جستجوی مقالات مرتبط با کلیدواژه « gravimetry » در نشریات گروه « فیزیک »

The Moho discontinuity is a boundary between the crust and upper mantle that reveals the difference between them with changes in seismic velocity, density, chemical structure, and constituents. Estimating the Moho depth and studying its lateral changes is one of the important goals of geophysical studies. The current study aims to estimate the depth and topography of the Moho discontinuity in the southwestern part of the Baltic Sea, including parts of the central European system, the Trans-European Suture Zone, Caledonian Crustal Suture, and the Ringkobing-Fyn High. This area has been one of the most attractive regions for Geoscientists in the last decades due to its complicated geological structures caused by different tectonic events. For this purpose, a three-dimensional model of the crustal structures based on gravity data forward modeling in the study area has been presented. Previous seismic / non-seismic results have been used to constrain the model and reduce its degree of freedom. This model includes sedimentary sequences, crustal thickness, Moho topography, and high-velocity lower crust expansion in the region and shows the tectonic structures of the study area. This study used a combination of marine, land, and EGM2008 gravity data and modeled them with IGMAS+, Interactive Gravity and Magnetic Application System. The interactive modeling program allows the user to change the geometry as well as the density and susceptibility of the primary model and observe results quickly during the processing. In the software, the model structure could be be more user friendly by eliminating additional details and dividing the whole model into vertical sections. Our primary model consists of three main layers of sediments, crust and upper mantle. The sedimentary layer is divided into two major parts, pre-Permian and post-Carboniferous. Also, the crustal layer is divided into the upper crust and the high-density lower crust. Besides, the upper crust is composed of the upper crust of the Baltica and the upper crust of Avalonia. The last layer of the model is a part of the upper mantle. The model space consists of 16 vertical planes stretching 385 kilometers east-west with an equal distance of 15 kilometers, covering the entire study area. The initial model was developed based on seismic sections and previous models, and it has been improved using interactive forward modeling of gravity data. The result shows a good agreement between the measured and modeled Bouguer anomaly, and the Root Mean Square Error of the model is 1.12 mGal. The model correlates clearly with major tectonic units. It indicates that the Caledonian collision resulted in the amalgamation of Baltica and Avalonia is the most prominent tectonic event in the area, and the Caledonian crustal suture between them is interpreted from changes in physical parameters at crustal levels. There is a relatively thick crystalline crust in the area, and the depth of Moho discontinuity varies from 26 to 42 km. The results also indicate that the transition from the Paleozoic crust of the Central European Basin to the Precambrian crust of the Eastern European Craton occurs within the Tornquist Zone.

In this paper, three-dimensional (3D) inversion of gravity data using graph theory is used. The methodology was initially introduced by Bijani et al. (2015) and, here, we provide more details for the steps and required parameters of the algorithm. An ensemble of simple point masses are used to model a homogenous subsurface body. Then, in the presented inversion methodology, the model parameters are the Cartesian coordinates of point masses and their total mass. Consequently, the algorithm is able to reconstruct the skeleton of the subsurface body and to yield its total mass. Here, the set of point masses is associated to the vertices of a weighted full graph in which the weights are computed by the Euclidean distances separating vertices in pairs. Then, the Kruskal’s algorithm can be used to solve the Minimum Spanning Tree (MST) problem for the graph. A stabilizer, called equidistance function, is obtained using the MST, which computes the statistical variance of the distances among point masses. The function restricts the spatial distribution of points, and suggests a homogeneous distribution for the point masses in the subsurface. Here, a non-linear global objective function for the model parameters comprising data misfit term and equidistance function with balancing provided by a regularization parameter that should be minimized. A genetic algorithm (GA) is used for the minimization of the objective function. GA consists of a random search algorithm based on the mechanism of natural selection and natural genetics. Then, to solve the optimization problem in our algorithm, there is no need to calculate the derivatives of the objective function with respect to model parameters, or any matrix operation. Simulations for two synthetic examples, including a vertical and a dipping dike, demonstrate the efficiency and effectiveness of the implementation of the present algorithm. The skeleton and total mass of the bodies are estimated very accurately. We also show that although the search limits for the model parameters must be used, they are not very limitative. Even with less realistic bounds, acceptable approximations of the body are still obtained. Unlike Bijani et al. (2015) which used the L-curve method for estimating the regularization parameter, here, we present a new strategy to approximate the parameter. We demonstrate that if: 1. the equidistance function converges almost monotonically to zero with increasing numbers of generation; 2. minimum of the objective function at the final iteration becomes small; and 3. the predicted data by the reconstructed model is approximately close to observed data, then, the selected regularization parameter is nearly optimum and the results are reliable. This provides a suitable and inexpensive methodology for estimating the regularization parameter. The method is tested on gravity data from the Mobrun ore body, north east of Noranda, Quebec, Canada. The anomaly is associated with a massive body of base metal sulfide, mainly pyrite, which has displaced volcanic rocks of middle Precambrian age (Grant and West, 1965). With application of the algorithm, a skeleton of the body is obtained which extends about 350 m in the east direction, and shows a maximum extension of 200 m in depth.

