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.

scholarly journals Application of Aeromagnetic Data to Assess the Structures and Solid Mineral Potentials in Part of North Central Nigeria

2020 ◽  
pp. 11-29
Author(s):  
M. D. Tawey ◽  
D. U. Alhassan ◽  
A. A. Adetona ◽  
K. A. Salako ◽  
A. A. Rafiu ◽  
...  
Keyword(s):  
Structural Characteristics ◽  
Signal Amplitude ◽  
Analytic Signal ◽  
Aeromagnetic Data ◽  
Euler Deconvolution ◽  
North Central ◽  
Vertical Derivative ◽  
Magmatic Intrusions ◽  
First Vertical Derivative ◽  
Tilt Derivative

Assessment of the structures and solid minerals was carryout to investigate subsurface structural characteristics and mineralization potential zones within part of north-central Nigeria. The residual magnetic intensity data of the area was reduced to magnetic pole after which several source edge detection/interpretation with depth determination techniques including, analytic signal; tilt derivative; first and second vertical derivatives and Euler deconvolution were applied to the aeromagnetic data. From the analytic signal map, three magnetic zones were delineated. These are: low to relatively low magnetic zone (LM) with amplitude range from 0.003 to 0.009, moderate magnetic zone (MM) with amplitude 0.009 to 0.106 and those with amplitudes above 0.106 were products of later magmatic intrusions into host with fractures, faults and joints. Tilt derivative helped in delineating location and extent of edges of causative sources while Euler deconvolution helps in determination of boundary, depth and geometry of the structures. From first vertical derivative map, structures were found to have high lineament density around the central portion of the area and span toward the western end of the map were delineated. The lineaments mapped trending in the ENE-WSW followed by WNW-ESE with some NE-SW, NNE-SSW and NNW-SSE trends. The second vertical derivative (SVD) map also helped in delineating structures and possible mineralization zones that are pronounced within the study area, around high analytic signal zones. Delineated possible and favorable mineralization zones from second vertical derivative map correlate with portion of the study area with rocks showing high analytic signal amplitude suggesting the rocks to be of later magmatic intrusions where mineralization fluids solidify within the host rocks.

Imaging depth, structure, and susceptibility from magnetic data: The advanced source-parameter imaging method

Geophysics ◽  
2005 ◽  
Vol 70 (4) ◽  
pp. L31-L38 ◽  
Author(s):  
Richard S. Smith ◽  
Ahmed Salem
Keyword(s):  
Source Parameters ◽  
Thin Sheet ◽  
Signal Amplitude ◽  
Horizontal Cylinder ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Imaging Method ◽  
Structural Index ◽  
Synthetic Test ◽  
Vertical Contact

An important problem in the interpretation of magnetic data is quantifying the source parameters that describe the anomalous structure. We present a new method that uses various combinations of the local wavenumbers for estimating the depth and shape (structural index) of the structure. Because the estimates are derived from third derivatives of the magnetic data, they are noisy. However, there are multiple ways of calculating the depth and index, and these solutions can be averaged to give a stable estimate. Even so, a synthetic test shows that the results are erratic away from the locations where the analytic-signal amplitude is large. Hence, when we generate images of the depth and structural index, we make the results most visible where the analytic-signal amplitude is large and less visible where the signal is small. The advantage of the method is that estimates can be obtained at all locations on a profile and used to generate continuous profiles or images of the source parameters. This can be used to help identify the locations where interference might be corrupting the results. The structural index image can be used to determine the most appropriate type of model for an area. Assuming this model, it is possible to calculate the depth that would be consistent with the model and the data. Knowing both the depth and model, the analytic-signal amplitude can be converted to apparent susceptibility. If a vertical-contact model is assumed, the susceptibility contrast across the contact can be imaged. For the thin-sheet and horizontal-cylinder models, we can image the susceptibility-thickness and susceptibility-area products, respectively.

On: “A case for upward continuation as a standard separation filter for potential‐field maps” by Bo Holm Jacobsen (GEOPHYSICS, 52, 1138–1148, August 1987)

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 723-723
Author(s):  
Nelson C. Steenland
Keyword(s):  
Cross Section ◽  
Potential Field ◽  
Thin Body ◽  
Thick Slab ◽  
Vertical Derivative ◽  
Upward Continuation ◽  
Original Field ◽  
First Vertical Derivative

This paper deals with gradients, not residuals. Computing a field up, then subtracting the “up” field from the original field to find residuals obviously involves shifting datums. Apparently the author got caught up in his equation (17) concerning the simple case of deriving the anomaly of a slab by subtracting the anomaly of one infinite prism from another of the same cross‐section but at a slightly smaller depth. That the anomaly of a slab behaves like the gradient (first vertical derivative) of the prism’s anomaly is apparent from the fact that the field of an infinitely thick slab attenuates by one power less than the field of a slab which approximates an infinitely thin body.

A combined analytic signal and Euler method (AN‐EUL) for automatic interpretation of magnetic data

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1952-1961 ◽  
Author(s):  
Ahmed Salem ◽  
Dhananjay Ravat
Keyword(s):  
Source Parameters ◽  
Euler Method ◽  
Analytic Signal ◽  
Magnetic Data ◽  
Euler Deconvolution ◽  
Automatic Interpretation ◽  
Different Depths ◽  
Ground Magnetic ◽  
Theoretical Simulations ◽  
Airborne Magnetic

We present a new automatic method of interpretation of magnetic data, called AN‐EUL (pronounced “an oil”). The derivation is based on a combination of the analytic signal and the Euler deconvolution methods. With AN‐EUL, both the location and the approximate geometry of a magnetic source can be deduced. The method is tested using theoretical simulations with different magnetic models placed at different depths with respect to the observation height. In all cases, the method estimated the locations and the approximate geometries of the sources. The method is tested further using ground magnetic data acquired above a shallow geological dike whose source parameters are known from drill logs, and also from airborne magnetic data measured over a known ferrometallic object. In both these cases, the method correctly estimated the locations and the nature of these sources.

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.

Magnetic source parameters of two‐dimensional structures using extended Euler deconvolution

Geophysics ◽  
2001 ◽  
Vol 66 (3) ◽  
pp. 814-823 ◽  
Author(s):  
Martin F. Mushayandebvu ◽  
P. van Driel ◽  
Alan B. Reid ◽  
James Derek Fairhead
Keyword(s):  
Homogeneous Function ◽  
A Priori ◽  
Source Parameters ◽  
Thin Sheet ◽  
Source Location ◽  
Euler Deconvolution ◽  
True Source ◽  
Susceptibility Contrast ◽  
Magnetic Profile ◽  
Constrained Solutions

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.

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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