  We consider the relativistic tidal effects on frequency shift of
clock-comparison experiments. The relativistic formulation for frequency shift
and time transfer is derived in the gravitational field of a tidal,
axisymmetric, and rotating Earth. With the help of Love numbers describing the
tidal response of solid Earth, we formulize the mathematical connection between
tidal effects from the ground-based clock-comparison experiments and the local
gravity tides from the gravimeters, which in turn provides us an approach to
eliminate tidal influences on clock comparison with the local gravity tides
data. Moreover, we develop a method of the perturbed Kepler orbit to determine
relativistic effects of clock comparison for space missions, which allows more
precise calculations comparing to the conventional method of unperturbed Kepler
orbit. With this perturbed method, it can give the perturbation of relativistic
effects due to the orbital changes under the influences of tidal forces,
Earth's oblateness etc. In addition, as the applications of our results, we
simulate tidal effects in frequency shift for the clock comparison on the
ground and also give some estimates for TianQin mission and GPS.
