Estimate of the effect of vibrations on quartz gravity meters

Summary Relations for computing the minimum amplitudes of ground vibrations which generate oscillations of the gravity meter reading beam at the limit of the resolution of the optical system, have been derived. The minimum amplitudes in the ground displacement period range of0.1 to10 s, for the assumed values of the fundamental parameters of quartz gravity meters (i.e. the periods and damping constants of the pendulum and the mechanico-optical magnification of the pendulum deflections), range from tenths of a micrometre to units of micrometres. Larger displacement amplitudes, due to, e.g., earthquakes and traffic, disrupt gravity measurements.     

Behaviour of quartz gravity meters under high frequency vertical motion

Summary Tests on the vertical vibrating table in the frequency range of70–110 Hz indicate that quartz gravity meters are10–100 times more sensitive at some frequencies than under low-frequency excitation. At high frequencies, the reading beam is at rest and deflected from the correct position. Slow fluctuations of amplitude and frequency near resonance could cause slow irregular motion of the beam with absence of low-frequency ground motion of sufficient intensity.

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unmauaum a mua um¶rt; ¶rt;uana amm 70–110u mam, m a m ammaaum 10–100 a mum nu uamm au. u amm au u a¶rt;um n m mu m nu. ¶rt; auauu anum¶rt; u amm au uu aa m am uamm u ua ¶rt;a mmmm uamm au n ¶rt;mam umumu.

     

A more precise mechanical theory of askania gravity meters

Summary The measuring systems of Askania gravity meters are assumed to have 3 degrees of freedom. The axis of rotation of the beam can also be displaced in the vertical and horizontal directions. The equations of equilibrium of this system (25)–(27) were used to derive the expressions for the effect of displacing the calibration ball, for the scale equation and for the sensitivity of the gravity meter. Equations (33), (34) and (39) refer to gravity meters with a photoelectric transducer, and Eqs (46), (47) and (49) to gravity meters with a capacitive transducer.

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uum umaum au n¶rt;naam 3 mnu ¶rt;. au aa m m nam mua uuma anau. au au m um (25)–(27) ¶rt; au ¶rt; ¶rt;mu nu au aua, ¶rt; aua a u ¶rt; mummuauma. aum mmuu mm m au (33), (34), (39), ¶rt;aum m mm au (46), (47), (49).

     

Sensitivity of the Sharpe and Worden gravity meters to vertical motion

Summary Using the least-squares method the constants of both gravity meters — seismometers — were derived from the amplitude responses, observed under vertical motion on a vibrating table in the 0.3–30 s range. The values of the seismogram amplitudes, above which seismic waves cause an observable displacement of the gravity meter reading beam, were determined for the SKD and Press-Ewing station seismographs.     

Direct BEM for high-resolution global gravity field modelling

The paper presents a high-resolution global gravity field modelling by the boundary element method (BEM). A direct BEM formulation for the Laplace equation is applied to get a numerical solution of the linearized fixed gravimetric boundary-value problem. The numerical scheme uses the collocation method with linear basis functions. It involves a discretization of the complicated Earth’s surface, which is considered as a fixed boundary. Here 3D positions of collocation points are simulated from the DNSC08 mean sea surface at oceans and from the SRTM30PLUS_V5.0 global topography model added to EGM96 on lands. High-performance computations together with an elimination of the far zones’ interactions allow a very refined integration over the all Earth’s surface with a resolution up to 0.1 deg. Inaccuracy of the approximate coarse solutions used for the elimination of the far zones’ interactions leads to a long-wavelength error surface included in the obtained numerical solution. This paper introduces an iterative procedure how to reduce such long-wavelength error surface. Surface gravity disturbances as oblique derivative boundary conditions are generated from the EGM2008 geopotential model. Numerical experiments demonstrate how the iterative procedure tends to the final numerical solutions that are converging to EGM2008. Finally the input surface gravity disturbances at oceans are replaced by real data obtained from the DNSC08 altimetryderived gravity data. The ITG-GRACE03S satellite geopotential model up to degree 180 is used to eliminate far zones’ interactions. The final high-resolution global gravity field model with the resolution 0.1 deg is compared with EGM2008.     

地震重力观测技术的新发展方向:绝对重力与重力梯度一体化观测

高精度绝对重力与重力梯度一体化和阵列式观测可有效提高不同深度重力场源体的识别精度。本文基于中国地震局发布的《中国地球物理站网（重力）规划（2020—2030）》中绝对重力观测技术的不足和发展方向,提出了绝对重力与重力梯度一体化的观测技术思路。在监测中发现,强震孕育过程中壳—幔热物质运移引起的微重力变化信号,有利于提升破坏性地震的中、短期和临震预测能力。有必要进一步拓展重力站网绝对重力控制能力等方面的应用,为我国专业地震台站探索重力观测技术新发展方向。      

Excel modelling of hydrological systems

This short paper describes the use of Excel spreadsheet Solver facility for deriving estimates in a solute mixing model equation with more than one unknown.     

