  If a non-reversible Finsler norm is the sum of a reversible Finsler norm and
a closed 1-form, then one can uniquely recover the 1-form up to potential
fields from the boundary distance data. We also show a boundary rigidity result
for Randers metrics where the reversible Finsler norm is induced by a
Riemannian metric which is boundary rigid. Our theorems generalize Riemannian
boundary rigidity results to some non-reversible Finsler manifolds. We provide
an application to seismology where the seismic wave propagates in a moving
medium.
