A simplified surface correction formulation is proposed to diminish the far-field spurious sound gener- ated by the quadrupole source term in Ffowcs Williams and Hawkings (FW-H) integrals. The proposed formulation utilizes the far-field asymptotics of the Green's function to simplify the computation of its high-order derivatives, which circumvents the difficulties reported in the original frequency-domain sur- face correction formulation. The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex. The results show that the proposed formulation success- fully eliminates the spurious sound. The applications of the proposed formulation to flows with some special parameters are also discussed.