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.     

Some critical factors for engineering and environmental microgravity investigations

The gravity method is one of the geophysical tools used for engineering and environmental investigations where the detection of cavities, karst phenomena, subsoil irregularities, or landfills is essential. In many cases, deep or small-scale heterogeneities generating low-amplitude anomalies have to be detected and the reliability of further interpretation requires highly accurate measurements, carefully corrected for any quantifiable disturbing effects. The purpose of this study is to investigate the factors likely to limit measurement quality and how to make improvements.Calibrations of a Scintrex gravimeter were made between French relative and absolute base stations, and the relative uncertainties on the calibration factors were estimated for these links. Ranging from 10⁻³, for calibration on an old gravity net, to 10⁻⁴, for a high amplitude absolute base line, this accuracy will be generally sufficient for microgravity surveys.Continuous gravity recordings of Scintrex gravimeters, installed at the same stable site, enabled the estimation of the stability and accuracy of the instruments and revealed that some of the time variations of g measurements, such as instrumental drift, tidal effects and seismic noise, are not entirely removed by standard processing procedures. The accuracy of corrected gravity measurements is mainly limited by inadequate corrections of tidal effects and by a poor estimation of ocean loading effects. In comparison with residual defaults in tidal corrections, instrumental and seismic noises are taken more properly into account by statistical data processing.In field operation, residual tidal effects are generally integrated into an experimental terrain drift estimated on the basis of frequent repeated measurements. A differential gravity approach, based on a fixed gravimeter reference whose recordings are used to correct measurements made with a mobile gravimeter, has also been investigated at a test site. Compared to standard processing, this method can help improve repeatability of gravity measurements.Microgravity surveys in the urban environment require effective and accurate consideration of the effects of infrastructures, nearby buildings and basements, as well as those of topography, in the vicinity of a gravity station. Correction procedures, applied at the same experimental site, where gravity points are located close to buildings, walls and basement slope, appear to have almost totally eliminated these disturbances.     

Microgravity and height changes caused by volcanic activity: Four

Microgravity measurements and levelling surveys on volcanoes are not always easy to make, but are useful for studying volcanic processes quantitatively. Gravity changes associated with volcanic activity are not always significant. Precision of microgravity measurements depend critically on the procedures adopted, and those applied in the present paper are described. Levelling technique is now orthodox, and some empirical laws relating ground deformation to volcanic activity are deduced from the accumulated data. Gravity changes occur at the same time and places as ground deformations. The relationship between microgravity and height changes are discussed from the standpoint of analyzing the data obtained on volcanoes. The observational results obtained on four volcanoes in Japan are separately analyzed because each volcano exhibits different patterns of gravity changes and deformations. During the 1977–1982 activity of Usu volcano, deformation was accompanied by microgravity changes frequently observed at a particular benchmark at the base of the volcano for about five years. The gravity changes prove to be not a direct effect of magma movements but to be caused by the deformations of ground strata and aquifers around the benchmark. The 1983 eruption of Miyakejima volcano was associated with local gravity changes around the eruptive fissures due to magma intrusion which was approximately modelled. Similarly the 1986 eruption of Ooshima volcano caused gravity changes on the volcano, but these were poorly correlated with elevation changes and their origins were not uniquely interpreted. To detect gravity changes associated with the activity of Sakurajima volcano, an equigravity point was selected at the north of the volcano besides the gravity points on and around the volcano itself. The probable gradual accumulation of magmas beneath the volcano for eight years is substantiated by observed microgravity and elevation changes.     

AUTOMATIC INTERPRETATION OF GRAVITY GRADIOMETRIC DATA IN TWO DIMENSIONS: VERTICAL GRADIENT1

The magnetic and gravity field produced by a given homogeneous source are related through Poisson's equation. Starting from this consideration, it is shown that some 2D interpretation tools, widely applied in the analysis of aeromagnetic data, can also be used for the interpretation of gravity gradiometric data (vertical gradient). This paper deals specifically with the Werner deconvolution, analytic signal and Euler's equation methods. After a short outline of the mathematical development, synthesized examples have been used to discuss the efficiency and limits of these interpretation methods. These tools could be applied directly to airborne gravity gradiometric data as well as ground gravity surveys after transformation of the Bouguer anomalies into vertical gradient anomalies. An example is given of the application of the Werner deconvolution and Euler's equation methods to a microgravity survey.     

