O problema epistemológico da complexidade

JOURNAL OF THE BALKAN GEOPHYSICAL SOCIETY, Vol. 4, No 2, May 2001, p. 29-44, 23 figs.

Estimation of some bodies parameters from the self potential method using Hilbert transform
Mustafa Akgün
Dokuz Eylül Uni. Müh. Fak. Jeofizik Müh. B. Bornova, 35100 Izmir, Turkey e-mail: mustafa [e-mail] (Received 4 April; accepted 3 July 2000)

Abstract: Structural parameters can be determined directly from the geophysical anomalies having two-dimensional distributions for the potential fields. In order to achieve this, more equations are constructed for the same parameter to be determined. The special properties of analytical functions of the complex gradients and the Hilbert Transforms can be used to reach the above-mentioned situation. Certain structural parameters of two-dimensional bodies such as horizontal cylinder and horizontal sheets, were directly determined from the anomalies of the self-potential method. Hilbert Transforms, which can be carried out in two different ways using the Fourier Transform and convolution methods, were used to provide the conversion between the complex gradients of the anomaly. Structural parameters were then determined from the solutions of the constructed equations (anomaly, amplitude and phase functions). Key Words: Self Potential, Inversion, 2D Bodies, Hilbert Transformation.

INTRODUCTION Although Hilbert Transform (HT) have been used in electrical engineering and signal analysis for a long time (Bracewell, 1965), their application in geophysical studies started following 1970's. The HT is a method of direct solution. The aim of using the HT in geophysical studies is to obtain more than one equations that contain the same structural parameters by utilizing the complex gradients of the available data. The roots and common intersection points of the anomaly and the complex gradients of the anomaly have been used to determine the structural parameters. Therefore, an error ±1 sampling interval is expected for the