravimetric data spanning more than 12 years are considered. During this time, more than 15 trips were made from the fundamental gravimetric point Ledovo to the first class point Zapolskoe and back using two CG 5 Autograv automated relative gravimeters. The most significant parameters that affect the readings of the instruments were identified: ambient temperature, the values of the zero drift of the sensing element of the gravimeter, and the direct increment of gravity. The zero drift was taken into account using a second-order polynomial prediction, and the remaining two parameters were described by a logarithmic dependence. The natural logarithm equation allows describing the functions by measuring the coefficient before the logarithm (logarithmic) and additional (linear). The value of the logarithmic coefficients characterizing the duration of transient processes has a linear dependence on temperature, which means that it can characterize the measurement time at the point in the case of a significant temperature change. The magnitude of the linear coefficients characterizing the increase in gravity depends linearly on temperature when the instruments are moved to a colder environment. When the instruments are moved to a warmer environment (10°), the dependence becomes more complex, possibly random, which also requires an increase in the measurement time at the point. The usual duration of measurements at gravimetric stations is 10 min. The relevance of taking temperature into account at measurement points depends on the required accuracy, for example, for a temperature difference of 10°C, the RMS of gravimetric measurements was ±0.025 mGal.

The article provides a generalized retrospective of creating global models of the Earth's gravity field using satellite methods and modern global ultra-high-degree models; the most promising new solutions are considered. The main attention is given to reviewing techniques that affect the resolution of satellite methods, their development, and ways of further improvement. Modern combined models of the Earth's gravity field, which also include altimetry data, instrumental surveys and global topography, are most interesting. The areas of possible practical application of global models and applied problems solved with their help depend on an understanding of the nature of model data and methods for their modification. At present, the resolution of models up to 5540 degrees of field expansion in spherical harmonics is achievable; however, high values of their degree and order do not always determine the reliability of the presented model data (not verified by direct measurements). Therefore, along with the highest-degree solutions, this article considers most of the known models of the Earth's gravity field and their most characteristic modifications.

In this paper, the issues of modeling the Earth's gravitational field, the accuracy of modern models and the prospects for their further development are discussed.Ultra-high-degree combined models and their constituent parts that form these models in different frequency ranges were studied.The special attention is given to satellite methods that form the low-frequency basis of the combined ultra-high-degree model and to the satellite altimetry method, as the most effective means of obtaining high-frequency data on the global gravitational field in the waters of the World Ocean.The most typical areas of localization of model errors associated with the field gradient are identified and a method for predicting such areas for the preliminary assessment of the practical application of model data is proposed.Also, as a result of the analysis, the prospects of modeling the global gravity field on the basis of satellite methods were confirmed and directions for improving the methods for creating promising combined ultra-high-degree models were determined.

—Empirical comparative study of the modern global models of the Earth’s gravity field (EGF) in the form of geopotential spherical harmonics is carried out. The importance and topicality of this study is associated with the growing number of models and strengthening the requirements to the modeling results. The obtained comparative characteristics are based on the results of statistical processing of model quasi-geoid heights and gravity anomalies on global and regional scale (by the example of the Arctic region and territory of Russia). A large and diverse array of the examined models and the study method determine the novelty of the obtained results. Overall, 103 models have been studied, among which three are Russian and others are developed by foreign authors. The studied models include those with low-, medium-, high-, and super-high spatial resolution. The effect of convergence (nonparallelism) of meridians at the calculation points on the statistical characteristics of EGF models is estimated which, according to the obtained estimates, can be significant. It is shown that this effect can be taken into account by a modified approach that involves introducing the weighting factors. The discrepancies between models in different combinations are analyzed. Based on this analysis, the contribution of the new satellite geodetic data obtained with the use of satellite-to-satellite systems and satellite gradientometry is estimated. The importance of taking into account the intragroup, intergroup, and inter-regional differences between the studied models is shown.

The phenomenon of synchronous episodic increase in gravimetric noise at the stations distant by thousands of kilometers from each other is described. The comparison with microseismic noise suggests inertial rather than gravimetric origin of the recorded anomalies. The duration of anomalous enhancement in microvibrations ranges from a few hours to a few days. The nature of synchronous microvibrations involving significant segments of the Earth’s lithosphere is unclear; the probable causes are discussed. The conducted analysis has shown that among the key factors responsible for the increase in the microseismic noise in the European part of Russia is the influence of marginal seas, in particular, the storm-generated microseisms. The allowance for this phenomenon is necessary in planning and conducting high-precision gravity surveys and long-term gravity observations.

Aerogravimetric survey is a rapidly developing and promising method for studying the gravity field in remote regions of the Earth. However, its practical use involves difficulties. Thus, during flights, inertial interference occurs due to engine-induced vibration of the fuselage. Earlier, various options for antivibration designs were tested. During its annual aerogravimetric works, the Schmidt Institute of Physics of the Earth, Russian Academy of Sciences (IPE RAS), employs a quite efficient option, which, however, cannot be regarded as complete. For the first time, a high-frequency seismometer was used to evaluate the efficiency of a gravimeter antivibration system used in aerogravimetric operations. Vibration suppression was assessed in a wide frequency range. During experimental flights, a decrease in vibration noise was detected at a frequency of 2 Hz, which is relevant for gravimetric equipment. The experimental results confirm the adequacy of the applied antivibration equipment. The antivibration platform developed at IPE RAS significantly reduces vibrations affecting the GT-2M aerogravimetric system. The possibility of using the Baikal-ACN high-frequency seismometer in an unconventional field of application is demonstrated.

Abstract—The empirical results on estimating the resolution and high-frequency noise in the Earth’s gravity models are presented. The Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences participated in a marine gravity survey in the Indian Ocean. Based on the survey data, gravity maps were constructed for ten regions with a total of 611 986 gravimetric points. The root mean square measurement error is at most 0.27 mGal. The differences between measured gravity and predictions by the EGM2008 gravity model are calculated. The statistical processing of the differences shows that they vary from –25 to 44 mGal on the shelf and from –7.4 to 6.2 mGal on the abyssal plain with a root mean square value of 1.33 mGal. The results of the survey indicate that the anomalies in the ultra-high-degree model can only be used for constructing gravity maps on the scale of 1 : 500 000 or smaller.

A modified method for S-approximations of anomalous potential fields is described; its advantages are discussed. Software has been developed to calculate deflections of the vertical (DOV) and geoid heights using the proposed technique. The results of DOV calculations for two regions of the Atlantic Ocean are given.

Modern methods of studying the Earth’s gravity field on a mobile base are discussed, among them aerogravimetric research. The features of creating a highly autonomous airborne gravimetric laboratory with a long flight duration for operations in remote territories and waters are described. The experience of creating an airborne laboratory based on AN-30D and AN-26BL aircraft is discussed in detail. The makeup of gravimetric and navigation equipment is substantiated; the need for installing additional thermal and vibration protection devices, backup power lines, and additional communication facilities is shown; and the device and operation of airborne gravimetric systems based on different principles of operation are considered. The aerogravimetric survey method and features of its implementation are discussed. The main provisions of the software packages for in situ and office processing of gravimetric and navigation information obtained both on board the aircraft and at GPS or GLONASS base (ground) stations are presented. Methods for taking into account corrections for aerogravimetric systems with different operating principles are discussed.