  In [Engquist et al., Commun. Math. Sci., 14(2016)], the Wasserstein metric
was successfully introduced to the full waveform inversion. We apply this
method to the earthquake location problem. For this problem, the seismic
stations are far from each other. Thus, the trace by trace comparison [Yang et
al., arXiv(2016)] is a natural way to compare the earthquake signals.
  Under this framework, we have derived a concise analytic expression of the
Fr\`echet gradient of the Wasserstein metric, which leads to a simple and
efficient implementation for the adjoint method. We square and normalize the
earthquake signals for comparison so that the convexity of the misfit function
with respect to earthquake hypocenter and origin time can be observed
numerically. To reduce the impact of noise, which can not offset each other
after squaring the signals, a new control parameter is introduced. Finally, the
LMF (Levenberg-Marquardt-Fletcher) method is applied to solve the resulted
optimization problem. According to the numerical experiments, only a few
iterations are required to converge to the real earthquake hypocenter and
origin time. Even for data with noise, we can obtain reasonable and convergent
numerical results.
