Hilbert transform in the interpretation of magnetic anomalies of various components due to a thin infinite dike

The Hilbert transform H(x) applicable to vertical (ΔZ), horizontal (ΔH), and total (ΔT) 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 analytic signal is given to locate the origin. The abscissa of the point of intersection of F(x) and the discrete Hilbert transform H(1.Δx) 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.