Variable Gravity Field Research Articles

Effect of Variable Gravity Field on Dual Component Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer With Temperature‐Dependent Heat Source

ABSTRACTThis study examines how gravity fluctuations, the couple stress parameter, anisotropic parameters, and heat source collectively influence dual‐component convection in the porous layer. The linear analysis is conducted utilizing the normal mode technique. The authors proposed three categories of gravity fluctuation, namely: (a) linear, (b) parabolic, and (c) exponential. Expressions for both stationary and oscillatory Rayleigh numbers are derived using the Galerkin approach. Neutral stability curves for both stationary and oscillatory modes are analyzed, with graphical representations to show the effects of various stability parameters, including gravity fluctuations, couple stress, anisotropy, and heat source. The results show that the mechanical anisotropy parameter and Vadasz number lead to system destabilization, while the couple stress parameter, Lewis number, gravity parameter, solute Rayleigh number, and thermal anisotropy parameter help to stabilize the system. Furthermore, the system is more stable with exponential gravity fluctuations and less stable with parabolic gravity fluctuations. This finding offers insights into thermal convective instability in porous media, impacting applications in geoscience, engineering, and environmental science.

Resolution analysis of the gravity survey network in the middle and south sections of Tan-Lu fault and recent changes in the gravity field

In this paper, we computed the fractal dimension of three survey areas within the central and southern sections of the Tan-Lu fault zone using fractal analysis. Subsequently, simulations were conducted to analyze the gravity response under a forward model of equivalent density changes. Additionally, we thoroughly investigated the seismic monitoring capabilities of the gravity network in the central and southern regions of the Tan-Lu fault. Expanding on these analyses. Recent gravity field variations were examined in the mid-southern segment of the Tan-Lu fault zone and its surrounding areas from 2013 to 2023. The results indicate that the observation capabilities of the northern network in the study area outperform those of the southern gravity network, with the northern network demonstrating a more evenly distributed coverage. The optimal gravity anomaly recovery effect for the entire study area is achieved at a resolution of 0.5° × 0.5°. With an equivalent observable signal in the range of 30 × 10−8 m/s2 to 40 × 10−8 m/s2, the spatial resolution of the gravity network's field source is estimated to be approximately 55 km. From 2013 to 2023, a significant positive change has been observed in the gravity field within the study area. The Tan-Lu fault zone plays a crucial role in governing the crustal movement in this region, with the dextral strike-slip movement trend of the fault persisting. Small earthquakes occur more frequently in the southern section of the fault zone, while strong earthquakes are less common. The alignment of gravity field changes with the fault strike indicates ongoing activity in the fault zone without any signs of locking. In the central segment of the Tan-Lu fault zone in the Shandong region, there appears to be a weaker correlation between gravity field changes and fault trends. This discrepancy may suggest that the area is locked, resulting in the accumulation of stress and strain. It is imperative to monitor the continuous evolution of the gravity field in this region to gain insights into potential seismic risks.

Effects of variable gravity on stability in couple-stress fluids across various conducting boundaries

This work aims to inspect the effect of variable gravity field on the convective stability of couple stress fluid for different combinations of bounding surfaces. Both linear and nonlinear analyses are conducted to obtain eigenvalue problems. For this analysis, three different combinations of bounding surfaces have been considered. Normal mode analysis is used for linear analysis, while the energy method is used for nonlinear analysis. The numerical values of critical Rayleigh numbers are calculated using the single-term Galerkin technique. It is found that the Rayleigh numbers for the two analyses coincide, suggesting global stability. It is found that the increase in the value of couple stresses stabilize the system. The variable gravity can enhance or reduce the stability of the system depending on the direction of gravity variation which can be easily controlled by its parameter values. It is also observed that fluid confined in rigid-rigid bounding surface is more thermally stable, which is suitable for convection in couple stress fluid.

