Gravity Disturbance Research Articles

Geoid determination with Hotine’s integral based on terrestrial gravity data in Semarang city

GNSS surveys can accurately determine the geodetic position, but the elevation values do not have physical meaning for the purposes of engineering work. Physical height can be determined through the gravimetric geoid model representing the relationship between the geometric and physical shapes of the earth. Theoretically, the gravimetric geoid model is a solution of Boundary Value Problems (BVP) to obtain the boundary value in the form of the geoid surface. Before the era of GNSS, a BVP was calculated using Stokes or Molodensky approaches. Another approach that was quite difficult to be practiced in that era was Hotine approach. This approach requires gravity disturbance data on surface of the earth or on the geoid itself. This paper presents an accurate gravimetric geoid modelling based on terrestrial gravity data in Semarang using Hotine’s approach. The main gravity data was measured in March 2016 using Scintrex CG-5 gravimeter which has an accuracy of 5 microgal. It covered an area about 1 arc degree squares. Additional gravity data for improving the accuracy of the geoid models was measured by some government and private agencies using analogue gravimeters. It covered Jawa island. The global geopotential model was GECO with maximum degree 2190. The results showed that the computation of Hotine’s integral for modelling the geoid of Semarang city had an accuracy of ± 0.044 m. In the region of land subsidence, the geoid model is quite prospective to be implemented as the Vertical Reference System (VRS). Measurement of elevation of a distant point using geoid can be completed in a matter of hours, while using spirit levelling completed within a matter of days.

Two-dimensional Kalman filter approach to airborne vector gravimetry

Abstract The paper presents a new approach to the airborne vector gravimetry problem. The idea of the approach is to take into account spatial correlation of the gravity field to improve observability of horizontal components of the gravity disturbance vector (GDV). We consider the GDV determination problem given airborne data at a set of parallel survey lines assuming that lines are flown in the same direction at a constant height above the reference ellipsoid. We use a 2-D random field model for the gravity field at the flight height. The random field is governed by two autoregressive equations (one in the direction along the lines, the other across the lines). Then we pose the estimation problem simultaneously for the GDV horizontal components and systematic errors of an inertial navigation system at all the lines simultaneously. The developed estimation algorithm is based on 2D Kalman filtering and smoothing techniques. Numerical results obtained from simulated data processing showed improved accuracy of the gravity horizontal component determination.

The modified integral method for the determination of gravity disturbance near the Earth’s surface

Abstract For the calculation of gravity disturbance in the Earth’s external gravity field, the Stokes-Pizzetti integral is a commonly used method. However, when the target point approaches the Earth’s surface, such problems as singularity and discontinuity arise due to the Stokes kernel structure itself. To settle the problems, firstly the reason for singularity and discontinuity was discussed, and then modification was made to the integral formula, by which the singularity at the surface point is eliminated. Finally the non-singular integral formulas for the calculation of disturbing gravity were derived. In numerical experiments, an area in China was selected to test the modified formula. Numerical results show that the modified formula performs much better than classical Stokes-Pizzetti integral formula when dealing with the calculation of the radial component of gravity disturbance near the Earth’s surface.

Improving the Strapdown Airborne Vector Gravimetry by a Backward Inertial Navigation Algorithm.

Strapdown airborne gravimetry is an efficient way to obtain gravity field data. A new method has been developed to improve the accuracy of airborne vector gravimetry. The method introduces a backward strapdown navigation algorithm into the strapdown gravimetry, which is the reverse process of forward algorithm. Compared with the forward algorithm, the backward algorithm has the same performance in the condition of no sensor error, but has different error characteristics in actual conditions. The differences of the two algorithms in the strapdown gravimetry data processing are presented by simulations, which show that the two algorithms have different performance in the horizontal attitude measurement and convergence of integrated navigation filter. On the basis of detailed analysis, the procedures of accuracy improvement method are presented. The result of this method is very promising when applying to an actual flight test carried out by a SGA-WZ02 strapdown gravimeter. After applying the proposed method, the repeatability of two gravity disturbance horizontal components were 1.83 mGal and 1.80 mGal under the resolution of 6 km, which validate the effectiveness of the method. Furthermore, the wavenumber correlation filter is also discussed as an alternative data fusion method.

