Summary Common Middle Point seismic sections and their successive time migration provide extremely important knowledge about the internal structure of the 3D heterogeneous geological media and are key elements for successive geological interpretation. Full scale numerical simulation, that is one which starts with single shot seismograms, provides a deep understanding how the features of the image are linked with its subsurface prototype. Unfortunately, this kind of simulations for realistic geological media and 3D seismic surveys needs huge computer resources, especially for simulation of seismic waves’ propagation through multiscale media like cavernous fractured reservoirs. In order to significantly reduce the query of computer resources we propose to model these 3D seismic cubes directly rather than shot-by-shot simulation with subsequent CMP stacking. In order to do that the well known “exploding reflectors principle” is modified for 3D heterogeneous multiscale media. Its parallel implementation allows modeling of realistic 3D Common Middle Point stacks with reasonable computational costs. Numerical results for simulation of Common Middle Points sections and their time migration are presented and discussed.

Common Middle Point seismic sections and their successive time migration provide extremely important knowledge about the internal structure of the 3D heterogeneous geological media and are key elements for successive geological interpretation. Full scale numerical simulation, that is one which starts with single shot seismograms, provides a deep understanding how the features of the image are linked with its subsurface prototype. Unfortunately, this kind of simulations for realistic geological media and 3D seismic surveys needs huge computer resources, especially for simulation of seismic waves' propagation through multiscale media like cavernous fractured reservoirs. In order to significantly reduce the query of computer resources we propose to model these 3D seismic cubes directly rather than shot-byshot simulation with subsequent CMP stacking. In order to do that the well known "exploding reflectors principle" is modified for 3D heterogeneous multiscale media. Its parallel implementation allows modeling of realistic 3D Common Middle Point stacks with reasonable computational costs. Numerical results for simulation of Common Middle Points sections and their time migration are presented and discussed.

New numerical method for large-scale computer simulation of seismic waves in multiscale heterogeneous media is developed. As multiscale hereafter we mean media with heterogeneities of extremely different scales. In the paper some specific multiscale medium is dealt with – karst intrusions within thin layered package. Karsts are produced as a result of interaction of water (surface or ground) with underlying bedrock, often limestone or marble. This causes very complicated, extremely irregular structure of karst intrusions - as a rule they form conjunction of local heterogeneities of different scales and very complicated shape. In order to be able to perform reliable finite-difference simulation of seismic wave’s propagation through these structures we develop finite-difference techniques based on grids with local spatial refinement within karstic areas.