Crustal Apparent Density Variations in the Middle Segment of the North Tianshan Mountains and Their Tectonic Significance

In this study, we collected mobile gravity observations in the middle segment of the North Tianshan Mountains from August 2016 to July 2022 and carried out classical adjustment calculations under the constraint of the absolute gravity datum to obtain the spatiotemporal variation pattern of the local gravity field. We used equivalent source inversion to obtain the spatiotemporal variation characteristics of crustal apparent density. We also extracted the coseismic deformation field from SAR data, using the 2016 Hutubi earthquake as an example, and constructed a model of the seismogenic fault. The gravity monitoring network in the study area performed well in resolving the earthquake source parameters. Both the time-varying gravity field and equivalent apparent density variation pattern show prominent zoning characteristics with a smoothly evolving spatial distribution over time. The variation trends of the gravity field and equivalent apparent density are in line with the orientation of tectonic structures, and their anomalous signals can be detected before and after an earthquake. The constructed seismogenic structure of the 2016 Hutubi earthquake indicates a typical thrust earthquake, probably occurring on a north-dipping blind fault beneath a region with intense crustal deformation. The subsurface tectonic system reflected by this earthquake can be informatively extended to the entire middle segment of the North Tianshan Mountains by subsurface configuration. Our findings can serve as a reference for analyzing the source characteristics of the time-varying gravity field and interpreting anomalous pre-seismic signals, and aid in understanding earthquake preparation zones and the mode of crustal tectonic movements.

The variable viscosity and variable gravity field on the onset of convective motion in a porous layer with throughflow

In the present article, the combined influence of the changeable gravity field and temperature-reliant viscosity on the porous bed is considered for investigation numerically by the Galerkin technique in the presence of upward vertical throughflow. The temperature-reliant viscosity is known to be exponential. The porous matrix is subjected to continuous downward gravity fluctuations varying with distance across the medium and vertical upward throughflow. Four different cases of gravity variance were discussed. A parametric analysis is conducted by adjusting the following parameters: throughflow parameter, viscosity parameter, and gravity parameter. Results show that the beginning of the convective moment would be delayed by all three parameters throughflow, temperature-reliant viscosity, and gravity variance. It has been shown that the fluidic system is more inconsistent in case (iii) and more consistent in case (iv).

Penentuan Fasies Sentral Gunung Api Purba Menggunakan Metode Gravitasi Pada Kawasan Gunung Ijo, Pegunungan Kulonprogo

The Kulon Progo Mountains are a range of Old Volcanoes that are no longer active so that the body is difficult to identify as a volcano body. One of the old volcanoes in the Kulon Progo Mountains is Mount Ijo. The description of the subsurface through the characteristics of the existence of ancient volcanoes uses a geophysical method approach, namely the gravity method with supporting data in the form of geological studies of the Mount Ijo area. This is done to get the distribution of variations in the subsurface gravity field of Mount Ijo. The gravity data used is GGMPlus gravity satellite data with a lot area of 8.32 x 14.23 Km with a point distribution of 2368 points. In the processing process, a derivative analysis is carried out using Total Horizontal Derivative (THD) and Total Derivative (TDR). The results obtained from the ABL value of the Mount Ijo area illustrate the distribution of gravity anomaly values with high values ranging from 0.2 mGal to 3.5 mGal in the center of the map indicating the presence of the peak of Mount Ijo which is the central facies of Mount Ijo. Supported by the presence of structures in the form of faults and intrusion hills included in the proximal facies surrounding the central facies. The 2.5-dimensional model of the 2 incisions of the residual anomaly map has a depth of 800m and produced a picture of the central facies, proximal facies and a small part of the medial facies of Mount Ijo.

Evaluating groundwater balance and its spatial Distribution as part of NASA GRACE mission for Blue Nile River (Ethiopia, East Africa)

The paper introduces a methodology for estimating groundwater balance on the example of the Blue Nile basin by means of NASA GRACE space technologies. The international Gravity Recovery and Climate Experiment (GRACE) was launched in 2002 to measure time-space variations in the Earth's gravity field. It is a system for remote determination of changes in gravitational force associated with variations of mass within the Earth. The study involves a gravity recovery and climate experiment together with The Global Land Data Assimilation System to calculate groundwater storage as applied to the Blue Nile River basin, based on processing satellite data and spatial localization of the Blue Nile River using an optimal window function with specific scan line. Groundwater storage and its dynamics were investigated from 2003 to 2010. Considering surface water storage, surface runoff and soil moisture, the authors estimated groundwater budget in the Blue Nile River basin. According to the obtained results, the average groundwater storage in the area under study comprised 1100.0 mm/year. Due to a lack of land hydrological studies, verification of the data obtained was not carried out, but was recommended as a matter for future research in this area.

