Surface Gravity Field Research Articles

High-Resolution Gravity Measurements on Board an Autonomous Underwater Vehicle: Data Reduction and Accuracy Assessment

Gravity on Earth is of great interest in geodesy, geophysics, and natural resource exploration. Ship-based gravimeters are a widely used instrument for the collection of surface gravity field data in marine regions. However, due to the considerable distance from the sea surface to the seafloor, the spatial resolution of surface gravity data collected from ships is often insufficient to image the detail of seafloor geological structures and to explore offshore natural minerals. Therefore, the development of a mobile underwater gravimetry system is necessary. The GraviMob gravimeter, developed for a moving underwater platform by Geo-Ocean (UMR 6538 CNRS-Ifremer-UBO-UBS), GeF (UR4630, Cnam) and MAPPEM Geophysics, has been tested over the last few years. In this study, we report on the high-resolution gravity measurements from the GraviMob system mounted on an Autonomous Underwater Vehicle, which can measure at depths of up to several kilometres. The dedicated GraviMob underwater gravity measurements were conducted in the Mediterranean Sea in March 2016, with a total of 26 underwater measurement profiles. All these measurement profiles were processed and validated. In a first step, the GraviMob gravity measurements were corrected for temperature based on a linear relationship between temperature and gravity differences. Through repeated profiles, we acquired GraviMob gravity measurements with an estimated error varying from 0.8 to 2.6 mGal with standard deviation after applying the proposed temperature correction. In a second step, the shipborne gravity data were downward continued to the measurement depth to validate the GraviMob measurements. Comparisons between the corrected GraviMob gravity anomalies and downward continued surface shipborne gravity data revealed a standard deviation varying from 0.8 to 3.2 mGal and a mean bias value varying from −0.6 to 0.6 mGal. These results highlight the great potential of the GraviMob system in measuring underwater gravity.

A New Global Bathymetry Model: STO_IEU2020

To address the limitations in global seafloor topography model construction, a scheme is proposed that takes into account the efficiency of seafloor topography prediction, the applicability of inversion methods, the heterogeneity of seafloor environments, and the inversion advantages of sea surface gravity field element. Using the South China Sea as a study area, we analyzed and developed the methodology in modeling the seafloor topography, and then evaluated the feasibility and effectiveness of the modeling strategy. Based on the proposed modeling approach, the STO_IEU2020 global bathymetry model was constructed using various input data, including the SIO V29.1 gravity anomaly (GA) and vertical gravity gradient anomaly (VGG), as well as bathymetric data from multiple sources (single beam, multi-beam, seismic, Electronic Navigation Chart, and radar sensor). Five evaluation areas located in the Atlantic and Indian Oceans were used to assess the performance of the generated model. The results showed that 79%, 89%, 72%, 92% and 93% of the checkpoints were within the ±100 m range for the five evaluation areas, and with average relative accuracy better than 6%. The generated STO_IEU2020 model correlates well with the SIO V20.1 model, indicating that the proposed construction strategy for global seafloor topography is feasible.

Hayabusa2 Landing Site Selection: Surface Topography of Ryugu and Touchdown Safety

One of the primary goals of Hayabusa2 is to land on the asteroid Ryugu to collect its surface materials. The key for a successful touchdown is to find a promising landing site that meets both scientific and engineering requirements. Due to the limited availability of pre-arrival information about Ryugu, the landing site selection (LSS) must be conducted based on proximity observations over a limited length of time. In addition, Ryugu was discovered to possess an unexpectedly high abundance of boulders with an absence of wide and flat areas, further complicating the LSS. To resolve these problems, we developed a systematic and stepwise LSS process with a focus on the surface topography of Ryugu and the associated touchdown safety. The proposed LSS scheme consists of two phases: Phase-I LSS, a comprehensive survey of potential landing areas at the 100-m scale based on the global mapping of Ryugu, and Phase-II LSS, a narrowing-down process of the candidate landing sites at the 10-m scale using high-resolution images and a local terrain model. To verify the feasibility of a precision landing at the target site, we also investigated the landing dispersion via a Monte Carlo simulation, which incorporates the effect of the irregular surface gravity field. One of the major characteristics of the Hayabusa2 LSS developed in this study is the iterative feedback between LSS analyses on the ground and actual spacecraft operations near the target asteroid. Using the newly developed method, we chose a landing site with a radius of 3 m, and Hayabusa2 successfully conducted its first touchdown on February 21, 2019. This paper reports the methodology and results of the stepwise iterative LSS for the first Hayabusa2 touchdown. The touchdown operation results reconstructed from flight data are also provided, demonstrating the validity of the adopted LSS strategy.

