A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

In mountainous regions with scarce gravity data, gravimetric geoid determination is a difficult task that needs special attention to obtain reliable results satisfying the demands, e.g., of engineering applications. The present study investigates a procedure for combining a suitable global geopotential model and available terrestrial data in order to obtain a precise regional geoid model for Konya Closed Basin (KCB). The KCB is located in the central part of Turkey, where a very limited amount of terrestrial gravity data is available. Various data sources, such as the Turkish digital elevation model with 3 ?? × 3?? resolution, a recently published satellite-only global geopotential model from the Gravity Recovery and Climate Experiment satellite (GRACE) and the ground gravity observations, are combined in the least-squares sense by the modified Stokes?? formula. The new gravimetric geoid model is compared with Global Positioning System (GPS)/levelling at the control points, resulting in the Root Mean Square Error (RMS) differences of ±6.4 cm and 1.7 ppm in the absolute and relative senses, respectively. This regional geoid model appears to be more accurate than the Earth Gravitational Model 2008, which is the best global model over the target area, with the RMS differences of ±8.6 cm and 1.8 ppm in the absolute and relative senses, respectively. These results show that the accuracy of a regional gravimetric model can be augmented by the combination of a global geopotential model and local terrestrial data in mountainous areas even though the quality and resolution of the primary terrestrial data are not satisfactory to the geoid modelling procedure.     

海域航空重力快速构建区域大地水准面

我国在海域开展了大规模的航空重力勘探,这些资料对构建高精度大地水准面具有重要价值.基于此,本文提出一种利用海域航空重力测量数据快速构建大地水准面的方法.该方法基于移去-恢复法思想,利用位场最小曲率方法对航空重力数据进行高精度向下延拓并获取相应的扰动位,实现航空重力测量快速构建海域大地水准面.与斯托克斯积分计算相比,采用了处理效率更高的频率域位场转换,解决了向下延拓及垂向积分时航空重力异常数据空白及扩边问题,具有较高的位场转换精度.本文应用EGM2008模拟航空重力数据进行模型验证,计算结果与其给出的水准面的精度相当;同时,也选取GRAV-D计划的航空重力数据进行实际验证,计算结果与xGEOID18B水准面模型精度基本一致.模型验证和实际应用验证了本方法的实用性.

     

Testing Stokes-Helmert geoid model computation on a synthetic gravity field: experiences and shortcomings

We report on testing the UNB (University of New Brunswick) software suite for accurate regional geoid model determination by use of Stokes-Helmert’s method against an Australian Synthetic Field (ASF) as “ground truth”. This testing has taken several years and has led to discoveries of several significant errors (larger than 5mm in the resulting geoid models) both in the UNB software as well as the ASF. It was our hope that, after correcting the errors in UNB software, we would be able to come up with some definite numbers as far as the achievable accuracy for a geoid model computed by the UNB software. Unfortunately, it turned out that the ASF contained errors, some of as yet unknown origin, that will have to be removed before that ultimate goal can be reached. Regardless, the testing has taught us some valuable lessons, which we describe in this paper. As matters stand now, it seems that given errorless gravity data on 1′ by 1′ grid, a digital elevation model of a reasonable accuracy and no topographical density variations, the Stokes-Helmert approach as realised in the UNB software suite is capable of delivering an accuracy of the geoid model of no constant bias, standard deviation of about 25 mm and a maximum range of about 200 mm. We note that the UNB software suite does not use any corrective measures, such as biases and tilts or surface fitting, so the resulting errors reflect only the errors in modelling the geoid.     

Surface deformation, gravity and the geoid from a three-dimensional convection model at low Rayleigh numbers

The two-dimensional surface deformation, gravity field and geoid are calculated from the temperature fields of a number of numerical models of constant viscosity three-dimensional convective flows, heated from within and from below, using the appropriate Green's functions. The admittance is positive, with positive gravity anomalies above hot rising regions, except for large aspect ratio circulations with undeformable lower boundaries. The surface deformation and the geoid are insensitive to the short wavelength features of the temperature variation. The gravity field is less smooth, though still does not clearly indicate the narrowness of the upwelling and downwelling regions at large Rayleigh numbers. When the lower boundary of the convecting region is deformable, the gravity field is dominated by lateral temperature variations within the upper thermal boundary layer, even when their contribution to the overall circulation is small. The variation of surface deformation with Rayleigh number agrees well with that expected from simple boundary layer arguments when the circulation is driven by heating from below, but less well when the heating is internal. These results suggest that the convective upwelling beneath regions showing positive geoid and residual depth anomalies is more localized than the horizontal extent of these features would suggest.     

