Computers & Geosciences Vol. 19, No. 5. pp. 705-715, 1993 0098-3004/93 $6.00 + 0.00 Printed in Great Britain. All rights reserved Copyright "c 1993 Pergamon Press Ltd A FORTRAN PROGRAM FOR THE COMPUTATION OF 2-DIMENSIONAL INVERSE FILTERS IN MAGNETIC PROSPECTING C. B. PAPAZACHOS and G. N. TSOKAS Geophysical Laboratory, University of Thessaloniki, P.O. Box 352-I, GR-54006 Thessaloniki, Greece (Received 8 June 1992, accepted 17 November 1992) A~tract--A FORTRAN program has been designed for the construction and application of 2-D inverse filters for magnetic prospecting. When these filters are convolved with magnetic anomalies, they result in the corresponding distribution of magnetization and also delineate the shape of the disturbing bodies. The efficiency of these filters is demonstrated by examples. Key Word~: Convolution, Magnetization, Parallelepiped prism, Inverse filter. INTRODUCTION Convolutional models for the computation of the anomaly of a dynamic field caused by "disturbing" bodies have been introduced widely in exploration geophysics (Bhattacharyya and Navolio, 1975; Bhattacharyya and Chan, 1977). Usually the anomaly is the result of convolution of various terms con- trolled by the geometrical features of the disturbing body and the distribution of the causative parameter (density, magnetic susceptibility, etc.) within the body. In these situations the inverse problem is to construct appropriate deconvolution filters for the determin- ation of some of the model variables, provided that the remaining ones are specified. Convolution and deconvolution usually are per- formed in the frequency domain where they trans- form into multiplication and division operations. For this purpose it is necessary to calculate theoretical expressions for the spectrum of the anomaly (e.g. Gudmundsson, 1966; Bhattacharyya, 1966). These expressions can be used to remove the effect of the known variables by simple divisions in the frequency domain, leaving a filtered spectrum which will give us the desirable information in the space domain (Gunn, 1975). Our intention is to construct a purely space-domain inverse operation. That operation should result in the rectification of the magnetic anomalies in order that their maxima or minima is located over the epicenters of the disturbing bodies. Furthermore, the new anomalies should delineate the spatial extend of the bodies and give an estimate of their magnetiz- ation. For this reason space-domain inverse filters are designed that transform the magnetic anomalies into the corresponding 2-D distribution of the magnetiz- ation. The main advantage of a space-domain oper- ation, once these inverse filters are calculated, is that they can be applied easily in situ, even with a hand calculator. CONVOLUTIONAL MODEL AND INVERSE FILTER DESIGN Tsokas and Papazachos (1990, 1992) used a previously defined formula (Grant and West, 1965; McGrath and Hood, 1973) in order to define the magnetic anomaly, AT, of any block-like body, as the accumulation of the contribution of thin plates. It is shown that the anomaly at a data point (x,.v) [body is at the origin (0, 0)] can be expressed as AT(x,y) = D. R(x, y) (1) where D is the body's magnetization, reasonably termed as the "amplitude" function and R is a func- tion of the body's geometrical features, the direction angles of the magnetization and of the total field, 7", termed as the "shape" function. In order to proceed to the convolutional model we make the assumption that the magnetization is of induced type or, at least, is of known direction, Then, an ensemble of bodies placed at the same depth at points x/=Ax I=LI ..... L, y,,,=Ay m =Mr ..... M_~, can be considered. Assuming the validity of the superposition principle, the total field anomaly at each point (x,,yi) is L, M 2 AT(x,,y,)= ~ ~ Dr.,, ,'R(x,-x t,)',-y,,,) I=LI m=Mi i = L t ..... L2j = M] ..... M,. 705