Perfect transmission and asymptotic solutions for reflection of ice-coupled waves by inhomogeneities

Dissimilar imperfections such as cracks and pressure ridges in sea ice result in similar reflection coefficients when they scatter ice-coupled waves, being highly reflective at short wavelengths, highly transmissive at long wavelengths, and having some periods at which transmission is perfect (although associated with a change in phase). The causes of the zeroes in the reflection coefficient are not well understood and where analytic solutions can be found physical interpretations are difficult. Here we examine simplified systems that are amenable to such an interpretation. For a single crack in an ice sheet we present an asymptotic solution for a very thin sheet and furnish a new interpretation of the existing wide-spacing approximation that suggests that the zero is caused by destructive interference of waves reflected from each of the two sides of the crack. For a simple rectangular pressure ridge we report a small feature approximation that also shows that the zero arises from destructive interference but, for this case, interference of waves reflected from the mass and rigidity of the ridge.