  Reciprocity theorems are established for the elastic sea level fingerprint
problem including rotational feedbacks. In their simplest form, these results
show that the sea level change at a location x due to melting a unit point mass
of ice at x' is equal to the sea level change at x' due to melting a unit point
mass of ice at x. This identity holds irrespective of the shoreline geometry or
of lateral variations in elastic Earth structure. Using the reciprocity
theorems, sensitivity kernels for sea level and related observables with
respect to the ice load can be readily derived. It is notable that calculation
of the sensitivity kernels is possible using standard fingerprint codes, though
for some types of observable a slight generalisation to the fingerprint problem
must be considered. These results are of use within coastal hazard assessment
and have a range of potential applications within studies of modern-day sea
level change.
