PROCESSING AND APPLICATIONS IN MICROGRAVITY SURVEYS*

An economic and precise processing system for microgravity surveys is presented. Three computer processing modes covering areal ground and underground measurements, measurements in vertical shafts, and measurements of vertical gravity gradients with a 3 m high tower are dealt with. Diagrams for manual calculation of gravity effects of prismatic walls, vertical shafts, and horizontal galleries, as well as programs for calculation of accurate terrain corrections and corrections for gravity effects of bodies with complicated ground-plan are proposed. The method of processing microgravity data is two to three times quicker than any traditional way, with maximum accuracy preserved in resulting gravity micro-anomalies. Applications from the field of mining geophysics and archaeology are included.     

CORRECTION OF ACCURATE GRAVITY SURVEYS BY CAREFULLY OBSERVED VERTICAL GRADIENTS OF GRAVITY*

Gravity surveys in western Texas with station spacing of about 400 m were complemented by carefully observed vertical gradients of gravity making use of specially designed and automated instrumentation. The presented areal surveys of 51 and 52 stations taken in relatively flat terrain are parts of a large survey of close to 1000 stations complemented by an equal number of vertical gradient measurements. Quite irregular anomalous vertical gravity gradients surpassing 10 microgal/m were often encountered. Assuming the causative density contrasts to be located not more than 10 m below ground surface then free air correction errors of ± 0.1 mgal and more must be accepted. From a practical point of view there seems to be no other way to control such unpredictable errors than to carefully observe the local variation of vertical gravity gradients with adequate equipment. Making use of very closely spaced gravity measurements to derive these anomalous features seems more costly and cumbersome.     

UNDERGROUND GRAVITY SURVEY IN ALPINE REGIONS*

An underground gravity study was carried out under extreme conditions of the Alpine regions. The lead–zinc mine Bleiberg, Carinthia, was selected as an example to show the possibilities and limitations of the subsurface gravity method. For in situ density determinations, gravity measurements were made in two vertical mine shafts passing through Triassic sedimentary rocks of the Bleiberg Unit. The main prblem in gravity data reduction in extremely rugged topography is the accurate calculation of the terrain effect on underground stations. A general discussion of the various corrections required for the gravity measurements in the mine is presented. The mean interval densities in the two shafts, in limestone, dolomite, and schists formations, were determined as 2.76 and 2.77 g/cm³, respectively, with an accuracy of better than 0.01 g/cm³ for a depth interval of 50 m. The interval densities provide valuable information about the lithological and structural changes in the shaft surroundings and also agree well with the representative hand sample densities. In the second part, the applications of subsurface horizontal gravity surveys in exploration are discussed. Since the influence of topography is less underground because of the greater distance to the surface, subsurface surveys have definite advantages over surface surveys and can be very helpful in locating anomalous density zones in the mines. An example of gravity survey with a station spacing of 10 m at a depth of about 540 m is presented.     

Line integrals of potential field data1

Information on the mass and the spatial location of an arbitrary source body can be obtained by performing suitable integrations of 3D gravity and magnetic data along an infinite straight line. No assumptions on the density/magnetization distribution or the shape and location of the source are required. For an oblique borehole, a relationship between the lower limit of the source mass and the distance to the body is obtained. The mass contrast and the magnetic moment of the source can also be estimated. For a vertical borehole, both gravity and vertical magnetic component anomalies have equal areas to the left and right of the depth axis. The particular case of a horizontal gallery not intersecting the body is also studied. If the source is intersected, a lower limit is estimated for the maximum thickness of the body along the gallery. Information on the vertical coordinate of the centre of mass of the source can also be obtained. Numerical tests with synthetic gravity data support the theoretical results.     

