Shape and depth solutions from magnetic data using a parametric relationship

Abdelrahman, E. M.; Hassanein, Hamdy I. E.

doi:10.1190/1.1444703

Cited by 14 publications

(13 citation statements)

References 13 publications

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“…BARBOSA et al (1999), HSU (2002) and GEROVSKA and ARAUZO-BRAVO (2003) presented criteria for determining the correct structural index that is related to the shape of the source and is applied in magnetic interpretation using the Euler deconvolution method. ABDELRAHMAN and HASSANEIN (2000) developed a parametric-curves method (window-curves method) to determine simultaneously the shape and the depth of a buried structure from a residual magnetic anomaly profile. SALEM et al (2004) presented a method for interpreting a residual magnetic anomaly where a linear equation involving a symmetric anomalous field and its horizontal gradient is derived to provide the depth and the shape of the buried structures.…”

Section: Introductionmentioning

confidence: 99%

A New Method for Depth and Shape Determinations from Magnetic Data

Abdelrahman

Essa

2014

Pure Appl. Geophys.

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We present in this paper a new formula representing the magnetic anomaly expressions produced by most geological structures. Using the new formula we developed a simple and fast numerical method to determine simultaneously the depth and shape of a buried structure from second-horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths. The method involves using a nonlinear relationship between the depth to the source and the shape factor and a combination of observations at four points with respect to the coordinate of the source center with a free parameter (window length). The relationship represents a parametric family of curves (window curves). For a fixed free parameter, the depth is determined for each shape factor. The computed depths are plotted against the shape factors representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is read at the common intersection of the window curves. This method can be applied to residuals as well as to the observed magnetic data consisting of the combined effect of a local structure and a second-order regional or less. The method is applied to synthetic data with and without random errors and tested on three field examples from India, Brazil and the USA. In all cases the shape and depth of the buried structures are in good agreement with the actual ones.

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Section: Introductionmentioning

confidence: 99%

A New Method for Depth and Shape Determinations from Magnetic Data

Abdelrahman

Essa

2014

Pure Appl. Geophys.

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“…Figure 6 also shows an acceptable agreement between observed and computed anomalies. According to ABDELRAHMAN and HASSANEIN's (2000) results, the depth of the magnetic dike causing this anomaly is 2.1 meters, while this depth is estimated to be 3.5 meters, according to ABDELRAHMAN and SHARAFELDIN (1996) and SILVA (1989) where this result is considered as an overestimate of the real depth, (Table 7). …”

Section: Field Examplesmentioning

confidence: 99%

“…Parameters ABDELRAHMAN and SHARAFELDIN (1996) SILVA (1989) ABDELRAHMAN and HASSANEIN (2000) Present method z in meters 3.5 3.5 2.1 2.26 ± 0.09 h F in degrees 33.3 --47.11 ± 1.13 C F in nT )58.6 --)59.81 ± 1.54 216 J. Asfahani and M. Tlas Pure appl.…”

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confidence: 99%

Nonlinearly Constrained Optimization Theory to Interpret Magnetic Anomalies Due to Vertical Faults and Thin Dikes

Asfahani

Tlas

2004

Pure and Applied Geophysics

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A new and simple method based on a nonlinearly mathematical optimization concept has been proposed in this research to interpret magnetic anomalies due to vertical faults and thin dikes. This proposed interpretative method consists of three main steps. The first step is to formulate nonlinearly constrained optimization problems to describe the geophysical problems related to the studied structures. The second step is to suggest an interior penalty function in order to convert these nonlinearly constrained optimization problems into nonlinearly unconstrained optimization ones. The third step is to solve the converted nonlinearly unconstrained optimization problems by using the famous Hooke and Jeeves's algorithm in order to estimate the geophysical parameters of the studied structures such as: depth, amplitude coefficient, and index parameter. The Hooke and Jeeves's algorithm is purposely chosen for being robust and also its application to magnetic data converges rapidly towards the optimal estimation of parameters. This method was first tested on theoretical models with different random noise, where a very close agreement was obtained between the assumed and evaluated parameters.The validity of this new method was also tested on practical field examples taken from Australia, India, United States, and Brazil, where available magnetic data existed and was previously analyzed by different interpretative methods. The agreement between the results obtained by our developed method and those obtained by the other geophysical methods is good. The advantages of this newly proposed method, compared with the other published interpretative methods, also have been discussed and demonstrated.

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“…The magnetic anomaly expression produced by most geologic structures with center located at x i = 0 can be represented by the following function (Abdelrahman and Hassanein, 2000) H(x i , z, θ) = KW(x i , z, θ), i = 1, 2, ... N,…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…These methods include, for example, the use of correlation factors between successive leastsquares residual magnetic anomalies (Abdelrahman, 1990), the use of a parametric relationship (Abdelrahman and Hassanein, 2000) and higher derivative analysis techniques (Abdelrahman and Abo-Ezz, 2001). However, effective quantitative interpretations using a numerical method based on the analytical expression of second moving average residual magnetic anomalies are yet to be developed.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

Abdurrahman¹,

El-Araby²,

Essa³

2004

ear

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ABSTRACT. We have developed a numerical method to estimate the depth of a buried structure from second moving average residual anomalies obtained from magnetic data using filters of successive graticule spacings. The problem of depth determination has been transformed into the problem of finding a solution to a nonlinear equation of the form z = f(z). Formulas have been derived for a dike, horizontal cylinder, geologic contact, and a sphere. The method involves using simple models convolved with the same second moving average filters as applied to the observed magnetic data. As a result, our method can be applied not only to residuals but also to observed magnetic data. The method is applied to synthetic data with and without random errors. The validity of the method is tested in detail on a field example from Canada. In all cases examined, the depth obtained gives satisfied results with actual depth.

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Shape and depth solutions from magnetic data using a parametric relationship

Cited by 14 publications

References 13 publications

A New Method for Depth and Shape Determinations from Magnetic Data

A New Method for Depth and Shape Determinations from Magnetic Data

Nonlinearly Constrained Optimization Theory to Interpret Magnetic Anomalies Due to Vertical Faults and Thin Dikes

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

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