Review Paper: Historical development of the total normalized gradient method in profile gravity field interpretation

Abstract

In the Russian school, the total normalized gradient method belongs to the most wide‐spread of direct interpretation methods for potential field data. This method was also used and partly developed by many experts from abroad. The main advantage of the total normalized gradient method is its relative independence of parameters such as the expected differential density of interpreted structures. The method is built from a construction of a specially transformed field (total normalized gradient) on a section crossing the potential field sources. The special properties of this transformed field allow it to be used to detect the source positions. From the 1960s, the mathematical basis of the method underwent enormous development and several modifications of the method have been elaborated. The total normalized gradient operator itself represents a relatively complicated, non‐linear band‐pass filter in the spectral domain. The properties of this operator can be handled by means of several parameters that act to separate the information about field sources at different depth levels. In this contribution, we describe the development of the method from its very beginning (based mostly on qualitative interpretation of simple total normalized gradient sections) through to more recent numerical improvements to the method. These improvements include the quasi‐singular points method, which refines the filter properties of the total normalized gradient operator and defines an objective criteria (so called criterion ‘α’ and ‘Г') for the definition of source depths in the section. We end by describing possibilities for further development of the method in the future.

Depth Estimation of Potential Field by Using a New Downward Continuation Based on the Continued Fraction in Space Domain

“…Although numerous methods have been proposed to improve the calculation stability and accuracy (Xu 2007;Pašteka et al 2012;Zhang et al 2013;Zeng et al 2013;Pilkington and Boulanger 2017;Zhou et al 2018;Zhang et al 2018), downward continuation methods are not developed enough to over cover depths equal to or greater than the depth at which the field becomes singular (Fedi and Florio 2011). Therefore, depth estimation methods based on downward continuation, such as the normalized total gradient (NTG) and the singular (quasi-singular) point method, usually require additional calculations (Elysseieva and Pašteka 2009;Fedi and Florio 2011;Elysseieva and Pašteka 2019). In fact, these methods are similar in basic normalized theory.…”

“…If we want to obtain the depth information (the singular point) by using Taylor series, the term of m must be infinite  . It is conflict with the finite potential filed data we measured or modeled, and it is very difficult to implement the method using infinite m. To overcome the limitation, a normalized algorithm was proposed (Elysseieva and Pašteka 2009;Elysseieva and Pašteka 2019).…”

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

“…An important topic in potential‐field data interpretation is the concept of singular points (Elysseieva & Pasteka, 2018). Singular point methods are based on the idea that the position of potential field data sources is very close to the position of singular points of a specially transformed field during the downward continuation or analysis of complex functions from special transformations.…”

“…An important method of this type is the normalized full gradient (NFG) method introduced in early papers of Berezkin and Buketov (1965), Berezkin and Buketov (1966), Berezkin (1967) and Berezkin (1968). A historical overview of the development of this method can be found in the studies of Elysseieva and Pasteka (2018).…”

Depth Estimation of Potential Field Sources by Using Improved Chebyshev‐Padé Downward Continuation in Wave Number Domain

“…In fact, stable downward continuation with low‐pass filtering is a promising technique for estimating the depth of sources. The most widely accepted method is the “normalized full gradient” and “quasi‐singular points method”, proposed by the Russian geophysical school (Elysseieva & Pašteka, 2009, 2019). This type of approach was developed or used for many years by other authors (e.g., Aydin, 2007; Florio & Fedi, 2018; Zeng et al, 2002; Zhang & Meng, 2015; Zhang et al, 2005; Zhou, 2015).…”