Journal articles: 'Euler deconvolution'

1

Florio, Giovanni, and Maurizio Fedi. "Multiridge Euler deconvolution." Geophysical Prospecting 62, no. 2 (October 11, 2013): 333–51. http://dx.doi.org/10.1111/1365-2478.12078.

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Hansen, R. O., and Laura Suciu. "Multiple-source Euler deconvolution." GEOPHYSICS 67, no. 2 (March 2002): 525–35. http://dx.doi.org/10.1190/1.1468613.

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Rapid three-dimensional (3-D) source location methods can be extremely useful in framing a subsurface structural model from gravity or magnetic data. However, existing implementations of Euler deconvolution are limited to a single source in each window. This can be a significant limitation in areas of complex structure. We have generalized the method to the multiple-source case, and implemented the 3-D algorithm. Results from synthetic data and from the Gold Acres mining district in Nevada suggest that the new algorithm can be a useful interpretive tool.

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Nabighian, Misac N., and R. O. Hansen. "Unification of Euler and Werner deconvolution in three dimensions via the generalized Hilbert transform." GEOPHYSICS 66, no. 6 (November 2001): 1805–10. http://dx.doi.org/10.1190/1.1487122.

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The extended Euler deconvolution algorithm is shown to be a generalization and unification of 2‐D Euler deconvolution and Werner deconvolution. After recasting the extended Euler algorithm in a way that suggests a natural generalization to three dimensions, we show that the 3‐D extension can be realized using generalized Hilbert transforms. The resulting algorithm is both a generalization of extended Euler deconvolution to three dimensions and a 3‐D extension of Werner deconvolution. At a practical level, the new algorithm helps stabilize the Euler algorithm by providing at each point three equations rather than one. We illustrate the algorithm by explicit calculation for the potential of a vertical magnetic dipole.

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Zhang, Changyou, Martin F. Mushayandebvu, Alan B. Reid, J. Derek Fairhead, and Mark E. Odegard. "Euler deconvolution of gravity tensor gradient data." GEOPHYSICS 65, no. 2 (March 2000): 512–20. http://dx.doi.org/10.1190/1.1444745.

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Tensor Euler deconvolution has been developed to help interpret gravity tensor gradient data in terms of 3-D subsurface geological structure. Two forms of Euler deconvolution have been used in this study: conventional Euler deconvolution using three gradients of the vertical component of the gravity vector and tensor Euler deconvolution using all tensor gradients. These methods have been tested on point, prism, and cylindrical mass models using line and gridded data forms. The methods were then applied to measured gravity tensor gradient data for the Eugene Island area of the Gulf of Mexico using gridded and ungridded data forms. The results from the model and measured data show significantly improved performance of the tensor Euler deconvolution method, which exploits all measured tensor gradients and hence provides additional constraints on the Euler solutions.

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Keating, Pierre B. "Weighted Euler deconvolution of gravity data." GEOPHYSICS 63, no. 5 (September 1998): 1595–603. http://dx.doi.org/10.1190/1.1444456.

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Euler deconvolution is used for rapid interpretation of magnetic and gravity data. It is particularly good at delineating contacts and rapid depth estimation. The quality of the depth estimation depends mostly on the choice of the proper structural index and adequate sampling of the data. The structural index is a function of the geometry of the causative bodies. For gravity surveys, station distribution is in general irregular, and the gravity field is aliased. This results in erroneous depth estimates. By weighting the Euler equations by an error function proportional to station accuracies and the interstation distance, it is possible to reject solutions resulting from aliasing of the field and less accurate measurements. The technique is demonstrated on Bouguer anomaly data from the Charlevoix region in eastern Canada.

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FitzGerald, Desmond, Alan Reid, and Philip McInerney. "New discrimination techniques for Euler deconvolution." Computers & Geosciences 30, no. 5 (June 2004): 461–69. http://dx.doi.org/10.1016/j.cageo.2004.03.006.

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Mu, Yaxin, Xiaojuan Zhang, Wupeng Xie, and Yaoxin Zheng. "Automatic Detection of Near-Surface Targets for Unmanned Aerial Vehicle (UAV) Magnetic Survey." Remote Sensing 12, no. 3 (February 1, 2020): 452. http://dx.doi.org/10.3390/rs12030452.

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Great progress has been made in the integration of Unmanned Aerial Vehicle (UAV) magnetic measurement systems, but the interpretation of UAV magnetic data is facing serious challenges. This paper presents a complete workflow for the detection of the subsurface objects, like Unexploded Ordnance (UXO), by the UAV-borne magnetic survey. The elimination of interference field generated by the drone and an improved Euler deconvolution are emphasized. The quality of UAV magnetic data is limited by the UAV interference field. A compensation method based on the signal correlation is proposed to remove the UAV interference field, which lays the foundation for the subsequent interpretation of UAV magnetic data. An improved Euler deconvolution is developed to estimate the location of underground targets automatically, which is the combination of YOLOv3 (You Only Look Once version 3) and Euler deconvolution. YOLOv3 is a deep convolutional neural network (DCNN)-based image and video detector and it is applied in the context of magnetic survey for the first time, replacing the traditional sliding window. The improved algorithm is more satisfactory for the large-scale UAV-borne magnetic survey because of the simpler and faster workflow, compared with the traditional sliding window (SW)-based Euler method. The field test is conducted and the experimental results show that all procedures in the designed routine is reasonable and effective. The UAV interference field is suppressed significantly with root mean square error 0.5391 nT and the improved Euler deconvolution outperforms the SW Euler deconvolution in terms of positioning accuracy and reducing false targets.

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Mushayandebvu, Martin F., P. van Driel, Alan B. Reid, and James Derek Fairhead. "Magnetic source parameters of two‐dimensional structures using extended Euler deconvolution." GEOPHYSICS 66, no. 3 (May 2001): 814–23. http://dx.doi.org/10.1190/1.1444971.

