Due to non-uniqueness of GEOPHYSICAL INVERSE PROBLEMS and measurement errors, the inversion uncertainties within the model parameters are one of the most significant necessities imposed on any modern INVERSE theory. Uncertainty analysis consists of finding equivalent models which sufficiently fit the observed data within the same error bound and are consistent with the prior information. In this paper, we present a non-parametric block-wise bootstrap resampling method called moving block bootstrapping (MBB) for uncertainty analysis of GEOPHYSICAL INVERSE solutions. In contrast to conventional bootstrap in which the dependence structure of data is ignored, the block bootstrap considers the dependency and correlation among the observed data by resampling not individual observations, but blocks of observations. The application of the proposed strategy to different synthetic INVERSE PROBLEMS as well as to synthetic and real datasets of geo-electrical sounding inversion is presented. The results demonstrated that through the block bootstrap, it is possible to effectively sample the equivalence regions for a given error bound.

Imaging and inversion of potential field geophysics data permit the estimation of the source-property distribution in2D/3D space. In this work, the advantages and performances of a fast gradient-based imaging technique, known as the normalized full gradient (NFG), are examined to depict the source distribution in 2D space. In addition, a conventional Tikhonov norm-based inversion technique is used to estimate physical properties in 3D space. The functionality of these approaches are evaluated first for synthetic data sets, which involve three scenarios of a single source, a sloping source and a combination of them. Where the constructed sources and property distributions (i. e. density contrast and magnetic susceptibility) were compared. Then, algorithms were employed to the potential field data pertaining to the Shavaz iron-bearing deposit in Iran. Both methods have shown accurately the centroid depth of all sources, but the boundary is better preserved by the inversion method for simulated sources and the real data set. Iron ore occurrence is in the forms of hematite and magnetite lens which mainly has an elongation along a NW-SE strike, indicating the impact of the Dehshir-Baft fault on trapping the iron. It is worth pointing out that the inversion method led to more accurate information on geometry of the sought source by estimating density contrast and magnetic susceptibility values, but with higher execution time. In addition, the NFG algorithm took less time to run, more sensitive to noisy data, and severely smeared-out the border of the source responsible for potential field anomaly.

GEOPHYSICAL data inversion has a prominent role in geo-structural investigations. In this study, the corrected GEOPHYSICAL data of Doroh mining area were modeled to obtain the underground body's shape and other parameters such as susceptibility. At first, magnetic data were filtered and then modeled by the magnetic compact inversion method (Last & Kubik) and properties including depth, susceptibility and the deposit shape were provided. This inversion can be described according to basic principles to minimize the cross-sectional area of the sources. The under-surface area was divided into horizontal prisms with an extreme length and fixed magnetic susceptibility. The simulation was performed using synthetic magnetic anomalies generated by compact bodies embedded in an inducing magnetic field. It was shown that this modeling was capable of solving underdetermined PROBLEMS with good accuracy in the presence of moderate noise data. At first, a MATLAB code was employed to implement the algorithm. The output results from the synthetic model demonstrated the accuracy of the code. The code was then applied to real magnetic data. The results showed acceptable accuracy.A statistical analysis was also carried out on the IP&Rs normalized data. Normalization was done because the statistical analysis was tender to data dispersion. Therefore, the outlier data was identified by a box plot of SPSS software and replaced using the Q method. Then the correlation coefficient was used to determine the dispersion extent. The statistical analysis showed a compact and rich body under the surveyed profiles. Then for providing more information on this area, apparent resistivity and induced polarization data were modeled by the RES2DINV software. RES2DINV is a computer program that automatically creates a two-dimensional resistivity model for the electrical data of the subsurface. In this software, the under-surface area is divided into horizontal prisms with an extreme length. In some situations, particularly where there are large resistivity variations near the ground surface, better results can be obtained by using narrower model cells. In almost all cases, this gives the optimum results. A forward modeling subroutine was used to calculate the apparent resistivity values, and a non-linear least-square optimization technique was used for the routine inversion. The program supports both finite-difference and finite-element forward modeling techniques.The studied area is located in Flysch zone in the Southeast of Doroh City in Sarbishe in the South Khorasan Province. Lithology of this area includes shale, sandstone and thin layer limestone, here and there. In this area, magnetic surveys were done via 40 profiles with a north eastern-south western strike and 1200 survey points. Apparent resistivity and induced polarization surveys were done in five profiles with a dipole-dipole array and 700 survey points. The magnetic consideration results showed three compact bodies under the surveyed profiles which were named A, B and C. The depths of these bodies were 80 –100 meters. The results of IP & Rs modeling showed that these anomalies were located near the surface and are dyke-shaped. The results of magnetic compact inversion methods and modeling are in agreement with IP & Rs inversion results. For an exact review of this body, a few points were eventually proposed for drilling.

The problem of constructing a matrix by its spectral information is called INVERSE eigenvalue problem (IEP) which arises in a variety of applications. In this paper, we study an IEP for arrowhead matrices in different cases. The problem involves constructing of the matrix by some eigenvalues of each of the leading principal submatrices and one eigenpair. We will also investigate this problem and its variants in the cases of matrix entries being real, nonnegative, positive definite, complex and equal diagonal entries. To solve the PROBLEMS, a new method to establish a relationship between the IEP and properties of symmetric and general form of matrices is developed. The necessary and sufficient conditions of the solvability of the PROBLEMS  are obtained. Finally, some numerical examples are presented.

After offering an overview of some of the main themes of Popper’s political thought, the paper argues that his account faces two PROBLEMS relating to institutions. The first is that while Popper stresses the ‘rational unity of mankind’, and the potential for any of us to furnish criticisms of public policy, it is not clear what institutional means currently exist for this to enable this to take place. Second, Popper has stressed the conjectural character of even our best theories. However, at any point, some theories will have fared better in the face of criticism than others, and they may give us important information about constraints on our actions. At the same time, as ordinary citizens we may not be in a good position to understand the theories in question, let alone appraise the state of the specialised discussion of them. There is, it is suggested, a case for thinking of ways to institutionally entrench such fallible theories, especially in the current setting in which social media play an important role

In this paper, we represent an inexact INVERSE subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=lBx [Q.Ye and P. Zhang, Inexact INVERSE subspace iteration for generalized eigenvalue PROBLEMS, Linear Algebra and its Application, 434 (2011) 1697-1715]. In particular, the linear convergence property of the INVERSE subspace iteration is preserved.

In this paper a new method for solving nonlinear INVERSE PROBLEMS is presented. In order to overcome severe nonlinear behaviors, the domain is divided into several sub-domains. In each sub-domain, by using an optimization method and finite element method and also by employing the information obtained by the previous sub-domain, the unknown boundary conditions are determined.To show the efficiency of the proposed method, an INVERSE non-linear heat conduction problem and an INVERSE non-linear thermoelastic problem are analyzed by both the whole domain and the present methods. According to the obtained results, it is shown that the presented domain decomposition method is more efficient and accurate than the whole domain method.

In this paper, first a great number of INVERSE PROBLEMS which arise in instrumentation, in computer imaging systems and in computer vision are presented.Then a common general forward modeling for them is given and the corresponding inversion problem is presented. Then, after showing the inadequacy of the classical analytical and least square methods for these ill posed INVERSE PROBLEMS, a Bayesian estimation framework is presented which can handle, in a coherent way, all these PROBLEMS. One of the main steps, in Bayesian inversion framework is the prior modeling of the unknowns. For this reason, a great number of such models and in particular the compound hidden Markov models are presented. Then, the main computational tools of the Bayesian estimation are briefly presented. Finally, some particular cases are studied in detail and new results are presented.