Gravity Reduction Research Articles

Numerical study of reservoir permeability effects on gravity changes associated with CO2 geological storage: implications for gravimetric monitoring feasibility

AbstractGravimetric methods are used for monitoring the migration of CO2 stored in the reservoir. Reservoir permeability is crucial for injectivity and potentially important for gravity changes associated with CO2 storage. Nevertheless, its effects on gravity changes have not been investigated systematically. After conducting numerical simulations of CO2 injection and storage using models with varying permeability conditions (50–1000 mD), we calculated surface gravity changes. Results show that two mechanisms affect gravity decrease, related to differences in CO2 density and in CO2 spatial patterns. Under low‐permeability conditions, gravity decrease is minimal during injection because of increases in pressure and the resulting relative high density of CO2. Gravity decrease is enhanced after injection ceases because of the pressure release and resulting CO2 expansion. These effects are strong at shallow depths, at which CO2 is near the critical point and highly compressible. Under higher permeability conditions, rapid spreading of the CO2 plume causes smaller gravity reduction rate after some decades of injection. After injection ceases, upward CO2 migration because of buoyancy and plume spreading increase gravity above the injection zone. The time required for gravity change detection depends on permeability. Detection during injection can be made earlier under higher permeability conditions and under lower permeability conditions after injection ceases. These points suggest that permeability affects the feasibility of gravimetric methods. Moreover, designing monitoring programs based on permeability and depth conditions is necessary for successful monitoring. © 2020 Society of Chemical Industry and John Wiley & Sons, Ltd.

Effect of Qattara Depression on gravity and geoid using unclassified digital terrain models

The determination of the gravimetric geoid is based on the magnitude of the gravity observed at the topographic surface of the Earth. In order to satisfy Laplace’s equation, the masses between the surface of the Earth and the geoid must be removed or shifted inside the geoid. Then the gravity values have to be reduced to the geoid, forming the boundary values on the boundary surface. Gravity reduction techniques using unclassified Digital Terrain Models (DTM) usually presume that negative elevations are reserved for ocean stations. In case of Qattara Depression, the elevations are negative, i.e., below sea level. This leads to an obvious error in the topographic-isostatic reduction using, for example, TC-program employing unclassified DTM by assuming water masses filling the depression instead of air, besides computing at the non-existing sea level instead of computing at the actual negative topography. The aim of this paper is to determine the effect of Qattara Depression on gravity reduction and geoid computation, as a prototype of the effect of the unclassified land depressions on gravity reduction and geoid determination. The results show that the effect of Qattara Depression on the gravity reduction reaches 20 mGal and is restricted only to the depression area, while its effect on the geoid exceeds 1 m and has a regional effect which extends over a distance of about 1000 km.

Assessment of local covariance estimation through Least Squares Collocation over Iran

Abstract. Covariance determination as the heart of Least Squares Collocation gravity field modeling is based on fitting an analytical covariance to the empirical covariance, which is stemmed from gravimetric data. The main objective of this study is to process different local covariance strategies over four regions with different topography and spatial data distribution in Iran. For this purpose, Least Squares Collocation based on Remove – Compute – Restore technique is implemented. In the Remove step, gravity reduction in regions with a denser distribution and a rougher topography is more effective. In the Compute step, the assessment of the Collocation estimates on the gravity anomaly control points illustrates that data density is more relevant than topography roughness to have a good covariance determination. Moreover, among the different attempts of localizing the covariance estimation, a recursive approach correcting the covariance parameters based on the agreement between Least Squares Collocation estimates and control points shows better performance. Furthermore, we could see that covariance localization in a region with sparse or bad distributed observations is a challenging task and may not necessarily improve the Collocation gravity modeling. Indeed, the geometrical fitness of the empirical and analytical covariances – which is usually a qualitative test to verify the precision of the covariance determination – is not always an adequate criterion.

Gravity for Geodetic Purpose: Geoid-Ellipsoid Separation and Orthometric Height System

Gravity plays very crucial role in geodetic issues as gravity field determines the shape of the earth. This paper reviews – beginning from defining the gravity, various applications of gravity in geodesy and in other fields, nature of gravity field of our terrain, instruments of gravity measurement, and techniques of gravity survey. This paper first gives information about gravity networks in Nepal, presents an equation to compute orthometric correction (OC) from height obtained from levelling. Gravimetric geoid-determination method is explained here with various gravity reduction methods and topographic-isostatic gravity reduction method is recommended for N- separation computation as this method results gravity anomalies near to zero.