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The Euler homogeneity relation expresses how a homogeneous function transforms under scaling. When implemented, it helps to determine source location for particular potential field anomalies. In this paper, we introduce an additional relation that expresses the transformation of homogeneous functions under rotation. The combined implementation of the two equations, called here extended Euler deconvolution for 2-D structures, gives a more complete source parameter estimation that allows the determination of susceptibility contrast and dip in the cases of contact and thin‐sheet sources. This allows for the structural index to be correctly chosen on the basis of a priori knowledge about susceptibility and dip. The pattern of spray solutions emanating from a single source anomaly can be attributed to interfering sources, which have their greatest effect on the flanks of the anomaly. These sprays follow different paths when using either conventional Euler deconvolution or extended Euler deconvolution. The paths of these spray solutions cross and cluster close to the true source location. This intersection of spray paths is used as a discriminant between poor and well‐constrained solutions, allowing poor solutions to be eliminated. Extended Euler deconvolution has been tested successfully on 2-D model and real magnetic profile data over contacts and thin dikes.

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Mushayandebvu, M. F., V. Lesur, A. B. Reid, and J. D. Fairhead. "Grid Euler deconvolution with constraints for 2D structures." GEOPHYSICS 69, no. 2 (March 2004): 489–96. http://dx.doi.org/10.1190/1.1707069.

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The conventional formulation of 3D Euler deconvolution assumes that the observed field in each Euler window varies in all directions. Where the source is 2D, this assumption leads to the production of poorly constrained solutions. If the source is 2D, the problem leads to a rank deficient normal equations matrix having an eigenvector associated with a zero eigenvalue. This vector lies in the horizontal plane and is pointing along the strike direction, thus allowing for the identification of a 2D structure and its strike. Finding a pseudoinverse via eigenvector expansion allows accurate source location, and the strike information allows the automatic implementation of profile‐based techniques like extended Euler deconvolution to gridded data, thus allowing for the first time the estimation of strikes, dips, and susceptibilities from grids using an automatic process. We present a grid‐based version of Euler deconvolution that has the ability to define within an Euler operating window whether the source is 2D or 3D in character so that the solutions can be treated differently. We illustrate the new approaches on model and real data.

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Cooper, G. R. J. "Euler deconvolution in a radial coordinate system." Geophysical Prospecting 62, no. 5 (April 23, 2014): 1169–79. http://dx.doi.org/10.1111/1365-2478.12123.

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Cooper, Gordon R. J. "Euler Deconvolution Applied to Potential Field Gradients." Exploration Geophysics 35, no. 3 (September 2004): 165–70. http://dx.doi.org/10.1071/eg04165.

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Rodrigues, Rafael Saraiva, David Lopes de Castro, and João Andrade dos Reis Júnior. "CHARACTERIZATION OF THE POTIGUAR RIFT STRUCTURE BASED ON EULER DECONVOLUTION." Revista Brasileira de Geofísica 32, no. 1 (March 1, 2014): 109. http://dx.doi.org/10.22564/rbgf.v32i1.400.

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ABSTRACT. The Euler deconvolution is a semi-automatic interpretation method of potential field data that can provide accurate estimates of horizontal position and depth of causative sources. In this work we show the application of 3D Euler Deconvolution in gravity and magnetic maps to characterize the rift structures of the Potiguar Basin (Rio Grande do Norte and Ceará States, Brazil) using the structural index as a main parameter, which represents an indicator of the geometric form of the anomalous sources. The best results were obtained with a structural index equal to zero (for residual gravity anomalies) and 0.5 (for magnetic anomalies reduced to the pole), a spatial window size of 10 km, which is used to determine the area that should be used in the Euler Deconvolution calculation, and maximum tolerance of error ranging from 0 to 7%. This parameter determines which solutions are acceptable. The clouds of Euler solutions allowed us to characterize the main faulted limits of the Potiguar rift, as well as its depth, dip and structural relations with the Precambrian basement. Keywords: Euler deconvolution, potential field, structural index, Potiguar rift. RESUMO. A deconvolução de Euler é um método de interpretação semiautomático de dados de métodos potenciais, capaz de fornecer uma estimativa da posição horizontal e da profundidade de fontes anômalas. Neste trabalho, mostraremos a aplicação da deconvolução de Euler 3D em mapas gravimétricos e magnéticos para caracterizar as estruturas rifte da Bacia Potiguar (RN/CE), utilizando como principal parâmetro o índice estrutural, que representa um indicador da forma geométrica da fonte anômala. Os melhores resultados foram obtidos com um índice estrutural igual a zero (para as anomalias gravimétricas residuais) e 0,5 (para as anomalias magnéticas reduzidas ao polo), tamanho da janela espacial igual a 10 km, que ´e utilizada para determinar a área que deve ser usada para o cálculo da deconvolução de Euler, e tolerância máxima do erro variando de 0 a 7%, que determina quais soluções são aceitáveis. As nuvens de soluções de Euler nos permitiram caracterizar os principais limites falhados do rifte Potiguar, bem como suas profundidades, mergulho e relações estruturais com o embasamento Pré-cambriano. Palavras-chave: deconvolução de Euler, métodos potenciais, índice estrutural, rifte Potiguar.

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Davis, Kristofer, Yaoguo Li, and Misac N. Nabighian. "Effects of low-pass filtering on the calculated structural index from magnetic data." GEOPHYSICS 76, no. 4 (July 2011): L23—L28. http://dx.doi.org/10.1190/1.3587216.

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Euler and extended Euler deconvolution applications use an assumed structural index (SI) or calculate the SI, respectively, for magnetic anomaly data within a specified window. The structural index depends on the source type: specifically, the rate at which the field produced by the source decays. We have examined the effects that the application of low-pass filtering to magnetic data has on estimating the SI. Using a simple low-pass filter, we derived the SI for filtered-field solutions directly over, and away from, a target based on the magnetic potential of a vertical dipole [Formula: see text]. We validated this approach by applying extended Euler deconvolution to synthetic and field examples. In general, filtered magnetic data will decrease the numerically determined SI to a value lower than the theoretical one. The slope and cutoff wavelength of the filter directly affect the estimated SI solutions. The results prove that one must take into account filtering for the application of Euler deconvolution to locate dipole anomalies for unexploded ordnance detection.

