Abstract：The seismic reflection travel-times are often represented approximately by various progression forms of offsets and its precision decreases along with the increase of offset-to-depth ratio. The paper discussed four time-distance curve equation of seismic waves in vertical heterogeneous media; analyzed and compared the errors of ray paths and travel-time curves under the approximation of different velocity function in four layered media models;demonstrated that the mean-square-root errors of hyperbolic-fitted ray paths are much greater than that fitted by other several velocity model. The travel-time approximations in two kinds of velocity models: slowness being linear change with depth and with vertical one-way travel-time are suitable to describe the formation structure with slowly-changed velocity in low velocity layer and fast-changed velocity in high-velocity layer; but the travel-time approximations in two other kinds of velocity models: velocity being linear change with depth and with vertical one-way travel-time are suitable to describe the formation structure with stable change of velocities. The NMO results of theoretical records showed above mentioned NMO results of four fittings are superior to that by four-order curve fitting.
