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The extraction of kinematic parameters from wave propagation through traveltimes is one of the great challenges in seismic data processing. In this context, we modify the common-reflection-surface (CRS) traveltime to improve its accuracy and also interpret its parameters via paraxial ray theory in an anisotropic medium obtaining information about the wavefront curvatures measured at surface. The proposed method consists of searching for the best stacking parameters that fit the data set followed by the extraction of kinematic information from the measured waves. Numerical tests show the effectiveness of our assumptions and that the results obtained in the fitting and parameter extraction in anisotropic media achieve better accuracy than conventional CRS.

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The effective application of normal moveout correction processes mainly depends on four factors: the chosen traveltime approximation, the stretching associated with the given traveltime, crossing events and phase changes, the last two being inherent to the seismic data. In this context, we conduct a quantitative analysis on stretching considering a general traveltime expression depending on half‐offset and midpoint coordinates. Through this analysis, we propose a mathematically proven procedure to eliminate stretching, which can be applied to any traveltime approximation. The proposed method is applied to synthetic and real data sets, considering different traveltime approximations and achieved complete elimination of stretching.