A computational model of reverberation at low frequencies in an ice-covered environment is developed. The model is built on a full-field perturbation approach and includes elastic parabolic equation solutions for the acoustic field and its horizontal and vertical derivatives near water-ice and water-air interfaces. Our previous work demonstrated that average reverberation intensity is sensitive to both elasticity and thickness of the ice at mid-frequencies, where the ice layer thickness is on the order of or larger than both compressional and shear wavelengths. Here we address what happens to the reverberation when ice thickness approaches zero. Reverberation estimates for rough free surface and those from rough ice-water interface with increasing ice layer thickness are compared to determine at what ice thicknesses and acoustic frequencies the long-range reverberation distinguishes between the two cases. To isolate effects of ice thickness, we assume roughness is the same in both environments. Frequencies will be varied from very low, where the ice layer is practically transparent, to moderately low where the presence of the ice becomes noticeable in the reverberation. Numerical examples for reverberation in a typical Arctic environment with upward refracting sound-speed profile are presented and discussed. [Work supported by ONR.]A computational model of reverberation at low frequencies in an ice-covered environment is developed. The model is built on a full-field perturbation approach and includes elastic parabolic equation solutions for the acoustic field and its horizontal and vertical derivatives near water-ice and water-air interfaces. Our previous work demonstrated that average reverberation intensity is sensitive to both elasticity and thickness of the ice at mid-frequencies, where the ice layer thickness is on the order of or larger than both compressional and shear wavelengths. Here we address what happens to the reverberation when ice thickness approaches zero. Reverberation estimates for rough free surface and those from rough ice-water interface with increasing ice layer thickness are compared to determine at what ice thicknesses and acoustic frequencies the long-range reverberation distinguishes between the two cases. To isolate effects of ice thickness, we assume roughness is the same in both environments. Frequencie...