A Least-squares Window Curves Method for Interpretation of Magnetic Anomalies Caused by Dipping Dikes E. M. ABDELRAHMAN, E. R. ABO-Ezz, K. S. SOLIMAN, T. M. EL-Araby, and K. S. ESSA Abstract—We have developed a least-squares method to determine simultaneously the depth and the width of a buried thick dipping dike from residualized magnetic data using filters of successive window lengths. The method involves using a relationship between the depth and the half-width of the source and a combination of windowed observations. The relationship represents a family of curves (window curves). For a fixed window length, the depth is determined for each half-width value by solving one nonlinear equation of the form f (z) = 0 using the least-squares method. The computed depths are plotted against the width values representing a continuous curve. The solution for the depth and the width of the buried dike is read at the common intersection of the window curves. The method involves using a dike model convolved with the same moving average filter as applied to the observed data. As a result, this method can be applied to residuals as well as to measured magnetic data. Procedures are also formulated to estimate the amplitude coefficient and the index parameter. The method is applied to theoretical data with and without random errors. The validity of the method is tested on airborne magnetic data from Canada and on a vertical component magnetic anomaly from Turkey. In all cases examined, the model parameters obtained are in good agreement with the actual ones and with those given in the published literature. Key words: Magnetic dipping dike, depth and width solutions, least- squares method, window curves method. 1. Introduction In numerous exploration problems, it is valid to assume a geologic structure which is related to a dipping dike. The model is frequently used in magnetic interpretation to find the depth and the width of a class of geologic structures. Several graphical methods have been developed for interpreting magnetic anomalies due to dipping dikes (PETERS, 1949; COOK, 1950; WERNER, 1953; HUTCHISON, 1958; GAY, 1963; BRUCKSHAW and KUNARATNAM, 1963; GRANT and WEST, 1965; RAO et al., 1967; KOULOMZINE et al., 1970; RAO and MURTHY, 1978; and many others). However, most of these methods use a few characteristic points and distances, Geophysics Department, Faculty of Science, Cairo University, Giza, Egypt. E-mail: sayed5005@ yahoo.com Pure appl. geophys. 164 (2007) 1027–1044 0033–4553/07/051027–18 DOI 10.1007/s00024-007-0205-8 Ó Birkha ¨ user Verlag, Basel, 2007 Pure and Applied Geophysics