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The application of the horizontal-to-vertical spectral ratio (HVSR) modeling and inversion techniques is becoming more and more widespread for assessing the seismic response and velocity model of soil deposits due to their effectiveness, environmental friendliness, relative simplicity and low cost. Nevertheless, a number of issues related to the use of these techniques in difficult natural conditions, such as in the shelf areas of the Arctic seas, where the critical structures are also designed, remain poorly understood. In this paper, we describe the features of applying the HVSR modeling and inversion techniques to seismic records obtained by ocean-bottom seismographs (OBS) on the outer shelf of the Laptev Sea. This region is characterized by high seismotectonic activity, as well as sparse submarine permafrost distribution and the massive release of bubble methane from bottom sediments. The seismic stations were installed for one year and their period of operation included periods of time when the sea was covered with ice and when the sea was ice-free. The results of processing of the recorded ambient seismic noise, as well as the wave recorder data and ERA5 and EUMETSAT reanalysis data, showed a strong dependence of seafloor seismic noise on the presence of sea ice cover, as well as weather conditions, wind speed in particular. Wind-generated gravity waves, as well as infragravity waves, are responsible for the increase in the level of ambient seismic noise. The high-frequency range of 5 Hz and above is strongly affected by the coupling effect, which in turn also depends on wind-generated gravity waves and infragravity waves. The described seafloor seismic noise features must be taken into account during HVSR modeling and interpretation. The obtained HVSR curves plotted from the records of one of the OBSs revealed a resonant peak corresponding to 3 Hz, while the curves plotted from the records of another OBS did not show clear resonance peaks in the representative frequency range. Since both OBSs were located in the area of sparse distribution of submarine permafrost, the presence of a resonance peak may be an indicator of the presence of a contrasting boundary of the upper permafrost surface under the location of the OBS. The absence of a clear resonant peak in the HVSR curve may indicate that the permafrost boundary is either absent at this site or its depth is beyond the values corresponding to representative seismic sensor frequency band. Thus, HVSR modeling and inversion techniques can be effective for studying the position of submarine permafrost.