The current induced by removing a gate separating two fluids of close densities is simulated using a developed Smoothed Particle Hydrodynamic (SPH) model. The simulation is performed for fluids with density ratios between 0.9 and 1.0. To develop the two-phase model, no significant changes are applied to the basic SPH formulations, regarding the low density difference between the two fluids. The classic SPH equations are used with a small change: the speed of sound and the reference density are changed in order to produce the same reference pressure for both phases.In addition, density re-initialization is applied for each phase separately. The resulted in viscid flow has characteristics very close to or the same as the experimental results. The flow depth and the flow front speed are two parameters selected to validate the simulations. The effects caused by the variations in the density differences to the phenomenon and effectiveness of the applied Method are evaluated by performing a series of simulations of different density ratios and resolutions.

Gravity anomalies always include the total effects (combination of the structures which have different densities and depths) of the study area and beyond.The regional-residual resolution of the potential field continues to be a topic of considerable interest among geophycists even to a present time. In spite of a large number of sophisticated analytical techniques both in the space and frequency domain, there are instances where interpreters are not satisfied with the regional and residual components obtained by this Method.The finite element Method (FEM), which has been used in potential field interpretation for decades, makes complex problems to be solved easily and accurately.A regional Gravity anomaly, based on element shape functions used in finite element analysis, is developed. The first step of FEM is to identify the elements and then to decide onthe boundary of the solution space, the solution space is divided into elements. After determination of the geometrical structure of the solution space, the most suitable elements should be chosen for this geometrical structure. The agreement between the geometry and the elements is quite important for the convergence to the best possible solution.In this work FEM was applied to a theoretical model and to Gravity data from salt dome structure in Qom to produce the regional and residual anomalies.

Applying 2D algorithms for inverting the potential field data is more useful and efficient than their 3D counterparts, whenever the geologic situation permits. This is because the computation time is less and modeling the subsurface is easier. In this paper we present a 2D inversion algorithm for interpreting Gravity data by employing a set of constraints including minimum distance, smoothness, and compactness. Using different combination of these constraints provide either smooth images of the underground geological structures or models with sharp geological boundaries. We model the study area by a large number of infinitely long horizontal prisms with square cross-sections and unknown densities. The final density distribution is obtained by minimizing an objective function that is composed of the model objective function and equality constraints, which are combined using a Lagrangian multipliers. Each block's weight depends on depth, a priori information on density and the allowed density ranges for the specified area. A MATLAB code has been developed and tested on a synthetic model consists of vertical and dipping dikes. The algorithm is applied with different combinations of constraints and the practical aspects are discussed. Results indicate that when a combination of constraints is used, the geometry and density distribution of both structures can be reconstructed. The Method is applied on Zereshlu Mining Camp in Zanjan - Iran, which is well known for the Manganese ores. Result represents a high density distribution with the horizontal extension of about 30 m, and the vertical extension shows a trend in the E - W direction with a depth interval between 7 to 22 m in the east and 15 to 35 m in the west.

Summary Edge detection is a fast and qualitative interpretation Method to achieve information from potential field (e. g. Gravity) anomalies. In the edge detection Methods, the separation of overlapping amplitudes of anomalies and accuracy of edge detection are very important. There are various Methods for edge detection. Most of these Methods are based on the gradients of the potential field data. The gradients are sensitive to noise. Statistical Methods have been used to increase the accuracy of edge detection. Normalized standard deviations (NSTD) and correlation coefficient of multidirectional standard deviations (CCMS) are among these Methods. Introduction There are several edge detection Methods based on gradients of data. Each of these Methods has some strengths and some weaknesses. In the selection of these Methods for a particular case, simplicity and better performance are considered. These Methods include: total horizontal derivative (THD), Theta angle, Tilt angel, hyperbolic tilt angle (HTA) and a new Method based on the gradients, called normalized total horizontal derivative (NTHD). In addition, the semi-statistical Method of NSTD and statistical Method of CCMS are among these Methods that have been explained in this paper. The NSTD Method is obtained from the standard deviation of the gradients, however, the CCMS Method does not use the gradients. This Method is completely a statistical Method, which is based on correlation coefficient and standard deviation. Methodology and Approaches In this paper; after examining the above-stated edge detection Methods, they have been applied on both synthetic and real data. The performances of these Methods are compared in the presence of noisy data, overlapping amplitudes of anomalies and their accuracies in edge detection. Results and Conclusions The results of applying the above-stated edge detection Methods on the synthetic data show that the gradient-based edge detection Methods are sensitive to noise, depths of anomalies and overlapping amplitudes of anomalies. The NTHD, NSTD and CCMS Methods are less sensitive to noise than the other edge detection Methods. These Methods detect anomalies with different depths and separate anomalies with overlapping amplitudes. In all of these Methods, as the depths of anomalies increase, the accuracy of edge detection decrease. This study show that the CCMS Method has the best result when applied on the synthetic data. Furthermore, applying the CCMS Method on the real data yields better results in comparison with the other edge detection Methods. The results of edge detection by this Method have been shown on the bouguer map. Thus, this Method reduces complexities of edge detection that can be useful for the interpreter.

