The application of the local wavenumber for depth estimation of magnetic data; Case study: Siriz Iron Mine

Depth detection of magnetic bodies is the most important goal in magnetic data interpretation, and there are so many different methods for this  purpose. After Nabighian (1972) proposed the analytic signal and used it for magnetic data interpretation, so many authors and researchers have used the definition of analytic signal in magnetic data interpretation (Roest et all,1992; Hsu et all, 1996, 1998; Thurston and Smith, 1997; Smith et all, 1998; Thurston et all, 2002; Salem et all, 2005, 2008; Keating, 2010).
The analytic signal is a complex relation, which its real and imaginary parts are horizontal and vertical derivatives of the magnetic field, respectively. Therefore, the analytic signal can be introduced by amplitude and phase. The amplitude of an analytic signal is equal to the root square of horizontal and vertical derivatives () and its phase is equal to . Both amplitude and phase can be used in magnetic data interpretation. The maximum amplitude of an analytic signal can be used for edge detection (the maximum amplitude of an analytic signal is located on the body), and also for depth estimation. The depth estimation methods based on the amplitude of the analytic signal use the maximum amplitude of different orders of the analytic signal.
    The local wavenumber is based on the gradient of phase and recently it has been used in magnetic data interpretations, such as edge and depth detection of magnetic sources. Like the amplitude of the analytic signal, high orders of the local wavenumber are calculated and used in magnetic data interpretation.
The local wavenumber is used for depth detection in two ways:
1) Depth estimation based on the maximum value of local wavenumber: The maximum value of the local wavenumber is located on the magnetic bodies and with a priori knowledge about the model of magnetic bodies (for example: contact, thin dike, horizontal cylinder, …), magnetic source depth can be estimated. In this way, the depth detection’s equation only use the second order derivative of magnetic field. Therefore, it is more suitable for interpretation of noisy data. However, in early stages of exploration, usually there is not any knowledge about the model of sources. Also, the depth can be estimated without any prior knowledge about the model, but it uses the third order derivative of the magnetic field.
2) The estimation of depth and horizontal location of source using the enhanced local wavenumber. In this method, a linear equation was obtained that estimates the depth and the horizontal location of the magnetic bodies without any prior knowledge about the model. A window is passed over the data and this linear relation is solved by the least square method. These methods only use the second order derivative of the magnetic field. 
These methods are applicable on profile and gridded data.
    In this study, the local wavenumber-based methods are introduced and their advantages and disadvantages are discussed by applying to synthetic data. For these methods, we have developed code in MATLAB software. These methods are also applied to a magnetic anomaly in Ciriz in Kerman Province, Iran.