5th Symposium on Terrestrial Gravimetry: Static and Mobile Measurements (TG-SMM 2019)

Methods to measure absolute gravity and deflections of the vertical on a moving base are presented. The breadboard of integrated gravimetric system is described. The first results of experimental studies confirmed the possibility of high-precision measurement of the absolute values of gravity and deflection of the vertical at sea.

In recent years, it was shown that the quality of strapdown airborne gravimetry using a navigation-grade strapdown inertial measurement unit (IMU) could be on par with “classical” airborne gravimeters as the 2-axis stabilized LaCoste and Romberg S-type gravimeter. Basically, two processing approaches exist in strapdown gravimetry. Applying the indirect method (also referred to as “inertial navigation approach” or “one-step approach”), all observations – raw GNSS observations or position solutions, IMU specific force and angular rate measurements – are combined in a single Kalman Filter. Alternatively, applying the direct method (also referred to as “accelerometry approach” or “cascaded approach”), GNSS position solutions are numerically differentiated twice to get the vehicle’s kinematic acceleration, which is then directly removed from the IMU specific force measurement in order to obtain gravity. In the scope of this paper, test runs for the application of strapdown airborne and shipborne gravimetry are evaluated using an iMAR iNAV-RQH-1003 IMU. Results of the direct and the indirect methods are compared to each other. Additionally, a short introduction to the processing scheme of the Chekan-AM gravimeter data is given and differences between Chekan-AM and strapdown results of the shipborne campaigns are analysed. Using the same data set, the cross-over residuals suggest a similar accuracy of 0.39 mGal for the Chekan-AM and 0.41 mGal for the adjusted strapdown results (direct method).

In this article, we propose a technique for processing airborne gravimetry measurements at repeat drape lines. To model gravity along a line, we use cubic B-splines. The unknown parameters of the model (the spline coefficients) are to be estimated from the measurements. In order to take into account dependance of gravity on position, the same set of the spline coefficients is assumed for gravity modeling at each repeat line. Gravity estimation is performed with the Kalman filter. The spline coefficients are included in the state vector of the filter as unknown constants. The developed estimation algorithm was tested using measurements of the GT-2A gravimeter collected at repeat drape lines. The gravity estimates obtained with the use of B-splines are more accurate compared with those obtained with the standard technique, in which gravity is modeled as a stochastic process in the time domain.

The article presents the description of two algorithms used for processing of the raw data of a gravity gradiometer. These algorithms are intended for estimation of some instrument errors. The first algorithm is applicable for the instrument operation in its stationary mode, the second proposes the use of a special test bench. Rotary gravity gradiometer of the accelerometric type was taken as a prototype for relevant mathematical models. Nowadays this type of gradiometer is brought to the stage of practical implementation and serial production.

In development of a rotating accelerometer gravity gradiometer (RAGG), it is difficult for us to distinguish the measurement signals and error components in the RAGG output without a verified and correctness RAGG analytical model. In addition, many key techniques, such as RAGG analytical model validation, online error compensation, post motion error compensation, are difficult to be verified. RAGG numerical model can provide validation platform for solving all the above problems, which can speed up the development of the RAGG. In this study, based on the principle and configuration of the RAGG, we synthetically consider almost all the error factors, such as circuit gain mismatch, installation errors, accelerometer scale-factor imbalance, and accelerometer second-order error coefficients, construct a parameters adjustable RAGG numerical model. In multi-frequency gravitational gradient simulation experiment, we use the RAGG numerical model simulating the situation that a test mass rotates about the RAGG with time-varying angular velocity to generate multi-frequency gravitational gradient excitations; the experiment results are consistent with the theoretical ones; the RAGG numerical model can recur some phenomenons of a actual RAGG.