Quantifying the differences between gravity reduction techniques

Gravity data processing (reduction) generally utilises the best-available formulae. New and improved formulae have been introduced over time and the resulting newly processed gravity will not match the old. Additionally, mistakes made in the gravity reduction process, as well as the incompatibilities between various equations, will inevitably lead to errors in the final product. This can mean that overlapping gravity surveys are often incompatible, leading to incorrect geological interpretations. In this paper I demonstrate the magnitude of change that results when different information is introduced at various stages of the gravity reduction process. I have focussed on differences relating to calibration factors, time zones and time changes, height, geodetic datums, gravity datums and the equations involved therein. The differences range from below the level of detection (0.01 mGal) to over 16.0 mGal.The results not only highlight the need to be diligent and thorough in processing gravity data, but also how it is necessary to document the steps taken when processing data. Without proper documentation, gravity surveys cannot be reprocessed should an error be identified.

Impact of Nasser Lake on gravity reduction and geoidal heights for Egypt

In the course of the IAG African Geoid Project, it is needed to study the impact of the lakes on the gravity reduction and geoidal heights. The aim of this paper is to study the impact of the water in Nasser Lake on gravity reduction and geoidal heights for Egypt. The determination of the gravimetric geoid is based on the well-known remove-restore technique. The problem of the lakes occurs because the popular programs widely used in practice (e.g., TC-program (Forsberg, 1984)) assume that all positive elevations are filled with rock topography, and all negative elevations are filled with ocean water. This is, however, not true for the case of Nasser Lake, which lies completely above sea level, at about 180 m elevation, with a water depth of about 20 m. The paper presents an approach on estimating the impact of Nasser Lake on gravity reduction and geoidal heights using TC-program with some tricky cases. The results show that the impact of Nasser Lake on both gravity anomalies and geoid undulation is limited to the area of the lake. The impact of Nasser Lake on the gravity anomalies is in the order of sub mgal, while the impact of Nasser lake on the geoid undulation is significant and reaches few centimeters.

Density structure of the crust in the Emeishan large igneous province revealed by the Lijiang- Guiyang gravity profile

The Emeishan large igneous province (hereafter named by its acronym ELIP) is the first accepted large igneous region in China. The current study tries to reconstruct the density structure of the crust in this region. For this purpose, we conducted the gravity survey along an 800-km-long profile, which stretched laterally along the latitude 27°N from Lijiang (Yunnan province) to Guiyang (Guizhou province). The fieldwork included 338 gravity measurements distributed from the inner zone to the outer zone of the mantle plume head. After a series of gravity reductions, we calculated the Bouguer gravity anomaly and then constructed the density model for ELIP by iterative forward modeling from an initial density model tightly constrained by wide-angle seismic reflection data. The topography of the Moho, here physically interpreted as a density discontinuity of ~0.4 g·cm–3, gradually rises from the inner zone (~50 km deep) to the outer zone (~40 km), describes a thicker crust in the inner zone than in any other segment of the profile and largely reproduces the shape of the Bouguer gravity anomaly curve. Both the Bouguer gravity and the density structure show significant differences with respect to the inner zone and the other two zones of ELIP according to the commonly accepted partition of the Emeishan area. A thicker and denser middle-lower crust seems to be the main feature of the western section of the profile, which is likely related to its mafic magmatic composition due to magmatic underplating of the Permian mantle plume.

Human Locomotion in Hypogravity: From Basic Research to Clinical Applications.

