The authors use the common offset ground penetrating radar ( GPＲ) data inversion based on ray theory to estimate interval velocity and to obtain the relative permittivity． In the ray-tracing based inversion，the input data are the offset distance between antennas，the velocity of the first layer，the pick-up amplitude and reference amplitude of each reflection layer． The thickness and velocity of each layer are calculated by this recursive method． Firstly，the horizontal homogeneous layered medium model is established，and the ideal inversion results are obtained． Subsequently，Monte Carlo method is used to establish a randomly undulating homogeneous layered medium model． The common offset GPＲ data for the built geological model is then simulated by finite-difference time-domain ( FDTD) ． It proved that this ray-tracing based inversion method is feasible for the horizontal layered geological model，even the layered geological model with random undulation． Undulation，represented
by ＲMS height and CL ( correlation length) ，influences the inversion results． Finally，a more complex geological model--pinch-out model was established． In the pinch-out model，the pinch-out interface can be clearly identified，though there is a false anomaly，which will not significantly affect the identification of the underground medium structure．
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