Electrical resistivity tomography (ERT) is a widely used for investigating subsurface properties, particularly in near-surface studies. It has found broad application in various fields, such as groundwater exploration, archaeology, environmental monitoring, and hydrogeophysical research, including the evaluation of aquifer parameters. In ERT, electrodes are strategically placed according to the survey goals and site characteristics to gather data. These measurements, which represent the distribution of potential or apparent resistivity, are then analyzed using inverse modeling techniques to obtain the actual resistivity distribution. This process involves solving a nonlinear inverse problem, which aims to minimize discrepancies between field data and theoretical predictions by optimizing an objective function.     The method is based on forward modeling, which simulates the physical behavior of the system, often by solving Poisson’s equation through a finite difference approach. Accurate forward modeling is crucial for effective inversion. In this study, resistivity responses are derived by simulating the flow of current through the Earth's surface, with Poisson's equation serving as the guide. A finite-difference algorithm is employed to discretize the models, incorporating mixed boundary conditions to enhance precision and reliability. One key advantage of the finite-difference method over other approaches is its established ability to quickly approximate solutions for complex and arbitrary structural models, often providing faster results than the finite-element method. The partial differential equations that describe the resistivity problem are derived using the principles of charge conservation and the continuity equation. To solve the inverse problem, the equations are linearized through iterative processes.     A central focus of this study is the application of inverse modeling to electrical resistivity data. The forward and inverse problem formulations, along with their respective solutions, have been implemented in MATLAB, with performance improvements achieved through C programming for computational efficiency. Field data are subject to noise, which may arise from factors such as imperfect measuring instruments, suboptimal field conditions, operator errors, and geological influences. These noise components can significantly affect the inversion process, given the inherent challenges of the inverse problem.     This study investigates the impact of data weighting matrices on the accuracy of geoelectrical data inversion, with focus on electrical resistivity data. The Occam inversion method was utilized as the primary framework for applying various weighting matrices and constraints during the inversion process. Our analysis shows that due to the presence of random noise, variations in the signal-to-noise ratio, the spacing between current and potential electrodes, the different arrays used along a profile, and geological complexities at the data acquisition site, employing data weighting matrices is essential for accurate inversion. Results from synthetic and field models demonstrate that applying a weighting matrix significantly improves the representation of conductive layers and reduces inversion errors. In field studies, validation using agricultural water wells confirmed that inversion results with a weighting matrix closely match geological realities. Additionally, the evaluation of inversion sections using resolution density, upper bounds of the resistivity variation, and sensitivity pattern indicates that the application of weighting matrices produces more reliable results.

The presence of noise in geophysical measurements has undesirable effects on the seismic data. One of the important problems in seismic data processing is attenuation of the noise to the desired form and keeping the original signal. Contamination of seismic data with noise prevents obtaining a proper image of geological structures and seismic data interpretation. In some of the receivers the noise has erratic values and the amplitude is large in relation to other receivers, surprising and do not follow a Gaussian distribution. In reality, not all observed data follow the Gaussian distribution. There may be a group of atypical data that are far away from the majority of data. Atypical data are referred to as outliers or gross errors, which follow other distributions or there is no clear distribution to describe them. These are called erratic noises that do not follow the Gussian distribution. Conventional methods for noise suppression assume Gaussian noise distribution and their performance decreases in the case of erratic noise. The rank reduction based techniques are applied to attenuate weak random seismic noise in a least squares sense. The rank reduction methods are very sensitive to erratic noises and the different results provide. Even a little of erratic noises extremly degrades the performance of the rank reduction methods. More robust estimates are needed such that they are acceptable even when the data do not strictly follow the given distribution. The non-Gaussian and erratic noise are usually produced by wind, incorrect polarity, cultural and traffic noises and so on. In order to solve this problem a new filter based on repeating the reduction of the rank of Hankel matrix is introduced. The method is called iteratively reweighted rank reduction (IRRR). This method is combination of iterative weighted least squares procedure (IRLS) and weighting low-rank approximations (WLRA). In this method after transferring data into the frequency domain, for each constant frequency slice an individual Hankel matrix is created and then by using singular value decomposition (SVD) a rank reduced matrix is obtained. Later on using the iterative algorithm, until the desired convergence is achieved, the combined weight values are obtained from the original matrix and rank reduced matrix. Parameter that controls the convergence of the method is the weighting function. The role of weighting function is reducing or completely removing of the erratic noise from data. Here the weighting function we used was Tukey’s Biweight function. In order to maintain the statistical performance and the ability of the method we define regulation parameter τB. Regulation parameter is calculated based on the estimates to the median and the median absolute deviation. These two estimates are not sensitive to erratic noise. The advantage of this method in comparison to the other rank reducing methods is the attenuation of erratic noise and at the same time random noise. This method is application to 2D and 3D seismic data. Performance of the method was tested on synthetic and real seismic data. The results showed superior performance of the method in attenuating erratic noises.

