Summary: One of the most important problems in the interpretation of GRAVITY or magnetic data is to obtain information about the sources position (geometry and depth). Potential field automatic interpretation techniques can significantly decrease the interpretation workload of a geophysicist and are widely used. Automatic interpretation methods can be classified into two major groups: modeling and analytical. Euler Deconvolution, Werenr Deconvolution and recently, Tilt-Depth method are the commonly used (practical goals) analytical methods. The basic idea in Tilt-Depth method is simultaneous application of tilt angle for edge and depth estimation of magnetic contact model. In this method, the vertical and horizontal GRADIENTs of magnetic contact substituted in tilt equation lead to an equation for depth estimation. This paper generalizes the tilt-depth method to GRAVITY data using the horizontal cylinder and the buried sphere models.Introduction: Salem et al, (2007) introduced the tilt-depth method for the magnetic anomaly over a contact. Previously Miller and Singh had developed the tilt angle as a method of enhancing images of the vertical derivative of potential field data. The tilt-depth method only depends on mapping specific contours of the magnetic tilt angles. The zero contours delineate the spatial location of the magnetic source edges whilst the depth to the source is the distance between the zero and either the –45° or the +45° contour or their average. The tilt-depth method adds to the arsenal of geophysical methods currently in use to estimate magnetic source depths, many of which use second- and/or third-order derivatives. These include methods based on Euler’s equation and the local wavenumber, both of which calculate the source depths for a range of source-body geometries, and, more recently, for the simultaneous estimation of both source depth and source type. Methodology and Approaches: In this paper, the tilt-depth method will be both generalized (by applying it to GRAVITY models) and extended (by using all values of the ratio of the field GRADIENTs, not just a single value). The GRAVITY models used are 2D horizontal cylinder and buried sphere. In this regard we developed a MATLAB code for applying the proposed method to synthetic and real data. In this code the selection of the ratio of the vertical to horizontal derivatives are done on the basis of the signal to noise ratio of the dataset. Also for the consistency of result the vertical derivative is calculated using Hilbert transform. The final equation was solved by Newton method. Results and Conclusions: The efficiency of the proposed method tested using various synthetic GRAVITY models. The sensitivity of methods to noise and interface was tested using synthetic data. On the basis of observations the method is sensitive to noise, but if the data continued upward before applying the algorithm or using of the stable derivative operator the inconsistency of the result decreases seriously. For overcome in body overlapping phenomena we suggest anomaly windowing or insulating by means of Bott (1966) algorithm. This method applied on 2 GRAVITY profiles from Shavaz Iron ore in Yazd province. Then the results compared with power spectrum depth analysis. Accordance to this comparison the proposed method could produce the same result as power spectrum. In this case w upward GRAVITY data to 2m in order to decrease noise content.

Summary: Chromite exploration is really important in mineral exploration. GRAVITY method is really important in chromite exploration. Edge detection methods are used to determine lenses of chromite. In this paper, we used the curvature GRAVITY GRADIENT tensor (CGGT) along with the tilt angle method to detect chromite lenses. Application of the methods on synthetic and real GRAVITY data showed that the CGGT can determine the edges of chromite lenses better than the tilt angle method. Introduction: Chromite is a strategic mineral. Therefore, the exploration of chromite mineral reserves is the main mineral exploration priorities. Chromite has a marked density contrast with the host rock, so the GRAVITY method can be applied for exploration of the chromite ore bodies. The boreholes locations are usually determined after finding the edges of the chromite lenses by edge detection of the GRAVITY anomalies. There are various edge detection methods. Most of the edge enhancement techniques are interpreted qualitatively. The Tilt angle method is a traditional method that can detect edges of subsurface structures quantitatively. The value of Tilt angle is zero above edges of subsurface bodies. The curvature GRAVITY GRADIENT tensor (CGGT) was also used to interpret the geological structure quantitatively. The value of eigenvalues of CGGT are zero above edges of subsurface bodies. In this paper, we used CGGT for edge detection of chromite lenses. Methodology and Approaches: In order to obtain CGGT, at first, horizontal vector GRADIENTs of GRAVITY GRADIENT tensors are computed from the vertical component of GRAVITY data with a Fourier transform technique. Then the eigenvalues of CGGT are obtained. The large eigenvalue determines the edges of negative density bodies while the small eigenvalue only can be used to outline edges of positive density bodies. The chromite has positive density contrast with the host rock and produce positive GRAVITY anomaly. Therefore, we choose the small eigenvalue to outline edges of the chromite lenses. Finally, the tilt angle is also applied to compare with the CGGT. Results and Conclusions: The robustness of the codes used for the edge enhancement is tested with GRAVITY field anomaly map caused by four prisms of synthetic bodies. The results indicated that the proposed method can enhance the edges of the synthetic bodies with zero contour of the small eigenvalue of the CGGT. Then, the proposed method has been applied on the real GRAVITY data from chromite deposits In Camaguey province, Cuba. The results showed that the zero contour of the small eigenvalue of the CGGT can outline the edges of synthetic bodies and chromite lenses better than the zero contour of the tilt angle method. Therefore, we can use the small eigenvalue of the CGGT to detect edges of chromite lenses precisely.

