Seismic monitoring of the accumulation and burial of greenhouse gases in a reservoir is attracting increasing attention due to its relevance to mitigating the effects of climate change. Changes in properties in the reservoir during gas injection demonstrate how seismic data changes. Among the seismic surveys, specialists are modeling the propagation of seismic wave fields for seismic monitoring. However, such methods are too resource-intensive, especially when solving for a large number of known velocity models and the number of sources in the acquisition system. Therefore, new effective algorithms for tracking changes in seismic data are needed. The work uses a neural network, which is used in two stages: to refine and obtain seismograms at the next step of seismic monitoring using a coarse computational grid and to suppress numerical dispersion. The developed algorithm makes it possible to accelerate classical seismic monitoring up to 3 times, taking into account the physics of multiphase flows.