The East Siberian Arctic shelf is the area where the largest natural gas reserves are concentrated. The formation of permafrost of the Arctic shelf during the Ice Age contributed to the emergence of a zone of stable existence of gas hydrates in the sedimentary layer, and subsequent flooding of the shelf led to its gradual degradation, the thawing of gas hydrates and the subsequent emissions of methane into the atmosphere. In the first part of the paper, we use mathematical modeling to study the processes of the formation of subsea permafrost on the Arctic shelf considering changes in the sea levels over the past 200 thousand years. Numerical simulations show the influence of climate warming up to 2200 on the degradation of subsea permafrost and the violation of the conditions for the stable existence of methane hydrates in bottom sediments using the example of the East Siberian shelf. The second part of the paper proposes a method for seismic monitoring of the state of gas hydrates based on a solution of multi-parameter inverse seismic problems. In particular, the degree of attenuation of seismic energy is one of the objective parameters for assessing the consolidation of gas hydrates: the closer they are to the beginning of decomposition, the higher the attenuation and, hence, the lower the quality factor. In this publication, we do not solve a multi-parameter inverse seismic problem for a real geological object. This would be impossible due to the lack of necessary data. Instead, we focus on substantiating the possibility of correct solutions for the problem of the reconstruction of the absorption and velocities for a viscoelastic medium in relation to the problem of monitoring the state of gas hydrate deposits. As noted in a range of publications, the thawing of gas hydrates leads to an increase in the fluid saturation of the geological medium followed by an increase in the absorption of seismic energythat is, a decrease in the quality factor. Thus, the methods of seismic monitoring of the state of gas hydrates to predict the possibility of developing dangerous scenarios should be based on solving a multi-parameter inverse seismic problem. This publication is devoted to the presentation of this approach.