Interpretation of potential field anomalies using source parameter imaging method (SPI)

One important goal in the interpretation of magnetic data is to determine the type and location of the magnetic source. This has recently become particularly important due to the acquisition of large volumes of magnetic data both in environmental and geological applications. Interpretation of the magnetic data involves determining the parameters that characterize the source of the observed anomaly. In this regard, depth to the top of the source is the most important parameter. To this end, there are generally two different approaches, namely the manual and automatic methods. Manual methods, as implied in the name need simple tools such as rulers, calculators and are commonly used in processing 2-D datasets or profiles. Additionally, these methods can be performed in the field, allowing the user to distinguish the noises from signals without recourse to the computer (due to their simplicity). However, because of the large amount of magnetic data that are being collected in the field of geology, using of more rapid and powerful methods are necessary. In contrast to manual methods, automatic methods have the ability to perform in both 2-D and 3-D datasets more rapidly and with at least as much precision. A large number of automatic methods exist for interpreting magnetic data. These methods can be applied to profile data (Hartman, 1971; Naudy, 1971; Nabighian, 1972; Jian, 1976; Thompson, 1982; Atchuta Rao et al.). There are numerous methods that work on grided data, including 3-D Euler deconvolution (Reid et al., 1990), the 3-D analytic signal (Roest et al., 1992) and the enhanced analytic signal technique (Hsu et al., 1996). The results of these methods are usually displayed by plotting a symbol superimposed in the magnetic map in the source location. Consequently, the source boundary (horizontal location) must be evaluated by common edge detection methods, namely, zero crossing of the second-order vertical derivative or maximum value of the analytic signal prior to running a depth estimation method. In general, all automatic methods use derivatives of the magnetic data which is computed either in the space domain by the finite difference method or in the frequency domain by the Fast Fourier (FF) technique. Then, an appropriate equation is developed for depth estimation starting from a simple geometry model, such as sphere, dyke, or horizontal cylinder. The depth to top of the body measure is assessed by solving this equation either in the space or frequency domain. The proposed method extends the theory of the complex analytic signal by computing three complex attributes including instantaneous amplitude of the analytic signal, instantaneous phase and instantaneous frequency. It must be noted that the instantaneous concept is applied in the analysis of the temporal series (time dependent dataset) and because the magnetic data are spatial, analogous to temporal, we use the term local instead of instantaneous. These three quantities are obtained as shown below: (1) (2) (3) where, A, and f are amplitude, phase and frequency, respectively. Phase variation of potential field data can be used as an interpretation method. This idea appears in edge detection with tilt angle or phase angle. The advantages using of this quantity include its independence of body magnetization direction and its ease of computation. In this paper variations of this quantity, termed local frequency, are used for source parameter estimation, such as body depth and susceptibility. This method has been applied on the synthetic magnetic data from a vertical cylinder in both noiseless and noisy data. The presence of the noise causes the estimated depth to differ from the actual body depth; therefore, in practice, the noise should be removed by the upward continuation technique. This method was also applied on real magnetic data from Anomaly No.2 in the Gol-Gohar mining area. In order to remove the superficial noise, the magnetic anomaly was continued to 12.5m elevation. Using this method, it was found that causative body depth varies from 40 to 120 meters in different locations, which has broad correlation with explorative drilling results.