Estimating source parameters of 2D magnetic sources from special function: euler deconvolution, analytic signal and analytical expression of the anomalies

 









^*نگارنده رابط:          تلفن: 3395509-0273            دورنگار: 3395509-0273                   kamkarr@yahoo.com E-mail:
 





 



Generally, the analytic-signal and the Euler-deconvolution techniques have been widely used for estimating subsurface magnetic or gravity source parameters. The main advantage of using these two techniques is that we can delineate geological boundaries and determine depths to sources without considering the ambient earth magnetic parameters. However, in the traditional Euler-deconvolution method, an a priori selected structural index is usually used to estimate the causative source position. Unfortunately, the geometric type of a subsurface magnetic source is also a parameter that a geologist or geophysicist would wish to determine. Moreover, the datum level of a magnetic anomaly usually involved in the traditional Euler-deconvolution method is difficult to determine unambiguously, that results in the dependence of the structural index on the datum level. An incorrect structural index causes spatially diffuse Euler solutions.
Estimation of the depth of a buried structure from the magnetic data has drawn considerable attention. Different numerical methods have been given in the geophysical literature. The most commonly used of these methods are Werner deconvolution and Euler deconvolution. In these methods, the depth determination problem is transformed into the problem of finding a solution to a system of linear equations. The methods are sensitive to errors both in anomaly amplitude resolution and in determination of vertical and horizontal gradients, which are highly sensitive to noise.
A variety of semi-automatic methods, based on the use of derivatives of the magnetic anomalies, have been developed for the determination of causative source parameters, such as locations of boundaries and depths. One of these techniques is the analytic signal method, which was initially used in its complex function form and makes use of the Hilbert transform. It does not require knowledge of the magnetization direction and therefore it is useful in cases of remanent magnetization. Initially, it was successfully applied on profile data. The method was further developed by Roest et al. (1992) for the interpretation of aeromagnetic maps. In the analytic signal method, it is typically assumed that the causative sources are 2D geological structures, such as contacts, dikes and horizontal cylinders. For these models, depths can be obtained either from the width of the analytic signal anomalies or based on the ratio of the analytic signal to its higher derivatives if the source type is assumed. However, correct estimation of the depth is obtained only when the source corresponds to the chosen model. Several attempts have been made to use the analytic signal method to provide both the depth and model type of magnetic sources  However, all these attempts are based on the location of the maximum for defining the source location and the value of the maxima being used to define the type of source.
Few methods have been developed to determine the shape of the buried structure from magnetic data. Barbosa et al. (1999) presented a criterion 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.
We propose an interpretational approach using the analytic signal and Euler deconvolution to estimate the magnetic source parameters of a 2D contact, a thin dike and a cylinder. The major advantage of using a joint analysis is that not only we can determine the depths and possible geometric types (structural indices) of magnetic sources, but also we can estimate the structural dips and magnetization contrast. The results can avoid solution bias from an inappropriate magnetic datum level and can determine the horizontal locations, depths, structural types (indices), magnetization contrasts and/or structural dips. The synthetic models show that the feasibility of the proposed method is quite good. However, if the magnetic interference between two adjacent structures is too large, the method fails to solve the magnetic parameters. The maximum amplitudes (peaks) of the analytic signal in the 2D profile can also be used as an auxiliary method for judging the existence of probable solutions at the same locations. In real data, the structural index of a simple 2D model must be assigned for further estimation of the magnetization contrast and structural dip of the model. To demonstrate the feasibility of the proposed method, we analyze a magnetic profile across the Formosa Canyon, south-west Taiwan. For this real data, several different data windows were tried in order to obtain the best depth and structural-index solutions. Results show that good depth and structural-index solutions are placed at the locations where the analytic signal generally displays maximum amplitudes (peaks). Also the proposed method tested on ground magnetic profile from Surk Iron ore in Yazd Province in which the depth and structural index have broad correlation with exploratory drilling.