The presence of hot springs, travertine outcrops, hydrothermal altered area and active tectonic in the north-east of Takab city in the West Azarbayjan province indicate that there is a geothermal system in the area. In order to characterize the geological structures associated to the geothermal system in the region, a Gravity survey was carried out in 140 stations which covered an area about 600 km2. Necessary modifications such as Bouguer, topography and free air were applied over data to obtain complete Bouguer anomaly field. Then, residual Gravity anomaly field was calculated by subtracting the regional Gravity field from complete Bouguer field. The regional Gravity field was calculated by fitting a three-order polynomials surface over the complete Bouguer field. The calculated residual Gravity map shows two negative anomaly zones (A1 and A2) in the study area. In geothermal exploration, negative Gravity anomalies are considered as probable reservoir of geothermal systems. The horizontal and vertical derivative maps show complicated fracture zones in the study area. To obtain more information, the depth estimation carried out using Euler Method. Estimated depth for the top of negative anomaly source in zone 1 is between 1000 and 2000 m. Finally, 3D inversion of the data was performed using Li and Oldenburg algorithm to show an image of the reservoir in the depth. The results of 3D inversion show a significant negative density contrast that occurred only in zone 1. Therefore, the reservoir of the Takab geothermal system is located in the depths between 3000 and 5000 m in A1 anomaly zone.

In order to properly understand the subsurface structures, the issue of inversion of geophysical data has received much attention from researchers. Since accurate reconstruction of the shape and boundaries of the mass using gravimetric data is very important in some issues, it is important to use an effective and efficient Method that has a high ability to draw and reconstruct the boundaries of a mass. In recent years, the level set Method introduced by Asher and Stein has been widely used to solve this problem. From the expansion of the level set function in some bases of the problem, the effective number of parameters is greatly reduced and an optimization problem is created which its behavior is better than the least squares problem. As a result, the level set parameterization Method will be presented for the reconstruction of inversion models. A common advantage of the parametric level set Method is the careful examination of the boundary for optimum sensitivities, which significantly reduces the dimensional problem, and many of the difficulties of traditional level set Methods, such as regularization, reconstruction, and basis function. Level set parameterization is performed by radial basis functions (RBF),which causes an optimal problem with an average number of parameters and high flexibility,and the computational and optimization process for Newton's Method is more accurate and smooth. The model is described by the zero contour of a level-set function, which in turn is represented by a relatively small number of radial basis functions. This formulation includes some additional parameters such as the width of the radial basis functions and the smoothness of the Heaviside function. The latter is of particular importance as it controls the sensitivity to changes in the model. In this algorithm adaptively chooses the required smoothness parameter and tests the Method on a suite of idealized Earth models. In this evolutionary approach, the reduction gradient Method usually requires many iterations for convergence, and the functions are weakened for low-sensitivity problems. Although the use of Quasi-Newton Methods to improve the level set function increases the degree of convergence, they are computationally challenging, and for large problems and relatively finer grids, a system of equations must be solved in each iteration. Moreover, based on the fact that the number of underlying parameters in a parametric approach is usually much less than the number of pixels resulting from the discretization of the level set function, we make a use of a Newton-type Method to solve the underlying optimization problem. In this research, the algorithm is used to investigate its strengths and weaknesses for applying geophysical Gravity data, coding and programming, and it is tested using several two-dimensional synthetic models. Finally, the Method is tested on Gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada. The results of this study show that the application of the optimization algorithm of the level set function will lead to a relatively more accurate and realistic detection of mass boundaries. It shows that the tested mass has spread from a depth of 10 meters to a depth of 160 meters.

Progressive collapse studies generally assess the performance of the structure under Gravity and blast loads, while earthquakes may also lead to the progressive collapse of a damaged structure. In this study, the progressive collapse response of concentrically braced dual systems with steel moment-resisting frames was assessed under seismic loads through pushover analysis using triangular and uniform lateral load patterns. Two different bracing types (X and inverted V braces) were considered, and their performances were compared under different lateral load patterns using the nonlinear static alternate path Method recommended in the Unified Facilities Criteria (UFC) guideline. Eventually, the seismic progressive collapse resistance of models was compared to their progressive collapse response under Gravity loads. These studies showed that models under the seismic progressive collapse loads satisfied UFC acceptance criteria and limited rehabilitation objective. The structures had better performance under seismic progressive collapse than models under Gravity loads because of more resistance, ductility, suitable load redistribution, and more structural elements that participated in load redistribution. Furthermore, despite studies on progressive collapse under Gravity loads, the dual system with X braces showed better progressive collapse performance (more resistance, residual reserve strength ratio and ductility) under seismic loads than the model with inverted V braces.