地形-均衡补偿重力、大地水准面异常频谱分析

将地形高、地球内部质量异常以及重力、大地水准面展开成球谐级数,依据岩石圈弹性挠曲均衡补偿理论建立地形—均衡补偿重力、大地水准面异常的球谐级数表达式.由此我们可以研究地形—均衡补偿重力、大地水准面异常与球谐级数阶次的关系,以及不同波长地形荷载与岩石圈挠曲补偿的关系,探讨地形—均衡补偿重力、大地水准面的频谱特性.从观测大地水准面异常和自由空气重力异常扣除地形—均衡补偿大地水准面、重力异常,可以得到均衡大地水准面异常和均衡重力异常.均衡大地水准面异常已经消除了浅层物质不均匀的影响,反映的是地球深部物质密度不均匀分布.均衡重力异常显示出中短波长特性,反映的是地壳上地幔物质分布的失衡和物质调整的动力学特征.     

Interpretation of gravity and magnetic data in the Phlegraean fields geothermal area, Naples, Italy

Available gravity and magnetic data of the Phlegraean Fields geothermal area, Naples, Italy, have been interpreted and the obtained structural models discussed in the light of the other available geological, volcanological and geophysical data.On the basis of the results of a previous seismic reflection survey in the Gulf of Naples and in the Pozzuoli Bay, which delineated a basement characterized by a seismic velocity of 4–6 km/s, it has been possible to evaluate the gravity anomaly connected with the morphology of this horizon ( = 2.7 g/cm³).The residual anomaly map, obtained after subtraction of the regional long-wavelength components relative to mantle and deep crustal structures and the computed components relative to the above-mentioned seismic basement, shows up as a circular low with an amplitude of 10 mgal centred in the Pozzuoli Bay. This gravity low has been interpreted as due to the occurrence, in the centre of Pozzuoli Bay, of light (Δ = −0.2 g/cm³) material with a maximum thickness of about 2 km. However, a contribution to the anomaly due to a narrow magmatic body intruded in the basement, as suggested by volcanological and ground deformation data, cannot be excluded.The aeromagnetic map of the Phlegraean Fields is characterized by three main anomalies which have been fitted by superficial tridimensional parallelepipedic bodies, schematically representing lava flows and domes. Their anomalies have been subsequently subtracted from the observed field, obtaining as a residual a large anomaly centred in the southwestern area of the Pozzuoli Bay. It has been interpreted as being due to a lowmagnetized body which, taking into account the thermal state of the area, should represent that part of the pyroclastic sequence which has lost part of its magnetization by thermo-chemical alteration.     

Conditionality of inverse solutions to discretised integral equations in geoid modelling from local gravity data

The eigenvalue decomposition technique is used for analysis of conditionality of two alternative solutions for a determination of the geoid from local gravity data. The first solution is based on the standard two-step approach utilising the inverse of the Abel-Poisson integral equation (downward continuation) and consequently the Stokes/Hotine integration (gravity inversion). The second solution is based on a single integral that combines the downward continuation and the gravity inversion in one integral equation. Extreme eigenvalues and corresponding condition numbers of matrix operators are investigated to compare the stability of inverse problems of the above-mentioned computational models. To preserve a dominantly diagonal structure of the matrices for inverse solutions, the horizontal positions of the parameterised solution on the geoid and of data points are identical. The numerical experiments using real data reveal that the direct gravity inversion is numerically more stable than the downward continuation procedure in the two-step approach.     

On calculation of the vertical deflection and the geoid undulation from gravity anomalies

Specific features of the calculation of the vertical deflection and the geoidal undulation in the Arctic from gravity anomalies are discussed. Basic requirements to the initial model of the anomalous field are described. The technique of calculating the vertical deflection with arbitrarily fine detail is proposed. The ways for improving the models of gravity anomalies for solving the stated problems are suggested.     

Regional compensation of subducted lithosphere: effects on geoid,gravity and topography from a preliminary model

It is proposed that the anomalous mass of subducted lithospheric slabs is partially compensated by two mechanisms: (a) by stresses transmitted up the slab to the surface lithosphere, causing the trench, and (b) by stresses transmitted through the mantle wedge overlying the slab, which cause a broad shallow depression. Results calculated from a preliminary two-dimensional model show that it can give a first-order account of observed topography, gravity and geoid anomalies. In particular, the model can reconcile the large mass anomaly predicted for the slab by thermal conduction theory with the smaller than expected gravity and geoid anomalies. Preliminary results indicate substantial compensation by mechanism (a), implying rather large stresses at the top of the slab: these could be important for theories of earthquake mechanisms and plate driving mechanisms. Roughly 50% of the possible compensation by mechanism (b) is indicated: the resulting depression, the order of 500 m deep and over 500 km wide, could explain anomalously deep marginal basins and some marine transgressions of continents.     

