A B S T R A C TThe founder of the Russian school of direct interpretation of potential fields (with minimal prior geological-geophysical information) was V.M. Berezkin, who introduced the operator of total normalized gradient for the 2D interpretation of profile gravity data sets. This operator was successfully applied in searches of hydrocarbon reservoirs. The further development of this approach (the so-called quasi-singular points method) has allowed solution also to various structural problems, using mathematical criteria for the transition from extremes of total normalized gradient fields to coordinates of anomalous sources. The main numerical evaluation strategy is based on stabilized downward continuation of field derivatives and specific use of the filtration properties of Fourier series approximation. The characteristic properties of the quasi-singular points method are: 1) presentation of a more general total normalized gradient function through additional parameters (derivative order m, form of smoothing function Q, number of Fourier coefficients N * with maximal N), optimum values being chosen during a peak-spectrum analysis of the interpreted function; 2) calculation of the set of total normalized gradient fields for various values of N * /N, representing coordinate systems {x,N * /N} as an 'axes tree' of extrema, where each 2D total normalized gradient field is representationally compressed in a 1D line, permitting a) immediate overview of the positions of the axes in all variants of the calculated fields and b) reduction of the retained information, as required in subsequent interpretation; 3) development of two criteria for transition from extrema of total normalized gradient fields to the coordinates of anomaly sources. The quasisingular points method is intended for tracing limiting gently-sloping boundaries, if their micro-relief features are sources of the interpreted anomaly but sub-vertical contacts may also be traced. The method has been tested in delineating various geological structures. One of the most challenging, successfully achieved, was tracing of the Moho discontinuity and study of the upper mantle, using only Bouguer anomaly data along interpretation profiles. This is attested in an example of two regional profiles intersecting the European part of Russia. The central part of one of them coincides with the results from a deep seismic profile.

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.

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