Ranking fuzzy numbers plays a very important role in decision making and some other fuzzy application systems. Many different Methods have been proposed to deal with ranking fuzzy numbers. Constructing ranking indexes based on the centroid of fuzzy numbers is an important case. But some weaknesses are found in these indexes. The purpose of this paper is to give a new ranking index to rank various fuzzy numbers effectively. Finally, several numerical examples following the procedure indicate the ranking results to be valid.

Summary:Potential field data (Gravity and magnetic data) are usually analyzed by employing linear transformations, the spectral Method, inversion techniques and analytic signal Methods. Nowadays, there are different Methods of modeling the Gravity data; but each has limitations. One of the limitations of these Methods is the assumption of a simple shape for buried structures whereas the actual shape could be entirely different. This study uses cubic units (3D model) to solve this limitation because affords the ability to make any shape for unknown underground structures by arranging these cubics.In this paper, a new Method called Forced Neural Networks (FNN) to find the density variation of buried deposits or underground structures in different depth sections by assuming the cubic model is described. The aim of the geological modeling is to determine the shape and location of underground structures in 3-D sections. Here, one neuron network and back propagation algorithm are applied to discover the density difference. In this Method, weights of the neurons are assigned as density for each cubic and the activation function has a linear property such that the outputs are the same as the inputs. After using the back propagation, densities for each cubic are updated and the output of the neurons gives the Gravity anomaly. Hence, the density differences are found. However, the results of this system are insufficient because non-uniqueness and horizontal locations are constrained; therefore, the value of density difference is set to zero if its value is very close to zero according to the density difference which is obtained from geological features of the region. Otherwise these values are set to the density difference of the geological region after back propagation.Using a forced neural network, after sufficient epoch is applied, fixed values are assigned to the output of the neuron according to the density difference, and this process is continued until the mean square error of the output becomes sufficiently small. The Method is used for both noise-free and noise-corrupted synthetic data and, after obtaining satisfactory results for three synthetic data models, this Method was used for modeling of the real data.The Dehloran Bitumen map in Iran was chosen as a real data application. The area under consideration is located in the Zagros tectonic zone, west of Iran where we are looking for Bitumen. Layers of Medium-bedded limestone with intermediate marllimestone are the dominant formations in the area and the hydrocarbon zone is one of the most important characteristics of the area. A program was written using the Anomaly modeling Method. The final result of this Method shows that the deposit begins from the low depth to approximately less than 40 meters. This modeling yeilded satisfactory results for the drilling in the region. The results of the drillings show that the lowest depth of the deposit varies from 7 to 10 meters. This Method can easily be applied for Gravity, microGravity and magnetic data especially for porphyry deposits.

Gravity dams are vital structures whose proper design and evaluation for stability are quite important. One of the effective forces on stability of concrete dams is the uplift force and its distribution below the dam base. Uplift pressure resulting from headwater and tail-water not only exists through dam cross sections and the dam base, but also within the foundation below the dam base. In many Gravity dams uplift pressure is the major active force that must be included in the stability and stress analysis to ensure structural adequacy. There have been different Methods employed since past to the present to assess and calculate the uplift load. In each of these Methods, depending on the degree of simplification, the accuracy of the answers will be reduced. Due to the limitations of each of these Methods, available numerical Methods may be used nowadays to estimate the values of pore pressure within the porous medium. As far as seepage forces have a great effect on stability of Gravity dams, understanding the seepage in rock masses has a great importance, because the Gravity dams are generally built on rock foundations. The actual influential phenomenon encountered in saturated jointed rock media is the joints hydro-mechanical interaction effect. Finite element Method as a general and systematic Method is one of the most common numerical Methods for solving engineering problems. Also, this Method has significant application in hydraulic and hydrodynamic problems. In addition, the uplift load pattern and distribution according to common codes are influenced by some factors such as head and tail water, assuming a segmented linear load distribution below the dam. In this research, to investigate the sensitivity of the load pattern to dam height, a number of Gravity dams of Pine Flat type with different heights and their foundations are modeled. An enhanced modeling approach is employed to estimate the equivalent uplift load distribution at the dam base for application in the standard finite element modeling procedures. Coupled p-u finite element analysis is performed accounting for the seepage and stress field simultaneously. Dam body is considered to be completely impervious. The foundation rock is assumed as homogeneous and uniform, in terms of elasticity and permeability. The stresses generated in the dam interface for each case of the coupled hydro-mechanical analysis is compared against that of the conventional load pattern according to the U. S. Army Corps of Engineers regulation for the same dam model. It was found that the error magnitude due to the conventional pattern has a direct relationship with the dam height. As the dam height increases, the amount of error of calculated stress increases. In particular, the error at the critical zones of the foundation such as at the dam heel, may raise even up to 40%. In the group of dams studied, the error increases even up to 12 times in respect to the expected error in the shorter dams. The deficiency could in some cases completely affect the safety of the dam. This research indicates the necessity of using more accurate Methods of estimating uplift load under high Gravity dams.