An interferometric form of Fermat's principle is derived that converts travel times of free-surface multiples into those for lower-order events such as primary reflections. These primary reflection travel times can then be used to tomographically invert for layer velocities more accurately than standard travel time tomography applied to multiples. As an example, Fermat's interferometric principle converts VSP (vertical-seismic-profile) travel times of receiver-side ghosts and direct waves to those for CDP (common-depth-point) primary reflections. These CDP travel times can be used to estimate, e.g., statics velocities for a 3D survey, which is impossible by conventional VSP tomography applied to primary travel times. This procedure is exact in the high frequency approximation, and it can be extended to multiples in CDP and earthquake data. Fermat's interferometric principles presents new opportunities for imaging multiples and greatly extends the illumination area of VSP, CDP and earthquake travel time tomography.