vahid e. ardestani

Potential field data play a crucial role in the interpretation of various geological structural features. The application of edge detection techniques significantly improves the capacity to delineate subsurface structures. In recent years, a variety of methodologies have been developed to identify edges; however, each of these methodologies possesses distinct advantages and limitations. This study presents a novel edge enhancement technique that employs the Total Horizontal Derivative (THD) in conjunction with the Rootsig activation function (RTHD). This technique is applied to the interpretation of potential field data to enhance structural mapping. The effectiveness of the RTHD is evaluated through the interpretation of synthetic gravity and magnetic anomalies, both with and without the presence of noise, including sources located at various depths. Furthermore, the RTHD technique is applied to investigate gravity field data from the Považský Inovec Mountains, located in the Western Carpathians of Slovakia. In this region, the boundaries of the primary anomalies, as well as the Považie and Ripňany faults, are distinctly delineated. The results demonstrate that the RTHD approach effectively delineates edges and balances the amplitudes of both shallow and deep-seated sources, in contrast to traditional edge enhancement methods. The findings indicate that the RTHD represents a more effective strategy for structural mapping when utilizing gravity and magnetic data.

In standard gravimetric correction methods, after the raw gravity data sets were corrected for drift, tide, latitude, and free-air effects to obtain free air anomalies, the effect of the mass between the reference surface and ground surface is eliminated in two steps including Bouguer and terrain corrections. But this study removes this effect in one step through the forward modeling method. To do this, two things are necessary for finding more accurate answers. First, how is the underground discretization, and to what extent a network of Digital Terrain Model (DTM) is available? Quad tree mesh accessible in Simulation and Parameter Estimation in Geophysics (SimPEG) is a very accurate and advanced meshing algorithm to discretize subsurface based on our requirements. This meshing system can choose the size of cells in the desired locations. Hence, using this flexible discretization, it is possible to define the smaller cells in borders, near the topographic region, which helps a for more precise answers. Having a dense DTM, the SRTM GeoTiff pictures are downloaded from USGS Earth explorer with 1 arc-second (90 m) resolution (https://doi.org/10.5066/F7PR7TFT), and then height information is extracted from these pictures through GeoToolkit (http://toolkit.geosci.xyz) script. Assuming a flat geoid for our study area, topography is extracted from the SRTM and the pictures are interpolated to estimate the elevation at the gravity observation points. The gravity effect of the model space (the space between the reference surface and topography) is computed via numerical forward modeling assuming a constant density (2.67 gr/cm3). This procedure is done by the Simulation module in SimPEG and is considered as the Bouguer and terrain corrections simultaneously. These corrections are subtracted from the free-air anomalies, which yields the complete Bouguer anomaly. This method is powerful in contrast to other standard methods. In standard methods, Bouguer correction considers Bouguer slab approximation. Therefore, accuracy is lost. Also, in large-scale problems, curvature correction becomes necessary. Also, terrain correction for removing the effects of the mass between the lowlands and heights of the region is inevitable. Terrain correction considers two approximations. First, it uses average height. Hence this procedure has a low precision. Secondly it divides the surrounding area into three zones (near, middle, and far) and computes the effects of middle and far zones with lower precision. Therefore, it decreases the accuracy of the results. The mentioned method is tested on 399 ground gravity data with a grid spacing of about 5 km prepared by the National Cartographical Center of Iran (NCC) in an area of about 200 km in 200 km located in parts of Central Zagros and Central Iran. The results obtained from this one-stage correction method are more accurate and less complicated in doing compared to the results of the usual procedure. Because in this method, we have no simplifying assumptions such as infinite Bouguer slab in Bouguer correction or using relative heights in terrain correction that exist in standard methods.

The gravity and the magnetic data sets are utilized to model the Hematite ore body. The cross-gradient joint inversion is used to invert the data sets simultaneously. To discretize the model space, the advanced meshing algorithm (Octree mesh) has been applied. The sparse norm and cross-gradient inversion modules in Python, accessible through Simulation and Parameter Estimation in Geophysics (SimPEG, version 0.17.0) website, have been applied to the inversion process. The sparse norm inversions do not provide reasonable results, particularly for the gravity data set. The estimated density contrasts through the inversion process are very low and unrealistic and on the other hand, the north-south cross sections do not represent a real image from the subsurface sources. The magnetic modeling results obtained through sparse norm inversion also show unrealistic characters, particularly for the 3-dimensional figure of the subsurface anomaly.The cross-gradient inversion acts quite successfully for both gravity and magnetic models in spite of high noise level in gravity data and the weak signal of magnetic data. The results are in good agreement with geological evidences and also former geophysical survey in the survey area. The priority of cross-gradient inversion of gravity and magnetic data sets to separate inversion is quite clear, despite the weak magnetic signal.

