Application of the Normalized Full Gradient (NFG) Method to Resistivity Data

Adopting normalized full gradient method for regional‐scale gravity modelling: A case study for Northwestern Iran

“…}\left( {\frac{1}{M}\mathop \sum \nolimits_{i = 1}^M \sqrt {{{\left( {{{\left( {\frac{{\partial G\left( {{x_i},\;{z_j}} \right)}}{{\partial x}}} \right)}^2} + {{\left( {\frac{{\partial G\left( {{x_i},\;{z_j}} \right)}}{{\partial z}}} \right)}^2}} \right)}^v}} }\right),\end{equation}$$in which i is the counter of observation data, j is the counter of interesting depth, M is the number of observations,$$\;\partial G( {{x_i},\;{z_j}} )/\partial x$$ and$$\;\partial G( {{x_i},\;{z_j}} )/\partial z$$ are the derivatives of $$G( {{x_i},\;{z_j}} )$$ and v is called the degree of the NFG operator, which controls two important shaping parameters of an envelope, the peak value and the anomaly width of the NFG sections. Although v can be taken as 1, 2, 4, 8 and so forth, v = 1 is generally used for the potential field data (Aydin, 1997). Karsli (2001) suggested that higher order values are more reasonable for seismic applications because they narrow the recorded signal's width and improve the seismic resolution.…”

“…q can be equal to any integer number; however, Berezkin (1973) showed that q = 2 could provide better results for oil–gas exploration. Previous research studies (Aydin, 1997; Aghajani et al., 2009a; Dondurur, 2005; Karsli, 2001; Oruç, 2011) proposed that q values of 1 and 2 give a good result in the downward continuation and help to find more accurate depth estimation of subsurface features from geophysical data. Anyhow, this parameter should be defined on field data via a parameter analysis.…”

“…In the conservative NFG method, the optimal number of harmonics is estimated by N value analysis (Zeng et al., 2012). N ‐restricted processing was discussed by Aydin (1997), Aghajani et al. (2009a, 2009b, 2011), Berezkin (1988), Dondurur (2005), Sindirgi et al.…”

“…Analytical continuation discriminates certain structural anomalies which cannot be distinguished in the observed gravity field (Aydin, 2007). Downward analytical continuation of the observed gravity data shows irregular variations during the passage of the mass giving rise to the anomaly (Berezkin, 1988; Aydin, 1997). The NFG of the gravity anomaly is often used rather than the gravity anomaly in underground spaces because it is stable and indicates the locations of source bodies.…”

“…Moreover, NFG gives a useful interpretation of electromagnetic data (e.g. Zeng et al., 2002; Dondurur, 2005), resistivity data (Aydin, 2010), gravity and magnetic data (e.g. Aydin, 2007; Zeng et al., 2002), self‐potential data (e.g.…”