In this article, a fabulous method for database retrieval is proposed. The multiresolution modified wavelet transform for each of image is computed and the standard deviation and average are utilized as the textural features. Then, the proposed modified bitbased color histogram and edge detectors were utilized to define the high level features. A feedback-based dynamic weighting of shape, color and textural features composition produce a resistant feature vectors for image retrieval and recall. A comprehensive and unified matching scheme based on matrix error rate technique was accomplished for similarity of image and retrieval procedure. The feature vectors size in our algorithm is the least one evaluated to the different techniques. Furthermore, the calculation time of previously published techniques is much more than the presented algorithm which is a benefit in proposed retrieval method. The experimental results illustrates that novel algorithm obtains more precious in retrieval and the efficiency in evaluating with the other techniques and algorithms at Corel color image database.

Background and Objectives: The accurate prediction of soil hydraulic parameters is essential to simulate the transport of water, solutes and contaminants in soil, management of the agricultural water, management of production and conservation of soil and water. The least squares regression is the most common method applied for fitting the soil-water retention curve (SWRC) function to the observed data-points to optimize its parameters. However, the variance of SWRC data varies in different moisture content and therefore, unlike the wet-end of SWRC, the conventional unweighted regression method may not be sufficiently effective in estimating its dry-end (higher suctions). While, selected soil processes, such as soil moisture redistribution or transport of contaminants in soil occur in low soil moisture contents which correspond to the dry-end of the curve. Consequently, in fitting different hydraulic functions to SWRC, the accuracy of SWRC parameters would be improved in the low-moisture range content by determining the appropriate weights for data points. Accordingly, the objective of this study was to investigate the effect of properly weighting the SWRC data points on increasing the accuracy of the estimated soil hydraulic parameters. Materials and Methods: In this study, undistributed soil samples were collected from 20 cm soil depth with six replications. The SWRC of the samples were measured at suctions of 0 to 15000 cm. In order to fit the van Genuchten equation of SWRC on measured values of h(θ ) and to estimate its hydraulic parameters through RETC code, the weighted least squares regression method was also used along with the conventional standard least squares regression method. For this purpose, some weights were assigned to the data points as the inverse of the variance of the measured volumetric soil water content in six replications, so that, the effect of the curve estimation error in low moisture contents were considered by assigning larger weights in the regression fitting. Finally, the accuracy of unweighted and weighted regression in the fitting of the SWRC model on the measured data was compared using statistical criteria and a suitable method for the averaging of hydraulic parameters was introduced. Results: Comparison of the fitted hydraulic parameters by unweighted and weighted regression showed that the mean values of the residual water content (Ɵ r), saturated water content (Ɵ s) and α parameter (reciprocal of air-entry suction) in the weighted method were lower than the unweighted method, however the n parameter values obtained by the weighted method were higher than unweighted method. The extraction of SWRC based on hydraulic parameters estimated by both unweighted and weighted methods showed that the weighted method increases the accuracy of the estimation and reduces the percentage of point error in lower moisture contents (higher suctions) compared to the unweighted method. Although, the weighting method generally increased the error of SWRC estimation and decreased the correlation between estimated and observed moisture content. Comparison of two methods of averaging of soil hydraulic parameters in the replicates showed that in both unweighted and weighted regression, the method II (averaging of volumetric water contents at different suctions and estimating hydraulic parameters) had a lower error in compression to method I (averaging of hydraulic parameters). However, in estimation of SWRC in lower moisture contents, the method I had lower point error than that of method II. The method I reduced the error percentage in the weighting method. Conclusion: Assigning proper weight to SWRC data points improves curve fitting in lower moisture range, which is very important in simulating redistribution of moisture or transfer of contaminants transport in the soil processes, particularly in arid and semi-arid conditions.

The neoclassical growth model is tested by use of panel data procedure in this research. In the econometric test, simoultanously time series and cross detection will be compared on the basis of panel data method through which their observed points increase and consequently the estimation efficiency will be increased. The examination of neoclassical growth theory has been done with reference to external & internal factors of 52 selected countries from 1960 to 2000. The independent variable of model has been selected on the basis of the result of previous research which explains the result in three separate models: developed countries, developing countries, and whole countries. These factors are such as: Gross National Products with lag of period, work force age, growth rate, education level, the change of capital accumulation and economic trade volum. The consequences of this research is that: neoclassical growth model can explain the major part of economic growth of the countries with use of internal variables. Also with the use of panel procedure of fixed effect, we can see the fundamental differences and structure of the growth process for different countries; and show how the economic, and social conditions affect on the growth.