We have considerable knowledge about the mechanisms underlying compensation of Earth gravity during locomotion, a knowledge obtained from physiological, biomechanical, modeling, developmental, comparative, and paleoanthropological studies. By contrast, we know much less about locomotion and movement in general under sustained hypogravity. This lack of information poses a serious problem for human space exploration. In a near future humans will walk again on the Moon and for the first time on Mars. It would be important to predict how they will move around, since we know that locomotion and mobility in general may be jeopardized in hypogravity, especially when landing after a prolonged weightlessness of the space flight. The combination of muscle weakness, of wearing a cumbersome spacesuit, and of maladaptive patterns of locomotion in hypogravity significantly increase the risk of falls and injuries. Much of what we currently know about locomotion in hypogravity derives from the video archives of the Apollo missions on the Moon, the experiments performed with parabolic flight or with body weight support on Earth, and the theoretical models. These are the topics of our review, along with the issue of the application of simulated hypogravity in rehabilitation to help patients with deambulation problems. We consider several issues that are common to the field of space science and clinical rehabilitation: the general principles governing locomotion in hypogravity, the methods used to reduce gravity effects on locomotion, the extent to which the resulting behavior is comparable across different methods, the important non-linearities of several locomotor parameters as a function of the gravity reduction, the need to use multiple methods to obtain reliable results, and the need to tailor the methods individually based on the physiology and medical history of each person.

Evaluation of ASTER GDEM in the northeastern margin of Tibetan Plateau in gravity reduction

In this paper, we first transferred the normal height of ASTER GDEM v2 to GPS ellipsoidal height based on the EGM96, and analyzed the precision of this digital elevation model in the northeastern margin of Tibetan Plateau (NETP) combining with 89 ground GPS measurements. The results demonstrate that the standard deviation of the difference between ASTER GDEM and GPS results is 9.3 m, and the precision of ASTER GDEM in this region is approximately 10 m. We also calculated the free-air gravity anomalies using the relative gravity data and DEM model in NETP. The results show that the gravity anomalies are generally negative with local positive values, ranging from −156 to 43 mGal (10−5 m/s2). At last, we compared the EGM2008 free-air gravity anomalies (FGAs) with the ground gravity measurements, and their spatial patterns are similar. While the point-to-point difference between the modeling and measuring results shows great discrepancy. The free-air gravity anomalies of EGM2008 in this region range from −154 to 96 mGal, and the difference between EGM2008 and the ground measurements ranges from −102 to 50 mGal. The mean difference is −17.34 mGal, and the standard deviation is 46.69 mGal, which demonstrates that the EGM2008 has poor precision in the northeastern margin of Tibet Plateau.

Insights on the structure of Lusi mud edifice from land gravity data

Since May 2006, the active Lusi mud eruption has continuously erupted boiling mud. During the early stages of the eruption in 2006, previous gravity studies showed that the piling up of the mud constructed a large edifice that subsides within the unconsolidated sediment especially around a large area over the active crater. After ten years of continuous eruption, the size of the edifice has grown significantly over a surface framed by 10 m tall containment embankments. In 2015 and 2016, several land gravity surveys were carried out to investigate the structure of the mud edifice and the effect of local geological active features. The new residual Bouguer anomaly map, calculated for a reference density of 2670 kg m−3, shows significant changes in the local gravity field in comparison to the previous 2006-gravity map survey. The new data set shows that the gravity decrease is generally restricted along the faulted and fractured zones, around erupting vents, and in the southern part of the mud edifice. Maximum gravity variations reach 1.4 mGal in some areas of the mud edifice. In the region outside the embankment, the gravity reductions are 0.6 mGal E-W and 1.0 mGal N-S. A second vertical derivative analysis of gravity data indicates that the mud edifice continues to pile up and subside mostly in the western and southern part of the edifice. Results of a 3D forward model of a vertical cylinder shape allowed characterising the extent of compacted material along the Watukosek fault system that originates from the neighbouring volcanic arc and crosses the mud edifice. Our results support the hypothesis of local pinched volume of mud ongoing between the subsided and uplifted masses of mud. The density of compacted mud breccia material increases between 16 and 27%. Gravity data also shows that the Lusi mud edifice is built over an extended NW-SE gravity increase, interpreted as a sediment density variation within the basin, and which is parallel to the trend of the Basin.

Gravity Reduction View: A Radiographic Technique for the Evaluation and Management of Weber B Fibula Fractures.