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Stavrev, Petar, and Alan Reid. "Euler deconvolution of gravity anomalies from thick contact/fault structures with extended negative structural index." GEOPHYSICS 75, no. 6 (November 2010): I51—I58. http://dx.doi.org/10.1190/1.3506559.

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The concept of extended Euler homogeneity of potential fields is examined with respect to all variables of length dimension in their analytical expressions. This reveals the possible existence of positive degrees of homogeneity or corresponding negative structural indices considered as extensions of the Thompson’s structural indices in Euler deconvolution. This approach is implemented for a contact gravity model, represented by a 2D semi-infinite slab with large thickness relative to its depth. Applying Euler deconvolution on synthetic and field data indicates that the positive degree of homogeneity, i.e., the extended negative structural index, is the appropriate one for the inversion of gravity anomalies from contact structures.

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15

Florio, G., M. Fedi, and R. Pasteka. "On the application of Euler deconvolution to the analytic signal." GEOPHYSICS 71, no. 6 (November 2006): L87—L93. http://dx.doi.org/10.1190/1.2360204.

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Standard Euler deconvolution is applied to potential-field functions that are homogeneous and harmonic. Homogeneity is necessary to satisfy the Euler deconvolution equation itself, whereas harmonicity is required to compute the vertical derivative from data collected on a horizontal plane, according to potential-field theory. The analytic signal modulus of a potential field is a homogeneous function but is not a harmonic function. Hence, the vertical derivative of the analytic signal is incorrect when computed by the usual techniques for harmonic functions and so also is the consequent Euler deconvolution. We show that the resulting errors primarily affect the structural index and that the estimated values are always notably lower than the correct ones. The consequences of this error in the structural index are equally important whether the structural index is given as input (as in standard Euler deconvolution) or represents an unknown to be solved for. The analysis of a case history confirms serious errors in the estimation of structural index if the vertical derivative of the analytic signal is computed as for harmonic functions. We suggest computing the first vertical derivative of the analytic signal modulus, taking into account its nonharmonicity, by using a simple finite-difference algorithm. When the vertical derivative of the analytic signal is computed by finite differences, the depth to source and the structural index consistent with known source parameters are, in fact, obtained.

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Li, Hai Xia, Hai Long Yu, and Xiao Ling Zhang. "Application Effect Analysis of Magnetic Gradients Data Continuation from Undulate Surface to Plane." Advanced Materials Research 779-780 (September 2013): 643–46. http://dx.doi.org/10.4028/www.scientific.net/amr.779-780.643.

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Application effect of magnetic gradients data continuation from undulate surface to plane has been analyzed by model test. The gradient data of before and after the processing was used for the analytic signal and the Euler deconvolution method calculation respectively, comparing the calculated results show that the maxima of analytic signal calculated by gradients anomaly on undulate surface deviate obviously from the center location of the prism magnetic source, and the position of prism boundaries are not clear. However, the analytic signal calculated by gradients anomaly after continuation from undulate surface to plane can be successfully used to estimate the center and boundaries position of prism. The solutions of Euler deconvolution method calculated by gradients anomaly on undulate surface are dispersive, the solutions calculated by gradients anomaly after continuation from undulate surface to plane are relatively clustering, and can outline clearly the positions of prism corners. The results demonstrate that continuation from undulate surface to plane processing of gradients anomaly can improve the application effect of analytic signal and Euler deconvolution technique.

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Amaral Mota, Elizangela S., Walter E. Medeiros, and Roberto G. Oliveira. "Can Euler deconvolution outline three‐dimensional magnetic sources?" Geophysical Prospecting 68, no. 7 (June 18, 2020): 2271–91. http://dx.doi.org/10.1111/1365-2478.12988.

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Reid, A. B., J. M. Allsop, H. Granser, A. J. Millett, and I. W. Somerton. "Magnetic interpretation in three dimensions using Euler deconvolution." GEOPHYSICS 55, no. 1 (January 1990): 80–91. http://dx.doi.org/10.1190/1.1442774.

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Magnetic‐survey data in grid form may be interpreted rapidly for source positions and depths by deconvolution using Euler’s homogeneity relation. The method employs gradients, either measured or calculated. Data need not be pole‐reduced, so that remanence is not an interfering factor. Geologic constraints are imposed by use of a structural index. Model studies show that the method can locate or outline confined sources, vertical pipes, dikes, and contacts with remarkable accuracy. A field example using data from an intensively studied area of onshore Britain shows that the method works well on real data from structurally complex areas and provides a series of depth‐labeled Euler trends which mark magnetic edges, notably faults, with good precision.

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Uieda, Leonardo, Vanderlei C. Oliveira, and Valéria C. F. Barbosa. "Geophysical tutorial: Euler deconvolution of potential-field data." Leading Edge 33, no. 4 (April 2014): 448–50. http://dx.doi.org/10.1190/tle33040448.1.

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In this tutorial, we will talk about a widely used method of interpretation for potential-field data called Euler de-convolution. Our goal is to demonstrate its usefulness and, most important, to call attention to some pitfalls encountered in interpretation of the results. The code and synthetic data required to reproduce our results and figures can be found in the accompanying IPython notebooks ( ipython.org/notebook ) at dx.doi.org/10.6084/m9.figshare.923450 or github.com/pinga-lab/paper-tle-euler-tutorial . The note-books also expand the analysis presented here. We encourage you to download the data and try them on your software of choice. For this tutorial, we will use the implementation in the open-source Python package Fatiando a Terra ( fatiando.org ).

