The Euler Deconvolution of Potential Field Gradients

2003 ◽  
Author(s):  
G.R.J. Cooper
Keyword(s):  
Potential Field ◽  
Euler Deconvolution ◽  
Field Gradients

scholarly journals Geophysical tutorial: Euler deconvolution of potential-field data

2014 ◽  
Vol 33 (4) ◽  
pp. 448-450 ◽  
Author(s):  
Leonardo Uieda ◽  
Vanderlei C. Oliveira ◽  
Valéria C. F. Barbosa
Keyword(s):  
Open Source ◽  
Potential Field ◽  
Field Data ◽  
Synthetic Data ◽  
Euler Deconvolution ◽  
Potential Field Data ◽  
Python Package

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 ).

Degrees of homogeneity of potential fields and structural indices of Euler deconvolution

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. L1-L12 ◽  
Author(s):  
Petar Stavrev ◽  
Alan Reid
Keyword(s):  
Potential Field ◽  
Variable Density ◽  
Point Sources ◽  
Index Formula ◽  
Potential Fields ◽  
Positive Zero ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Field Source ◽  
Definition Of

Homogeneity is a well-known property of the potential fields of simple point sources used in field inversion. We find that the analytical expressions of potential fields created by sources of complicated shape and constant or variable density or magnetization also show this property. This is true if all variables of length dimension are involved in the test of homogeneity. The coordinates of observation points and the source coordinates and sizes form an extended set of variables, in relation to which the field expression is homogeneous. In this case, the principal definition of homogeneity applied to a potential field can be treated as an operator of a space transform of similarity. The ratio between the transformed and original fields determines the value and sign of the degree of homogeneity [Formula: see text]. The latter may take on positive, zero, or negative values. The degree of homogeneity depends on the type of field and on the assumed physical parameter of the field source, and can be nonunique for a given field element. We analyze the potential field of one singular point as the simplest case of homogeneity. Thus, we deduce results for the structural index, [Formula: see text], in Euler deconvolution. The structural index can also be positive, zero, or negative, but it has a unique value. Analytical considerations, as well as numerical tests on the gravity contact model, confirm the proposed physical interpretation of [Formula: see text], and lead to an extended version of Euler’s differential equation for potential fields.

On the application of Euler deconvolution to the analytic signal

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. L87-L93 ◽  
Author(s):  
G. Florio ◽  
M. Fedi ◽  
R. Pasteka
Keyword(s):  
Potential Field ◽  
Harmonic Functions ◽  
Horizontal Plane ◽  
Homogeneous Function ◽  
Source Parameters ◽  
Analytic Signal ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Vertical Derivative ◽  
First Vertical Derivative

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.

CHARACTERIZATION OF THE POTIGUAR RIFT STRUCTURE BASED ON EULER DECONVOLUTION

2014 ◽  
Vol 32 (1) ◽  
pp. 109 ◽  
Author(s):  
Rafael Saraiva Rodrigues ◽  
David Lopes de Castro ◽  
João Andrade dos Reis Júnior
Keyword(s):  
Potential Field ◽  
Window Size ◽  
Gravity Anomalies ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Potential Field Data ◽  
3D Euler Deconvolution ◽  
Maximum Tolerance ◽  
Para Determinar ◽  
Spatial Window

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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