The putative Saginaw impact structure, Michigan, Lake Huron, in the light of gravity aspects derived from recent EIGEN 6C4 gravity field model

Abstract The hypothetical impact structure in the Saginaw Bay (Michigan, USA, Lake Huron) has been tested by the gravity data derived from the recent gravity field model EIGEN 6C4 (expanded to degree and order 2190, with ground resolution of ~9 km). The following gravity field aspects were used: the gravity disturbances/anomalies, second derivatives of the disturbing potential (Marussi tensor), two of three gravity invariants, their specific ratio (known as 2D factor), the strike angles, and the virtual deformations. These gravity aspects are sensitive in various ways to the underground density contrasts. For the Saginaw Bay area, we confirm that we do not see any typical impact crater in terms of gravity disturbance or the radial second order derivative, possibly because of the thick layer of the ice located at the place and time of the impact. But the “combed” strike angles (one type of the gravity aspects we use) disclose a trace of high pressure to the SE/S/SW of the Bay and may be due to an impacting body. Thus, we provide circumstantial evidence of the Younger Dryas impact hypothesis.

Experiences with the use of mass-density maps in residual gravity forward modelling

In many modern local and regional gravity field modelling concepts, the short-wavelength gravitational signal modeled by the residual terrain modelling (RTM) technique is used to augment global geopotential models, or to smooth observed gravity prior to data gridding. In practice, the evaluation of RTM effects mostly relies on a constant density assumption, because of the difficulty and complexity of obtaining information on the actual distribution of density of topographic masses. Where the actual density of topographic masses deviates from the adopted value, errors are present in the RTM mass-model, and hence, in the forward-modelled residual gravity field. In this paper we attempt to overcome this problem by combining the RTM technique with a high-resolution mass-density model. We compute RTM gravity quantities over New Zealand, with different combinations of elevation models and mass-density assumptions using gravity and GPS/levelling measurements, precise terrain and bathymetry models, a high-resolution mass-density model and constant density assumptions as main input databases. Based on gravity observations and the RTM technique, optimum densities are detected for North Island of ~2500 kg m−3, South Island of ~2600 kg m−3, and the whole New Zealand of ~2590 kg m−3. Comparison among the three sets of residual gravity disturbances computed from different mass-density assumptions show that, together with a global potential model, the high-resolution New Zealand density model explains ~89.5% of gravitational signals, a constant density assumption of 2670 kg m−3 explains ~90.2%, while a regionally optimum mass-density explains ~90.3%. Detailed comparison shows that the New Zealand density model works best over areas with small residual heights. Over areas with larger residual heights, subsurface density variations appear to affect the residual gravity disturbance. This effect is found to reach about 30 mGal over Southern Alpine Fault. In order to improve the RTM modelling with mass-density maps, a higher-quality mass-density model that provides radially varying mass-density data would be desirable.

INTEGRATION OF INS AND GNSS FOR GRAVIMETRIC APPLICATION WITH UAS

Abstract. The integration based on Inertial Navigation System (INS) and Global Navigation Satellite System (GNSS) has been successfully developed in observing the gravity. Therefore, this study integrates a navigation-grade INS, iNAV-RQH from iMAR and GNSS from NovAtel to develope an Unmanned Aerial System (UAS) using unmanned helicopter for gravimetric application. The advantages include its good flexibility, and it is an intermediate system between the airborne and terrestrial survey in terms of the coverage and spatial resolution. On the other hand, based on the characteristics of vertical take-off and landing, in addition to the kinematic mode as the measure method in the acquisition of gravimetric results, the Zero Velocity Update (ZUPT) mode is implemented as a novel method with the developed UAS. The preliminary results in kinematic mode show that the internal accuracies of horizontal and vertical gravity disturbance at crossover points are approximately 6–11 mGal and 4 mGal, respectively, with a 0.5-km resolution. As expected, the accuracy in down component is higher than that in horizontal components because the orientation errors could cause large error in horizontal components. Moreover, the repeatability in ZUPT mode is evaluated with accuracies of approximately 2–3 mGal. The capability of developed UAS for gravimetric application has been demonstrated through various scenarios in this study.