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Williams, Simon E., J. Derek Fairhead, and Guy Flanagan. "Comparison of grid Euler deconvolution with and without 2D constraints using a realistic 3D magnetic basement model." GEOPHYSICS 70, no. 3 (May 2005): L13—L21. http://dx.doi.org/10.1190/1.1925745.

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We describe the application of a 2D-constrained grid Euler deconvolution method which is able to determine for each solution window whether the source structure is two dimensional, three dimensional, or poorly defined and to estimate the source location and depth. In each solution window, eigenvalues and eigenvectors are derived from the Euler equations and compared to threshold levels. A single eigenvalue below the given threshold and lying in the x–y-plane is shown to indicate a 2D source, while the absence of such an eigenvalue indicates a 3D source geometry. Two small eigenvalues indicate the field in the window has no distinct source. Applying these criteria to each solution window allows us to generate a map of source-geometry distribution. We evaluate the effectiveness of 2D-constrained grid Euler deconvolution using synthetic magnetic data generated from a 3D basement model based on real topography from an area with surface-exposed faulting. This modeling strategy provides a complex, nonidealized data set that compares Euler depth estimates directly to the known basement surface depth. Our results indicate that noninteger structural indices can be the most appropriate choice for some data sets, and the 2D-constrained grid Euler method images magnetic basement structure more clearly and unambiguously than the conventional grid Euler method.

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Ugalde, Hernan, and William A. Morris. "Cluster analysis of Euler deconvolution solutions: New filtering techniques and geologic strike determination." GEOPHYSICS 75, no. 3 (May 2010): L61—L70. http://dx.doi.org/10.1190/1.3429997.

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Euler deconvolution often presents the problem of filtering coherent solutions from uncorrelated ones. We have applied clustering and kernel density distribution techniques to a Euler-generated data set. First a kernel density distribution algorithm filters uncorrelated Euler solutions from those consistently located near an anomalous magnetic-gravimetric source. Then a fuzzy [Formula: see text]-means clustering algorithm is applied to the filtered data set. The computation of cluster centers reduces the size of the data set considerably, yet maintains its statistical consistency. Finally, the computation of eigenvectors and eigenvalues on the cluster centers yields an estimate of the geologic strike of the anomalous sources responsible for the observed geophysical anomalies. Therefore, we can obtain an improved strike and depth estimation of the magnetic sources. Although the algorithm can filter and cluster any Euler data set, we recommend obtaining the best solutions possible before any clustering. Hence, we have used a hybrid 3D extended Euler and 3D Werner deconvolution algorithm. We have developed synthetic and real examples from the Bathurst Mining Camp (New Brunswick, Canada). The output of this algorithm can be used as an input to any 3D geologic-modeling package.

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Melo, Felipe F., and Valéria C. F. Barbosa. "Correct structural index in Euler deconvolution via base-level estimates." GEOPHYSICS 83, no. 6 (November 1, 2018): J87—J98. http://dx.doi.org/10.1190/geo2017-0774.1.

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In most applications, the Euler deconvolution aims to define the nature (type) of the geologic source (i.e., the structural index [SI]) and its depth position. However, Euler deconvolution also estimates the horizontal positions of the sources and the base level of the magnetic anomaly. To determine the correct SI, most authors take advantage of the clustering of depth estimates. We have analyzed Euler’s equation to indicate that random variables contaminating the magnetic observations and its gradients affect the base-level estimates if, and only if, the SI is not assumed correctly. Grounded on this theoretical analysis and assuming a set of tentative SIs, we have developed a new criterion for determining the correct SI by means of the minimum standard deviation of base-level estimates. We performed synthetic tests simulating multiple magnetic sources with different SIs. To produce mid and strongly interfering synthetic magnetic anomalies, we added constant and nonlinear backgrounds to the anomalies and approximated the simulated sources laterally. If the magnetic anomalies are weakly interfering, the minima standard deviations either of the depth or base-level estimates can be used to determine the correct SI. However, if the magnetic anomalies are strongly interfering, only the minimum standard deviation of the base-level estimates can determine the SI correctly. These tests also show that Euler deconvolution does not require that the magnetic data be corrected for the regional fields (e.g., International Geomagnetic Reference Field [IGRF]). Tests on real data from part of the Goiás Alkaline Province, Brazil, confirm the potential of the minimum standard deviation of base-level estimates in determining the SIs of the sources by applying Euler deconvolution either to total-field measurements or to total-field anomaly (corrected for IGRF). Our result suggests three plug intrusions giving rise to the Diorama anomaly and dipole-like sources yielding Arenópolis and Montes Claros de Goiás anomalies.

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Olurin, Oluwaseun Tolutope. "Interpretation of high resolution airborne magnetic data (HRAMD) of Ilesha and its environs, Southwest Nigeria, using Euler deconvolution method." Materials and Geoenvironment 64, no. 4 (December 1, 2017): 227–41. http://dx.doi.org/10.1515/rmzmag-2017-0013.

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AbstractInterpretation of high resolution aeromagnetic data of Ilesha and its environs within the basement complex of the geological setting of Southwestern Nigeria was carried out in the study. The study area is delimited by geographic latitudes 7°30′–8°00′N and longitudes 4°30′–5°00′E. This investigation was carried out using Euler deconvolution on filtered digitised total magnetic data (Sheet Number 243) to delineate geological structures within the area under consideration. The digitised airborne magnetic data acquired in 2009 were obtained from the archives of the Nigeria Geological Survey Agency (NGSA). The airborne magnetic data were filtered, processed and enhanced; the resultant data were subjected to qualitative and quantitative magnetic interpretation, geometry and depth weighting analyses across the study area using Euler deconvolution filter control file in Oasis Montag software. Total magnetic intensity distribution in the field ranged from –77.7 to 139.7 nT. Total magnetic field intensities reveal high-magnitude magnetic intensity values (high-amplitude anomaly) and magnetic low intensities (low-amplitude magnetic anomaly) in the area under consideration. The study area is characterised with high intensity correlated with lithological variation in the basement. The sharp contrast is enhanced due to the sharp contrast in magnetic intensity between the magnetic susceptibilities of the crystalline and sedimentary rocks. The reduced-to-equator (RTE) map is characterised by high frequencies, short wavelengths, small size, weak intensity, sharp low amplitude and nearly irregular shaped anomalies, which may due to near-surface sources, such as shallow geologic units and cultural features. Euler deconvolution solution indicates a generally undulating basement, with a depth ranging from −500 to 1000 m. The Euler deconvolution results show that the basement relief is generally gentle and flat, lying within the basement terrain.