In this paper the 3D inversion of gravity data using two different regularization methods, namely Tikhonov regularization and truncated singular value decomposition (TSVD), is considered. The earth under the survey area is modeled using a large number of rectangular prisms, in which the size of the prisms are kept fixed during the inversion and the values of densities of the prisms are the model parameters to be determined. A depth weighting matrix is used to counteract the natural decay of the kernel, so the inversion obtains reliable information about the source distribution with respect to depth. To generate a sharp and focused model, the minimum support (MS) constraint is used, which minimizes the total area with non zero departure of the model parameters from a given a priori model. Then, the application of iteratively reweighted least square algorithm is required to deal with non-linearity introduced by MS constraint. At each iteration of the inversion, a priori variable weighting matrix is updated using model parameters obtained at the previous iteration. We use the singular value decomposition (SVD) for computing Tikhonov solution, which also helps us to compare the results with the solution obtained by TSVD. Thus, the algorithms presented here are suitable for small to moderate size problems, where it is feasible to compute the SVD. In Tikhonov regularization method, the optimal regularization parameter at each iteration is obtained by application of the parameter-choice method. The method is based on the statistical distribution of the minimum of the Tikhonov function. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data and, when the regularization term is considered to be weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional becomes a random variable that follows a distribution. Then, a Newton root-finding algorithm can be used to find the regularization parameter. For truncated SVD regularization, the Picard plot is used to find a suitable value of truncation index. In math literature, a plot of singular values together with SVD and solution coefficients is often referred to as Picard plot. To test the algorithms, a density model which consists of a dipping dike embedded in a uniform half-space is used. The surface gravity anomaly produced by this model is contaminated with three different noise levels, and are used as input for introduced inversion algorithms. The results indicate that the algorithms are able to recover the geometry and density distribution of the original model. In general, the reconstructed model is more sparse using TSVD method as compare with Tikhonov solution. This especially happens for high noise level, where there is an important difference between two solutions. In this case, while TSVD produces a sparse model, the solution of Tikhonov regularization is not sparse. Furthermore, the number of iterations, which is required to terminate the algorithms, is more for TSVD as compare with Tikhonov method. This feature, along with automatic determination of regularization parameter, makes the implementation of the Tikhonov regularization method faster than TSVD. The inversion methods are used on real gravity data acquired over the Gotvand dam site in the south-west of Iran. Tertiary deposits of the Gachsaran formation are the dominant geological structure in this area, and it is mainly comprised of marl, gypsum, anhydrite and halite. There are several solution cavities in the area so that relative negative anomalies are distinguishable in the residual map. A window of residual map consists of 640 gridded data, which includes three negative anomalies, that is selected for modeling. The reconstructed models are shown and compare with results obtained by bore holes.