INDUCED GRAVITY ANOMALIES AND ROCK-BURST RISK IN COAL MINES: A CASE HISTORY1

The use of the gravity method to predict rock bursts in mines is based on the relationship between the development of a dilatancy process in the exploited rock mass and the time-dependent gravity anomalies induced by this phenomenon. The differences between successive observations of anomalies and the time behaviour of their trend amplitudes as precursors of preceding changes of rock stability are interpreted. The centres of zones of induced rock density variation are determined by computing the position of singular points of the differences between anomalies. Two gravity surveys have been carried out in the Radbod coal mine (Germany). The first survey took place at the level of the Dickebank seam (depth 1030 m), the second in the Sonnenschein seam (depth 1090 m). The observations were made with Worden and LaCoste-Romberg (D-type) gravimeters. The differences between successive anomalies were less than 100 μGal. In the case of the Dickebank seam, the position of singular points demonstrates the effect of two approaching longwalls on a previously mined-out seam and on the gallery in which the gravity observations were made. In the case of the Sonnenschein seam, the trend amplitudes show distinct variations in the formation of the approaching longwall below the edges of all previously mined-out seams. In particular, the effect of a remnant pillar has caused the largest gravity gradients. This result corresponds to the existence of a zone of rock-burst hazard known from test drilling. The computed singular points are grouped together under the remnant pillar indicating two local hazard zones. Both results, the observed development of rock instability with time and the information about the position of the disturbed rock mass relative to the mine workings, are of importance, subsurface gravity surveying can therefore be a valuable tool for predicting rock-bursts.     

Error estimation and optimization of gravity surveys1

Gravity data are often acquired over long periods of time using different instruments and various survey techniques, resulting in data sets of non-uniform accuracy. As station locations are inhomogeneously distributed, gravity values are interpolated on to a regular grid to allow further processing, such as computing horizontal or vertical gradients. Some interpolation techniques can estimate the interpolation error. Although estimation of the error due to interpolation is of importance, it is more useful to estimate the maximum gravity anomaly that may have gone undetected by a survey. This is equivalent to the determination of the maximum mass whose gravity anomaly will be undetected at any station location, given the data accuracy at each station. Assuming that the maximum density contrast present in the survey area is known or can be reasonably assumed from a knowledge of the geology, the proposed procedure is as follows: at every grid node, the maximum mass whose gravity anomaly does not disturb any of the surrounding observed gravity values by more than their accuracies is determined. A finite vertical cylinder is used as the mass model in the computations. The resulting map gives the maximum detection error and, as such, it is a worst-case scenario. Moreover, the map can be used to optimize future gravity surveys: new stations should be located at, or near, map maxima. The technique is applied to a set of gravity observations obtained from different surveys made over a period of more than 40 years in the Abitibi Greenstone Belt in eastern Canada.     

利用激光雷达测量重力波三维结构

激光雷达观测得到的密度、温度等数据被广泛应用于大气重力波研究.瑞利激光雷达可以获取激光路径上的大气密度、温度数据.对于大气中的三维波动而言,单条路径上的观测参量能提取得到的波动信息有限.本文首先以单色重力波为例,分析了利用激光雷达直接观测三维波动结构的可行性.激光雷达垂直观测即可得到重力波的垂直波长,当激光雷达以一定的天顶角斜向测量时,所得到的波长包含了重力波的垂直波长以及水平波长信息.因此,利用激光雷达同时以三个方向(垂直、向南(天顶角30°)以及向西(天顶角30°))测量,可以提取得到重力波的垂直波长和水平波长.本文利用中国科学院国家空间科学中心研制的车载532nm瑞利激光雷达的经向系统和纬向系统同时以不同的指向角观测大气重力波,对利用激光雷达获取三维波动结构的方法进行了分析研究.本文给出了北京地区激光雷达观测重力波的诸多案例,分析了30~60km高度范围内北京地区大气重力波的垂直及水平波长信息.并以2017年11月7日观测的准单色重力波为例,结合再分析资料的风场数据,分析了该重力波的水平波长,垂直波长及传播方向等信息.     

Assessment of Density‐Induced Tracer Movement in Groundwater Velocity Measurements with Point Velocity Probes (PVPs)

The concept of equivalent freshwater head was adapted to predict the conditions under which density‐driven flow would adversely impact measured groundwater velocities using point velocity probes (PVPs). Theoretically, vertical flow will result from any density contrast between the PVP tracer and the groundwater. However, laboratory testing of tracers with salinities ranging from 0 to 2000 mg NaCl/L showed that horizontal velocities could be determined with good accuracy with up to 60% of the total flow being vertical due to density effects in a gravel medium. The available data suggest that density effects are less likely to be pronounced in sandy sediments. The relative amount of vertical flow due to tracer density can be estimated from vertical and horizontal velocities measured with PVPs, or from the ratio of vertical to horizontal hydraulic gradients. The equivalent freshwater gradient produced from a given tracer salinity at 10 °C (a typical groundwater temperature at moderate latitudes) can be estimated from 7.80 × 10^?7 × (M_NaCl), where M_NaCl is the mass of NaCl added, in mg, to 1 L of site groundwater in the mixing of the tracer. Equations for other temperatures were also determined.     

