Generally, the measured secondary field data is inverted into resistivity using two principal models; the homogeneous half-space model and the layered half-space model. While the homogeneous half-space Inversion uses single frequency data, the Inversion is done individually for each of the frequencies used, the multi-layer 1D Inversion is able to take the data of all frequencies available into account. The resulting parameter of the half-space Inversion is the apparent resistivity which is the inverse of the apparent conductivity. It's possible that using the fast method to calculate the apparent resistivity, if the distance between the HEM sensor and the top of the half-space is known. Unfortunately, the dependency of the secondary field on the half-space resistivity is highly non-linear. Thus, the Inversion is not straightforward and the apparent resistivities have to be derived by the use of look-up tables, curve fitting or iterative Inversion procedures (Fraser, 1978; Siemon, 1997; Siemon, 2001).The usual technique for Inversion of airborne electromagnetic data frequency domain (HEM) data is a 1D single site Inversion, because of the 2D and 3D Inversion of HEM data wants very powerful computer hardware. Some Inversion method for electromagnetic data Inversion suggested. Usually this method updated for ground electromagnetic methods. One of the methods employed in the Inversion of airborne electromagnetic data frequency domain (HEM), Levenberg-Marquardt method Inversion (MLI) is looking for smoothing fitted to the data in the Inversion algorithm; this Inversion method based on least squares criteria, seeking a modelby minimizing the residuals of an objective function. Marquardt’s Inversion only pursuits the largest fitting of simulation data to original measurements, and has the characteristics of simple algorithm and fast calculation. In this procedure usually HEM data smoothed and then used in the Inversion procedure, but any variation in data change results. For stability of Inversion procedure, it is suggested that stitched-together 1-D models along the profile that each sounding inverted by Constrained neighbor sounding and each layer of each sounding inverted by depth Constrained neighbor layers. In addition used smoothing Constrained in Inversion procedure instead of smoothing a data like Marquardt–Levenberg Inversion.In this paper, Starting model determined for apparent resistivity with Mundry technique and for centroied depth with Weidelt technique. To using this method, the auto Inversion cod written in MATLAB software environment that inputs are real and imaginary part of data with sensor altitude and output is inverted model with misfit. In the following this algorithm tested on standard synthetic data, the model chosen for the generation of synthetic data represents a layered earth structure having an inhomogeneous top layer in order to study the influence of shallow resistivity variations on the appearance of deep horizontal conductors in one-dimensional Inversion results. The Inversion of synthetic data results shown this technique for Inversion HEM data improved the results and is much more accurate than Marquardt–Levenberg Inversion. Finally the Inversion algorithm used to invert a set of real DIGHEM field data from Mirgah Naqshineh area in Saqqez of Kurdistan and interpretation of results according to geology information of area.