The role of local thermal non-equilibrium on the instability analysis in the presence of variable gravity field with throughflow

The influence of variable gravity on the stability analysis has been investigated in a horizontal porous region with throughflow under a local thermal non-equilibrium (LTNE) situation. Flow inside the porous region is considered to be followed by the Darcy model. Also, the linear varying gravity field with height and nonlinear (parabolic, cubic, and exponential) changing gravity field depth have been considered to address the investigation. The obtained eigenvalue problem for the perturbed state is solved via bvp4c technique in MATLAB. Finally, we investigated the convective boundaries of the system due to the governing parameters, such as gravity variation parameter (λ), porosity-modified conductivity ratio (γ), interphase heat transfer parameter (H), and throughflow parameter (Q). The outcomes assure that the interphase heat transfer parameter has a significant impact on the breakdown of the convection inside of its intermediate range, while the local thermal equilibrium (LTE) state occurred when H converges both the limiting cases, i.e. H→0 and H→∞. It has also been observed that the gravity variation parameter and throughflow parameter have a stabilizing effect, whereas the porosity-modified conductivity ratio destabilizes the flow. Further, it is distinguished that the instability boundaries are unchanged by H when γ≥10. In addition, the flow field is more delayed for exponential changing gravity field, whereas more advanced for cubic varying gravity field.

High spatial resolution marine gravity trend determined from multisatellite altimeter data over Bay of Bengal

SUMMARY Mass redistribution in the Earth system induce variations of the Earth's gravity field. Now, the time-varying gravity models from the Gravity Recovery and Climate Experiment (GRACE) mission can only estimate the large-scale gravity changes, so the high-resolution marine gravity trend (MGT) model is urgently required to detect small-scale Earth's mass migration. The sea level change is a significant response to marine gravity field change. Here, we propose to estimate the high-resolution MGT using the sea level trend (SLT). Firstly, the SLT model caused by marine mass change (MMC) on 5′ × 5′ grids covering the Bay of Bengal (BOB) is established based on multisatellite altimetry data and EN4 quality-controlled ocean data, named BOB_MMC_SLT. Then, the marine mass trend (MMT) is calculated using the BOB_MMC_SLT. The spherical harmonic function (SHF) method is applied to estimate MGT using the MMT, and this MGT model on 5′ × 5′ grids, named BOB_SHF_MGT, is used to study marine gravity changes and their associated geophysical processes. The results show that, the MGT mean of BOB_SHF_MGT is about 0.14 μGal yr−1, which indicates that marine gravity in BOB is rising. The earthquakes mainly occur in the southeastern BOB where MGT is obviously rising, which may be related to the increased density of the Burma Plate due to the subduction of the India Plate and the Australia Plate. BOB_SHF_MGT shows that the marine gravity rise rate is increasing from the 85°E ridge to Andaman–Nicobar ridge, with a maximum at the location where the India Plate subducts to the Burma Plate. The MGT model based on altimetry data constructed by SHF method is important for the study of small-scale mass migration near the subduction boundaries.

Using a SPATIAL INS/GNSS MEMS Unit to Detect Local Gravity Variations in Static and Mobile Experiments: First Results.