Error sources and data limitations for the prediction of surface gravity: a case study using benchmarks

Gravity-based heights require gravity values at levelled benchmarks (BMs), which sometimes have to be predicted from surrounding observations. We use the Earth Gravitational Model 2008 (EGM2008) and the Australian National Gravity Database (ANGD) as examples of model and terrestrial observed data respectively to predict gravity at Australian National Levelling Network (ANLN) BMs. The aim is to quantify errors that may propagate into the predicted BM gravity values and then into gravimetric height corrections (HCs). Our results indicate that an approximate ±1 arc-min horizontal position error of the BMs causes maximum errors in EGM2008 BM gravity of ~22 mGal (~55 mm in the HC at ~2200 m elevation) and ~18 mGal for ANGD BM gravity because the values are not computed at the true location of the BM. We use RTM (residual terrain modelling) techniques to show that ~50% of EGM2008 BM gravity error in a moderately mountainous region can be accounted for by signal omission. Non-representative sampling of ANGD gravity in this region may cause errors of up to 50 mGals (~120 mm for the Helmert orthometric correction at ~2200 m elevation). For modelled gravity at BMs to be viable, levelling networks need horizontal BM positions accurate to a few metres, while RTM techniques can be used to reduce signal omission error. Unrepresentative gravity sampling in mountains can be remedied by denser and more representative re-surveys, and/or gravity can be forward modelled into regions of sparser gravity.     

Explicit formula for the geoid-quasigeoid separation

The explicit formula for the geoid-to-quasigeoid correction is derived in this paper. On comparing the geoidal height and height anomaly, this correction is found to be a function of the mean value of gravity disturbance along the plumbline within the topography. To evaluate the mean gravity disturbance, the gravity field of the Earth is decomposed into components generated by masses within the geoid, topography and atmosphere. Newton’s integration is then used for the computation of topography-and atmosphere-generated components of the mean gravity, while the combined solution for the downward continuation of gravity anomalies and Stokes’ boundary-value problem is utilized in computing the component of mean gravity disturbance generated by mass irregularities within the geoid. On application of this explicit formulism a theoretical accuracy of a few millimetres can be achieved in evaluation of the geoid-to-quasigeoid correction. However, the real accuracy could be lower due to deficiencies within the numerical methods and to errors within the input data (digital terrain and density models and gravity observations).     

微重力探测城市地下空间试验及正演模拟分析

随着国家城市快速发展,城市地下空间探测与开发利用需求加大,传统物探方法在人文活动区域受干扰因素较多,无法获取真实准确的探测数据。微重力方法相对而言受干扰因素较小,对于城市建筑物和人类活动遗迹干扰可以通过模型正演校正的方法消除,从而获取高精度重力数据,进而通过有效的反演方法,可以获得城市地下空间的隧道、采空区、空洞、塌陷区、管廊等空间位置信息。本文用地面移动式高精度重力测量仪器,进行城市探测中受影响的因素进行试验性探测与分析,并结合正演模型校正研究,微重力方法在城市地下空间探测上有不错的效果。      

Вычисление первой и второй вертикальных производных силы тяжести

Summary Following Molodensky's suggestions anomalies of the vertical gradient of gravity were used to achieve a greater accuracy in the determination of the figure of the Earth by gravimetrical methods. The existing methods of computing this quantity do not take into account inclinations of the physical surface of the Earth. Using the Laplace equation, the second derivative ∂² T/∂v ² (1) of the disturbing potentialT is expressed by the second derivatives ofT along the tangentsτ ₁ andτ ₂ to the physical surface of the Earth in mutually perpendicular planes and by the derivatives of gravity anomalies (2). The derivatives ∂² T/∂τ ₁ ² and ∂² T/∂τ ₂ ² have been determined using the Molodensky method [4] of solving his integral equation for the single layer density. In the zero approximation, the Noumerov formula [2] was obtained; however, the results obtained using this formula should be referred to the physical surface of the Earth, not to the Listing geoid. The correction of the first approximation is given by formula (16). The second vertical derivative of gravity anomalies can be determined using the expression (20).      

preliminary discussion on horizontal gravity gradient and its application to seismic gravity precursor research