The paper presents an approach to determination of the gravity disturbance vector from airborne gravimetry measurements at an aircraft’s flight path. A navigation-grade inertial navigation system (INS) and the carrier-phase differential mode of GNSS are assumed. To improve observability of the gravity horizontal components, which are observed in combination with the INS systematic errors, we use a spatial model of gravity. We parameterize the disturbing potential in the observation area using the spherical scaling functions. The unknown coefficients of the parameterization and the INS systematic errors are estimated simultaneously using the Kalman filter. Due to ill-conditioning of the estimation problem, the information form of the Kalman filter and regularization are used. The numerical results obtained from simulated data processing shows that the approach based on spatial modeling is capable to improve accuracy of the gravity horizontal component determination comparing to a typical modeling of gravity in the time domain.

The initial information for the development of high-degree models of the Earth's gravitational field (EGF) are the results of satellite and ground-based measurements. At the same time, satellite measurements carry information on the long-wave structure of the EGF. Information on the short-wave structure of the EGF can be obtained only on the basis of ground-based measurements. Having organized the determination of deflection of vertical (DOV) with a resolution of several kilometers, the local structure of the EGF can be restored with the highest possible resolution. This can be done using digital zenith camera systems (DZCS). They are automated and allow to determine the components of the DOV at the point of placement in real time. The article presents the developed measurement technique with a DZCS and the results of its tests at various geographical points in the field. The proposed technique, unlike the existing traditional technique, allows to evaluate and take into account the calibration coefficients of the DZCS in each series of observations. In addition, the new proposed technique does not impose requirements on the accuracy of rotation of the telescope around the axis in the horizontal plane and the rigidity of the base of the DZCS. The test results of the new technique showed that the standard deviation of measurements is about 0.1^″–0.3^″.

Long-term recordings of temporal gravity variations were made with the gPhoneX # 117 spring gravimeter at the Center of Geodesy, Cartography and SDI (TsNIIGAiK). The purpose of the observations is to obtain reliable parameters of the Earth tides and non-tidal component for a site located within the territory of Moscow. At a later stage, these parameters will be used to process absolute gravity observations. One year of recordings were chosen (April 1, 2016–March 03, 2017). Preliminary data processing is fully automated and runs in a program written in Python. In the course of the research, the parameters of the instrument drift were determined by the method of piecewise linear approximation of the observations. The estimated parameters of the Earth tides were obtained according to the algorithms of the ETERNA 3.4 program (Wenzel, Bulletin d’Informations des Marées Terrestres 124:9425–9439, 1996). The non-tidal gravity changes (the difference between the experimental and local model data) were compared with the model of temporal variations of the gravity field caused by atmospheric loading. Theoretical values were provided by EOST Loading Service.

The studies presented here, are unique for Moscow site and they are one of the first attempts to use high-precision recordings of spring gravimeters while computing observed tidal and non-tidal parameters.

At present, the uncertainty in measurements of free fall acceleration (FFA) by the designed absolute ballistic gravimeter (ABG), developed in VNIIM, attains microgal values (1 Gal = 1 cm/s²). At such a high level of accuracy, the effects of the interaction of a test body (TB) falling in the vacuum chamber of the ABG in the geomagnetic field could comprise sources of systematic errors. Furthermore, individual units and systems of the ABG itself also can be sources of the magnetic field (MF). We report about more rigorous calculations of the possible effects than those performed in the past. A consecutive self-consistent method of calculation of the desired correction to the FFA has been developed. It results in the differential equation, including not only the field itself, but also its vertical first and second derivatives and variation of the velocity along the trajectory. The desired correction is obtained by its numerical solution on the basis of the parameters of the field generated by the magnet of the stepper motor. The derived correction proved to be at the level of a tenth part of microgal.

