On the estimation of the structural index from low-pass filtered magnetic data

The estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data, such as Euler deconvolution. However, these estimates are unstable even in the presence of a weak amount of noise, and Euler deconvolution of noisy data leads to an underestimation of structural index and depth. We have studied how the structural index and depth estimates are affected by applying low-pass filtering to the data. Physically based low-pass filters, such as upward continuation and integration, have been shown to be the best choice over a range of altitudes (upward continuation) or orders (integration filters), mainly because their outputs have a well-defined physical meaning. In contrast, mathematical low-pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields. The C-norm criterion is a reliable strategy to produce a stabilized vertical derivative, and we discourage Butterworth filters because they tend to a vertical integral filter, for a high cutoff wavenumber, thus complicating the interpretation of the estimated structural index. We found that the estimated structural index and depth to source increase proportionally with the amount of smoothing, unless in the case of overfiltering. In that case, the severe distortion of the original field may cause a decrease of the estimated structural index and depth to source.

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Effects of low-pass filtering on the calculated structural index from magnetic data

Geophysics ◽

10.1190/1.3587216 ◽

2011 ◽

Vol 76 (4) ◽

pp. L23-L28 ◽

Cited By ~ 5

Author(s):

Kristofer Davis ◽

Yaoguo Li ◽

Misac N. Nabighian

Keyword(s):

Magnetic Data ◽

Cutoff Wavelength ◽

Euler Deconvolution ◽

Structural Index ◽

Pass Filter ◽

Low Pass Filter ◽

Source Type ◽

A Value ◽

Low Pass ◽

Unexploded Ordnance Detection

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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A stable truncated series approximation of the reduction‐to‐the‐pole operator

Geophysics ◽

10.1190/1.1443492 ◽

1993 ◽

Vol 58 (8) ◽

pp. 1084-1090 ◽

Cited By ~ 39

Author(s):

Carlos Alberto Mendonça ◽

João B. C. Silva

Keyword(s):

Synthetic Data ◽

Magnetic Data ◽

Theoretical Expression ◽

Source Depth ◽

Upward Continuation ◽

Low Pass ◽

Reduction To The Pole ◽

Low Pass Filters ◽

Infinite Sum ◽

Taylor’S Series

We combine a stabilized reduction‐to‐the‐pole and an upward continuation filter to produce meaningful reduced‐to‐the‐pole fields at low magnetic latitudes. The stabilizing procedure is based on the development, in Taylor’s series, of the theoretical expression for the reduction‐to‐the‐pole filter in the wavenumber domain. The filter instability is caused by the huge filter amplitudes along the magnetization azimuth, which are expressed by the infinite sum of terms close to unity. The stabilizing procedure reduces to simply truncating the infinite series. The upward continuation filter attenuates the high wavenumber component of the noise and allows us to design a stabilized filter closer to the theoretical one. Besides, quantitative interpretations of source depth based on the filtered field are more reliable when using upward continuation as compared with arbitrary low‐pass filters. The proposed filter was applied to synthetic data of a single prism uniformly magnetized along a supposedly known direction, and it produced a reduced‐to‐the‐pole field very close to the theoretical field at pole. We also applied the filter to magnetic data from Dixon Seamount assuming induced magnetization only. We obtained, within the central part of the anomaly, roughly circular contours of the reduced‐to‐the‐pole anomaly due to the nearly circular shape of the Seamount (evidenced by topographic data).

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Butterworth filters as tracking differentiators

10.36227/techrxiv.13646678.v1 ◽

2021 ◽

Author(s):

philip olivier

Keyword(s):

High Frequency ◽

Integral Form ◽

Frequency Noise ◽

Output Measurement ◽

Tracking Differentiator ◽

Noise Rejection ◽

Output Noise ◽

Low Pass ◽

Butterworth Filters ◽

Low Pass Filters

<div> <div> <div> <p>This letter describes how traditional Butterworth low pass filters can enhance the performance of the tracking differentiator introduced by Han by mitigating the effect of additive high frequency noise that corrupts the output measurement. The tracking differentiator obtains much of its utility from its realization in cascaded integral form. By combining the cascaded integral form realization of Butterworth low pass filters with its the noise rejection features one can design a tracking differentiator that is efficiently tuned to reject high frequency output noise. </p> </div> </div> </div>

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Butterworth filters as tracking differentiators

10.36227/techrxiv.13646678 ◽

2021 ◽

Author(s):

philip olivier

Keyword(s):

High Frequency ◽

Integral Form ◽

Frequency Noise ◽

Output Measurement ◽

Tracking Differentiator ◽

Noise Rejection ◽

Output Noise ◽

Low Pass ◽

Butterworth Filters ◽

Low Pass Filters

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CHARACTERIZATION OF THE POTIGUAR RIFT STRUCTURE BASED ON EULER DECONVOLUTION

