PAGEOPH, Vol. 123 (1985) 0033-4553/85/040557-1051.50+0.20/0 9 1985 Birkh/iuser Verlag, Basel Hilbert Transform in the Interpretation of Magnetic Anomalies of Various Components due to a Thin Infinite Dike N. SUNDARARAJAN, 1 N. L. MOHAN, I M. S. VIJAYA RAGHAVA 2 and S. V. SESHAGIRIRAO 1 Abstract--The Hilbert transform H(x) applicable to vertical (AZ), horizontal (AH), and total (AT) magnetic anomalies due to a thin dike of infinite depth extent is derived from the generalised expression of magnetic effect F(x). The depth and dip of the dike is extracted by a simple procedure making use of F(x) and H(x). A modified version of the amplitude of the analytical signal is given to locate the origin. The abscissa of the point of intersection of F(x) and the discrete Hilbert transform H(1. Ax) directly yields the depth to the top. An example for each case is considered theoretically to illustrate the process. Applicability of the method is examined on the vertical component of the well-known magnetic anomaly at Kiirunavaara in northern Sweden, originally described by Von Carlheim Gyllenskjold, as well as on total magnetic anomaly of Bensons Mines, U.S.A. Key words: Magnetic anomalies; Discrete Hilbert transform; Analytical signal; Amplitude; Abscissa. Introduction Quite a few papers have discussed the utility of Hilbert transform in the interpreta- tion of magnetic and gravity anomalies (NABIGHIAN, 1972; STANLEY and GREEN, 1976; and STANLEY, 1977). MOHAN et al. (1982) and SUNDERARAJAN (1982) formulated a new technique for the interpretation of vertical magnetic anomalies due to two dimensional bodies. SUNDARARAJAN et al. (1983) have extended the technique to analyse the gravity anomalies due to two dimensional fault structures. Basically the Hilbert transform involves a phase shift of 90 degrees, hence it would be appropriate to say that the Hilbert transform could also be used to convert the vertical component of a magnetic field into the horizontal component, or vice versa. The horizontal derivative component of the gravity field is also obtainable by such transformation of the vertical derivative of the gravity field. NAmBHIAN (1972) has stressed only the transformation of the derivatives. Nabighian's interpretation process is based on the properties of the amplitude of the analytical signal curve, whereas the present method yields the parameters in an elegantly simple mathematical way. Centre of Exploration Geophysics, Osmania University, Hyderabad-500007, India. 2 Presently with AI Fateh University, Tripoli, Libya.