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Reid, Alan B., Jörg Ebbing, and Susan J. Webb. "Avoidable Euler Errors - the use and abuse of Euler deconvolution applied to potential fields." Geophysical Prospecting 62, no. 5 (April 7, 2014): 1162–68. http://dx.doi.org/10.1111/1365-2478.12119.

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Barbosa, Valéria C. F., Joao B. C. Silva, and Walter E. Medeiros. "Making Euler deconvolution applicable to small ground magnetic surveys." Journal of Applied Geophysics 43, no. 1 (January 2000): 55–68. http://dx.doi.org/10.1016/s0926-9851(99)00047-6.

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Cooper, Gordon, Magdel Combrinck, and Duncan Cowan. "The application of Euler deconvolution to airborne EM datay." ASEG Extended Abstracts 2004, no. 1 (December 2004): 1–4. http://dx.doi.org/10.1071/aseg2004ab021.

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Schmidt, Phillip W. "Inversion using Euler deconvolution of the magnetic gradient tensor." ASEG Extended Abstracts 2006, no. 1 (December 2006): 1–3. http://dx.doi.org/10.1071/aseg2006ab159.

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Castro, Fabrício R., Saulo P. Oliveira, Jeferson de Souza, and Francisco J. F. Ferreira. "Constraining Euler Deconvolution Solutions Through Combined Tilt Derivative Filters." Pure and Applied Geophysics 177, no. 10 (June 24, 2020): 4883–95. http://dx.doi.org/10.1007/s00024-020-02533-w.

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de Souza, João Paulo Gomes, Marcelo Henrique Leão-Santos, Cantidiano de Oliveira Freitas, Fernando Martins Vieira Matos, and Diogo Luiz Orphão de Carvalho. "Applicability of standard Euler deconvolution, modeling, and amplitude magnetic data inversion in Greenfield programs: The Leite target case study, Carajás Mineral Province, Brazil." Interpretation 3, no. 3 (August 1, 2015): T131—T143. http://dx.doi.org/10.1190/int-2014-0192.1.

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The Leite target is located in Carajás Mineral Province and has a magnetic anomaly with 140 nT of amplitude, elongated in the northwest–southeast direction. Four exploratory drillholes were performed to test the magnetic anomaly. The test showed that the source of the anomaly is a narrow magnetite hydrothermal alteration zone bearing copper mineralization up to 2%. In addition, geologic and geochemical data, magnetic susceptibility (MS) measurements were collected to identify the lithotypes with ferromagnetic minerals. We use three different techniques to estimate the depth and geometry of the magnetic source: standard Euler deconvolution, total field magnetic anomaly modeling, and magnetic amplitude inversion. When visualized in 3D, the depth of solutions from Euler deconvolution crossed the real magnetic layer with less inclination. The modeling, using the solutions from Euler deconvolution, was performed, and the magnetic anomaly produced by the body modeled achieved a low misfit. The body used in the forward modeling is geometrically similar to the geologic magnetic layer. The magnetic amplitude inversion successfully recovered the MS distribution. Finally, we carried out a borehole magnetic survey in two drillholes to validate the obtained models and investigate the magnetic source. This survey confirmed that the models were intercepted and the magnetic anomaly was associated, a hydrothermal alteration zone, with magnetite intercepted by drillholes. In this study, we demonstrated that the use of those techniques was effective in Greenfield exploration programs.

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Guspí, Fernando, and Iván Novara. "Generalized Hilbert transforms of the effect of single magnetic sources." GEOPHYSICS 77, no. 3 (May 1, 2012): J7—J14. http://dx.doi.org/10.1190/geo2011-0188.1.

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The generalized Hilbert transforms of potential fields, particularly magnetic fields, provide a useful resource for improving interpretation. Even though [Formula: see text]- and [Formula: see text]-Hilbert transforms of a potential field on a plane can be approximately computed from the whole observed field, they are locally independent of the observations when working on reduced areas of the plane, and therefore, on those areas, Hilbert transforms can be combined with them to better constrain and stabilize local inversions. Extended Euler deconvolution, based on Euler’s homogeneity equation, makes extensive use of this principle. We investigated closed-form expressions for evaluating in the space domain the generalized [Formula: see text]- and [Formula: see text]-Hilbert transforms of magnetic fields generated by single point sources, given in the form of dipoles, monopoles, and Newtonian potential type sources. Apart from providing a way to calculate Hilbert transforms via equivalent sources, this approach, adding little computer effort, can be applied to solve local inverse problems as a way to improve the definition of a model previous to an inversion over a large area; the solution is modeled by point sources, and it enables matching not only the observations, but also the Hilbert transforms, thus providing stronger constraints. A synthetic example with noisy data demonstrated the resolving power of this approach in locally inverting for magnetization intensities of prismatic bodies using data windows either above or displaced from the sources. In an example from a magnetic anomaly over Sierra de San Luis, Argentina, the magnetization intensities of the basement are locally inverted for at each solution point of an extended Euler deconvolution. Results indicated a more coherent pattern when the Hilbert transforms were incorporated to the inversion, illustrating how local inversions with Hilbert transforms, which do not involve time-consuming operations, can accompany extended Euler deconvolutions to better outline characteristics of a model.

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Thurston, Jeff. "Euler deconvolution in the presence of sheets with finite widths." GEOPHYSICS 75, no. 3 (May 2010): L71—L78. http://dx.doi.org/10.1190/1.3428484.

