The effect of thermal lattice vibration on the system in semi infinite polar crystal within the magnetic field, which is weak coupling with bulk LO phonons and strong coupling with SO phonons, were studied. An expressions for the self trapping energy of the surface magnetopolaron as a function of the depth from the crystal surface, magnetic field and temperature were derived by using Huybrechts' linear combination operator and variational method. The numerical results of the self trapping energy for AgCl show that the contribution of interaction between the electron and the different branch of phonons to the self trapping energy and the it's changing with the depth from the crystal surface, magnetic field and temperature are greatly different.