Volcanic activities sometimes involve gravity changes, and this research is intended to establish an observation network surrounding an active volcano using compact absolute gravimeters. To simplify the configuration of absolute gravimeters, they are preferably operated with a light source distributed from a telecom band (wavelength of 1.5 μm) laser through optical fibers. To evaluate the accuracy of the absolute gravimeter with the telecom band laser, we conducted observations using a prototype gravimeter (TAG-1) with frequency-stabilized lasers at both 1.5 μm and 633 nm, and compared these results with the expected gravity at the site. Initially, both results showed offsets −187 μGal and −9.6 μGal for the 1.5-μm laser and the 633-nm laser, respectively (1 Gal = 10⁻⁸ m/s²). By correcting the systematic errors of the photo detectors measured by the synthetic chirp signal, the obtained absolute gravity was consistent with the expected value for both wavelengths; offsets from the expected gravity were reduced to 6.6 μGal and 5.4 μGal for 1.5 μm and 633 nm, respectively. We also evaluated the errors associated with long-distance transmission of the 1.5-μm laser using a reeled optical fiber (26 km) and an optical amplifier and found no degradation in the gravity data from the case of short transmission (10 m). These results allow networking of compact absolute gravimeters connected by telecom optical fibers that are operated using a common laser and expansion to volcanic areas to monitor the gravity change associated with volcanic activities.

For the measurement of the acceleration due to gravity, INRiM developed a transportable ballistic rise-and-fall absolute gravimeter, the IMGC-02. It uses laser interferometry to measure the symmetrical free rising and falling motion of a test mass in the gravity field. The launch system is composed of a moveable carriage fixed to two pairs of springs loaded by an electric stepper motor, which vertically throw up a corner cube retroreflector in vacuum. The interferometer system is a modified Mach-Zehnder interferometer where the launched corner cube acts as the reflector in one of the optical arms of the interferometer and the other retroreflector acts as inertial reference during the measurement. However, both systems entail some practical problems and uncertainty contributions that need to be reduced. In particular, the current launch system might cause beam shear and rotational effects due to unavoidable small different loadings of the springs, while the current interferometer system poses problems in the alignment of the mirrors, which is a highly time-consuming procedure and has to be performed before and, sometimes, during the measurement session. For this reason, a new launch system consisting of an electric linear motor which produces a linear force along its length, and a modified Jamin interferometer system entailing a simpler alignment and a better stability in time, have been designed. This works deals with the description of these new systems.

Absolute gravity measurements taken on a near-weekly basis at a single location is a rarity. Twelve years of data at the UK’s Space Geodesy Facility (SGF) provides evidence to show that the application of results from international comparisons of absolute gravimeters should be applied to data and are critical to the interpretation of theSGF gravity time series of data from 2007 to 2019. Though residual biases in the data are seen. The SGF time series comprises near weekly data, with exceptions for manufacturer services and participation in international instrument comparisons. Each data set comprises hourly data taken over 1 day, with between 100 and 200 drops per hour. Environmental modelling indicates that the annual groundwater variation at SGF of some 2 m influences the gravity data by 3.1 μGal, based upon some measured and estimated soil parameters. The soil parameters were also used in the calculation of the effect of an additional telescope dome, built above the gravity laboratory, and have been shown to be realistic. Sited in close proximity to the long-established satellite laser ranging (SLR) system and the global navigation satellite systems (GNSS) the absolute gravimetry (AG) measurements provide a complimentary geodetic technique, which is non space-based. The SLR-derived height time series provides an independent measurement of vertical motion at the site which may be used to assess the AG results, which are impacted by ground motion as well as mass changes above and below the instruments.

The paper presents research of the evolution of resolution capabilities and approximation accuracy of the last decade global geopotential models based on space gravimetric measurements of CHAMP, GRACE and GOCE missions using their spectral characteristics.

The comparison between the model data with point measurements data on gravity anomalies and quasigeoid heights for the territory of Novosibirsk region is shown. Based on the research results the conclusion was drawn that accuracy characteristics of current global models under test built by the results of satellite gravimetry missions do not achieve the specified accuracy of 1 cm and 1 mGal on the territory under investigation. The research has made it possible to state that at the current technological and methodical level the potential has been reached as concerns EGF models resolution and accuracy enhancement.

The paper reviews models of tidal and non-tidal variations of the Earth's gravitational field. Proposing an algorithm for the estimation of the Stokes coefficients based on inter-satellite measurements of low-orbit spacecrafts. By processing measurements of the GRACE mission, we obtained experimental estimates of gravity field monthly variations. The analysis of these values was carried out by calculating the change in the equivalent water height for a given area.

