Abstract: The traveltime formula based on Taylor expansion is a common method to calculate P-wave traveltime. The Taylor expansion is accurate only near the calculation point, and the inaccuracy of the traveltime approximation is further magnified in the medium of   transverse isotropy  with vertical  symmetry axis   (VTI). An improved method for calculating P-wave traveltime is presented in this paper. This method utilizes the 8th-order offset-traveltime equation based on the Taylor expansion, and the coefficient matching method is used to determine the coefficients of the series expansion. Then the integration processing is used to optimize the parameters. Finally, the 4th-order P-wave traveltime calculation method is formed  based on  coefficient matching and parameter integration. The test results for horizontal layered VTI medium models show that the proposed method has relatively small numerical errors and relatively good performance at the far offset. The experimental results for 3D VSP data show that after parameter adjustment, the method effectively analyzes the data, exhibiting stable performance at middle offsets and a certain advantage at far offsets. 

Key words: traveltime calculation, coefficient matching, parameter integration, VTI medium