重力球面外部校正技术

山区重力勘探中，重力外部校正是重力勘探料处理和解释的前提，其内容包括地形校正、中间层校正等。本文在分析常规外部校正方法的基础上，提出了一套适合于山区重力勘探的球面地形校正及有限球壳中间层校正方法，并严格推出了球面地形校正公式。对中国南方ZJJ地区重力资料处理结果表明，该方法提高了地形校正的精度，使山区重力资料品质达到或接近平原区的水平。     

Near-station topographic masses correction for high-accuracy gravimetric prospecting

The expanding role of gravity prospecting in mineral and hydrocarbon exploration as well as seismic and volcanic risk studies will be related to its ability to provide high-resolution anomalies. To achieve this goal it is necessary to consider the errors resulting from the topographic corrections, in particular near-station effects. Such errors are relevant not only for severe topographies but also for relatively flat surfaces involving microgravity applications and large-scale surveys.
Indeed, the errors introduced by low-resolution digital elevation models can be of the same order of magnitude as the anomalies of interest. This basic fact is demonstrated by tests on synthetic models. The results of this analysis are summarized in an intuitive graph that can be used to estimate what near-station topographic resolution is necessary for a specific survey. For the Vulcano Island test site (in Southern Italy), we also compare results obtained using three different representations of the topographic surface with different horizontal resolutions and vertical precisions: one from existing photogrammetric data, the second from a digitized map and the third from a very high-resolution laser scanning system. Among the three methods, laser scanning is shown to obtain the highest resolution topographic reconstructions in the shortest time. Some weaknesses of the laser scanning methodology are discussed and we suggest ways of overcoming them.     

Interpretation of vertical gravity and magnetic profiles

Summary Methods have been developed by quantitatively interpreting gravity and magnetic data in vertical bore-holes or shafts for geological bodies that can be approximated by spheres and cylinders. Master diagrams that can be directly used by the interpreter are provided.     

Allowance for the vertical gradient in an airborne gravity survey

When processing the results of an airborne gravity survey flown in the Arctic at flight heights of 2000 to 3000 m, the authors encountered conditions, when the values of the free-air anomaly of gravity exceeded the values taken from the anomaly map, with a trend towards “heavier” values. The formula for calculation of the vertical gradient as a function of the latitude of the locality has been refined. The tentative calculations reported in the paper also indicate that a free-air gravity anomaly above the mountainous areas will contain additional positive systematic components, since only the effect of the vertical gradient of the normal gravity field is taken into account here, and the flight’s height during an airborne gravity survey, above a mountainous area, should be held constant, otherwise it would be necessary to take into account additional systematic biases, obtained in different flights, which are caused by the different values of the vertical gradient at different heights.     

Tidal loading along a profile Europe-East Africa-South Asia-Australia and the Pacific Ocean

A knowledge of the vertical component of the oceanic tidal load to a precision of at least one microgal is essential for the geophysical exploitation of the high-precision absolute and differential gravity measurements which are being made at ground level and in deep boreholes. On the other hand the ocean load and attraction signal contained in Earth tide gravity measurements can be extracted with a precision which is sufficient to characterize the behaviour of the oceanic tides in different basins and this provides a check of the validity of the presently proposed cotidal maps. The tidal gravity profiles made since 1971 from Europe to Polynesia, through East Africa, Asia and Australia, with correctly intercalibrated gravimeters, comprise information from 91 tidal gravity stations which is used in this paper with this goal in mind.A discussion of all possible sources of error is presented which shows that at the level of 0.5 μgal the observed effects cannot be ascribed to computational or instrumental errors. Cotidal maps which generate computed loads in agreement with the Earth tide gravity measurements over a sufficiently broad area can be used with confidence as a working standard to apply tidal corrections to high-precision measurements made by using new techniques in geodesy, geophysics and geodynamics, satellite altimetry, very long baseline interferometry, Moon and satellite laser ranging and absolute gravity. The recent cotidal maps calculated by Schwiderski for satellite altimetry reductions agree very well with land-based gravimeter observations of the diurnal components of the tides (O₁, K₁ and P₁ waves) but his semi-diurnal component maps (M₂, S₂ and N₂ waves) strangely appear less satisfactory in some large areas. The maps of Hendershott and Parke give good results in several large areas but not everywhere. More detailed investigations are needed not only for several coastal stations but mainly in the Himalayas.     

