The normalized full gradient (NFG) method defined by Berezkin (1967, 1973 and 1998) is used for downward continuation maps. Analytical downward continuation is a method to estimate the field closer to the source and consequently results in a better resolution of underground rock distribution. However, the usefulness of this process is limited by the fact that the operation is extremely sensitive to noise. With noise free data, downward continuation is well defined; we do not attempt to continue below the source level. In the presence of noise, the amplification of high frequencies is so strong that it quickly masks the information in the original profile. Low-pass Fourier filtering, while suppressing such noise, also blurs the signal, overcoming the purpose of sharpening by downward continuation.
Despite the above-mentioned problems, most geophysical experts have long been interested in this technique because of its importance to the mineral exploration. Furthermore, this method is a fast and cheap way to determine the initial depth of the subsurface features, especially where there is no other geophysical or well-logging data. A good analytical downward continuation process could provide subsurface general images, allowing an enhanced interpretation. Also, analytical downward continuation has the ability to determine accurately both horizontal and vertical extents of geological sources.
This method is concisely described in the following section. The 2-D NFG of gravity anomalies is defined as (Berezkin, 1973):
(1)
Where GH(x, z) is the NFG at point (x, z) on a cross-section x-z; Vzz(x, z) and Vxz(x, z) are the first vertical derivative and the first horizontal (along the x-direction) derivative of gravity anomalies (or Vz) at point (x, z), respectively; G(x, z) is the full (total) gradient of gravity anomalies at point (x, z); GCP(z) is the average of the full gradient of gravity anomalies at level z; and M is the number of samples in a data set.
Berezkin (1973) expressed the gravity anomalies over the range (-L, L) by the finite Fourier sine series,
(2)
where
(3)
L is the integral interval or length of the gravity profile; and N is the number of harmonics of the series. From Eq. (2) it follows that
(4)
(5)
Defining a smoothing factor for eliminating high-frequency noise resulting from downward continuation, we have,
(6)
Where, m is known as the degree of smoothing. It was suggested to choose m =1 or 2 to reach reasonable results. Finally,
(7)
(8)
(9)
Substituting Eqs. 8 and 9 into Eq. 1, the NFG is calculated.
The NFG method nullifies perturbations due to the passage of mass depth during downward continuation. The method depends on the downwards analytical continuation of normalized full gradient values of gravity data. Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field. It can be used to estimate location, depth to the top and center of the deposit that is applied also for detecting oil reserviors and tectonic studies. One of the important parameter to estimate accurate shape of the deposit is true selection of the harmonic number. In this paper, the correct range of the harmonic number is determined and then this method will be tested for noise-free and noise-corruption synthetic data. Finally, 2D and 3D of this method are applied on real data, Dehloran Bitumen.