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Volume :28 Issue : 2 2001      Add To Cart                                                                    Download

A new least-squares minimization approach to depth determination from numerical horizontal self-potential gradient over a 2-D inclined sheet

Auther : E. M. ABDELRAHMAN*, A. GH. HASSANEEN** AND M. A. HAFEZ**

*Geophysics Department, Faculty of Science, Cairo University, Giza, Egypt

**National Research Institute of Astronomy and Geophysics, Helwan, Cairo, Egypt

ABSTRACT

We have developed a two-stage approach to determine the depth to the upper and lower edges of a buried inclined sheet from numerical horizontal self-potential gradients obtained from observed data using filters of successive window lengths. The method involves using a relation- ship between the length of the horizontal projection on the ground surface, the depth to the lower edge of the source, and a combination of observations at symmetrical points with respect to the coordinate of the source origin and a free parameter (window length). For a fixed window length, the depth to the lower edge is determined for each length of the horizontal projection of the sheet. The computed depths to the lower edge are plotted against the lengths of the horizontal projection representing a continuous monotonically decreasing curve. The solution for the length of the horizontal projection and the depth to the lower edge of the sheet is read at the common intersection of the window curves. Knowing both the length of the horizontal projection and the depth to the lower edge, a least-squares minimization method is then presented to estimate the depth to the upper edge of the buried structure. The problem of depth determination to the upper edge from numerical self potential gradient has been transformed into finding a solution to a nonlinear equation. Procedures are also formulated to determine the dip and the electric dipole constant of the sheet which is related to the current density and the resistivity of the medium. Finally the method is applied to theoretical data and is used to interpret self-potential measurements which were carried out above a graphite deposit in the southern Bavarian woods, Germany.

Keywords: Inclined sheet; least-squares method; SP interpretation; window curves.

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