Summary Radio magnetotelluric (RMT) and ground penetrating radar (GPR) are known as the near-surface geophysical methods in groundwater investigations. The RMT method provides information about the variation of the electrical resistivity of 50 m of the uppermost part of the ground. High-resolution structural information can be extracted from the GPR processed sections of the very shallow ground. Combining the obtained data using these two methods lead to valuable results on the identification of near-surface layers and structures. In this study, we propose a new constraint for the two dimensional (2D) Inversion of the RMT data. We have investigated a known aquifer located in Heby, Sweden, to assess the Constrained Inversion results using a joint interpretation approach. RMT and GPR surveys have been carried out along two survey lines having the lengths of 870 m and 550 m, respectively. The results show that thick saturated zones are distinguished quite well either in the joint interpretation results or when using the Constrained Inversion approach. In such cases, the main problem is to locate the water table in the inverted RMT sections. Imposing smooth regularization in the Inversion results turns rather sharp boundaries into the gradual transition zone in the final resistivity models. Thus, using the GPR common-offset (CO) reflections as constraints in the Inversion of the RMT can recover the water table as a sharp interface in the RMT inverted model. Thin saturated zone has not been recognized in the RMT sections, due to low resolution of the RMT method. For verification of the results, we have evaluated a synthetic model with similar physical properties to the study area. In such circumstances, the results need to be improved either in the joint interpretation or the Constrained Inversion approach using CO sections. Hence, harder constraints through our proposed scheme have been incorporated into the Inversion routine to detect a thin aquifer and achieve a more realistic model. Introduction The RMT and GPR methods are among the most useful non-invasive methods, which can provide continuous data for groundwater exploration. The RMT method due to its limited range of frequencies (10-250 KHz) has low resolution, especially at very shallow depth, and the GPR method itself suffers from its limited penetration depth. Hence, it seems that combining the modeling results of these two methods leads to a more accurate anomaly definition. Reflection (seismic or GPR) data are usually used as constraints in electromagnetic data Inversion. Although all reflectors in seismic and GPR sections are not attributed to the distinct resistivity contrasts, in GPR they are mainly related to the dielectric contrast or may occur due to the thin layers embedded in homogenous geological formations. Thus, we propose an alternative scheme to incorporate interfaces with distinct resistivity contrast in the RMT data Inversion. Methodology and Approaches Using all GPR reflections as constraints in the RMT data Inversion may cause some artifacts in the final inverted model. In low clay content formations, such as clean sand and gravel formations, dielectric constant and resistivity are mainly related to the volumetric water content. Therefore, we propose a new structural constraint based on the assumption that the resistivity and water content contrasts occur at the same boundaries. To establish this constraint, we have used common mid-point (CMP) velocity analysis as well as the combination of Topp’ s and Archie’ s relationships. As a result, an initial resistivity model has been deduced from the CMP velocity analysis that can be used as a priori information in the RMT data Inversion. Results and Conclusions Thick saturated zones (having thicknesses of more than 10 m) have been distinguished quite well by applying smooth constraint Inversion of the RMT data as the joint interpretation of The RMT and GPR data leads to a reasonable outcome in this regard. Although sharp boundaries are mapped as gradual interfaces in the inverted resistivity section of the RMT data, such interfaces are recovered well by incorporating the GPR result as a priori information in the Constrained Inversion of the RMT data. The water table at a depth of 10 to 20 m, and consequently, the saturated zone is resolved well in this Constrained Inversion method. It correlates to the borehole log information. On the other hand, thin saturated layers could not be distinguished in the RMT sections due to its low resolution. It means that the water table at a depth of 10 to 15 m is not mainly detected when only the determinant mode data are used. In such areas, the Constrained Inversion of the RMT data using the water table location deduced from the CO GPR data also fails. However, we have incorporated harder constraints through the model covariance matrix and prior information in our proposed Constrained Inversion routine. Using this approach, a local thin aquifer has been recognized well. Furthermore, our proposed technique can be used in the Inversion of other electric and electromagnetic data.

A Constrained nonlinear optimization method based on nonlinear programming techniques has been applied to map geometry of bedrock of sedimentary basins by Inversion of gravity anomaly data. In the Inversion, the applying model is a 2-D model that is composed of a set of juxtaposed prisms whose lower depths have been considered as unknown model parameters. The applied Inversion method is a nonlinear one, which minimizes the objective functions by definition of different objective functions and an initial simple model to improve the initial model parameters.In this study, for different cases, sufficient objective functions are defined based on the condition which is encountered in the inverse problem. To control the under- determinacy part of the inverse problem and to prevent unreasonable instability in the resultant model, damping terms are added to the objective function. The act of synthetic Inversion for different cases of parameterization has been examined and the results are analyzed. The results have almost depicted the recovery of the model and also fitting of the original and model response data. In addition, the method has been used to invert real gravity data in Aman Abad area. From the Inversion results, depths of the basin, features like fractures and uplift in bedrock, along specific profiles have been determined. Thicker parts of sediments in the basin along the profiles have also been recognized, which have the potential for exploring drinking water in this area.

Here we study slip distribution of the June 18, 2007 Mw 5. 5 Kahak and September 27, 2010 Mw 5. 9 Kazerun earthquakes by using Constrained non-negative least-squares linear slip Inversion method for regional broadband seismic data. Hundreds of Inversions were carried out to obtain the optimal parameters used in the process, including rupture velocity and rise time. We used the rupture velocity of 2. 6 km/s (0. 75 Vs) and the rise time of 1. 4 s for the first event, and 2. 8 km/s (0. 75 Vs) and 2. 1 s for the second one. Results show the rupture with the peak slip of 8. 6 cm and 14. 3 cm, and the total seismic moment release of 1. 59×1024 dyne-cm and 2. 80×1025 dyne-cm for the Kahak and Kazerun earthquakes, respectively. Owing to the non-uniqueness of the Inversion problem, we presented a set of solutions for both events. Furthermore, the sensitivity of the slip models to some influential parameters such as rupture velocity and rise time was explored. Moreover, we used two ways for identifying the main/preferred fault plane, which are compatible with one another: First, discerning the main fault plane by using the slip Inversion method,second, distinguishing the main fault plane by the use of aftershocks. To the best of our knowledge, this is the first time to apply the linear finite-fault Inversion method to moderate earthquakes in Central Iran and Zagros seismotectonic provinces to model a set of rupture histories at regional distances.