In this paper the inversion of gravity data using L1–norm stabilizer is considered. The inversion is an important step in the interpretation of data. In gravity data inversion, the goal is to estimate density and geometry of the unknown subsurface model from a set of known observation measured on the surface. Commonly, rectangular prisms are used to model the subsurface under the survey area. The unknown density contrasts within each prism are the parameters which should be estimated. The inversion of gravity data is an example of underdetermined and ill-posed problem, i.e. the solution can be non-unique and unstable. Thus, in order to find an acceptable solution regularization should be imposed. Solution is usually obtained by minimizing a global objective function consisting of two terms, data misfit and the regularization term. Data misfit measures how well an obtained model can reproduce the observed data. Usually, it is assumed noise in gravity data is Gaussian, therefore a L2–norm measure of the error between observed and predicted data is well suited for data misfit. There are several choices for a stabilizer, depends on type of features one wants to see from inverted model. A typical choice is a L2 –norm of a low-order differential operator applied to the model, which also a priori information and depth weighting can be incorporated (Li and Oldenburg, 1996). In this case the objective function is quadratic, then minimization of the function results a linear system to be solved. However, the models recovered in this way are characterized by smooth feature which are not always consistent with the real geological structures. There are situations in which the sources are localized and separated by sharp, distinct interfaces. To deal with this problem, during last decades, researchers have proposed a few types of stabilizer. Last and Kubik (1983) presented a compactness criterion for gravity inversion that seeks to minimize the area (or volume in 3D) of the causative body. Portniaguine and Zhdanov (1999) based on this stabilizer, who named the minimum support (MS), developed the minimum gradient support (MGS) stabilizer. For both constraint, the regularization term can be written as the weighted L2–type norm of the model. Therefore, the problem of the minimization of the objective function can be treated same as conventional Tikhonov functional. The only difference is that a priori variable weighting matrix for model parameters incorporated in the regularization term. Thus the Iteratively Reweighted Least Square (IRLS) algorithm is required to solve the problem. Other possibility for stabilizer is the minimization of the L1-norm of model or gradient of model, the latter indicates total variation regularization. The L1–norm stabilizer allows occurrence of large elements in the inverted model among mostly small values. Therefore, it can be used to obtain sharp boundaries and blocky features. Although the L1–norm stabilizer has favorable properties, in reconstruction of sparse models, its numerical implementation in a minimization problem can be difficult because its derivatives with respect to an element is not defined at zero. To overcome this difficulty, in this paper, the L1–norm stabilizer is approximated by a reweighted L2 –norm term. The algorithm is extended to gravity inverse problem, which needs depth weighting and other priori information to be included in the objective function. For estimating the regularization parameter, which balances between two terms of objective function, the Unbiased Predictive Risk Estimator (UPRE) method is used. The solution of the resulting objective functional is found using Generalized Singular Value Decomposition (GSVD), also provides for efficient determination of the regularization parameter at each iteration. Simulation using synthetic data of a dipping dike demonstrates that the method is capable to reconstruct focused image, boundaries and slop of the reconstructed model are close to those of the original model. The method is applied on gravity data acquired over the Gotvand dam site, in the south-west of Iran. The results show rather good agreement with those obtained from the boreholes.

In this paper the 3D inversion of gravity data is considered. The goal is to reconstruct models of subsurface density distribution using a set of known gravity observations measured on the earth surface. The subsurface under the survey area is divided into large number of rectangular blocks of known sizes and positions. The unknown density contrasts within each prism define the parameters to be estimated. This kind of parameterization is flexible for the reconstruction of the subsurface model, but requires more unknown model parameters than observations (here N << M, where N is the number of data and M is the number of model parameters). The final density distribution will be obtained by minimizing a global objective function consists of data misfit and a regularization term. The inverse problem is solved in data space, which needs inverse of matrix with N×N dimension, as compared with M×M dimension system in model space inversion. This methodology was used by Pilkington (2009) in 3D inversion of magnetic data. To solve the resulting set of linear equation, the conjugate gradient method is used. Combination of data-space method with conjugate gradient leads to keep the storage and computational time to a minimum. The iteratively-defined regularization matrix, which is used in objective function, is a combination of three diagonal matrix; namely depth weighting, compactness and hard constraint matrices. The compactness constraint was introduced in Last and Kubik (1983) and developed in Portniaguine and Zhdanov (1999), who used term "minimum support stabilizer", is considered here to produce models with non-smooth features. It is a suitable and well-known constraint for identifying geologic structures which have material properties that vary over relatively short distances. The depth weighting matrix, introduced in Li and Oldenburg (1998), is used in regularization term to counteract the natural decay of the kernel with depth. The hard constraint allows us to incorporated priori geological and geophysical information into inversion process. While depth weighting and hard constraint matrices both are independent of the iteration index, the compactness depends on iterations. In order to recover a feasible image of the subsurface, realistic lower and upper density bounds are imposed during the inversion process. The computer program is written in MATLAB and tested on synthetic data produced by a model consists of two cubes. The cubes have same dimension and density, but located at different depths. The results indicate that the algorithm is efficient to handle large-scale gravity inverse problems. For the shallow cube the geometry and density of the reconstructed model are close to those of the original model, but for the deeper body the resolution decrease and a smooth image of subsurface obtained. The gravity data acquired over the Safo mining camp in the north-west of Iran, which is well-known for manganese ores, are used as a real modeling case. The results show a density distribution in the subsurface from about 5 to 35-40 m in depth and about 35 m extent in the x direction, which are close to those obtained by bore-hole drilling on the site.