This primary purpose of this work was to develop control laws for three axis stabilization of a magnetic actuated satellite with a passive GRAVITY GRADIENT boom. the satellite shall be three axis stabilized with its boom pointing outwards. This was achieved by classical linearized control of satellite. in addition to a theoretical treatment, the theses contain a large portion of application considerations. Stability analysis was done to find the moment of inertia of a satellite, in order to reach the passive GRAVITY GRADIENT control with boom. The control concept considered was that interaction between the earth’s magnetic field and a magnetic field generated by a set of coils in the satellite can be used for actuation. magnetic torquing was found attractive for generation of control torques on small satellites. Since magnetic control systems are relatively lightweight, require low power and are inexpensive. However, this principle is inherently none linear and difficult to use, classical linearized control and fuzzy controllers were used to stabilized the satellite and their performance was tested via simulation.

One of the methodologies employed in gravimetry exploration is eigenvector analysis of GRAVITY GRADIENT Tensor (GGT) which yields a solution including an estimation of a causative body’ s Center of Mass (COM), dimensionality and strike direction. The eigenvectors of GGT give very rewarding clues about COM and strike direction. Additionally, the relationships between its components provide a quantity (I), representative of a geologic body dimensions. Although this procedure directly measures derivative components of GRAVITY vector, it is costly and demands modern gradiometers. This study intends to obtain GGT from an ordinary GRAVITY field measurement (gz). This Tensor is called Computed GGT (CGGT). In this procedure, some information about a geologic mass COM, strike and rough geometry, just after an ordinary gravimetry survey, is gained. Because of derivative calculations, the impacts of noise existing in the main measured GRAVITY field (gz) could be destructive in CGGT solutions. Accordingly, to adjust them, a “ moving twenty-five point averaging” method, and “ upward continuation” are applied. The methodology is tested on various complex isolated and binary models in noisy conditions. It is also tested on real geologic example from a salt dome, USA, and all the results are highly acceptable.

The normalized full GRADIENT (NFG) method defined by Berezkin (1967, 1973 and 1998) is already used for detecting reservoirs. We apply the method for delineating near-surface GRAVITY anomalies. 2-D rectangular prisms with different coordinates are used as the synthetic models to be detected by the method. The NFG is also applied to real microGRAVITY data to determine the place and depth of a subterranean water tunnel (ghanat).      

The effect of variable GRAVITY on the free convection in a horizontal porous layer with viscous dis-sipation is investigated. The bottom boundary is taken as adiabatic and there is a non-uniform temperature distribution along the upper boundary. The effect of viscous dissipation is significant and the top boundary temperature distribution is assumed to have a constant GRADIENT. The GRAVITY varies linearly with the height. A linear stability analysis of the basic flow is carried out. The critical horizontal Rayleigh number is calculated for oblique roll disturbances. The longitudinal rolls are found to be the most unstable ones. The viscous dissipation has a destabilizing effect. There is a drastic decrease in the value of critical horizontal Rayleigh number when modified variable GRAVITY parameter changes from -1 to 1.

Estimation of depth and horizontal location of anomalous bodies plays an important role for selecting exploration wells location. There are many methods for depth estimating, and most of them use high-pass filters. The Normalized Full GRADIENT (NFG) method is one of these methods that use Fourier series to remove deficiencies and eliminate the oscillations which appear on the downward continuation when passing through center of an anomalous body. In this paper, the main goals is calculation of NFG and present a new method for determining optimum number of Fourier terms and use them for synthetic and real two and three dimensional field data. The obtained results on synthetic data indicate that the estimated location and depth of the model is in 10 percent error with the real. The NFG method has also applied on two sets of real field GRAVITY data to determine the location and estimate depth of Humble salt dome (USA) and massive sulfide mineralization of Mobrun (Canada). For the first field data set the NFG has provided a depth to the centre equal to 4.8 km and for the second case the depth to the top section of mineralized body has been estimated 17 meters and its continuation to a depth more than 70 meters has also been confirmed.  The obtained results of the NFG method on real field data in each case are in good agreement to those provided by other independent information arises from drilling and other geophysical methods. The above matter clearly illustrates that the NFG method is able enough to locate anomalous bodies and estimate their burial depth precisely.

