In order to search for ultra-high energy cosmological earth-skimming muon neutrinos by the surface detector array (SD) similar to one of the Pierre Auger Observatory (PAO), we propose to use the transition electromagnetic radiation at the medium interface induced by earth-skimming muons for triggering a few of aligned neighboring Cherenkov SD stations. Simulations of the acceptance of a modeling SD array have been done to estimate the detection probability of earth-skimming muon neutrinos.