Characteristic curves for the inversion of magnetic anomalies of spherical ore bodies

Essa

2014

Pure Appl. Geophys.

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.

Section: Field Examplessupporting

confidence: 79%

Section: Theorymentioning

confidence: 99%

Section: Field Examplesmentioning

confidence: 99%

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A New Method for Depth and Shape Determinations from Magnetic Data

Essa

2014

Pure Appl. Geophys.

“…Following GAY (1963), PRAKASA RAO et al (1986), and PRAKASA RAO and SUBRAHMANYAN (1988), the magnetic anomaly produced by most geologic structures with the centre located at X i ¼ 0 can be represented by the following function…”

Section: Theorymentioning

confidence: 99%

“…These four simple geometric forms are convenient approximations to common geologic structures often encountered in the interpretation of magnetic data. Several graphical methods have been developed for interpreting residual magnetic anomalies due to simple models (GAY, 1963(GAY, , 1965PAUL, 1964;STANLEY, 1977;ATCHUTA RAO and RAM BABU, 1980;PRAKASA RAO et al, 1986;PRAKASA RAO and SUBRAHMANYAN, 1988). However, the drawback with these techniques is that they are highly subjective and therefore, can lead to major errors.…”

Section: Introductionmentioning

confidence: 99%

A Least-squares Minimization Approach to Depth Determination from Magnetic Data

Pure and Applied Geophysics

El-Arby

et al. 2003

We have developed a least-squares minimization approach to depth determination from magnetic data. By defining the anomaly value T ð0Þ at the origin and the anomaly value T ðN Þ at any other distance ðN Þ on the profile, the problem of depth determination from magnetic data has been transformed into finding a solution to a nonlinear equation of the form f ðzÞ ¼ 0. Formulas have been derived for a sphere, horizontal cylinder, dike, and for a geologic contact. Procedures are also formulated to estimate the effective magnetization intensity and the effective magnetization inclination. A scheme for analyzing the magnetic data has been formulated for determining the model parameters of the causative sources. The method is applied to synthetic data with and without random errors. Finally, the method is applied to two field examples from Canada and Arizona. In all cases examined, the estimated depths are found to be in good agreement with actual values.

Least-squares Minimization Approaches to Interpret Total Magnetic Anomalies Due to Spheres

El-Araby

Soliman

et al. 2007

Pure appl. geophys.

We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.