Abstract <p>In the context of a dynamically changing Arctic ice environment, it is important to use up-to-date mathematical modeling methods to visualize scenarios of acoustic signal transmission through complex ice formations. This paper presents the results of mathematical modeling of ultrasonic ice ridges surveys. We used the grid-characteristic numerical method on systems of overset Chimera meshes do describe complex shape of the interfaces and inhomogeneities in an ice ridge. A combined boundary value problem of elastic and acoustic wave equations was solved to correctly describe the propagation of ultrasonic waves in water, ice, and seabed sedimentary rocks. In the course of the study, a comparison of heterogeneities of the hummocks of different sizes, qualitative and quantitative is performed using the profiles of the vertical and horizontal components of the propagation velocities of the initial acoustic signal of P-waves. Due to the initial variability of the approach, it is possible to conduct modeling with a source of different frequencies. The size of the integration domain under consideration and the complexity of its structure depend on the available computational resources. The results of the conducted numerical experiments testify to the possibility of using the grid-characteristic approach for creating digital twins of hummocks and studying the dependence of the passage of an acoustic signal on the morphometry of the hummock.</p>