Comparison of different methods for the estimation of depth, location and source-type of magnetic and gravity fields

The main goal of interpretation of potential fields (gravity and magnetic) data is determination of the buried source parameters including the depth, horizontal position, the structural index and the physical properties, which is magnetic susceptibility in the magnetic cases and density for gravity fields. For a large number of data it is so expensive modelling the data by using the inversion algorithms. So, in the last decades a variety of algorithms have been developed for source parameters estimate (Nabighian et al, 2005a, b). The depth is often the most important parameter to being determined. Early depth to source methods were mainly graphically. The automatic methods began to appear owing to computers and digital data available in 2D and 3D cases, most of them being field derivative based methods. Many of these approaches have restricted use because of limiting assumptions in their theory.
Since there is no method being the best, it is wise to use a variety of methods. In this paper, firstly, some of the widely used methods are described, such as Euler deconvolution (Thompson, 1982), analytic signal (Nabighian, 1972, 1974), source parameter imaging (SPI) (Thurston and Smith, 1997), Improved source parameters imaging (iSPI) (Smith et al, 1998), enhanced local wavenumber (ELW) (Salem et al, 2005) and ANEUL (Salem and Ravat, 2003). These are applied to a synthetic data produced by a fairly complex model simulating a magnetic basement, in order to estimate the position and structural index of its structures.
The SPI method requires second-order derivatives of the field and uses the local wavenumber concept. The SPI is a fast and automatic method, assuming as source-model either a 2D sloping contact or a 2D dipping thin sheet model; it provides estimates of depth, dip, edge location and physical property contrast. iSPI uses the same concept as in SPI and is applied to 2D data. ELW is a combination of local wavenumber in Euler equation to determine source location and structural index. In this method a window is selected around the local-wave number peaks, and the source position is estimated by solving an over determined problem in each window. Once the source location is estimated, the structural index is obtained by using the main equations of the method. ANEUL is a fully automatic method, whose main equation is obtained by using analytic signal up to order 2 in Euler-homogeneity equation.
Since all the above mentioned methods make use of the field derivatives of different orders, high-quality datasets are needed, otherwise the final results may be affected by even severe errors.
Multiscale methods (Fedi and Pilkington, 2012), are a different class of interpretative methods, based on the behavior of the potential fields at different altitudes. They allow determination of depth, horizontal location and source-type. Taking advantage of a combined use of upward continuation and field differentiation, these methods are very stable and not sensitive to noise as the other methods are.
In this paper, among the several multiscale methods we use DEXP transformation (Fedi, 2007), automatic DEXP (Abbas et al, 2014) and Geometric method (Fedi et al, 2009, 2012). By DEXP transformation the field is calculated at some altitudes and it is scaled by using a power-law of the altitude. The depth can be obtained by finding the extreme points of the DEXP field. Automatic DEXP is based on computing the local wavenumber (of any order) at several latitudes and then scaling with a proper function to estimate the structural index and the source position. This new version of the DEXP transform is fully automatic and does not need any priori information. By the geometric approach, the maxima of the field at various scales are located along lines that are called ridges. Extrapolating the true ridges below the measurement surface, is enough to find the source position at the ridge intersection.
In spite of using noise-free data set in the synthetic case, it is shown that the classical methods do not provide results as accurate as those by multiscale methods. Comparison among more methods and evaluation of their consistency will be really important and practical, in real cases, to evaluate the final results and to make decision about individuating the best ones.
We conclude the paper by applying all the methods to a magnetic profile over a 2D structure, in order to estimate its parameters. None of these methods is restricted to the magnetic fields, and they can be also applied to gravity fields or its derivatives as well.