In this paper, according to the synthetic gravity anomaly of a horizontally infinite cylindrical geologic body, gravity gradient in horizontal direction was calculated by potential field discrete cosine transformation in frequency domain. In the calculation, the minimum curvature method was used to extend edge lines. We found that the gravity gradient field from the potential field transformation was dependable by comparison with synthetic gravity gradient, except the data in the edges. Then, the accumulative horizontal gravity gradients before Lushan M_S7.0 earthquake were calculated for the accumulative gravity anomaly from September 2010 to October 2012. In the north-south direction, gravity gradient in Daofu-Kangding-Shimian and Markang-Lixian-Lushan exhibited a positive high value, and the strike of the high value zone was in line with the strike of Xianshuihe Faults and Markang Faults. In the east-west direction, high value zone was not as obvious as that in the north-south direction. Gravity gradients in the direction along and vertical to the strike of Longmenshan Faults were calculated by the definition of directional derivative. In the along-strike direction, high gravity gradient values appeared in Markang-Lixian areas along Markang Faults and Daofu-Kangding-Shimian areas along Xianshuihe Faults, and extremum appeared in Kangding-Shimian and the area nearby Lixian. In the direction vertical to the strike of Longmenshan fault zone, high gravity gradient values appeared in Lixian-Lushan-Kangding-Shimian areas, and the extremum appeared in the area nearby Kangding. The results indicate that gravity gradient in the direction along and vertical to the strike of faults can better show the relative gravity change on the two sides of faults. Lushan M_S7.0 earthquake is located at the transition zone between the two high value zones of gravity gradient. The total horizontal gravity gradient shows that the location and strike of the high value zone are basically consistent with regional faults, and the extremums of total horizontal gravity gradient appeared nearby Lixian, Kangding and Shimian.     

Nighttime E region plasma irregularities over an equatorial station Trivandrum

In situ measurements of electron density were made over Trivandrum (8.5°N, 76.9°E) during nighttime to study E-region plasma density irregularities. Irregularities, with vertical scale sizes from a few km to 15 cm, were detected during rocket ascent and descent. Electron density profiles during ascent and descent of an earlier nighttime rocket flight from Trivandrum are also presented. Some of the important results are as follows: (i) horizontal gradients in electron density exist in 110–120 km region with horizontal scale size of at least 40 km, (ii) based on the presence/absence of electron density structures during ascent and descent of both flights, the horizontal distance over which the gradient drift instability operates is found to be at least 80 km and 90 km, for both the flights, (iii) observed irregularities in regions of negative density gradient are suggested to be produced through the gradient drift instability (GDI) driven by vertical polarization electric field as well as by electric field produced through wind shears and those in positive gradient regions by wind driven GDI, (iv) largest irregularity amplitude (≈30%) was associated with steepest gradients and so was the presence of smallest vertical scale sizes (12 m to 15 cm), which were absent at other altitudes, (v) the spectral index of irregularities was in the range of ?2.2±0.2 for large scales (few kilometers>λ>50 m), ?3.25±0.25 for medium scales (50 m>λ>10 m) and ?2.6±0.1 for smaller scales (10 m>λ>1 m) and (vi) irregularities in large and medium scales are expected to be produced directly through GDI and the small and sum-meter scales through non-linear GDI.     

An objective algorithm for reconstructing the three-dimensional ocean temperature field based on Argo profiles and SST data

While global oceanic surface information with large-scale, real-time, high-resolution data is collected by satellite remote sensing instrumentation, three-dimensional (3D) observations are usually obtained from in situ measurements, but with minimal coverage and spatial resolution. To meet the needs of 3D ocean investigations, we have developed a new algorithm to reconstruct the 3D ocean temperature field based on the Array for Real-time Geostrophic Oceanography (Argo) profiles and sea surface temperature (SST) data. The Argo temperature profiles are first optimally fitted to generate a series of temperature functions of depth, with the vertical temperature structure represented continuously. By calculating the derivatives of the fitted functions, the calculation of the vertical temperature gradient of the Argo profiles at an arbitrary depth is accomplished. A gridded 3D temperature gradient field is then found by applying inverse distance weighting interpolation in the horizontal direction. Combined with the processed SST, the 3D temperature field reconstruction is realized below the surface using the gridded temperature gradient. Finally, to confirm the effectiveness of the algorithm, an experiment in the Pacific Ocean south of Japan is conducted, for which a 3D temperature field is generated. Compared with other similar gridded products, the reconstructed 3D temperature field derived by the proposed algorithm achieves satisfactory accuracy, with correlation coefficients of 0.99 obtained, including a higher spatial resolution (0.25° × 0.25°), resulting in the capture of smaller-scale characteristics. Finally, both the accuracy and the superiority of the algorithm are validated.     