Inversion of magnetic data is one of the important steps in the interpretation of practical magnetic data. The Inversion result can be obtained by minimization of Tikhonov objective function. The determination of an optimal regularization parameter is highly important in magnetic data Inversion. In this paper, an attempt has been made to use unbiased predictive risk estimator (UPRE) method in selecting the best regularization parameter for 3D Constrained Inversion of magnetic data using gradient projection reduced Newton (GPRN) algorithm. To achieve this goal, an algorithm has been developed to estimate this parameter. The validity of the proposed algorithm has been evaluated by magnetic data acquired from a synthetic model. The results have been compared with the results of generalized cross validation (GCV) method. The GCV method failed to estimate the regularization parameter, but the UPRE method could find the best regularization parameter. Then, the algorithm was used for Inversion of real magnetic data obtained from Allah Abad iron deposit. The results of three-dimensional (3-D) Inversion of magnetic data from this iron deposit show that the GPRN algorithm can provide an adequate estimate of magnetic susceptibility and geometry of subsurface structures of mineral deposits. A comparison of the Inversion results with drilling data clearly indicate that the proposed algorithm can be used for 3-D Inversion of magnetic data to estimate precisely the magnetic susceptibility and geometry of magnetized ore bodies.

This paper examines the work of Immanuel Kant in the light of a new theory on the nature of truth, knowledge and falsehood (the Inversion Theory of Truth). Kant’s idea that knowledge could be absolutely certain, and that its truth must correspond with reality, is discredited by a dissection of the Correspondence Theory of Truth. This examination of the nature of truth, as well as knowledge and falsehood, is conducted with reference to Sir Karl Popper’s writings on regulative ideas, the criterion of demarcation and the principle of falsifiability. It is argued that if truth is to be regarded as certain, it should be used to describe objects and events in the objective (noumenal) state, and that subjective knowledge must contain (and is improved by) falsehood. Perceptions and knowledge are obtained by the biological and evolutionary process of Active Subjectivism. Ideas we have knowledge of can be metaphysical or scientific, according to Popper’s Criterion of Demarcation. Kant’s “Copernican revolution” claim that our intellect imposes absolutely true laws on nature could not allow for the possibility that ideas might be constructed from fallible perceptions, and hence that all knowledge is uncertain. Instead, he developed a Critique of Practical Reason in which religion, though not provable through logical reasoning, could be proved by our innate moral sense, giving us a Categorical Imperative that could lead to perverse results. By rejecting the absolute certainty of a priori knowledge, and admitting a degree of essential falsehood, we arrive at a more reasonable grounding for moral behavior.

This study was aimed at examining the types of Inversion and their severity using the thermodynamic indices of the atmosphere such as SI, LI, KI and TT at Bandar Abbas Station for 2010-2020. In this study, Radioosvand data at the Bandar Abbas Station was obtained and used from the University of Wioming for the last 11 years (3. 5 local) during the last 11 years (2010 to 2020). The results of the analysis showed that the average number of Inversion phenomenon in Bandar Abbas was 501 cases per year, as in some days several types of Inversion were observed at different altitude. Of these Inversion, about 31. 6 % are related to radiation temperature Inversion, 4. 3 % front, and another 64. 1 % for subsidence Inversion. Due to the air session underneath, the share of subsidence Inversions is more than other types of Inversion. In the meantime, the most severe Inversion of subsidence was 1354 and the weakest Inversions were with 29 cases and fronts. In general, the long-term average intensity coefficient of Inversion of Bandar Abbas station with a coefficient of 0. 062 indicates that the intensity of the city's Inversion is mostly extremely severe, which can be very destructive effects both environmentally and physical health in the city's residents. Bandar Abbas follow. The correlation between the Inversion elements also showed that by reducing the thickness of the Inversion layer, the intensity of temperature Inversion also increased.