On the detection of the Wilkes Land impact crater

The definitive existence of a giant impact crater, two times larger than the Chixulub crater in the Yucatan peninsula, from an extraterrestrial origin, 1.6 km beneath Wilkes Land, East Antarctica, remain controversial. Here, we use the latest high-resolution gravito-topographic geopotential (SatGravRET 2014) model over Antarctica to offer a plausible confirmation of its existence. SatGravRET 2014 has a spatial resolution between 1 and 10 km at most places and included contemporary space gravimetry and gradiometry data from GRACE and GOCE, and other data including Bedmap 2 bedrock topography. We computed the gravity disturbances, the Marussi tensor of the second derivatives of the disturbing potential, the gravity invariants and their specific ratio, the strike angles and the virtual deformations to quantify the detailed geophysical features for the Wilkes Land anomaly. This set of the gravitational parameters revealed enhanced and more detailed geophysical features on the Wilkes Land Crater than previously possible only with the traditional gravity anomalies. Our findings support prior studies stating that in the Wilkes Land there is a huge impact crater/basin with detectable gravity mascon which is mostly consistent with the characteristics of an impact crater.

A New Tool for Airborne Gravimetry Survey Simulation

Airborne gravimetry represents nowadays probably the most efficient technique to collect gravity observations close to the Earth’s surface. In the 1990s, thanks to the development of the Global Navigation Satellite Systems (GNSS), which has made accurate navigational data available, this technique started to spread worldwide because of its capability to provide measurements in a fast and cost-effective way. Differently from other techniques such as shipborne gravimetry, it has the advantage to provide gravity measurements also in challenging environments which can be difficult to access otherwise, like mountainous areas, rain forests and polar regions. For such reasons, airborne gravimetry is used for various applications related to the regional gravity field modelling: from the computation of high accurate local geoid for geodetic applications to geophysical ones, specifically related to oil and gas exploration activities or more in general for regional geological studies. Depending on the different kinds of application and the final required accuracy, the definition of the main characteristics of the airborne survey, e.g., the planar distance between consecutive flight tracks, the aircraft velocity, etc., can be a difficult task. In this work, we present a new software package, which would help in properly accomplishing the survey design task. Basically, the developed software solution allows for generating a realistic (from the observation noise point of view) gravimetric signal, and, after that, to predict the accuracy and spatial resolution of the final retrievable gravimetric field, in terms of gravity disturbances, given the flight main characteristics. The proposed procedure is suited for airborne survey planning in order to be able to optimize the design of the survey according to the required final accuracy. With the aim to evaluate the influence of the various survey parameters on the expected accuracy of the airborne survey, different numerical tests have been performed on simulated and real datasets. For instance, it has been shown that if the observation noise is not properly modeled in the data filtering step, the survey results degrade about 25%, while not acquiring control lines during the survey will basically reduce the final accuracy by a factor of two.

A study of PID and L1 adaptive control for automatic balancing of a spacecraft three-axis simulator