Regional geoid modeling in the area of subglacial Lake Vostok,Antarctica

We present a geoid model for the area of Lake Vostok, Antarctica, from a combination of local airborne gravity, ice-surface and ice-thickness data and a lake bathymetry model. The topography data are used for residual terrain modeling (RTM) in a remove–restore approach together with GOCE satellite data. The quasigeoid is predicted by least-squares collocation (LSC) and subsequently converted to geoid heights. Special aspects of that method in presence of an ice sheet are discussed.It is well known that a body freely floating in water is in a state of hydrostatic equilibrium (HE). This usually applies, e.g., to ice shelves or sea ice. However, it has been shown that this is valid also for the ice sheet covering the subglacial Lake Vostok. Thus, we demonstrate the use of such a refined regional geoid model for glaciological and geophysical applications by means of the HE surface of that lake. The mean quadratic residual geoid signal (0.56 m) w.r.t. the GOCE background model exceeds the residual variations of the estimated apparent lake level (ALL) (0.26 m) within the central part of the lake. An approach considering the actual geopotential at the ALL has been derived and subsequently applied. In this context, downward continuation of the potential field within the ice sheet as well as the latitudinal tilt of off-geoid equipotential surfaces are discussed. In view of the accuracy of the ice-thickness measurements that dominate the total error budget of the estimated ALL these effects are negligible. Thus, the HE surface of subglacial lakes may safely be described by a constant height bias in small-scale regional applications. However, field continuation is significant with respect to the formal uncertainty of the quasigeoid, which is at the level of 5 cm given that accurate airborne gravity data (±2 mGal) are available.     

The Campania-Campi Flegrei area: a contribution to discern the best structural model from gravity interpretation

Structural interpretations of negative gravity anomalies at Campi Flegrei and Campania are reviewed. The interpretations are not uniquely determined, as different models correspond to equally good anomaly fits.These models are examined using a new method based on the interpretation of the apparent density map computed from the gravity anomaly map.As regards the Campi Flegrei anomaly, a funnel-shaped caldera 3D model is readily obtained. This is more appropriate than previous interpretations, as not only anomaly but also apparent densities are fitted.As about the regional structures, the used approach suggests that the more pertinent model is a large magmatic intrusion, 9 to 14 km deep.A final scheme is proposed linking this intrusion to the funnel-shaped caldera as the main regional reservoir.     

Ability of the EGM2008 high degree geopotential model to calculate a local geoid model in Valencia,Eastern Spain

A new generation of global geopotential models (GGM) is being developed. These solutions offer a file with fully-normalized spherical harmonic coefficients of the Earth’s gravitational potential up to a degree greater than 2000 with very low commission errors. This paper analyses the recent Earth Gravitational Model EGM2008, developed up to degree and order 2159 with additional coefficients to degree 2190 and order 2159, which means recovering the gravitational field up to approximately 20 km wavelengths. 223 GPS/levelling points of the new Spanish High Precision Levelling Network in the Valencia region (Eastern Spain) are used as external tool for evaluation in that particular region. The same evaluation has been performed to other different global (EGM96 and EIGENCG03C), continental (EGG97), regional (IGG2005 and IBERGEO2006) and local (GCV07) geoid models for comparison purposes only. These comparisons show that EGM2008 is the geoid model that best fits to the GPS/levelling data in that region.     

Employing the bilateral filter to improve the derivative-based transforms for gravity and magnetic data sets

Studia Geophysica et Geodaetica - In the literature, there are numerous derivative-based transforms for gravity and magnetic data sets, with which relevant features can be highlighted. However,...     

大地水准面异常在湖南地区的地球物理解释

以湖南地区为例,利用超高阶地球重力位模型EGM2008计算了研究区的重力大地水准面,并采用棱柱体公式和球体公式相结合的方法分别进行了完全地形改正和Airy-Heiskanen局部均衡改正,得到布格大地水准面和均衡大地水准面.对三种大地水准面进行不同波长分量的分离处理,得到包含不同深度异常信息的剩余大地水准面,并结合其他地球物理资料对研究区进行了详细的地球物理解释.结果表明,剩余重力大地水准面可以有效地反映出研究区内的深部构造特征,如深大断裂带分布、构造块体位置、上地幔密度横向分布等,但对地壳内异常结构反映不明显;研究区岩石圈密度变化相对平缓,厚度由东向西增加;根据剩余均衡大地水准面及研究区Airy局部均衡莫霍面,可以大致推测出研究区的莫霍面起伏形态以及均衡状态,可作为一种有用的参考信息.     