In this study, we present the feasibility of using gravity measurements made with a small inertial navigation system (INS) during in situ experiments, and also mounted on an unmanned aerial vehicle (UAV), to recover local gravity field variations. The INS operated is the SPATIAL one developed by Advanced Navigation, which has three-axis accelerometers. When the temperature bias is corrected, these types of INS are powerful enough to present the periodic signal corresponding to the solid Earth tides. There is also a clear correlation with the data measured at different altitudes by a CG5 gravimeter. However, these data were recorded on static points, so we also studied the INS in a moving platform on a UAV. Because there are a lot of vibrations recorded by the INS (wind, motor, on-board computer), the GPS and accelerometric data need to be filtered extensively. Once the data are corrected so they do not show thermal bias and low-pass filtered, we take the second derivative of the altitude (GPS) data to find the radial accelerometry of the drone and compare it to the radial accelerometry measured directly by the INS, in order to isolate the accelerometric signal that is related to the area that is being studied and the altitude. With a high enough precision, this method could be used to obtain the gravity variations due to the topography and density variations in the ground.

Uncertainty of Low‐Degree Space Gravimetry Observations: Surface Processes Versus Earth's Core Signal

AbstractSpace gravity measurements have been mainly used to study the temporal mass variations at the Earth's surface and within the mantle. Nevertheless, mass variations due to the Earth's core might be observable in the gravity field variations as measured by Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow‐On satellites. Earth's core dynamical processes inferred from geomagnetic field measurements are characterized by large‐scale patterns associated with low spherical harmonic degrees of the potential fields. To study these processes, the use of large spatial and inter‐annual temporal filters is needed. To access gravity variations related to the Earth's core, surface effects must be corrected, including hydrological, oceanic or atmospheric loading (Newtonian attraction and mass redistribution). However, these corrections for surface processes add errors to the estimates of the residual gravity field variations enclosing deep Earth's signals. As our goal is to evaluate the possibility to detect signals of core origin embedded in the residual gravity field variations, a quantification of the uncertainty associated with gravity field products and geophysical models used to minimize the surface process signatures is necessary. Here, we estimate the dispersion for GRACE solutions as about 0.34 cm of equivalent water height (EWH) or 20% of the total signal. Uncertainty for hydrological models is as large as 0.89–2.10 cm of EWH. We provide estimates of Earth's core signals whose amplitudes are compared with GRACE gravity field residuals and uncertainties. The results presented here underline how challenging is to get new information about the dynamics of the Earth's core via high‐resolution, high‐accuracy gravity data.

Propagation of crust deformation anomalies related to the Menyuan MS 6.9 earthquake

Decoding the variation laws of the deformation field before strong earthquakes has long been recognized as an essential issue in earthquake prediction research. In this paper, the temporal and spatial distribution characteristics of deformation anomalies in the northeastern margin of the Qinghai-Tibetan Plateau before and after the Menyuan MS 6.9 earthquake were studied by using the Fisher statistical test method. By analyzing the characteristics of these anomalies, we found that: 1) The deformation anomalies are mainly distributed in the marginal front area of the Qinghai-Tibetan Plateau, where short-term deformation anomalies are prone to occur due to a high gradient of gravity; 2) The deformation anomalies along the northeastern margin of the Qinghai-Tibetan Plateau are characterized by spatial propagation, and the migration rate is about 2.4 ​km/d. The propagation pattern is counterclockwise, consistent with the migration direction of MS ​≥ ​6.0 earthquakes; 3) The time and location of the Menyuan earthquake are related to the group migration of earthquakes with MS ​≥ ​6.0. Finally, based on the results of gravity field variation and the theory of crust stress wave, the law of deformation anomaly distribution was discussed. We suggest that both the deformation propagation along the northeastern margin of the Qinghai-Tibetan Plateau and the earthquake migration are possibly associated with the variation of the stress field caused by subsurface mass flow.

Designing Satellite Constellations to Observe Earth’s Time-Varying Gravity from Clock Frequency Comparisons

The nondominated sorting genetic algorithm III (NSGA-III) is used to design nonsymmetric satellite constellations to observe large-scale high-frequency gravity variations that would serve as complementary systems to other dedicated gravity field mapping missions such as the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On missions. The functionality of the NSGA-III method is validated by reproducing optimal surface-coverage satellite constellations from the literature. Then, NSGA-III is used to generate nondominated constellations tuned to detect short-term long-wavelength gravity field variations. The constellations are used to generate subweekly gravity field solutions from clock frequency comparison measurements. The effectiveness of NSGA-III for optimizing nonsymmetric constellations was demonstrated because the constellations obtained from NSGA-III were consistently superior in performance than traditional symmetric constellations. Furthermore, the results showed that the time-varying signals of interest (that is, gravity coefficients through the spherical harmonic degree and order of seven at daily intervals) can be unambiguously resolved by assuming an optical clock with a fractional frequency uncertainty representative of current technology. The ability to monitor these short-term long-wavelength signals on a global scale would observe a spectrum of the gravity field inherently undetectable by GRACE-like missions, and it would provide new insight to the understanding of global mass redistribution processes.