PurposeThe three-axis simulator relies on the air film between the air bearing and the bearing seat to achieve weightlessness and the frictionless motion condition, which is essential for simulating the micro-disturbance torque of a satellite in outer space. However, at the beginning of the experiment, the disturbance torque caused by the misalignment between the center of gravity of the simulator and the center of rotation of the bearing is the most important factor restricting the use of the space three-axis simulator. In order to solve this problem, it is necessary to set the balance adjustment system on the simulator to compensate the disturbance torque caused by the eccentricity. The paper aims to discuss these issues.Design/methodology/approachIn this paper, a study of L1 adaptive automatic balancing control method for micro satellite with motor without other actuators is proposed. L1 adaptive control algorithm adds the low-pass filter to the control law, which in a certain sense to reduce the high-frequency signal and speed up the response time of the controlled system. At the same time, by estimating the adaptive parameter uncertainty in object, the output error of the state predictor and the controlled object can be stabilized under Lyapunov condition, and the robustness of the system is also improved. The automatic balancing method of PID is also studied in this paper.FindingsThrough this automatic balancing mechanism, the gravity disturbance torque can be effectively reduced down to 10−6 Nm, and the automatic balancing time can be controlled within 7 s.Originality/valueThis paper introduces an automatic balancing mechanism. The experimental results show that the mechanism can greatly improve the convergence speed while guaranteeing the control accuracy, and ensuring the feasibility of the large angle maneuver of spacecraft three-axis simulator.

Moho Depth and Crustal Architecture Beneath the Levant Basin from Global Gravity Field Model

The study of the discontinuity between the Earth crust and upper mantle, the so-called Moho, and of the lithospheric architecture in general, has several important applications in exploration geophysics. For instance, it is used to facilitate the inversion of seismic-related data, in order to obtain important information on the sedimentary layers or to study the Earth’s heat flux. In this paper, the Levant crustal structure is being investigated starting from the inversion of gravity disturbances coming from a global geopotential field model based on ESA GOCE satellite mission integrated with seismic derived information. In the considered area, which is of particular interest because of its richness from the resources point of view, the deep crustal structure is still a matter of study due to the presence of a thick sequence of sedimentary layers, deposited within geological eras by the Nile River. Within the current work, the shape of the Oceanic domain in correspondence to the Herodotus Basin and the Cyprus Arc has been clearly defined. Moreover the nature of the Levantine Basin and of the Eratosthenes crust has been investigated by a set of ad hoc tests, finding the presence of continental crust. Finally, the Moho depth and the crustal density distribution have been retrieved. Several localized anomalies, in the Cyprus area, have been identified and modelled too, thus confirming the presence of heavy material, with a thickness up to 10 km, in the sedimentary layer and shallower part of the crust.

A Combined Gravity Compensation Method for INS Using the Simplified Gravity Model and Gravity Database.

In recent decades, gravity compensation has become an important way to reduce the position error of an inertial navigation system (INS), especially for a high-precision INS, because of the extensive application of high precision inertial sensors (accelerometers and gyros). This paper first deducts the INS’s solution error considering gravity disturbance and simulates the results. Meanwhile, this paper proposes a combined gravity compensation method using a simplified gravity model and gravity database. This new combined method consists of two steps all together. Step 1 subtracts the normal gravity using a simplified gravity model. Step 2 first obtains the gravity disturbance on the trajectory of the carrier with the help of ELM training based on the measured gravity data (provided by Institute of Geodesy and Geophysics; Chinese Academy of sciences), and then compensates it into the error equations of the INS, considering the gravity disturbance, to further improve the navigation accuracy. The effectiveness and feasibility of this new gravity compensation method for the INS are verified through vehicle tests in two different regions; one is in flat terrain with mild gravity variation and the other is in complex terrain with fierce gravity variation. During 2 h vehicle tests, the positioning accuracy of two tests can improve by 20% and 38% respectively, after the gravity is compensated by the proposed method.

Gravito-topographic signal of the Lake Vostok area, Antarctica, with the most recent data

By using SatGravRET2014 gravito-topography model, based also on satellite GRACE and GOCE data, we computed and plotted the gravity disturbances, the Marussi tensor of the second derivatives of the disturbing potential, the gravity invariants and their specific ratio, the strike angle and the virtual deformations for the Lake Vostok (LV) area in Antarctica. This set of gravity “aspects” provides more detailed and clearer information than the traditional gravity anomalies. Maps with the bedrock topography from Bedmap 2 are added. Some of our estimates and results confirm independent findings of other specialists, some results presented here are new. LV is divided not only into its N and S parts by a ridge, but also to E and W parts. A tension across LV has a prevailing direction E-W. We identified at least three candidates for subglacial lakes south of the lakes 90 E and Sovetskaya. In the gravity aspects this area looks like a basin, where the mentioned lakes might be just a remnant of a large bowl; the orientation of this basin is the same as that of LV; the size comparable to LV. A subglacial connection between all the mentioned lakes is possible and documented via the gravity aspects, namely by the virtual deformations.