The actual problem of creation of gravity maps which can be used as correctors in map-matching- navigation systems (MMNS) is considered. It is assumed to use information from two sources: available gravity maps and measurement data of various parameters of the Earth’s gravity field (EGF) (acceleration of gravity, deflection of the vertical, horizontal gradients of the potential).

Obtaining the required amount of measurement data of a specified accuracy is considered as a problem of planning primary measurements. At the first stage of its solution, the number of measurements necessary to achieve the required accuracy of the parameters of the gravitational map is minimized. It takes into account the accuracy and performance of measuring devices. The second stage assumes that the human operator specifies the position of the points at which to measure the parameters of the EGF with a known accuracy.

Joint processing of information is carried out on the basis of the collocation method. The estimation of EGF navigation quality is considered in a specified point and its nearest neighborhood. This approach is reasonable, if in the future it is required to optimally form the trajectory of the MMNS in a specified area or to a specified destination point. It is assumed rectilinear motion of the object from this point with a known initial level of coordinate errors. Position errors are defined as functions of distance from the initial point and direction of movement.

The current state of satellite altimetry development allows the use of altimetry data in determining the detailed characteristics of the Earth’s gravity field on the surface of the ocean in the form of models of geoid heights, deflection of vertical and gravity anomalies. The article presents the bistatic altimetry method based on the reflected signals of global navigation satellite systems (GNSS). In this method, measurement redundancy is necessary to solving the problem of determining the height of the geoid with high spatial resolution. The experiments showed the possibility of using the code and phase of the received signal. The experiments showed the possibility of using method of bistatic GNSS-altimetry to determine the height of the geoid.

Gravity changes associated with volcanic processes occur over a wide range of time scales, from minutes to years and with magnitudes between a few and a few hundred microGal. High-precision instruments are needed to detect such small signals and both time-lapse surveys along networks of stations, and continuous measurements at single points, are accomplished. Continuous volcano gravimetry is mostly carried out through relative gravimeters, either superconducting instruments, providing higher quality data, or the more widely used spring meters. On the other hand, time-lapse surveys can be carried out with relative (spring) gravimeters, that measure gravity differences between pairs of stations, or by absolute gravimeters, capable of measuring the absolute value of the gravitational acceleration at the observation point. Here we present the state-of-the-art of terrestrial gravity measurements to monitor and study active volcanoes and the possibilities of new gravimeters that are under development. In particular, we present data from a mini array of three iGrav superconducting gravimeters (SGs) at Mount Etna (the first network of SGs ever installed on an active volcano). A comparison between continuous gravity measurements recorded through the iGrav#016 superconducting gravimeter at Serra La Nave station (1730 m a.s.l.) and absolute gravity data collected with the Microg LaCoste FG5#238 gravimeter in the framework of repeated campaigns is also presented. Furthermore, we introduce the Horizon 2020 NEWTON-g project (New Tools for Terrain Gravimetry), funded under the FET-OPEN Research and Innovation Actions call, Work Programme 2016–2017 (Grant Agreement No 801221). In the framework of this project, we aim to develop a field-compatible gravity imager, including an array of low-costs Micro-Electro-Mechanical Systems (MEMS)-based relative gravimeters, anchored on an absolute quantum gravimeter. After the design and production phases, the gravity imager will be field-tested at Mt. Etna (Italy) during the last 2 years of the project.

The paper analyzes the effect of preliminary processing of gravity measurements on the accuracy of the marine gravity-aided navigation. The preliminary processing of the measurements is implemented in the filtering and smoothing modes. Obtained results are illustrated by a one-dimensional example of gravity-aided navigation problem.

The work considers the results of filtering and smoothing of the gravity disturbance vector horizontal components and focuses on the sensitivity of these results to the model parameters in the case when the inertial-geodesic method is applied in the framework of a marine survey on a sea vessel.