基于单元细分H-自适应有限元全张量重力梯度正演

在重力梯度各阶张量正演中,难于求取复杂地质体的解析式,转而利用已知解析解的简单规则几何形体近似剖分地质体,其会引起较大的几何拟合误差.本文首先从全张量重力梯度解析公式出发结合等参变换基于有限元分析给出了满足地下复杂地质体正演的型函数,引入体积分的误差指示器用以估计全张量重力梯度误差,提出了适用于全张量重力梯度正演的自适应计算的策略及迭代算法,数值算例证明了本文方法的正确性和有效性.     

The effect of the magnetic field on the accuracy of measurements with Worden and Sharpe gravity meters

Summary The effect of an additional homogeneous magnetic field with an intensity of 0–4.5 Oe on the Worden quartz gravity meter No. 961 and on Sharpe quartz gravity meters Nos 173 and 174 was tested. Whereas no effect was observed with the Worden gravity meter, the magnetic field had a measurable effect on both the Sharpe gravity meters. The largest deviation of the reading beam is caused by the horizontal component of the magnetic field which acts in the plane of oscillation of the gravity-meter arm. The Sharpe gravity meter No. 173 is considerably sensitive; a field of 0.2 Oe intensity, corresponding to the magnitude of the horizontal component of the geomagnetic field in mid-latitudes, causes an error in the measurement of gravity of as much as 0.08 mGal. With a view to the different behaviours of the individual quartz gravity meters of the same type in a magnetic field, it should prove expedient to carry out check measurements with all gravity meters and, with regard to the sensitivity of the gravity meter to the magnetic field and the required accuracy of the gravity determination, take into account this perturbing factor in field measurements, as well as laboratory tests of gravity meters.     

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

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

A comparison of satellite systems for gravity field measurements

A detailed and accurate Earth gravity field model is important both to geophysical progress and to the precise tracking necessary for interpretation of geophysical experiments. Various satellite techniques which may be used to determine the Earth's gravity field are compared and their ability to recover the long wavelength and short wavelength features of the field are described.A high-low configuration satellite-to-satellite tracking mission is recommended for the determination of the long wavelength portion of the gravity field. Satellite altimetry and satellite gradiometry experiments are recommended for determination of the short wavelength portion of the gravity field.     

On integral approach to regional gravity field modelling from satellite gradiometric data

Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case, satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential (geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies show that by integrating T _zz with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly, the errors of the recovered geoids from T _xz,yz and T _{xx-yy, 2xy} are 13 and 21 cm, respectively.     

Transient analysis of concrete gravity dam-reservoir systems by Wavenumber-TD approach

The Wavenumber approach was initially introduced as an ideal substitute for the rigorous type of analysis which had been the basis of extensive studies in seismic analysis of concrete gravity dams. The former technique is formulated in the context of pure finite element programming, while the latter relies heavily on a two-dimensional semi-infinite fluid element (i.e., hyper-element). Recently, a variation of Wavenumber method was proposed which was referred to as Wavenumber-TD approach. The approximation to the original technique improves its realm of application and allows it to be carried out in time domain as well as frequency domain. In that study, the formulation was examined for harmonic type of excitation which proved to be promising. Herein, this will be evaluated for its real intended application, which is transient analysis of dam-reservoir systems. For this aim, the prepared special purpose finite element program is modified and the analysis of Pine Flat dam is considered as a typical example. Several models are considered with different values of normalized reservoir length. In each case, the reservoir truncation surface is treated by Wavenumber-TD and the extensively utilized Sommerfeld conditions. The dynamic loading considered is the S69E component of Taft earthquake record. Furthermore, two types of reservoir bottom condition of full reflective as well as absorptive, are adopted. Overall, this will allow for a thorough examination and evaluation of Wavenumber-TD approach in regard to its effectiveness.     