Brazilian Journal of Geophysics ◽

10.22564/rbgf.v32i1.400 ◽

2014 ◽

Vol 32 (1) ◽

pp. 109 ◽

Cited By ~ 5

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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Automatic interpretation of magnetic data based on Euler deconvolution with unprescribed structural index

Computers & Geosciences ◽

10.1016/s0098-3004(03)00101-8 ◽

2003 ◽

Vol 29 (8) ◽

pp. 949-960 ◽

Cited By ~ 46

Author(s):

Daniela Gerovska ◽

Marcos J. Araúzo-Bravo

Keyword(s):

Magnetic Data ◽

Euler Deconvolution ◽

Structural Index ◽

Automatic Interpretation

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Continuous wavelet transform and the Euler deconvolution method and their application to magnetic field data of Jharia coal field, India

10.5194/gi-2016-22 ◽

2016 ◽

Author(s):

Arvind Singh ◽

Upendra Kumar Singh

Keyword(s):

Wavelet Transform ◽

Field Data ◽

Magnetic Anomalies ◽

Magnetic Data ◽

Deconvolution Method ◽

Euler Deconvolution ◽

Coal Field ◽

Potential Field Data ◽

Gravity And Magnetic ◽

Jharia Coal

Abstract. This paper deals the application of Continuous Wavelet Transform (CWT) and Euler deconvolution methods to estimate the source depth using magnetic anomalies. These methods are utilised mainly to focus on the fundamental issue for mapping the major coal seam and locating magnetic lineaments. These methods are tested and demonstrated on synthetic data and finally applied on field data from Jharia coal field. Prepared magnetic anomaly map that reflects clear tectonics control and nature of the underlying basement, demarcation of the basin, geological faults by steep gradients of magnetic anomaly. Analysis suggests that the CWT have a great utility in the magnetic data interpretation and the correlation between magnetic anomalies and geological features such as faults/joints and intrusive bodies over the basin. The CWT provides the consistent and reliable depth of the underlying basement with the results of Euler deconvolution and Tiltdepth methods without any priory information that is correlated well with borehole samples (Raja Rao, 1987). One of the fundamental issues is to detect differences in susceptibility and density between rocks that contain ore deposits or hydrocarbons or coal. These differences are reflected in the gravity and magnetic anomalies and also delineation of structural features, which are interpreted using several techniques (Blakely and Simpson, 1986). One of the most important objective in the interpretation of potential field data is to improve the resolution of underlying source, delineating lateral change in magnetic susceptibilities that provides information not only on lithological changes but also on structural trends. Especially, mapping the edges of causative bodies is fundamental to the application of potential field data to geological mapping. The edge detection techniques are used to distinguish between different sizes and different depths of the geological discontinuities (Cooper and Cowan 2006, 2008; Perez et al. 2005; Ardestani 2010; Hsu et al. 1996, 2002; Holschneider et al., 2003). The derivatives of magnetic data are used to enhance the edges of anomalies and improve significantly the visibility of such features. Sedimentary layer dominates the gravity and magnetic signature over Jharia Coal field (Verma et al., 1973, 1976, 1979). Thus the difference between the depths estimated using Euler deconvolution method (EDM) (Thompson 1982; Reid et al. 1990) and Tilt Depth Method (TDM) technique (Salem et al., 2007; Cooper 2004, 2011) may help to detect the thickness of the coalbed. Wavelet transform and Euler deconvolution method has been theoretically demonstrated on magnetic data. These methods provide source parameters such as the location, depth, geometry of geological bodies and interfaces in an easy and effective way. However, it may be more difficult to characterize the source properties in cases of extended sources (Sailhac et al., 2009). These methods executed over Jharia coal field, Dhanbad, India. This area forms an east west trending belt of Gondwana basin of Damodar valley at the north eastern part of India. This study region is mostly coal rich area of Gondwana basin. Analysis on Jharia coal field suggests that the magnetic anomalies provide encouraging results which are well correlated with available gravity data and some borehole informations.

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Correct structural index in Euler deconvolution via base-level estimates

Geophysics ◽

10.1190/geo2017-0774.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. J87-J98 ◽

Cited By ~ 5

Author(s):

Felipe F. Melo ◽

Valéria C. F. Barbosa

Keyword(s):

Standard Deviation ◽

Field Measurements ◽

Real Data ◽

Magnetic Anomalies ◽

Magnetic Data ◽

Total Field ◽

Minimum Standard ◽

Euler Deconvolution ◽

Structural Index ◽

Base Level

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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