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The 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 quasi-singular 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. [ABSTRACT FROM AUTHOR]

The change in reservoir pore pressure due to the production of hydrocarbons leads to anisotropic changes in the stress field acting on the reservoir. Reservoir stress path is defined as the ratio of the change in effective horizontal stress to the change in effective vertical stress from the initial reservoir conditions, and strongly influences the depletion-induced compaction behaviour of the reservoir. Seismic velocities in sandstones vary with stress due to the presence of stress-sensitive regions within the rock, such as grain boundaries, microcracks, fractures, etc. Since the response of any microcracks and grain boundaries to a change in stress depends on their orientation relative to the principal stress axes, elastic-wave velocities are sensitive to reservoir stress path. The vertical P- and S-wave velocities, the small-offset P- and SV-wave normal-moveout (NMO) velocities, and the P-wave amplitude-versus-offset (AVO) are sensitive to different combinations of vertical and horizontal stress. The relationships between these quantities and the change in stress can be calibrated using a repeat seismic, sonic log, checkshot or vertical seismic profile (VSP) at the location of a well at which the change in reservoir pressure has been measured. Alternatively, the variation of velocity with azimuth and distance from the borehole, obtained by dipole radial profiling, can be used. Having calibrated these relationships, the theory allows the reservoir stress path to be monitored using time-lapse seismic by combining changes in the vertical P-wave impedance, changes in the P-wave NMO and AVO behaviour, and changes in the S-wave impedance. [ABSTRACT FROM AUTHOR]