Combined discrete and continuous gravity observations at Mount Etna

Systematic investigation of discrete gravity measurements has continued at Mount Etna since 1986. The network now covers an area of 400 km² with about 70 stations 0.5–3 km apart. Mass redistributions occurring at depths ranging between about 8 km below sea level and a few hundred metres below the surface (magma level changes within the shallower parts of the feeding conduits) have been identified from these data. Conventional (discrete) microgravity monitoring on a network of stations furnishes only instantaneous states of the mass distribution at continuously active systems. In order to obtain information on the rate at which the volcanic processes (and thus mass transfers) occur, three stations for continuously recording gravity where installed on Mount Etna in 1998. A 16-month long sequence from one of the continuously running stations (PDN, located 2 km from the active northeast crater at the summit of Etna volcano) is presented. After removing the effects of Earth Tide and tilt, the correlation of the residual gravity sequence with simultaneous recordings of meteorological parameters acquired at the same station was analysed. Once the meteorological effects have also been removed, continuous gravity changes are within 10 μGal of gravity changes measured using conventional microgravity observations at sites very close to the continuous station. This example shows how discrete and continuous gravity observations can be used together at active volcanoes to get a fuller and more accurate picture of the spatial and temporal characteristics of volcanic processes.     

断裂构造精细解释技术——三方向小子域滤波

针对利用重磁场资料解决地质构造的精细划分和解释问题,提出三方向小子域滤波方法. 根据直立岩脉重力异常曲线特征和DCT理论,分析了直立岩脉重力异常π/２相位偏移技术,给出了突出三方向直立岩脉特征的平面重力异常及其π/2相移的DCT转换的理论公式. 模型实验证实,经过坐标变换后的偏移结果,其异常梯度最大值的水平位置与铅垂台阶断面在地面上的投影位置相一致;利用传统的小子域滤波分别检测每个方向偏移处理结果中的梯级带,突出三方向的异常分界特征,从而实现三方向小子域滤波的数值计算. 在应用中表明,传统的小子域滤波只能识别出黑龙江虎林盆地11条断裂带,而三方向小子域滤波法检测出33条断裂,这说明三方向小子域滤波法大大增强了对平面断裂水平位置信息的识别.     

Variations of the earth's gravity field due to the free nutation

Summary Expressions for the time variation of gravity and for deformations of equipotential surfaces due to the free nutation of the Earth have been derived. The possibility has been shown of determining the polar motion by means of accurate gravity observations under the assumption that the other effects, particularly tidal, may be expressed with sufficient accuracy theoretically. The necessity of introducing gravity corrections due to the polar motion has been pointed out in investigating the secular variations of gravity and in accurate gravity measurements (standard error of the order of 0.01 mgal and less), in general.     

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.     

Three-Dimensional Gravity Modeling In All Space

We review available analytical algorithms for the gravity effect and gravity gradients especially the vertical gravity gradient due to a right rectangular prism, a right polygonal prism, and a polyhedron. The emphasis is placed on an investigation of validity, consistency, and especially singularities of different algorithms, which have been traditionally proposed for calculation of the gravity effect on ground (or outside anomalous bodies), when they are applied to all points in space. The rounding error due to the computer floating point precision is estimated. The gravity effect and vertical gradient of gravity in three dimensions caused by a cubic model are calculated by different types of algorithms. The reliability of algorithms for the calculation of gravity of a right polygonal prism and a polyhedron is further verified by using a regular polygonal prism approximating a vertical cylinder and a regular polyhedron approximating a sphere, respectively. By highlighting Haáz-Jung-Plouff and Okabe-Steiner-Zilahi-Sebess' formulae for a right rectangular prism, Plouff's algorithm for a right polygonal prism, and Gouml;tze and Lahmeyer's algorithm for a polyhedron and removing their singularities, we demonstrate that these formulae and algorithms can be used to model the gravity anomaly and its vertical gradient at all possible computation positions.     

Free core nutation period inferred from the gravity measurements at Józefosław

The Free Core Nutation (FCN) is an important eigenmode which affects both Earth rotation and body tide. The FCN parameters, the resonance period and the quality factor are important for understanding the dynamics of the Earth at nearly diurnal periods. Those parameters are usually estimated either from the Very Long Baseline Interferometry (VLBI) observations of nutation, or from the tidal gravity measurements. In this paper we investigate the determination of the FCN parameters from gravity records covering a period of more than three years, collected with the use of a LaCoste&Romberg Earth Tide no. 26 gravimeter, located at Józefos?aw observatory near Warsaw. From the resonant enhancements of gravimetric factors and phases of diurnal tidal gravity waves, we could infer the FCN period to be equal to 430 sidereal days. This result is in very good agreement with previous gravimetric and VLBI nutation results, confirming the discrepancy in the dynamic flattening of the outer liquid core from its theoretical value based on the hydrostatic equilibrium assumption. The estimated FCN quality factor (Q ≈ 1300) is considerably smaller than the VLBI nutation result, which confirms that the local gravity measurements are more sensitive than VLBI global analyses to site-dependent phenomena (such as atmospheric and indirect ocean tidal effects). We also investigated the importance of gravimetric corrections in the FCN analysis, including numerical tests and simulations. This allowed us to estimate the uncertainty of FCN parameters due to improper or incomplete set of environmental corrections. We took also into account the impact of gravimetric factor errors and tidal wave selection on estimated FCN parameters. We demonstrated that despite relatively noisy measurements due to unfavorable gravimeter location, we were able to obtain very good results in case when proper correction and tidal wave selection were applied.     

