Kawaguchi space, Zermelo's condition and seismic ray path

Based on Kawaguchi space, a seismic ray path through an anisotropic medium corresponds to an arclength under Zermelo's condition. From a special function in Kawaguchi space, we obtain some Finslerian metrics (mth root metric or 1-form metric). Considering a variational problem of the seismic ray, Snell's law is derived from Euler's vector, and envelopes of seismic wavefront are classified by m-values in seismic Finsler metric. Moreover, we discuss the relation between Kawaguchi space and another ray theory.