Analytical signal and Euler deconvolution techniques uses as a semi
automatic interpretation of magneic data to identify magnetic causative body,
location-depth relationship (Keating & Pilkington, 2004; Ndlovu et al.,
2015). The analytic signal is most easily derived in the wavenumber domain,
since it involves the calculation of derivatives of magnetic anomalies. The
following convention is used for the forward and inverse 2-D Fourier transform

with k, and ky, the wavenumbers in x and y directions. Using this
equation wavenumber domain relations can be derived between the Fourier
transforms of a magnetic anomaly M and of its orizontal and vertical
derivatives (Nabighian, 1972, 1984)

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Defining 

  as unit vectors in x, y, and z directions,
allows the 3-D analytic signal of a potential field anomaly M to be written as

From the above equation Roesr et al., (1992)  showed that the amplitude function is formed
through a combination of the horizontal and vertical gradients of a magnetic
anomaly.

The analytic signal has a form over causative bodies (Fig.5B ) that depends on
the locations of the bodies but not on their directions of magnetization. The
signals maxima mark the edges of the magnetized bodies or the magnetization
contrasts occurs and is independent of the ambient magnetic field and source
magnetization directions (Nabighian, 1984; Roest et al., 1992;  Macleod et al., 1993).  The Locations of these maxima demarcate
the  outlines of magnetic sources and
since these  anomalies are caused by
vertical contacts, the breadth of the peak 
of analytic signal can be used to estimate depths to magnetic sources (Reid
et al., 1990; Roest et al.,  1992) while
Hsu et al., (1996) used it for geological boundary demarcation. The analytic
signal is useful in locating the edges of magnetic source bodies, particularly
where low magnetic latitudes and/or remanent magnetization complicates the
interpretation. (Fig. 5B)