While various radiographic parameters and application of manual/gravity stress have been proposed to elucidate instability for Weber B fibula fractures, the prognostic capability of these modalities remains unclear. Determination of anatomic positioning of the mortise is paramount. We propose a radiographic technique, the Gravity Reduction View (GRV), which helps elucidate non-anatomic positioning and reducibility of the mortise. The patient is positioned lateral decubitus with the injured leg elevated on a holder with the fibula directed superiorly. The x-ray cassette is placed posterior to the heel, with the beam angled at 15° of internal rotation to obtain a mortise view. Our proposed treatment algorithm is based upon the measurement of the medial clear space (MCS) on the GRV versus the static mortise view (and in comparison to the superior clear space (SCS)) and is based on reducibility of the MCS. A retrospective review of patients evaluated utilizing the GRV was performed. 26 patients with Weber B fibula fractures were managed according to this treatment algorithm. Mean age was 50.57 years old (range:18-81, SD=19). 17 patients underwent operative treatment and 9 patients were initially treated nonoperatively. 2 patients demonstrated late displacement and were treated surgically. Using this algorithm, at a mean follow-up of 26 weeks, all patients had a final MCS that was less than the SCS (final mean MCS 2.86 mm vs. mean SCS of 3.32) indicating effectiveness of the treatment algorithm. The GRV is a radiographic view in which deltoid competency, reducibility and initial positioning of the mortise are assessed by comparing a static mortise view with the appearance of the mortise on the GRV. We have proposed a treatment algorithm based on the GRV that we found it useful in our patients in guiding treatment and achieving anatomic mortise alignment.

Quantifying the errors in gravity reduction

Mistakes in processing gravity data lead to errors in the final product. This can mean that overlapping gravity surveys are often incompatible, and can lead to incorrect geological interpretations. In this paper I demonstrate the magnitude of the errors introduced at various stages of the gravity reduction process. I have focussed on errors relating to calibration factors, time zones and time changes, height, geodetic datums, gravity datums, and the equations involved therein. The errors range from below the level of detection, to many milligals. The results highlight the need to not only be diligent and thorough in processing gravity data, but also how it is necessity to document the steps taken when processing data. Without properly documented gravity surveys they cannot be reprocessed should an error be identified.

Gravity Reduction View

Category: Trauma Introduction/Purpose: The determination of stability and ultimate need for operative stabilization of Weber B fibula fractures largely depends on the presence of a competent deltoid ligament. While various radiographic parameters and the application of manual or gravity stress have been proposed to elucidate instability, the prognostic capability of these modalities remains unclear. Given that a recent study found no difference between operative and nonoperative treatment for stress-positive Weber B ankle fractures, the value of stress views is questionable; what may be ultimately more important is the determination of anatomic positioning of the mortise. We propose a novel view, the Gravity Reduction View (GRV), which helps elucidate non-anatomic positioning and reducibility of the mortise. We also propose a treatment algorithm based on the use of the GRV. Methods: To obtain the GRV, the patient is positioned in lateral decubitus with the injured fibula directed upward and elevated with a leg holder. The x-ray cassette is placed posterior to the heel, with the beam angled at 15˚ of internal rotation to obtain a mortise view. Our treatment algorithm is based upon the measurement of the medial clear space (MCS) on the GRV versus the static mortise view. If the MCS on GRV remains wide or decreases, surgery is recommended as the GRV confirms a non- anatomic mortise. If the MCS remains within normal limits on the static and GRV views, a trial of nonoperative treatment with immobilization and repeat radiographs in 1-2 weeks is undertaken. If the MCS is normal on repeat weightbearing x-rays, the patient is treated conservatively; if increased, surgery is recommended. To further assess mortise stability, the MCS is compared to the superior clear space (SCS). Results: 23 patients with Weber B distal fibula fractures were managed according to this treatment algorithm. The mean age was 49.1 years old (range: 18-74). Of these patients, 15 underwent operative treatment and 10 patients were initially treated nonoperatively, although 2 patients demonstrated late displacement and were treated surgically. Using this algorithm, all patients had a final MCS that was less than the SCS (final mean MCS for patients treated operatively or nonoperatively 2.85 mm vs. mean SCS of 3.34), indicating effectiveness of the treatment algorithm. Conclusion: The Gravity Reduction View is a novel radiographic view in which deltoid competency, reducibility and initial anatomic positioning of the mortise are assessed by comparing a static mortise view with the appearance of the mortise on the reduction view (GRV). We have developed a treatment algorithm based on the GRV and have found it to be predictive of mortise alignment and useful in guiding treatment.