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Euler deconvolution of magnetic fields, induced by sheets with nonnegligible widths, provides source-location estimates that are biased away from the true locations. I have derived formulas for these biases and used the equations to model diffuse solution patterns that are owing to the interplay between integer structural indices and finite sources. These patterns closely match solutions deconvolved from aeromagnetic data over northern Canada. Motivated out of the necessity that complete harmonics be integral degreed, I have investigated and discovered the ineffectiveness of noninteger structural indices in remediating the aforementioned biases. In fact, real numbers impart similar errors to multiple Euler solutions, causing ensembles of estimated origin loci to reside below the middle of the tops of wide sheets. I have devised an approach requiring the inclusion of a term in the Euler deconvolution kernel whose independent variable is the second horizontal derivative of the total field, and whose partial slope (to be solved) is the sheet width. This approach is appropriate only if the thickness does not exceed the depth. However, precision could be sacrificed in favor of accuracy because of the presence of the second derivative. The application to aeromagnetic data over a diabase dike in northern Canada yields a depth effectively coincident with a drilling depth.

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Mikhailov, Valentin, Gwendoline Pajot, Michel Diament, and Antony Price. "Tensor deconvolution: A method to locate equivalent sources from full tensor gravity data." GEOPHYSICS 72, no. 5 (September 2007): I61—I69. http://dx.doi.org/10.1190/1.2749317.

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We present a method dedicated to the interpretation of full tensor (gravity) gradiometry (FTG) data called tensor deconvolution. It is especially designed to benefit from the simultaneous use of all the FTG components and of the gravity field. In particular, it uses tensor scalar invariants as a basis for source location. The invariant expressions involve all of the independent components of the tensor. This method is a tensor analog of Euler deconvolution, but has the following advantages compared to the conventional Euler deconvolution method: (1) It provides a solution at every observation point, without the use of a sliding window. (2) It determines the structural index automatically; as a consequence, the structural index follows the variations of the field morphology. (3) It uses all components of the measured full gradient tensor and gravity field, thus reducing errors caused by random noise. It is based on scalar invariants that are by nature insensitive to the orientation of the measuring device. We tested our method on both noise-free and noise-contaminated data. These tests show that tensor solutions cluster in the vicinity of the center of causative bodies, whereas Euler solutions better outline their edges. Hence, these methods should be combined for improved contouring and depth estimation. In addition, we use a clustering method to improve the selection of solutions, which proves advantageous when data are noisy or when signals from close causative bodies interfere.

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Silva, João B. C., and Valéria C. F. Barbosa. "3D Euler deconvolution: Theoretical basis for automatically selecting good solutions." GEOPHYSICS 68, no. 6 (November 2003): 1962–68. http://dx.doi.org/10.1190/1.1635050.

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We derive the analytical estimators for the horizontal and vertical source positions in 3D Euler deconvolution as a function of the x‐, y‐, and z‐derivatives of the magnetic anomaly within a data window. From these expressions we show that, in the case of noise‐corrupted data, the x‐, y‐, and z‐coordinate estimates computed at the anomaly borders are biased toward the respective horizontal coordinate of the data window center regardless of the true or presumed structural indices and regardless of the magnetization inclination and declination. On the other hand, in the central part of the anomaly, the x‐ and y‐coordinate estimates are very close to the respective source horizontal coordinates regardless of the true or presumed structural indices and regardless of the magnetization inclination and declination. This contrasting behavior of the horizontal coordinate estimates may be used to automatically delineate the region associated with the best solutions. Applying the Euler deconvolution operator inside this region would decrease the dispersion of all position estimates, improving source location precision.

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Indriana, Rina Dwi. "Distribution of subsurface anomalies in the Muria Peninsula and depth analysis with euler deconvolution." International journal of physical sciences and engineering 3, no. 3 (November 6, 2019): 21–30. http://dx.doi.org/10.29332/ijpse.v3n3.355.

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Muria Peninsula is one of the regions in Central Java that is uniquely formed. The Muria Peninsula was originally separated from Java and is now connected. To complement the studies that have been done before, subsurface analysis using euler deconvolution method is carried out. Gravity data used is satellite data provided free by BGI. The results of the processing produced a residual anomaly which showed a fault that passed in the middle of the peak of Muria towards Mount Genuk. The anomaly depth of Mt. Muria is 1000 m to 2000 m, in the peak area of Muria and Genuk <1000 m, and in the east and west of the study area the anomaly depth is more than 2000 m. Euler deconvolution index 0 illustrates the body boundaries of Mt. Muria and Genuk in the form of dike and steep.

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Davis, Kristofer, Yaoguo Li, and Misac Nabighian. "Automatic detection of UXO magnetic anomalies using extended Euler deconvolution." GEOPHYSICS 75, no. 3 (May 2010): G13—G20. http://dx.doi.org/10.1190/1.3375235.

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We have developed an algorithm for the automatic detection of prospective unexploded ordnance (UXO) anomalies in total-field or gradient magnetic data based on the concept of the structural index (SI) of a magnetic anomaly. Identifying magnetic anomalies having specific structural indices enables the direct detection of potential UXO targets. The total magnetic field produced by a dipolelike source, such as a UXO, decays with inverse distance cubed and therefore has an SI of three, whereas the gradient data have an SI of four. The developed extended Euler deconvolution method based on the Hilbert transform provides a reliable means for calculating the spatial location, depth, and SI of compact and isolated anomalies; it has enabled us to perform automatic anomaly selection for further analysis. Our method first examines the anomaly decay and selects possible UXO anomalies based on the expected SI. We refine the result further by post-Euler amplitude analysis using the relative source strength of the anomalies selected in the first stage. The amplitude analysis statistically identifies weak anomalies that are due to noise in the data. This enhances the final result and eliminates automatic picks that fall within the noise level. We have demonstrated the effectiveness of the method using synthetic and field data sets.