Cap integration in spectral gravity forward modelling: near- and far-zone gravity effects via Molodensky’s truncation coefficients

Spectral gravity forward modelling is a technique that converts a band-limited topography into its implied gravitational field. This conversion implicitly relies on global integration of topographic masses. In this paper, a modification of the spectral technique is presented that provides gravity effects induced only by the masses located inside or outside a spherical cap centred at the evaluation point. This is achieved by altitude-dependent Molodensky’s truncation coefficients, for which we provide infinite series expansions and recurrence relations with a fixed number of terms. Both representations are generalized for an arbitrary integer power of the topography and arbitrary radial derivative. Because of the altitude-dependency of the truncation coefficients, a straightforward synthesis of the near- and far-zone gravity effects at dense grids on irregular surfaces (e.g. the Earth’s topography) is computationally extremely demanding. However, we show that this task can be efficiently performed using an analytical continuation based on the gradient approach, provided that formulae for radial derivatives of the truncation coefficients are available. To demonstrate the new cap-modified spectral technique, we forward model the Earth’s degree-360 topography, obtaining near- and far-zone effects on gravity disturbances expanded up to degree 3600. The computation is carried out on the Earth’s surface and the results are validated against an independent spatial-domain Newtonian integration ( $$1\,\upmu \mathrm {Gal}$$ RMS agreement). The new technique is expected to assist in mitigating the spectral filter problem of residual terrain modelling and in the efficient construction of full-scale global gravity maps of highest spatial resolution.

Compensation of Horizontal Gravity Disturbances for High Precision Inertial Navigation.

Horizontal gravity disturbances are an important factor that affects the accuracy of inertial navigation systems in long-duration ship navigation. In this paper, from the perspective of the coordinate system and vector calculation, the effects of horizontal gravity disturbance on the initial alignment and navigation calculation are simultaneously analyzed. Horizontal gravity disturbances cause the navigation coordinate frame built in initial alignment to not be consistent with the navigation coordinate frame in which the navigation calculation is implemented. The mismatching of coordinate frame violates the vector calculation law, which will have an adverse effect on the precision of the inertial navigation system. To address this issue, two compensation methods suitable for two different navigation coordinate frames are proposed, one of the methods implements the compensation in velocity calculation, and the other does the compensation in attitude calculation. Finally, simulations and ship navigation experiments confirm the effectiveness of the proposed methods.

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation.

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method.

Quantifying the motor power of trees

Wood maturation strains can be estimated from the change in curvature that occurs when a stem grown staked in tilted position is released from the stake. Trees have a motor system to enable upright growth in the field of gravity. This motor function is taken on by reaction wood, a special kind of wood that typically develops in leaning axes and generates mechanical force during its formation, curving up the stem and counteracting the effect of gravity or other mechanical disturbances. Quantifying the mechanical stress induced in wood during maturation is essential to many areas of research ranging from tree architecture to functional genomics. Here, we present a new method for quantifying wood maturation stress. It consists of tilting a tree, tying it to a stake, letting it grow in tilted position, and recording the change in stem curvature that occurs when the stem is released from the stake. A mechanical model is developed to make explicit the link between the change in curvature, maturation strain and morphological traits of the stem section. A parametric study is conducted to analyse how different parameters influence the change in curvature. This method is applied to the estimation of maturation strain in two different datasets. Results show that the method is able to detect genotypic variations in motor power expression. As predicted by the model, we observe that the change in stem curvature is correlated to stem diameter and diameter growth. In contrast, wood maturation strain is independent from these dimensional effects, and is suitable as an intrinsic parameter characterising the magnitude of the plant’s gravitropic reaction.