Calculation of the New Gravity Wall Composed of Three Flat Slabs by the Equations of Bending Theory of Shells

Background/Objectives: In this paper, for the weight reduction of concrete gravity walls and reduction of wall thickness, flat slabs with the retaining walls have been matched and offered a new wall. Methods/Statistical Analysis: In this article, flat slabs are adapted with concrete gravity walls. Then to calculate new retaining wall, a new method, based on the principles of mathematics and engineering mechanics, is presented. In solving the new retaining wall, Fourier series and shells theory and the classical analysis method are used. Findings: In this research, a new structure form to reduce the material used in concrete gravity retaining walls and a new method for analyzing the new retaining walls have been offered. In addition, equations of bending theory of cylindrical shells considering with physical and mathematical aspects in solving the new retaining wall consisting of three flat slabs as well as engineering mechanics bases and classical analysis method have been indicated. Moreover, Fourier series to solve the new retaining wall problem have been used. Also, the studies showed that the use of the new retaining wall is more economical. Applications/Improvements: In various projects such as road, bridge building, landscaping, new retaining wall can be used. In general, new retaining wall can be used to stop the soil from falling everywhere.

한반도 지역에서의 상층중력장

The free-air anomalies are computed using a data set from various types of gravity measurements in the Korean Peninsula area. The gravity values extracted from the Earth Gravitational Model 2008 are used in the surrounding region. The upward continuation technique suggested by Dragomir is used in the computation of the external free-air anomalies at various altitudes. The integration radius 10 times the altitude is used in order to keep the accuracy of results and computational resources. The direct geodesic formula developed by Bowring is employed in integration. At the 1-km altitude, the free-air anomalies vary from -41.315 to 189.327 mgal with the standard deviation of 22.612 mgal. At the 3-km altitude, they vary from -36.478 to 156.209 mgal with the standard deviation of 20.641 mgal. At the 1,000-km altitude, they vary from 3.170 to 5.864 mgal with the standard deviation of 0.670 mgal. The predicted free-air anomalies at 3-km altitude are compared to the published free-air anomalies reduced from the airborne gravity measurements at the same altitude. The rms difference is 3.88 mgal. Considering the reported 2.21-mgal airborne gravity cross-over accuracy, this rms difference is not serious. Possible causes in the difference appear to be external free-air anomaly simulation errors in this work and/or the gravity reduction errors of the other. The external gravity field is predicted by adding the external free-air anomaly to the normal gravity computed using the closed form formula for the gravity above and below the surface of the ellipsoid. The predicted external gravity field in this work is expected to reasonably present the real external gravity field. This work seems to be the first structured research on the external free-air anomaly in the Korean Peninsula area, and the external gravity field can be used to improve the accuracy of the inertial navigation system.

Is Prone Position Ideal for Manipulation and Pinning of Displaced Pediatric Extension-type Supracondylar Fractures of Humerus? A Randomized Control Trial.

Closed reduction and percutaneous pin fixation is the standard of care for displaced supracondylar fractures of humerus in children. Although it is routinely performed in supine position, some authors recommend prone position to be advantageous as it aids in gravity reduction and avoids elbow hyperflexion. This study was conducted to compare the ease of manipulation and pinning, clinical, and radiologic outcomes in supine versus prone position. Fifty-two children with acute, grade III supracondylar humerus fractures without vascular injury were included in the study. They were grouped into prone (n=26) and supine (n=26) based on computer-generated block randomization. The duration of procedure, number of radiation exposures, attempts at closed reduction, and attempts at placing the pins were analyzed. Functional and radiologic outcomes were assessed for a minimum follow-up of 1 year. There was no significant difference between the 2 groups in the duration of procedure (P=0.422), number of radiation exposure (P=0.470), attempts at closed reduction (P=0.904), and attempts for pinning (P=0.745) and the final clinical and radiologic outcomes. One patient in prone group had cubitus varus of 8 degrees. Functionally, 2 in the supine group and 3 in prone group had poor outcomes. There is no significant difference in the ease of reduction and pinning between supine and prone positions. Grossly displaced fractures with skin puckering are difficult to manipulate in prone position. Supine position is ideal for closed reduction and pinning of all patterns of type III supracondylar fractures.