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Roy, Agarwal, and Shaw. "A new concept in Euler deconvolution of isolated gravity anomalies." Geophysical Prospecting 48, no. 3 (May 2000): 559–75. http://dx.doi.org/10.1046/j.1365-2478.2000.00203.x.

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COOPER, G. "Euler Deconvolution with Improved Accuracy and Multiple Different Structural Indices." Journal of China University of Geosciences 19, no. 1 (February 2008): 72–76. http://dx.doi.org/10.1016/s1002-0705(08)60026-6.

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Rim, Hyoungrae, Yeong-Sue Park, Mutaek Lim, Sung Bon Koo, and Byung Doo Kwon. "3D gravity inversion with Euler deconvolution as a priori information." Exploration Geophysics 38, no. 1 (March 2007): 44–49. http://dx.doi.org/10.1071/eg07010.

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Barbosa, Valéria C. F., João B. C. Silva, and Walter E. Medeiros. "Stability analysis and improvement of structural index estimation in Euler deconvolution." GEOPHYSICS 64, no. 1 (January 1999): 48–60. http://dx.doi.org/10.1190/1.1444529.

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Euler deconvolution has been widely used in automatic aeromagnetic interpretations because it requires no prior knowledge of the source magnetization direction and assumes no particular interpretation model, provided the structural index defining the anomaly falloff rate related to the nature of the magnetic source, is determined in advance. Estimating the correct structural index and electing optimum criteria for selecting candidate solutions are two fundamental requirements for a successful application of this method. We present a new criterion for determining the structural index. This criterion is based on the correlation between the total‐field anomaly and the estimates of an unknown base level. These estimates are obtained for each position of a moving data window along the observed profile and for several tentative values for the structural index. The tentative value for the structural index producing the smallest correlation is the best estimate of the correct structural index. We also propose a new criterion to select the best solutions from a set of previously computed candidate solutions, each one associated with a particular position of the moving data window. A current criterion is to select only those candidates producing a standard deviation for the vertical position of the source smaller than a threshold value. We propose that in addition to this criterion, only those candidates producing the best fit to the known quantities (combinations of anomaly and its gradients) be selected. The proposed modifications to Euler deconvolution can be implemented easily in an automated algorithm for locating the source position. The above results are grounded on a theoretical uniqueness and stability analysis, also presented in this paper, for the joint estimation of the source position, the base level, and the structural index in Euler deconvolution. This analysis also reveals that the vertical position and the structural index of the source cannot be estimated simultaneously because they are linearly dependent; the horizontal position and the structural index, on the other hand, are linearly independent. For a known structural index, estimates of both horizontal and vertical positions are unique and stable regardless of the value of the structural index. If this value is not too small, estimates of the base level for the total field are stable as well. The proposed modifications to Euler deconvolution were tested both on synthetic and real magnetic data. In the case of synthetic data, the proposed criterion always detected the correct structural index and good estimates of the source position were obtained, suggesting the present theoretical analysis may lead to a substantial enhancement in practical applications of Euler deconvolution. In the case of practical data (vertical component anomaly over an iron deposit in the Kursk district, Russia), the estimated structural index (corresponding to a vertical prism) was in accordance with the known geology of the deposit, and the estimates of the depth and horizontal position of the source compared favorably with results reported in the literature.

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McDonald, A. J. W., C. J. N. Fletchert, R. M. Carruthers, D. Wilson, and R. B. Evans. "Interpretation of the regional gravity and magnetic surveys of Wales, using shaded relief and Euler deconvolution techniques." Geological Magazine 129, no. 5 (September 1992): 523–31. http://dx.doi.org/10.1017/s0016756800021683.

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AbstractRegional gravity and aeromagnetic data of Wales have been processed using a variety of techniques. Image processing has greatly assisted qualitative interpretation, whilst automated procedures have provided additional quantitative information. The shaded relief images emphasize gradients in the potential fields, and are useful for displaying strong linear features. The Euler deconvolution method produces plotted solution maps, which define the position of the source of the gravity and magnetic anomalies. Euler solution maps of Wales and the adjacent continental shelf are presented for the first time. These maps are interpreted in relation to the known geology, with special emphasis on the Lower Palaeozoic Welsh Basin. It is proposed that the Euler solutions define a network of fault-bounded blocks within the Precambrian basement.

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Stavrev, Petar Y. "Euler deconvolution using differential similarity transformations of gravity or magnetic anomalies." Geophysical Prospecting 45, no. 2 (March 1997): 207–46. http://dx.doi.org/10.1046/j.1365-2478.1997.00331.x.

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Murdie, Ruth E., Peter Styles, Paula Upton, Phil Eardley, and Nigel J. Cassidy. "Euler deconvolution methods used to determine the depth to archaeological features." Geological Society, London, Special Publications 165, no. 1 (1999): 35–40. http://dx.doi.org/10.1144/gsl.sp.1999.165.01.03.

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Fedi, Maurizio, Giovanni Florio, and Tatiana A. Quarta. "Multiridge analysis of potential fields: Geometric method and reduced Euler deconvolution." GEOPHYSICS 74, no. 4 (July 2009): L53—L65. http://dx.doi.org/10.1190/1.3142722.

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A new method based on 3D multiridge analysis of potential fields assumes a 3D subset in the harmonic region and studies the behavior of potential field ridges, which are built by joining extreme points of the analyzed field computed at different altitudes. Three types of ridges are formed by searching for the zeros of the first horizontal and first vertical derivatives of the potential field (types I and II, respectively) and the zeros of the potential field itself (type III). This method uses a redundant set of ridges, called a multiridge set, to determine source type and location. For homogeneous potential fields generated by simple sources, all of the ridges are straight lines converging to the source position. This method analyzes the multiridges by using a geometric criterion to find the source position at the intersection of the multiridge set and by solving the three reduced Euler equations associated with ridge types I, II, and III. The reduced Euler type I and II equations are used to obtain the structural index and the vertical and horizontal source positions; equation type III estimates the horizontal and vertical source positions. Tests on synthetic as well as the Bishop model field yield good results even with noise-corrupted data. Results obtained using magnetic data collected over the wreck of a military ship in the Tyrrhenian Sea successfully determine its vertical and horizontal positions and the structural index.