On inverting gravity changes with the harmonic inversion method: Teide (Tenerife) case study

Abstract Here we investigate the applicability of the harmonic inversion method to time-lapse gravity changes observed in volcanic areas. We carry out our study on gravity changes occured over the period of 2004–2005 during the unrest of the Central Volcanic Complex on Tenerife, Canary Islands. The harmonic inversion method is unique in that it calculates the solution of the form of compact homogeneous source bodies via the mediating 3-harmonic function called quasigravitation. The latter is defined in the whole subsurface domain and it is a linear integral transformation of the surface gravity field. At the beginning the seeds of the future source bodies are introduced: these are quasi-spherical bodies located at the extrema of the quasigravitation (calculated from the input gravity data) and their differential densities are free parameters preselected by the interpreter. In the following automatic iterative process the source bodies change their size and shape according to the local values of quasigravitation (calculated in each iterative step from the residual surface gravity field); the process stops when the residual surface gravity field is sufficiently small. In the case of inverting temporal gravity changes, the source bodies represent the volumetric domains of temporal mass-density changes. The focus of the presented work is to investigate the dependence of the size and shape of the found source bodies on their differential densities. We do not aim here (yet) at interpreting the found solutions in terms of volcanic processes associated with intruding or rejuvenating magma and/or migrating volatiles.

Surface gravity and deformation effects of water storage changes in China's Three Gorges Reservoir constrained by modeled results and in situ measurements

Abstract The water impoundment of China's Three Gorges Reservoir (TGR), with the largest dam in the world, makes a large mass concentrated and thus influences the surface gravity field and crustal deformation field. In the TGR area, water impoundment began in 2003, and the Earth is responding to the ongoing changes of water storage. These responses can be investigated using the gravimeter and the GPS. In this paper, using a water load model derived from Digital Elevation Model (DEM) data and elastic loading Green's function, we modeled the surface gravity and displacement changes in the front area of TGR caused by water storage variations. Predictive results are compared with the measurements derived from absolute gravity by A10, continuous gravity by gPhone and GPS time series at the sites of front area in TGR. The observations agree well with the prediction spatially and temporally. The quantitative comparison and analysis indicate that the ground gravity and the vertical displacement are more sensitive to water storage changes than the horizontal displacement. The predictions from the water load model are consistent with the in situ measurements reported in this work and therefore can be utilized for water effect corrections for exacting the further signals related to lithospheric dynamics and geological hazards, such as abnormal deformation of active faults and landslides.

Estimates of [formula omitted] from GOCE data

The cold upper part of the lithosphere can support the elastic stresses that govern rigid plate movements and support the Earth's topography. In many regions the thickness Te of the layer involved can be estimated from the relationship between surface gravity measurements and topography. However, there are extensive regions of the continents where the topography is well determined, but the gravity field is not. The obvious solution to this problem is to use the satellite, rather than the surface, gravity field. The wavelength range of interest, 200–500 km, requires a satellite with a low orbit. The first satellite to satisfy this requirement is the Gravity field and steady state OCean Explorer (GOCE). Measurements of the elements of the gravity gradient tensor and determinations of the spherical harmonic coefficients of the gravity field based on GOCE observations are used to estimate Te. For Hawaii these estimates are 18.4 km and 21.4 km respectively, and agree well with a value of 18.2 km obtained from the surface gravity field determined from altimetry. An attempt to estimate the value of Te of the central North Atlantic using GOCE data was not successful, whereas surface data gives a value of about 4 km. Estimates for Tibet and surrounding regions, where the gravity field from surface measurements is poorly determined, are 25–32 km. The NW part of S. America gives 17–24 km. The difference in the values of Te from the two regions probably results from the difference in lithospheric thicknesses. Estimates of Te from central and southern Africa, of 31–34 km, are less well constrained than are those from Tibet and S. America. These results show that the data from GOCE can be used to estimate the value of Te where it is poorly determined from surface measurements, is greater than ∼15 km, and where large topographic loads produce large gravity anomalies.

A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders: Efficient computation at irregular surfaces

Fast spherical harmonic synthesis (SHS) at multiple points based on the lumped coefficients approach is a very well-established technique. However, this method cannot be applied to SHS at irregular surfaces, as the points must be regularly spaced and refer to a regular surface such as the sphere or the ellipsoid of revolution. In this paper we present a MATLAB®-based graphical user interface software for ultra-high degree (e.g. tens of thousands or even higher) SHS on grids at irregular surfaces, like the Earth surface. This software employs the highly efficient lumped coefficient approach for SHS at regular surfaces and the Taylor series expansions to continue the functionals to the irregular surfaces, e.g. the Earth surface. The generalized idea of continuing functionals using the Taylor series was presented by Hirt (2012) (J. Geod. 86, 729–744). We took advantage of the software GrafLab (Bucha and Janák, 2013. Comput. Geosci. 56, 186–196), which employs the lumped coefficients approach, and developed a new software isGrafLab (Irregular Surface GRAvity Field LABoratory). Compared to the commonly used “two loops” approach, the factor of increased computational speed can reach a value of several hundreds. isGrafLab allows accurate evaluation of 38 functionals of the geopotential on grids at irregular surfaces. High orders of the Taylor series can be used for the continuation. The new software offers all the other options available in GrafLab, such as the employment of three different approaches to compute the fully normalized associated Legendre functions, the graphical user interface or the possibility to depict data on a map.