Transcontinental tidal transect: European Atlantic coast-Southern Siberia-Russian Pacific coast

The paper presents results of measurements with digital tidal LaCoste-Romberg gravimeters on the European Atlantic coast-Southern Siberia-Russian Pacific coast transect in 1995–2005. The transect includes four West European (Chizé, Ménesplet, Mordelles, and Wikle), two South Siberian (Klyuchi and Talaya), and two Far Eastern (Zabakalskoe and Yuzhno-Sakhalinsk) stations. Gravimetric measurements at the Talaya station (SW Baikal rift zone) are supplemented by long-term laser extensometer observations. The position of the stations within the rectangle (45°–55°N, 0.4°–142°E) allows one to assess existing tidal strain models (WD93 and DDW99) and various ocean tide models (SCW80, CSR3, FES95, ORI96, CSR4, FES02, GOT00, NAO99, and TPX06). Data of intracontinental stations (with a small ocean effect at distances of 2000–3000 km) agree well with the DDW99 tidal strain model (with regard to the mantle viscosity). The uncertainty of digital tidal gravity measurements is 0.25%. Results of laser extensometer measurements are at the same accuracy level. Then, the Love and Shida numbers calculated at midlatitudes of the intracontinental zone of Eurasia from combined data are h = 0.6077 ± 0.0008, k = 0.3014 ± 0.0001, and l = 0.0839 ± 0.0001. The analysis of results of Pacific and Atlantic stations located at distances of 30–300 km from the ocean showed that the FES02, CSR4, GOT00, NAO99, and TPX06 ocean tide models are preferable.     

Full gravity gradient tensors from vertical gravity by cosine transform

We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ??Y?? type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.     

A study of the upward continuation of gravity data from a plane surface

Summary A summation method of upward continuation of gravity data has been considered under the assumption that observations are available at regular intervals. The upward continued value has been obtained as the sum of products of individual gravity values and corresponding theoretical coefficients. Besides the usual parameter involving horizontal and vertical distances, the theoretical coefficients have been generalized to be dependent also on i) the order of a low order polynomial assumed to represent the gravity variation around a grid point and ii) the weights assigned to the gravity values at the nearest four grid points used for least-squares determination of the polynomial. Since the observations in practical cases are available over a finite area only, the effect of truncation of the area of the integration has also been discussed separately. The method has been programmed and tested on a three-dimensional model, whose true gravity effects were computed at various levels over a finite area. Upward continued values have been computed under various assumptions about the gravity field in the outside region. Comparisons of these results with the true values indicate that the truncation effect becomes increasingly important for larger values of the ratio of elevation to grid separation and/or when the gravity field is not a local one. It has also been found that the greater is the above ratio, the less important is the effect of weights on the theoretical coefficients and practically vanishes(<10 ^–4 ) when the ratio is greater than5.0.     

Discussion of Mean Gravity Along the Plumbline

According to the definition of the orthometric height, the mean value of gravity along the plumbline between the Earth's surface and the geoid is defined in an integral sense. In Helmert's (1890) definition of the orthometric height, a linear change of the gravity with depth is assumed. The mean gravity is determined so that the observed gravity at the Earth's surface is reduced to the approximate mid-point of the plumbline using Poincaré-Prey's gravity gradient. Niethammer (1932) and later Mader (1954) took into account the mean value of the gravimetric terrain correction within the topography considering the constant topographical density distribution along the plumbline (for more details see Heiskanen and Moritz, 1967). Vaníek et al. (1995) included the effect of the lateral variation of the topographical density into the definition of Helmert's orthometric height. Recently, Hwang and Hsiao (2003) discussed the influence of the vertical gradient of disturbing gravity on the orthometric heights. In this paper, the mean integral value of gravity along the plumbline within the topography is defined so that the actual topographical density distribution and the change of the disturbing gravity with depth are taken into account. Based on the definition of the mean gravity, the relation between the orthometric and normal heights is discussed.     

重力剖面和激电测深联合勘测在涡河断裂研究中的应用

为查明涡河断裂的位置、性质等参数,选择重力剖面和激电测深联合勘测方法,对指定区域进行物探勘测工作。结果表明:由密度差异引起的重力异常位置和岩石电阻率、极化率异常位置基本吻合,说明以重力剖面和激电测深为手段的联合勘测是查找断裂的有效方法。