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Cooper, G. R. J. "An improved algorithm for the Euler deconvolution of potential field data." Leading Edge 21, no. 12 (December 2002): 1197–98. http://dx.doi.org/10.1190/1.1536132.

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Dewangan, Pawan, T. Ramprasad, M. V. Ramana, M. Desa, and B. Shailaja. "Automatic Interpretation of Magnetic Data Using Euler Deconvolution with Nonlinear Background." Pure and Applied Geophysics 164, no. 11 (November 3, 2007): 2359–72. http://dx.doi.org/10.1007/s00024-007-0264-x.

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Zhou, Wenna, Zeyu Nan, and Jiyan Li. "Self-Constrained Euler Deconvolution Using Potential Field Data of Different Altitudes." Pure and Applied Geophysics 173, no. 6 (February 19, 2016): 2073–85. http://dx.doi.org/10.1007/s00024-016-1254-7.

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Marson, I., and E. E. Klingele. "Reply by the authors to Craig Ferris." GEOPHYSICS 59, no. 11 (November 1994): 1786. http://dx.doi.org/10.1190/1.1487009.

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Our paper is a discussion aimed to show how the vertical gradient of gravity can be successfully used for quantitative interpretation in three dimensions (i.e., solving for the three coordinates [Formula: see text], [Formula: see text], and [Formula: see text] of the source body) with methods like analytic signal and Euler deconvolution.

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Nyaban, Christian Emile, Théophile Ndougsa-Mbarga, Marcelin Bikoro-Bi-Alou, Stella Amina Manekeng Tadjouteu, and Stephane Patrick Assembe. "Multi-scale analysis and modelling of aeromagnetic data over the Bétaré-Oya area in eastern Cameroon, for structural evidence investigations." Solid Earth 12, no. 4 (April 6, 2021): 785–800. http://dx.doi.org/10.5194/se-12-785-2021.

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Abstract. This study was carried out in the Lom series in Cameroon, at the border with Central African Republic, located between the latitudes 5∘30′–6∘ N and the longitudes 13∘30′–14∘45′ E. A multi-scale analysis of aeromagnetic data combining tilt derivative, Euler deconvolution, upward continuation, and 2.75D modelling was used. The following conclusions were drawn. (1) Several major families of faults were mapped. Their orientations are ENE–WSW, E–W, NW–SE, and N–S with a NE–SW prevalence. The latter are predominantly sub-vertical with NW and SW dips and appear to be prospective for future mining investigations. (2) The evidence of compression, folding, and shearing axis was concluded from superposition of null contours of the tilt derivative and Euler deconvolution. The principal evidence of the local tectonics was due to several deformation episodes (D1, D2, and D4) associated with NE–SW, E–W, and NW–SE events, respectively. (3) Depths of interpreted faults range from 1000 to 3400 m. (4) Several linear structures correlating with known mylonitic veins were identified. These are associated with the Lom faults and represent the contacts between the Lom series and the granito-gneissic rocks; we concluded the intense folding was caused by senestral and dextral NE–SW and NW–SE stumps. (5) We propose a structural model of the top of the crust (schists, gneisses, granites) that delineates principal intrusions (porphyroid granite, garnet gneiss, syenites, micaschists, graphite, and garnet gneiss) responsible for the observed anomalies. The 2.75D modelling revealed many faults with a depth greater than 1200 m and confirmed the observations from reduced-to-Equator total magnetic intensity (RTE-TMI), tilt derivative, and Euler deconvolution. (6) We developed a lithologic profile of the Bétaré-Oya basin.

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Stehlík, Milan, Ján Somorčík, Luboš Střelec, and Jaromír Antoch. "Approximation of Information Divergences for Statistical Learning with Applications." Mathematica Slovaca 68, no. 5 (October 25, 2018): 1149–72. http://dx.doi.org/10.1515/ms-2017-0177.

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Abstract In this paper we give a partial response to one of the most important statistical questions, namely, what optimal statistical decisions are and how they are related to (statistical) information theory. We exemplify the necessity of understanding the structure of information divergences and their approximations, which may in particular be understood through deconvolution. Deconvolution of information divergences is illustrated in the exponential family of distributions, leading to the optimal tests in the Bahadur sense. We provide a new approximation of I-divergences using the Fourier transformation, saddle point approximation, and uniform convergence of the Euler polygons. Uniform approximation of deconvoluted parts of I-divergences is also discussed. Our approach is illustrated on a real data example.

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Porzucek, Slawomir, and Monika Loj. "Depth estimation problems in microgravity survey." Acta Geophysica 69, no. 2 (February 25, 2021): 665–72. http://dx.doi.org/10.1007/s11600-021-00553-1.

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AbstractQualitative interpretation is one of the most important missions in geophysical methods, particularly the determination of the shape and depth of disturbing bodies. The characteristics of the gravity field make it difficult to unequivocally determine both of these parameters; therefore, the problem is solved by reducing the shape of the body by means of simple solid figures and on this basis an attempt to estimate their depth. This paper presents an analysis of depth estimation in microgravity surveys. The useful signal-to-error ratio in this survey causes an additional factor influencing the quality of the estimated depths. Werner deconvolution and Extended Euler deconvolution, as the most frequently applied methods, were used to resolving the problem. Based on the Werner method, a processing methodology was developed that minimizes the impact of the error on the calculation results. An algorithm was also created that allows obtaining a depth solution in this method. The results of the Werner method were compared with the results of the Extended Euler method. Tests have shown that despite the relatively high error to amplitude ratio of the anomaly, satisfactory results can be obtained with the appropriate methodology.

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Journal articles on the topic 'Euler deconvolution'

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