Karst areas occupy more than 14% of the world's land and cause serious economic losses, which are estimated at dozens of billions dollars, even without taking into account the physical danger. Among various geophysical methods that can be applied to detecting these objects, gravity and magnetic fields were selected (at the next stage the GPR data will be joined). The proposed approach to recognition of separate geophysical field peculiarities and geophysical integration consists in application of modern developments in the wavelet theory and data mining (Averbuch et al., 2016). Wavelet approach is applied for derivation of enhanced (e.g., coherence portraits) and combined images of geophysical fields simulated for the typical physical-geological models of karst development (different kinds of noise were added to the models). It is shown that the methodology based on the matching pursuit with wavelet packet dictionaries enables to extract desired signals even from strongly noised data. The recently developed technique of diffusion clustering combined with the abovementioned wavelet methods is utilized in to integrate the geophysical data and to detect existing irregularities in the subsurface structure. The most important factor is that these the results obtained at the stage of modeling could be applied for revealing karst targets from the field geophysical observations (on the basis of "learning" approach). The combination of the above approaches enables to create a new methodology, which in principle can enhance reliability and confidence of application of any individual geophysical method and geophysical method integration. This methodology could be an effective tool not only for hidden karst terranes delineation, but also for solving any typical geological (searching economic minerals, geological mapping, etc.), archaeological, ecological and other problems.