Geophysical Prospecting, 2005, 53, 399–410 Depth determination from a non-stationary magnetic profile for scaling geology A.R. Bansal ∗ and V.P. Dimri Fractals in Geophysics Group, National Geophysical Research Institute, 500 007 Hyderabad, India Received June 2003, revision accepted September 2004 ABSTRACT The conventional spectral analysis method for interpretation of magnetic data as- sumes stationary spatial series and a white-noise source distribution. However, long magnetic profiles may not be stationary in nature and source distributions are not white. Long non-stationary magnetic profiles can be divided into stationary subpro- files following Wiener filter theory. A least-squares inverse method is used to calculate the scaling exponents and depth values of magnetic interfaces from the power spec- trum. The applicability of this approach is demonstrated on non-stationary synthetic and field magnetic data collected along the Nagaur–Jhalawar transect, western India. The stationarity of the whole profile and the subprofiles of the synthetic and field data is tested. The variation of the mean and standard deviations of the subprofiles is sig- nificantly reduced compared with the whole profile. The depth values found from the synthetic model are in close agreement with the assumed depth values, whereas for the field data these are in close agreement with estimates from seismic, magnetotelluric and gravity data. INTRODUCTION The interpretation of magnetic data is carried out in both the space and frequency domains. Often the interpretation of the data is preferable in the frequency domain because (i) signal processing tools are easy to implement and (ii) the frequency- domain representations of potential field signals caused by a large variety of source models are simpler than their space- domain counterparts (Naidu and Mathew 1998). In the fre- quency domain, the estimation of the depth of anomalous sources is usually carried out by spectral analysis (Spector and Grant 1970; Treitel, Clement and Kaul 1971; Hahn, Kind and Mishra 1976; Negi et al. 1986; Mishra et al. 1995). The spectral method is strictly applicable only to stationary spa- tial series and white-noise source distributions. For realistic situations, geophysical spatial series are non-stationary. One of the simplest ways to deal with a non-stationary series is to divide it into a number of sections that can be considered ∗ E-mail: abhey bansal@ngri.res.in stationary. Previously, non-stationary profiles and maps were arbitrarily divided into windows or grids, without consider- ing the concept of non-stationarity (Curtis and Jain 1975; Connard, Couch and Gemperle 1983; Okubo et al. 1985; Negi et al. 1986). There are many ways to deal with non-stationary data. Dimri (1992) reviewed three ways to deal with non-stationary signals, i.e. (i) the gated Wiener filter, (ii) the Kalman filter, and (iii) adaptive filters. In the present study, the gated Wiener filter is applied to divide non-stationary profiles piecewise into sta- tionary subprofiles using the criterion of optimum gate length (Wang 1969; Dimri 1986). The second assumption of a white-noise source distribution of spectral analysis is generally made because of mathematical simplicity and limited information about the physical distribu- tion of subsurface sources. However, borehole studies such as those from the German Continental Drilling Program (KTB), the Canadian Shield, etc. have shown that the source distri- bution is scaling (Pilkington and Todoeschuck 1990, 1993, 1995; Maus and Dimri 1995, 1996). The concept of scaling C  2005 European Association of Geoscientists & Engineers 399