Effect of variable gravity field on the onset of convection in a Brinkman porous medium under convective boundary conditions

The effect of variable gravity on the onset of convection in a horizontal porous layer has been analyzed due to external heating. The third kind of thermal boundary conditions is considered on both the boundaries which are connected by Biot numbers B0 and B1. Also, the Brinkman model has been employed in the momentum equation. Further, linear and quadratic varying downward gravity fields depending on height have been taken to investigate the above observation. The bvp4c scheme is used in MATLAB to solve the eigenvalue problem for neutral stability mode. It is observed that the system's stability increases monotonically due to the rising effect of gravity variation parameter, Darcy number, and Biot numbers. Further, the onset of convection has been discussed for the two limiting cases of external heating on the boundaries where one boundary is associated with constant heat flux while another one is associated with an isothermal state. Finally, it is observed that the convection comes earlier for quadratic varying gravity field compared to linear varying gravity field when the external heat supplies from one boundary or both boundaries.

Nonlinear instability analysis of internally heated convection in a porous layer with the impact of magnetic field and variable gravity

AbstractThe impact of the magnetic field, heat source, and variable gravity field on the stability of convective phenomena in a porous layer are investigated numerically. Three types of gravity variations, such as linear, parabolic, and cubic functions are considered. For linear and nonlinear theories, the method of normal modes has been employed to solve governing dimensionless equations. It is found that the onset of convection is delayed by increasing the Hartmann number and gravity variation parameter and enhancement of the internal heat source makes the system stable. The subcritical instability region increases as the Hartmann number and gravity variation parameter increase.

Geodetic residual time series: A combined series by minimization of their internal noise level

This study aims to assess the hydrological effects of polar motion calculated from different combinations of geophysical excitations at decadal, seasonal, and non-seasonal periods. The geodetic residuals GAO, being a difference between observed geodetic excitation function of polar motion Geodetic Angular Momentum (GAM) and atmospheric (Atmospheric Angular Momentum—AAM) plus oceanic excitation functions (Oceanic Angular Momentum—OAM), are compared. Estimating hydrological effects on Earth’s rotation differs significantly, especially when using various oceanic models. Up to now, studies of geophysical excitations of polar motion containing AAM, OAM, and hydrological angular momentum (HAM) have not achieved entire agreement between geophysical (sum of AAM, OAM, and HAM obtained from the models) and geodetic excitation. Many geophysical models of the atmosphere, oceans, and land hydrology can be used to compute polar motion excitation. However, these models are very complex and still have uncertainties in the process descriptions, parametrization, and forcing. This work aims to show differences between various GAO solutions calculated from different mass and motion terms of various AAM and OAM models. Justifying to use one combination of GAO to estimate geodetic residuals is comparing those time series to hydrological excitations computed from Gravity Recovery and Climate Experiment (GRACE) data and the Land Surface Discharge Model (LSDM) model. Especially the quality of each geodetic residual time series is determined by estimating their noise level using a generalized formulation of the “three-cornered hat method” (3CH). This study presents a combined series of geodetic residuals GAO in polar motion (PM), wherein the internal noise level is shortened to a minimum by using the 3CH method. The combined GAO time series are compared with results obtained from the GRACE/GRACE Follow-On (GRACE-FO) solution provided by International Combination Service for Time variable Gravity Fields (COST-G) and the single solution elaborated by the Center for Space Research (CSR) and from the HAM LSDM hydrological model. The results show that higher consistency between GAO and HAM excitations can be achieved by minimizing the internal noise level in the GAO combined excitation series using the 3CH method, especially for the overall broadband and seasonal oscillations. For seasonal spectral bands, an agreement between combined GAO and the best-correlated series of GRACE CSR achieve correlations as high as 0.97 and 0.83 for the χ1 and χ2 equatorial components of PM excitation, respectively. This study’s combined geodetic residual time series slightly improved consistency between observed geodetic polar motion excitations and geophysical ones.

"Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium"

"Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium"

The study of internal heat and variable gravity field on the onset of convection in a sparsely packed porous medium

The qualitative influence of internal heat and variable gravity field on the onset of convection in a sparsely packed porous layer with horizontal fluid-saturated are investigated. Linear stability analysis is performed using the normal mode technique. The dimensionless governing equations with four cases of gravity field variation: (1) [Formula: see text], (2) [Formula: see text], (3) [Formula: see text], and (4) [Formula: see text] are solved using bvp4c in MATLAB R2020a and the corresponding eigenvalue problem is calculated for three types of boundaries, namely free-free, rigid-free, and rigid-rigid, respectively. The effect of an internal heat parameter [Formula: see text], Darcy number [Formula: see text], and gravity variation parameter [Formula: see text] for the stability of the system is investigated graphically. The critical value of the Rayleigh number and corresponding wavenumber are calculated for other fixed parameters. It is observed that internal heat parameters enhance the onset of convection, whereas the gravity variation parameter delays the same. It is also observed that the system becomes more stable for the exponential variable gravity function and less stable for the cubic variable gravity function.

Thermosolutal Instability of Couple Stress Rivlin Ericksen Ferromagnetic Fluid with Rotation, Magnetic and Variable Gravity Field in Porous Medium

In this paper thermosolutal instability of a couple stress Rivlin-Ericksen ferromagnetic fluid layerwith rotation, magnetic and variable gravity field in porous medium is studied. Using normalmode analysis technique the dispersion relation has been obtained and solved analytically. Forstationary convention, it is found that couple stress, magnetic field and permeability of mediumhave stabilizing effect on thermal instability under certain conditions. Rotation has stabilizingeffect if λ> 0 and destabilizing effect if λ< 0. Solute gradients has stabilizing effect either λ >0 or λ < 0. The presence of solute gradient, viscoelastic parameter, rotation and magnetic fieldintroduces oscillatory modes, stability in the system and principle of exchange of stability is notsatisfied if λ < 0 and system may be stable or unstable if λ > 0.

Exploiting the Combined GRACE/GRACE-FO Solutions to Determine Gravimetric Excitations of Polar Motion

Observations from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) missions can be used to estimate gravimetric excitation of polar motion (PM), which reflects the contribution of mass changes in continental hydrosphere and cryosphere to PM variation. Many solutions for Earth’s gravity field variations have been developed by institutes around the world based on GRACE/GRACE-FO data; however, it remains inconclusive which of them is the most reliable for the determination of PM excitation. In this study, we present a combined series of GRACE/GRACE-FO-based gravimetric excitation of PM computed using the three-cornered-hat (TCH) method, wherein the internal noise level in a combined solution is reduced to a minimum. We compare the combined series with results obtained from the combined GRACE/GRACE-FO solution provided by COST-G (International Combination Service for Time-variable Gravity Fields) and from the single solution elaborated by the Center for Space Research (CSR). All the gravimetric excitation series are evaluated by comparison with the sum of hydrological and cryospheric signals in geodetically observed PM excitation (called GAO). The results show that by minimizing the internal noise level in the combined excitation series using the TCH method, we can receive higher consistency with GAO than in the case of COST-G and CSR solutions, especially for the non-seasonal oscillations. For this spectral band, we obtained correlations between GAO and the best-combined series as high as 0.65 and 0.72 for the χ1 and χ2 equatorial components of PM excitation, respectively. The corresponding values for seasonal oscillation were 0.91 for χ1 and 0.89 for χ2. The combined series developed in this study explain up to 68% and 60% of overall GAO variability for χ1 and χ2, respectively.