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

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.