GRAVITY GRADIENT tensor is a matrix containing the second order derivatives of the Earth’s GRAVITY field, which has numerous applications in geodesy and geophysics. To date, much effort has been done for estimating GRAVITY GRADIENT tensor with reasonable accuracy. This quantity can be estimated via using various methods, and one of these methods is applying finite-difference method to GRAVITY observations. Finite-difference method can estimate GRAVITY GRADIENT tensor directly by using the mathematical concept of GRADIENT, regardless of extra assumptions. This ability of finite-difference method, from theoretical point of view, provides the possibility of accurate estimation of GRAVITY GRADIENT tensor without considering additional assumptions to the problem. This study tends to introduce and evaluate Finite difference method for estimating the GRADIENT tensor and present formulae for determining GRAVITY GRADIENT tensor from land-based GRAVITY observations. In this paper, the proposed equations are numerically tested by means of using a global GRAVITY model of the earth. Global GRAVITY model of the earth (EGM 2008) is a geopotential model of the earth consisting of spherical harmonic coefficients up to degree 2190 and order 2159. There are numerous uses for these high degree potential coefficient models. One of these uses is modeling and estimating GRAVITY GRADIENT tensor.Finally, GRAVITY GRADIENT tensor is estimated by the proposed method for 6350 GRAVITY stations located in Costal Fars region in a northern part of the Persian Gulf, between the latitudes from 26.5 N to 27.27 N and longitudes from 53.41 E to 55.58 E. The target area is about 10000 square kilometers. About 8500 square kilometers of the study area is located in moderate mountainous regions, and about 1500 square kilometers is located in flat coastal areas. The altitudinal distribution and spatial distribution of GRAVITY in study area are shown in figure 1 and 2 respectively. Numerical experiments of this study demonstrate the ability of this method in GRAVITY GRADIENT tensor estimation with acceptable accuracy. For example, numerical experiments showed that the proposed method can estimate diagonal components of GRAVITY GRADIENT tensor (second order derivatives of the Earth’s GRAVITY field in east, north and vertical directions) with the accuracy values of 12.46, 34.49 and 454.82 Eotvos respectively. The spatial distribution of the GRAVITY GRADIENT tensor components obtained from finite difference method in study area are shown in figure 3.Finally, according to the theoretical concepts discussed in this paper, It can be said because the finite difference method using from derivative and difference concepts directly for estimating GRAVITY GRADIENT tensor, it is expected that this method provide accurate estimation of GRAVITY GRADIENT tensor, As this is happen in the simulation conducted. However the accuracy of this method is very dependent on distances between sampling stations and by reducing distance between the stations, the accuracy of proposed method will be increased. The numerical results of this study also showed that the proposed method can provide accurately estimate of GRAVITY GRADIENT tensor components In some stations surrounded by suitable spatial distribution of gravitational observations.

Investigating the possibility of detection of underground structures is one of the complicated problems. In this paper, making use of GRAVITY GRADIENT data is introduced as an efficient technique to solve this problem. In order to analyze this problem thoroughly and take into account all parts of it, both direct and inverse problems are treated in this contribution. In the direct problem, with the assumption of the known size and position of the structure, GRAVITY GRADIENT signal is modeled. Then, using this modeled signal and by considering the noise level of the gradiometer, some points about the detectability of the structure are discussed. In the inverse problem, position of the underground target is estimated based on the Euler deconvolution, given the GRAVITY GRADIENT tensor. Finally, both of the direct and inverse problems are implemented based on simulated data and some suggestions are made to decrease the probability of detectability of the underground targets.

In this study we will review potential and GRAVITY GRADIENT changes due to Sumatra’s 9.2-magnitude earthquake on 26th Dec 2004 using data collected from GRACE Satellite. The GRAVITY GRADIENTs clearly show the variations of mass distributions in the ground. The previous studies have shown that filters and softening algorithms were used to elimination of stripe error of GRACE observations. In this study we find the application of GRAVITY GRADIENT in removing stripe error of observation of GRACE satellite and we see that with these GRADIENTs in direction, GRADIENT tensor components such as and cause eliminate GRACE observations strip errors however with these GRADIENTs in direction, GRADIENT tensor components such as and would cause fluctuations to intensify in north south direction. Also we find the maximum and minimum value of GRAVITY GRADIENT changes (1.5mE and -1.2mE) will be earned in direction.