Optimized system to improve pumping rate stability during aquifer tests

Aquifer hydraulic properties are commonly estimated using aquifer tests, which are based on an assumption of a uniform and constant pumping rate. Substantial uncertainties in the flow rate across the borehole-formation interface can be induced by dynamic head losses, caused by rapid changes in borehole water levels early in an aquifer test. A system is presented that substantially reduces these sources of uncertainty by explicitly accounting for dynamic head losses. The system which employs commonly available components (including a datalogger, pressure transducers, a variable-speed pump motor, a flow controller, and flowmeters), is inexpensive, highly mobile, and easily set up. It optimizes the flow rate at the borehole-formation interface, making it suitable for any type of aquifer test, including constant, step, or ramped withdrawal and injection, as well as sinusoidal. The system was demonstrated for both withdrawal and injection tests in three aquifers at the Savannah River Site. No modifications to the control system were required, although a small number of characteristics of the pumping and monitoring system were added to the operating program. The pumping system provided a statistically significant, constant flow rate with time. The range in pumping variability (95% confidence interval) was from +/- 2.58 x 10(-4) L/sec to +/- 9.07 x 10(-4) L/sec, across a wide range in field and aquifer conditions.     

Macroseismic attenuation in the Campanian area, southern Italy

The main objective of the present study is to evaluate seismic attenuation relationships for the Campanian area (southern Italy) using the felt intensity report data obtained from comprehensive historical databases (DOM 4.1). We focused our attention on the Campania region because it is characterized by a high seismic hazard and risk, particularly in the Naples area and its suburbs. In order to derive an attenuation relationship for the area, we fitted the observed data by using several functions. We found that a linear plus logarithmic model gives the best fits for the data in the Campanian region. Most of the attenuation relationships proposed up to now for the Italian Peninsula have an isotropic behavior and do not always properly describe the macroseismic attenuation. Therefore, in order to check the possible dependence of the attenuation on the azimuth of the seismic rays, we divided our data set in octants and performed for each of them the same analysis we carried out for the whole data set. The obtained results differ from octant to octant and the differences, besides being associated with the source effects, could be interpreted as probably due to the existence of lateral variations in the lithological and physical features of the crust at different depths, which could affect the patterns of attenuation.     

Combining T/P altimetric data with hydrographic data to estimate the mean dynamic topography of the North Atlantic and improve the geoid

The mean dynamic topography of the surface of the North Atlantic is estimated using an inverse model of the ocean circulation constrained by hydro-graphic and altimetric observations. In the North Atlantic, altimetric observations have no significant impact on the topography estimate because of the limited precision of available geoid height models. They have a significant impact, however, when uncertainties in the density field are increased to simulate interpolation errors in regions where hydrographic data are scarce. This result, which moderates the conclusion drawn by Ganachaud and co-workers of no significant contribution of altimetric observations to the determination of the large-scale steady circulation, reflects the simple idea that altimetric data are most useful near the surface of the ocean and in areas where the hydrography is poorly determined. One application of the present inverse estimate of the mean dynamic topography is to compute a geoid height correction over the North Atlantic which reduces the uncertainty in the geoid height expanded to spherical harmonic 40 down to a level of about 5 cm.     

Analysis of the tidal gravity observations in Three Gorges reservoir area

The comparative observations of the tidal gravity in Three Gorges reservoir area, recorded with the LCR-ET20 gravimeter from Institute of Geodesy and Geophysics, Chinese Academy of Sciences and the DZW-9 gravimeter from Institute of Seismology, China Earthquake Administration, are introduced. High-accuracy tidal gravity pa-rameters in this area are obtained, and the scale factor of the DZW-9 gravimeter is also estimated at a value of ?(756.06±0.05)×10?8 m?s?2V?1. The observed residuals of the corresponding instruments are investigated. Nu-merical results indicate that the long-term drift of the DZW-9 gravimeter appears a linear characteristic, and the observed accuracy is of the same order comparing with that of the LCR-ET20 gravimeter. The results given in the paper can provide with an effective reference model of the tidal gravity correction to the ground based and space geodesy.     

Normal gravity model of phobos

Summary The normal gravity field of Phobos defined by the sum a) of the gravitational potential of a homogeneous tri-axial ellipsoid representing the body of Phobos, b) of the potential of its centrifugal forces, c) of the constant part in the tidal-forming potential due to Mars, has been investigated. The radius-vector of the equipotential surface representing the normal model, as well as the gravity on it, have been derived. The long-term variations in the figure parameters and in gravity, due to the tidal evolution of the Mars—Phobos system, have been derived.

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