The aim of this study is 3-D inversion of magnetic data acquired from the Sorkheh-Dizej iron-bearing region in Zanjan province, Iran, in order to determine the geometrical distribution of the buried magnetic sources. For this purpose, our program discretizes the subsurface region into vertical right rectangular prisms and uses the nonlinear Marquardt-Levenberg algorithm to optimize the unknown parameters of the model, iteratively. To evaluate the applicability of the method, it has been first applied to modeling the synthetic data with added noise. The nonlinear inversion of potential field data has long been used for determining the unknown parameters of the source bodies. One of the major applications of this method is to determine the topography of the basement relief (see, e.g., Bott, 1960; Pedersen, 1977; Bhattacharayya, 1980). In this study, we use a similar approach for modeling the magnetic sources with complicated geological shapes. To do this, the region is discretized into vertical right rectangular prisms. As a result, the unknown geometrical parameters will be the depth to the top and depth to the bottom of each prism. The only other unknown parameter is magnetization which is constant for each prism A right rectangular prism is a widely used geometrical model for 3-D interpretation of magnetic source bodies. Bhattacharayya (1964) presented equations for computing the total field magnetic anomaly due to prismatic models. Kunaratnam (1981) simplified the logarithmic and arctangent terms in these equations using complex notation. The program used in this study uses these simplified expressions for forward modeling of magnetic data. To obtain the body parameters that best describe the observed data, our program uses the Marquardt-Levenberg optimization algorithm (Marquardt, 1963) in an iterative way to minimize the difference between the observed and calculated anomalies. The objective function to be minimized is the sum of the square-roots of the errors at all the data points (equation 1). Marquardt-Levenberg algorithm can be regarded as an interpolation between the Gauss-Newton and Steepest Descent methods. At points distant from the solution, this algorithm acts like the Steepest Descent method (for being faster), but as it approaches the solution it acts more like a Gauss-Newton technique, for being more accurate. This behavior is controlled by a damping factor which is automatically adjusted at each iteration according to the success or failure of the iteration in reducing the objective function. The program that is used in this study is the modified version of the FORTRAN-77 program presented by Rao and Babu (1993). For forming the Jacobian matrices, the program uses the expressions for derivatives from Rao and Babu (1991) and it uses the Cholesky decomposition technique for the factorization of the coefficient matrix (matrix D in equation 4). The input data to the program are the observed magnetic data and the magnetic properties of the region (i.e., magnetic declination and inclination and the regional constant). The program then generates an initial model of adjacent vertical prisms with similar upper and lower depths. There should be one data point above each prism on the surface of the earth. The goodness of fit between the observed data and calculated data is computed and then solving the inverse problem (equation 3) the increments that should be added to each body parameter to gain a smaller objective function in the next iteration are obtained. The iterations are continued until the desired objective function is reached or this residual is negligible. The geometrical configuration of the collection of the prisms at the end of the inversion shows the distribution of the magnetic source body. In order to evaluate the applicability of the method, first we apply it to modeling the synthetic data. The synthetic model consists of three separate rectangular blocks which represent a complex geological configuration (Fig. 1). The blocks have the same magnetization intensity (10 A/m) and the declination and inclination of the magnetization are assumed to be zero and 45 degrees, respectively. In order to make the generated synthetic data resemble the realistic field data, random noise with zero mean and standard deviation of 5 percent of each datum magnitude has been added to the data set. The terrain is discretized into a grid of 10x10 prisms, each with a surface data centered above it. The magnetization is supposed to be known and constant throughout the body. The result of the inversion after 100 iterations has a good similarity to the original model although it can be seen that the accuracy reduces with increasing depth (Fig. 3). We apply the inversion scheme to model the real field magnetic data from Sorkheh-Dizej region in Zanjan province, Iran. The shape of the anomaly map (the region isolated by the rectangle in Fig. 4) is typical of a large tabular body. As non-uniqueness is one of the major concerns in the inversion of potential field data, it is useful to limit the possible solutions by devising constraints on the variation of magnetization during the inversion procedure. The source body is completely buried with no outcrops, but the existence of several iron mines very close to the survey area, and the high amplitude of the anomaly intensity, suggest a similar genesis for the magnetic bodies of the region. Therefore, we performed magnetization intensity measurements on 15 core samples from the region which resulted in a range of 5-15 A/m for this parameter. We assume no remanent magnetization is present and the magnetization is only due to induction. The terrain is divided into a 17x15 grid of prisms and inversion performed for 100 iterations. Fig. 7 shows a view of the result body from East. The vertical extension of this dyke-like body is interpreted between -10 and -210 meters, and the average dip-angle of the body is 70 degrees towards North. The results have been compared with the results of the 3-D compact inversion of pseudo-gravity data. The good agreement between the two models shows the efficiency of the algorithm that is employed for the inversion of geomagnetic data in this study.