Application of the RTM-technique to gravity reduction for tracking near-surface mass-density anomalies: A case study of salt diapirs in Iran

We study a land-based gravity reduction technique for tracking near surface massdensity anomalies. For this purpose, we apply the residual terrain modeling (RTM) technique accompanied by a global geopotential model to provide a high-frequency reference gravity field. The proposed reference gravity field includes all required corrections for the corresponding gravity reduction; hence, it is subtracted from landbased gravity data to provide a kind of gravity anomaly that depends mainly on the massdensity anomalies of the near surface geological targets. As a case study, we examine the proposed reduction method to detect horizontal locations of some of known salt diapirs within the Zagros region. The numerical results indicate that the reduced gravity anomalies are sufficiently sensitive to locations of the salt diapirs.

Qinghai-Tibet Plateau crustal thickness derived from EGM2008 and CRSUT2.0

Abstract: Qinghai-Tibet Plateau is the most complex region for crustal thickness inversion, while high-resolution earth gravity model (EGM) makes it possible to obtain high precision gravity anomaly, which is a key parameter to depict the Earth’s inner structure in geodesy domain. On the basis of this principle, we calculated the Bouguer gravity anomalies in Qinghai-Tibet Plateau with EGM2008 and SRTM6. 0 by efficient high-degree spherical harmonic synthesis algorithm. In order to obtain the gravity anomaly caused by Moho density mutant, the noises caused by the topography was removed by wavelet details. Then, the crustal thickness was corrected on the basis of CRUST 2. 0 with the deep-large-scale single density interface formula. The inversion result indicates that the crustal thickness in Qinghai-Tibet Plateau is between 50 km and 75 km, which is in correspondence with the recent science research result. Compared with the 2 degree CRUST 2. 0 model, the spatial resolution of crustal thickness in our research can reach 40 arc minutes. In addition, there is a positive relationship between the inversed crustal thickness and topography, which can prove the effectiveness of Airy-Heiskanen isostatic model in gravity reduction.

Investigation of distribution of embedded shallow structures using the first order vertical derivative of gravity data

The utilization of the first order vertical derivative method, applied to a gravity field, in the determination of relatively low density and high density areas within the same unit can be helpful, defining such areas. In this study, the first order vertical derivative method was first applied to synthetic data and the workability of the method was investigated by creating scenarios having different densities within the same unit. Later, to compare the result of the scenarios, Adala-Manisa/Turkey and surroundings having a volcanic history were selected because of the existence of underground structures formed as a result of embedded volcanic areas. Real data set was obtained by using Scintrex CG-5 and Leica 1200 + GNSS for investigating the geological structure of the Adala-Manisa, at 400 stations. After the gravity reduction process the residual gravity anomaly values of the Adala-Manisa were obtained by removing a first order regional trend from the Bouguer gravity map. In the following process, the first order vertical derivative method was applied to the residual anomaly map. Thus, results of the synthetic anomalies and real data anomalies were compared and discussed by using the residual Bouguer gravity anomaly map. Consequently, the first order vertical derivative application in the determination of suppressed and undefinable shallow weak resources in the same media as Alluvial Fans and Alluvium units, especially on the Bouguer gravity anomaly map produces acceptable effective results.

New free-air and Bouguer gravity fields of Taiwan from multiple platforms and sensors

We construct 1′ × 1′ grids of free-air and Bouguer gravity anomalies around Taiwan with well-defined error estimates for quality assessment. The grids are compiled from land, airborne and shipborne gravity measurements, augmented with altimeter gravity at sea. Three sets of relative land gravity measurements are network-adjusted and outlier-edited, yielding accuracies of 0.03–0.09 mGal. Three airborne gravity sets are collected at altitudes 5156 and 1620 m with accuracies of 2.57–2.79 mGal. Seven offshore shipborne gravity campaigns around Taiwan and its offshore islands yield shallow-water gravity values with 0.88–2.35 mGal accuracies. All data points are registered with GPS-derived geodetic coordinates at cm–dm accuracies, allowing for precise gravity reductions and computing gravity disturbances. The various datasets are combined by the band-limited least-squares collocation in a one-step procedure. In the eastern mountainous (or offshore) region, Bouguer anomalies and density contrasts without considering the oceanic (or land) topographic contribution are underestimated. The new grids show unprecedented tectonic features that can revise earlier results, and can be used in a broad range of applications.