The Optimal Degree of Gravity Spherical Harmonic Model Calculation for Gravity Disturbance Compensation in Inertial Navigation

In recent years, the significant improvement of inertial navigation, leaves the gravity disturbance as the important factor which affects the accuracy of inertial navigation. This paper focus on the compensation for gravity disturbance with gravity spherical harmonic model, especially the optimal degree of gravity spherical harmonic model with which to calculate the gravity disturbance. The effect of gravity disturbance on inertial navigation is analysed based on the amplitude-frequency response characteristics of inertial navigation error differential equation, then the dominantly influential frequency band of gravity disturbance can be found which is the target of compensation. Combination the dominantly influential frequency band with the spatial resolution of the Earth’s gravity spherical harmonic model EGM2008 which is used to calculate the gravity disturbance, the optimal degree can be determined based on an algorithm proposed in this paper. Finally, shipborne inertial navigation experiment confirms the correctness and effectiveness of the proposed algorithm.

Mass properties identification and automatic mass balancing system for satellite attitude dynamics simulator

A Satellite Attitude Dynamics Simulator is a low-cost, ground-based system made to simulate the conditions of a weightless satellite in space. The identification of the mass characteristics is crucial for Satellite Attitude Dynamics Simulator application and so the center of mass place is necessary for balancing the platform and moment of inertia which is a significant factor in designing controllers and selecting actuators. The purposes of this paper are the mass properties identification and design, experimentation, and validation of an automatic mass balancing system, which is assembled on the Satellite Attitude Dynamics Simulator at the Space Research Laboratory. This paper presents a process of mass properties estimation for the Satellite Attitude Dynamics Simulator using classical Levenberg–Marquardt as an optimization method. By employing this technique lack of repeatability and difficulties in implementation will be eliminated. In order to verify this technique, a MATLAB® SIMULINK® model of the Satellite Attitude Dynamics Simulator is established. The gap between the center of mass and center of rotation is decreased by means of the automatic mass balancing system in order to remove gravity disturbance. The results of this identification process are compared to the recursive least square algorithm, which is commonly employed in identification of mass properties. The analytical and experimental results prove that the proposed characteristic estimation process using classical Levenberg–Marquardt algorithm is more effective and appropriate. Proper excitation of the platform will guarantee the accuracy of estimation and compensation of the center of gravity offset utilizing the balancing system.

Precise and efficient evaluation of gravimetric quantities at arbitrarily scattered points in space

Gravimetric quantities are commonly represented in terms of high degree surface or solid spherical harmonics. After EGM2008, such expansions routinely extend to spherical harmonic degree 2190, which makes the computation of gravimetric quantities at a large number of arbitrarily scattered points in space using harmonic synthesis, a very computationally demanding process. We present here the development of an algorithm and its associated software for the efficient and precise evaluation of gravimetric quantities, represented in high degree solid spherical harmonics, at arbitrarily scattered points in the space exterior to the surface of the Earth. The new algorithm is based on representation of the quantities of interest in solid ellipsoidal harmonics and application of the tensor product trigonometric needlets. A FORTRAN implementation of this algorithm has been developed and extensively tested. The capabilities of the code are demonstrated using as examples the disturbing potential T, height anomaly \(\zeta \), gravity anomaly \(\Delta g\), gravity disturbance \(\delta g\), north–south deflection of the vertical \(\xi \), east–west deflection of the vertical \(\eta \), and the second radial derivative \(T_{rr}\) of the disturbing potential. After a pre-computational step that takes between 1 and 2 h per quantity, the current version of the software is capable of computing on a standard PC each of these quantities in the range from the surface of the Earth up to 544 km above that surface at speeds between 20,000 and 40,000 point evaluations per second, depending on the gravimetric quantity being evaluated, while the relative error does not exceed \(10^{-6}\) and the memory (RAM) use is 9.3 GB.