A refined method of recovering potential coefficients from surface gravity data

Summary A new method for computing the potential coefficients of the Earth's external gravity field is presented. The gravimetric boundary-value problem with a free boundary is reduced to the problem with a fixed known telluroid. The main idea of the derivation consists in a continuation of the quantities from the physical surface to the telluroid by means of Taylor's series expansion in such a way that the terms whose magnitudes are comparable with the accuracy of today's gravity measurements are retained. Thus not only linear, but also non-linear terms are taken into account. Explicitly, the terms up to the order of the third power of the Earth's flattening are retained. The non-linear boundary-value problem on the telluroid is solved by an iteration procedure with successive approximations. In each iteration step the solution of the non-linear problem is estimated by the solutions of two linear problems utilizing the fact that the non-linear boundary condition may be split into two parts; the linear spherical approximation of the gravity anomaly whose magnitude is significantly greater than the others and the non-linear ellipsoidal corrections. Finally, in order to solve the problem in terms of spherical harmonics, the transform method composed of the fast Fourier transform and Gauss Legendre quadrature is theoretically outlined. Immediate data processing of gravity data measured on the physical Earth's surface without any continuation of gravity measurements to a reference level surface belongs to the main advantage of the presented method. This implies that no preliminary data handling is needed and that the error data propagation is, consequently, maximally suppressed.     

Modeling of two-phase flow in membranes and porous media in microgravity as applied to plant irrigation in space

In traditional applications in soil physics it is convention to scale porous media properties, such as hydraulic conductivity, soil water diffusivity, and capillary head, with the gravitational acceleration. In addition, the Richards equation for water flux in partially saturated porous media also contains a gravity term. With the plans to develop plant habitats in space, such as in the International Space Station, it becomes necessary to evaluate these properties and this equation under conditions of microgravitational acceleration. This article develops models for microgravity steady state two-phase flow, as found in irrigation systems, that addresses critical design issues. Conventional dimensionless groups in two-phase mathematical models are scaled with gravity, which must be assigned a value of zero for microgravity modeling. The use of these conventional solutions in microgravity, therefore, is not possible. This article therefore introduces new dimensionless groups for two-phase models. The microgravity models introduced here determined that in addition to porous media properties, important design factors for microgravity systems include applied water potential and the ratio of inner to outer radii for cylindrical and spherical porous media systems.     

Application of GPS data for tidal correction of marine gravity measurements

The possibility of applying the global positioning system (GPS) data for calculating the corrections for variations in the sea level to the results of a gravity survey and for improving the accuracy of marine gravity measurements is discussed.     

Calibration shifts in Scintrex CG‐3M gravimeters with an application to detection of microgravity changes at Iwo‐tou caldera,Japan

Calibration shift seriously influences gravity values measured using Scintrex CG‐3M gravimeters. We calibrated three Scintrex CG‐3M gravimeters three times (1999, 2003 and 2006) over eight years, using a calibration line with a gravity difference of 1.38 Gal. The scale factor correction coefficients (calibration factors) obtained here range from 0.9998–1.0005. The calibration factors vary with time by 89 ppm, ?102 ppm and ?126 ppm between the 1999–2003 surveys. The calibration shifts of two of the three gravimeters decreased to about 20 ppm or less in the second interval, the other remained about the same (142 ppm). The results indicate that they shifted at rates on the order of 10 ppm/year even several years after manufacturing. The large shift in calibration factors indicates that they must be corrected using calibrations done before and after the measurements to perform microgravity measurements when gravity differences between a reference gravity site and survey sites are on the order of a hundred milligals (mGal) or more. The results also indicate that the calibration factors change gradually with time, so their interpolation provides a good practical approximation for a specific survey time. We applied the time‐dependent calibration factors to microgravity monitoring at the Iwo‐tou caldera, Japan, where the gravity difference between the base site on the island and the reference site on Honshu (the mainland of Japan) is about 870 mGal mainly due to the 11° latitude difference. Gravity surveys were conducted every two years from 1998–2006. The correction of scale factors estimated from the repeated calibration surveys leads to satisfactory measurements, in which the average of the absolute differences between two Scintrex CG‐3M instruments in five surveys is reduced from 207μGal to 19μGal; for three of those surveys, it is less than 10 μGal. This result demonstrates the importance of repeated calibration surveys.