We describe a versatile method to determine Structural index (SI) and depth to source (z0) of potential fields. The method (SCALFUN) is based on the properties of the scaling function, introduced in the frame of the DEXP theory, and can be used in three ways:

a) to estimate independently the SI ;

b) to estimate independently the depth to source;

c) to obtain a simultaneous estimation of SI and z0.


Many semi-automated interpretation tools are suitable to the estimation of the source position and of a parameter characteristic of the type of the source. This parameter, called ‘Structural Index’ (SI) in the frame of the Euler deconvolution method, reflects the fall-off rate of the potential field anomaly with distance. The SI can be important in the interpretation of potential field data. In fact, it characterizes the anomaly source in terms of simple shapes, helping building a starting model for a forward method of interpretation. Moreover, other source parameters, such as susceptibility, can be determined by the knowledge of position and SI by inputting these parameters in the theoretical formula of the simple source suggested by the value of SI.

Methods to determine the scaling exponent

There are five groups of methods that were recently proposed to estimate the source position and SI:

1. Euler deconvolution techniques;

2. Continuous Wavelet Transform (CWT);

3. Analytic signal/Local Wavenumbers techniques;

4. Magnitude Magnetic Anomaly interpretation.

5. Depth from Extreme Points (DEXP)

1. The standard implementation of Euler deconvolution uses a predetermined value for SI and solve the equation for the source position and the background field. The possibility of a simultaneous estimate of position and SI in Euler deconvolution algorithms comes from different strategies to solve the problem of the presence of a regional field added to the measured data. In the algorithm of Stavrev (1997), the background is assumed as linear and the theory of differential similarity transformations is applied. Application of the Euler deconvolution to a (vertical) derivative was instead suggested by Hsu (2002) and the same attenuation of constant background trends is achievable by using the modulus of analytic signal (Keating and Pilkington, 2004; Florio et al., 2005). Another approach (Nabighian and Hansen, 2001) considers instead the (3D) Hilbert transforms of the potential field to be studied, allowing to eliminate the constant background and to use two equations (i.e. the Hilbert transform components along x and y) for each data point. The system is solved for the source coordinates and SI. All these methods solve simultaneously for depth and SI. Reid et al. (2005) proposed instead a ‘hybrid’ way to solve separately for position and SI, by first solving for position by considering an equation independent from SI, obtained by combining the two Hilbert equations, and then using the position results into the Hilbert equations to get the SI.

2. In the CWT method (f.i.: Sailhac and Gibert, 2003) the depth to the source can be achieved by two distinct analyses: i) a geometrical approach, by considering the position of the maxima of CWT coefficients at various dilations

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