Surface Gravity Fields for Asteroids and Comets

The characteristics of the interior gravity field are derived, summarized, and evaluated near the surface of an asteroid for the purpose of small body proximity operations. In order to characterize the gravity field of a body, the exterior gravity field is widely in use. However, the exterior gravity field expression breaks down when computing the potential and its gradients within the Brillouin sphere, meaning that spacecraft dynamics cannot be modeled accurately in close proximity to the body's surface. On the other hand, the convergence of the potential and its gradients are guaranteed within the Brillouin sphere of the interior potential, a feature that enables the gravity field modeling near the surface of a body. After derivation, a technique for converting an exterior gravity field or a polyhedral gravity field into an interior gravity field is outlined, a method to numerically approximate the interior spherical harmonic coefficients for a body with a homogeneous density distribution is introduced, and comparisons between the spacecraft dynamics propagated in the polyhedral gravity field and the interior gravity field are made. The results show that the interior gravity field models the gravity field environment well in close proximity to the body's surface.

Acoustic signal horizontal coherence variability: Relationship to internal tide and storm events.

Acoustic signal horizontal coherence has been extracted from a 31‐day data set taken during the late fall/early winter time period. The coherence variability for both 300‐ and 500‐Hz acoustic signals appears coupled to shelf/slope frontal motion, internal tides, and associate internal waves as well as changes in the surface gravity field. Acoustic signal and environmental data illustrating the coupling will be presented. The data were taken on the New Jersey Shelf with a 460‐m‐long bottomed array placed in ∼89 m of water. The cross shelf propagation range was ∼20 km. The acoustic sources were in ∼60 m of water.

Analytical Solutions of Love Numbers for a Hydrostatic Ellipsoidal Incompressible Homogeneous Earth

Tidal forces acting on the Earth cause deformations and mass redistribution inside the planet involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. Because for space geodesy it is now necessary to achieve the mm level in tidal displacements, we take into account the hydrostatic flattening of the Earth in the computation of the elasto-gravitational deformations. Analytical solutions are derived for the semi-diurnal tides on a slightly elliptical homogeneous incompressible elastic model. That simple analytical Earth’s model is not a realistic representation of any real planet, but it is useful to understand the physics of the problem and also to check numerical procedures. We rediscover and discuss the Love’s solutions and obtain new analytical solutions for the tangential displacement. We extend these analytical results to some geodetic responses of the Earth to tidal forces such as the perturbation of the surface gravity field, the tilt and the deviation of the vertical with reference to the Earth’s axis.

Testing the inverse-square law of gravity on a 465-m tower.

We have performed a test of Newton's universal theory of gravitation by comparing gravity measured on a tower to an upward continuation of the surface gravity field. We measured gravity at 12 heights on a 465-m tower at the Nevada Test Site and, in addition, made measurements at 281 locations on the ground. The surface points fell within 91 optimally chosen sectors that extended out to 2.6 km from the tower. These data were combined with 60 000 additional surface gravity measurements within 300 km of the tower. We used a surface integral derived from Laplace's equation to upward continue the surface gravity field and our observations are consistent with the Newtonian predictions to within (-60\ifmmode\pm\else\textpm\fi{}95)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}8}$ m ${\mathrm{sec}}^{\mathrm{\ensuremath{-}}2}$ at the top of the tower.

Statistics of narrow structures of the gravity field of the Earth: 1. General theory

With the increase in resolution and accuracy of gravity measurements it is becoming possible and increasingly important to concentrate on local analysis and on the role of elongated geophysical features. This paper deals with the statistical analysis of such features and develops for this purpose a new tool, the three‐ and four‐point correlation functions. Using an integration over the manifold of the rotation group, expressions are derived for these functions in terms of the spherical harmonic coefficients; I also discuss the corresponding quantities for a flat earth and show how this approximation is recovered for small features. To gain an understanding of the structure of these functions, a simple, heuristic model is constructed in which the surface gravity field is expressed as a random superposition of elliptical elementary disturbances with random orientations. The three‐point correlation function shows a characteristic behavior when the angle between its two vector arguments is of the order of the ratio of the axes of the ellipse. Another important piece of information contained in this function is the skewness of the gravity field.

Eccentric orbit generalization and simultaneous solution of binary star light and velocity curves

The computation of binary star light and radial velocity curves are discussed, including the effects of eccentric orbits and nonsynchronous rotation. Logical relations needed to impose physical constraints (semidetached condition, etc.) are specified. Some of the more important mathematical relations are also given. One can now model semidetached, detached, double-contact, and X-ray binaries for arbitrary rotation rates and orbital eccentricity. Contact binaries can also be modeled, but are restricted to the synchronous, circular orbit case. In all cases the figures of the components and the surface gravity fields are described by surfaces of constant potential energy.