The global distribution of gravity wave energy in the lower stratosphere derived from GPS data and gravity wave modelling: Attempt and challenges

Five years of global temperatures retrieved from radio occultations measured by Champ (Challenging Minisatellite Payload) and SAC-C (Satelite de Aplicaciones Cientificas-C) are analyzed for gravity waves (GWs). In order to separate GWs from other atmospheric variations, a high-pass filter was applied on the vertical profile. Resulting temperature fluctuations correspond to vertical wavelengths between 400 m (instrumental resolution) and 10 km (limit of the high-pass filter). The temperature fluctuations can be converted into GW potential energy, but for comparison with parameterization schemes GW momentum flux is required. We therefore used representative values for the vertical and horizontal wavelength to infer GW momentum flux from the GPS measurements. The vertical wavelength value is determined by high-pass filtering, the horizontal wavelength is adopted from a latitude-dependent climatology. The obtained momentum flux distributions agree well, both in global distribution and in absolute values, with simulations using the Warner and McIntyre parameterization (WM) scheme. However, discrepancies are found in the annual cycle. Online simulations, implementing the WM scheme in the mechanistic COMMA-LIM (Cologne Model of the Middle Atmosphere—Leipzig Institute for Meteorology) general circulation model (GCM), do not converge, demonstrating that a good representation of GWs in a GCM requires both a realistic launch distribution and an adequate representation of GW breaking and momentum transfer.     

Numerical modelling of coupled surface and subsurface flow systems

This paper presents and compares several numerical solutions of the coupled system of Navier–Stokes and Darcy equations. The schemes are based on combinations of the finite element method and the discontinuous Galerkin method. Accuracy and robustness of the methods are investigated for heterogeneous porous media. The importance of local mass conservation for filtration problems is also discussed.     

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.     

基于激光干涉法的地表重力垂直梯度测量系统设计及试验

基于激光干涉法对新型地表重力垂直梯度测量系统进行了研究并初步构建了原理样机． 该测量系统利用双光路干涉测量法, 获取垂直向间距为50 cm且同步自由下落的两个落体相对于参考点的时间和位移信息, 并通过差分运算得到该测点的重力垂直梯度值． 在系统设计过程中, 主要解决了双落体自由下落的同步自动控制和双干涉测量光路的垂直性调节问题． 试验结果表明, 本套测量系统可以获取双落体同步自由下落运动时的干涉条纹信号, 并完成重力垂直梯度测量, 且梯度测量精度优于100 E．      

The identifiability analysis for setting up measuring campaigns in integrated water quality modelling

Identifiability analysis enables the quantification of the number of model parameters that can be assessed by calibration with respect to a data set. Such a methodology is based on the appraisal of sensitivity coefficients of the model parameters by means of Monte Carlo runs. By employing the Fisher Information Matrix, the methodology enables one to gain insights with respect to the number of model parameters that can be reliably assessed. The paper presents a study where identifiability analysis is used as a tool for setting up measuring campaigns for integrated water quality modelling. Particularly, by means of the identifiability analysis, the information about the location and the number of the monitoring stations in the integrated system required for assessing a specific group of model parameters were gained. The analysis has been applied to a real, partially urbanised, catchment containing two sewer systems, two wastewater treatment plants and a river. Several scenarios of measuring campaigns have been considered; each scenario was characterised by different monitoring station locations for the gathering of quantity and quality data. The results enabled us to assess the maximum number of model parameters quantifiable for each scenario i.e. for each data set. The methodology resulted to be a powerful tool for designing measuring campaign for integrated water quality modelling. Indeed, the crucial cross sections throughout the integrated wastewater system were detected optimizing both human and economic efforts in the gathering of field data. Further, a connection between the data set and the number of model parameters effectively assessable has been established leading to much more reliable model results.     

Strategies for finite element modelling of three dimensional hydrodynamic systems

The simulation of a system composed entirely of three dimensional elements is computationally very expensive and little practical analysis has been undertaken. In an effort to reduce cost the author in a previous paper presented a simplified three dimensional model that used the hydrostatic pressure approximation to eliminate the vertical momentum equation and a transformation of the basic equations to directly solve for the free surface profile. This paper will examine approaches to the reduction of simulation costs within the framework of the original approach and modifications to the basic formulation to improve the performance of the model when the flow bath is over system with variable bed elevations. Examples will be presented to demonstrate the effectiveness of these modifications.     

Two‐dimensional modelling of ice cover effects for the dynamic analysis of concrete gravity dams

A two‐dimensional numerical model for determining the effects of the presence of an ice cover on the dynamic behaviour of large gravity dams is presented. Analytical predictions are compared to results obtained during a series of extensive dynamic tests on a large gravity dam. Data were obtained during summer and severe winter conditions to investigate the dynamic interactions between the dam, foundation, reservoir and the ice cover. The analysis includes ice‐reservoir interaction as well as the effects of water compressibility, flexible foundation and reservoir bottom absorption. Good agreement with the experimental findings is obtained. Copyright © 2002 John Wiley & Sons, Ltd.