Euler deconvolution of gravity anomalies from thick contact/fault structures with extended negative structural index

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. I51-I58 ◽  
Author(s):  
Petar Stavrev ◽  
Alan Reid
Keyword(s):  
Field Data ◽  
Gravity Anomalies ◽  
Potential Fields ◽  
Contact Structures ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Infinite Slab ◽  
Fault Structures ◽  
Structural Indices ◽  
Analytical Expressions

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.

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.

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.

PENCIRIAN SESAR-SESAR MAJOR DI SEKITAR SEMENANJUNG MALAYSIA BERDASARKAN TEKNIK SATELIT GRAVITI

2018 ◽  
Vol 80 (2) ◽  
Author(s):  
Nurul Fairuz Diyana Bahrudin ◽  
Umar Hamzah
Keyword(s):  
Gravity Data ◽  
Gravity Anomalies ◽  
Peninsular Malaysia ◽  
Gravity Inversion ◽  
Kuala Lumpur ◽  
Euler Deconvolution ◽  
Satellite Gravity ◽  
3D Euler Deconvolution ◽  
Major Fault ◽  
Fault Structures

Major fault structures of Peninsular Malaysia were interpreted by satellite gravity data obtained from EGM2008. Filtering including THD, TVD, TDR, TDX and Euler Deconvolution inversion techniuques were applied to the data and successfully delineated the major faults especially located in the area separating the granite and sedimentary rock such as Bok Bak, Kuala Lumpur, Bukit Tinggi and Lebir faults. The main finding of this research is the boundary separating the western and eastern belt of Peninsular Malaysia namely the Bentong-Raub Suture by the abrupt changes of gravity anomalies between the two belts. The average depths and dips of Kuala Lumpur, Bukit Tinggi and Seremban faults were estimated by gravity inversion 3D Euler Deconvolution. 

Analytical expressions for gravity anomalies due to homogeneous polyhedral bodies and translations into magnetic anomalies

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 730-741 ◽  
Author(s):  
M. Okabe
Keyword(s):  
Gravitational Potential ◽  
Computing Time ◽  
Gravity Anomalies ◽  
Magnetic Anomalies ◽  
Two Dimensions ◽  
First Derivative ◽  
Second Derivatives ◽  
Analytical Expressions ◽  
Derivatives Of ◽  
The Magnetic Field

Complete analytical expressions for the first and second derivatives of the gravitational potential in arbitrary directions due to a homogeneous polyhedral body composed of polygonal facets are developed, by applying the divergence theorem definitively. Not only finite but also infinite rectangular prisms then are treated. The gravity anomalies due to a uniform polygon are similarly described in two dimensions. The magnetic potential due to a uniformly magnetized body is directly derived from the first derivative of the gravitational potential in a given direction. The rule for translating the second derivative of the gravitational potential into the magnetic field component is also described. The necessary procedures for practical computer programming are discussed in detail, in order to avoid singularities and to save computing time.

scholarly journals Effects of Structure Boundary Conditions and Snow-Pack Properties on Snow-Creep Pressures

1989 ◽  
Vol 13 ◽  
pp. 175-179
Author(s):  
D.M. McClung ◽  
J.O. Larsen
Keyword(s):  
Theoretical Analysis ◽  
Field Data ◽  
Nonlinear Deformation ◽  
Design Consideration ◽  
Snow Pack ◽  
Deformation Law ◽  
Linear Creep ◽  
The Mean ◽  
Structure Boundary ◽  
Analytical Expressions

Structures placed in deep snow covers are subject to forces caused by interruption of the down-slope snow-pack deformation components. The resulting creep pressures are often the primary design consideration. In this paper, accurate field data (pressures) and theoretical analysis of the problem using a linear creep law to define snow deformation are presented. Results include analytical expressions for the pressures, and it is demonstrated that the resulting linear theory underestimates the mean pressures by about 20%. Higher accuracy will require that a nonlinear deformation law be formulated.

On: “Correction of topographic distortions in potential‐field data: A fast and accurate approach” by Jianghai Xia, Donald R. Sprowl, and Dana Adkins‐Heljeson (April 1993 GEOPHYSICS, p. 515–523).

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1874-1874
Author(s):  
David A. Chapin
Keyword(s):  
Point Source ◽  
Frequency Domain ◽  
Potential Field ◽  
Field Data ◽  
New Method ◽  
Potential Fields ◽  
Potential Field Data ◽  
Source Method ◽  
Equivalent Point ◽  
Breakthrough Technology

Xia et al. do an excellent job developing a new method for using the equivalent point source method in the frequency domain. The transformation from a varying datum to flat datum has always been a major problem in potential fields data. This is because the existing methods to perform this transformation have tended to be cumbersome, time‐consuming, and expensive. I congratulate the authors for this breakthrough technology.

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