An iterative least-squares approach to depth determination from residual magnetic anomalies due to thin dikes

Abdelrahman, E. M.; Sharafeldin, S.M.

doi:10.1016/0926-9851(95)00017-8

Cited by 34 publications

(45 citation statements)

References 11 publications

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“…4) of an arbitrary magnetized thin dike (2-D) is given as ATCHUTA RAO et al, (1980), and ABDELRAHMAN and SHARAFELDIN (1996): Vol. 161, 2004 Nonlinearly Constrained Optimization Theory 211…”

Section: Geophysical Problem Formulation Due To Thin Dikes Modelmentioning

confidence: 99%

“…By the same manner as presented in the case of vertical fault model, the evaluation of the parameters ðz; h F ; C F Þ could be obtained by solving the following nonlinearly constrained minimization problem. Knowing that the range of the angle h F is from À90 to þ90 (ABDELRAHMAN and SHARAFELDIN, 1996): Table 4 Interpretation of magnetic field anomaly on the south west of Dehri, Bihar, India …”

Section: Geophysical Problem Formulation Due To Thin Dikes Modelmentioning

confidence: 99%

“…Figure 5 also shows the theoretically computed field anomaly obtained according to the mentioned evaluated parameters, which obviously indicates the close agreement between observed and computed anomalies. ABDELRAHMAN and SHARAFELDIN (1996) interpreted the same anomaly and estimated the depth of the magnetic dike responsible for it to be 66 meters, while has estimated this depth to be 70 m (Table 6). Figure 6 is a total magnetic anomaly above a Mesozoic diabase dike intruded into Paleozoic sediments in the Parnaiba basin, Brazil (SILVA, 1989).…”

Section: Field Examplesmentioning

confidence: 99%

“…An excellent review is given by NETTLETON (1976) and BLAKELY (1994). The methods include, for example, matching standardized curves (PARKAR, 1963), characteristic points and distance approaches (GRANT and WEST, 1965;ABDELRAHMAN, 1994), monograms (PRAKASA et al, 1986), Hilbert transforms (MOHAN et al, 1982), Fourier transform techniques (BHATTACHARYA, 1965), correlation factors between successive least-squares residual anomalies (ABDELRAHMAN and SHARAFELDIN, 1996), and least-squares minimization methods (SILVA, 1989).…”

Section: Introductionmentioning

confidence: 99%

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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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“…4) of an arbitrary magnetized thin dike (2-D) is given as ATCHUTA RAO et al, (1980), and ABDELRAHMAN and SHARAFELDIN (1996): Vol. 161, 2004 Nonlinearly Constrained Optimization Theory 211…”

Section: Geophysical Problem Formulation Due To Thin Dikes Modelmentioning

confidence: 99%

Section: Geophysical Problem Formulation Due To Thin Dikes Modelmentioning

confidence: 99%

Section: Field Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…This anomaly was interpreted by several authors (Tlas and Asfahani, 2015, Abdelrahman and Essa, 2015, Asfahani and Tlas, 2007, Asfahani and Tlas, 2004, Abdelrahman and Sharafeldin, 1996, Gay, 1963 assuming a thin dyke model. The anomaly is interpreted using VFSA to obtain the different parameters.…”

Section: Pima Copper Deposit Arizona Usamentioning

confidence: 99%

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

Biswas

Parija²,

Kumar³

2017

Annals of Geophysics

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Applying Two‐Step Iterative Least Square Approach to Determine the Geometry and Physical Parameters of Magnetic Sphere Sources

Bian

Zhai³

et al. 2011

Chinese J of Geophysics

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Through the causation analysis of divergent solution in determining the magnetic sphere parameters with normal least square method, the result indicates that redundant parameters, especially the angle parameters, are the main factor to cause divergence in non‐linear equations. Therefore, an approach was proposed here to eliminate the influence of angle parameters by regarding magnetic anomaly components as observed value and substituting magnetic moment vector for magnetic inclination as well as magnetic declination. Based on the linear/non‐linear relationship between observed value and magnetic moment/center position, the geometry and physical parameters of magnetic sources could be precisely figured out by applying two‐step iterative least square approach. Considering the influence of background field and multi‐sources situation, corresponding data processing methods were also put forward. The effectiveness of the suggested techniques has been illustrated by real magnetic data from a collection of environmental ferro‐metallic objects. The conclusion shows that the presented approach is convergent and the calculated geometry together with physical parameters has very high precision

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An iterative least-squares approach to depth determination from residual magnetic anomalies due to thin dikes

Cited by 34 publications

References 11 publications

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

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

Global nonlinear optimization for the interpretation of source parameters from total gradient of gravity and magnetic anomalies caused by thin dyke

Applying Two‐Step Iterative Least Square Approach to Determine the Geometry and Physical Parameters of Magnetic Sphere Sources

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