Seismic traveltime tomography is an effective method to invert underground anisotropic parameters. Research about the anisotropic traveltime tomographic method remains insufficient. Most studies on this issue are based on weak anisotropy assumption which was proposed by Leon Thomsen according to previous research. But the degree of anisotropic property of strata and rocks is uncertain in real applications. Therefore, a kind of traveltime tomography by use of qP reflection waves is proposed to invert arbitrary anisotropic TI media. First arrival traveltime tomography is often used for near-surface and crosswell anisotropic parameters inversion. In fact, traveltime tomography of qP reflection waves has a much more extensive practical value, because the surface observation system is more economic and general than the systems of crossholes and vertical seismic profiles. Here, we present a new nonlinear traveltime inversion method for the surface observation system which combines several important features: (1) A robust reflected wave ray tracing method is used for arbitrary anisotropic TI media; ( 2) The first-order traveltime perturbation equation is not the eigenvector form of Cerveny's linearized formula, which suffers from a singularity problem for the two quasi-shear waves; ( 3) An effective computation of the Jacobian matrix is employed for an arbitrary anisotropic TI media; and (4) It adopts a fast, local minimization search style of nonlinear inversion. These features make the traveltime tomography of qP reflection waves can be used to invert anisotropic TI media with arbitrary anisotropic degree. In numerical simulation section, this seismic reflection tomography method was used to invert for a layered model and a blocky abnormal body model, respectively. The elastic moduli parameter and Thomsen parameter of these anisotropic models were obtained, respectively. Firstly, we used the traveltimes of qP reflection waves to invert the elastic moduli parameters of the layered model and blocky abnormal body model. (1) According to the tomograms of the layered model, the velocity image is not reconstructed very well although the ray paths can cover the whole model perfectly. The velocity values of the first and third layers differ from the true velocity value greatly. And the bottom interface of the second layer is not recovered very well. Fortunately, the elastic moduli parameters are all reconstructed very well. We can see these images are all very close to sections of the true elastic moduli parameters. (2) After inversion of the blocky abnormal body model, the velocity image is not reconstructed very well. Because the velocity values of the blocky abnormal body differ from the true velocity values greatly. On the contrary, the elastic moduli parameters are very close to the profiles of true elastic moduli parameters. But the c, parameter is not as good as the other three parameters. Secondly, we used the traveltimes of qP reflection waves to invert the Thomsen parameters of the layered model and blocky abnormal body model. (1) According to the tomograms of the layered model, the velocity image is still not reconstructed very well, because the velocity values of the second layer differ from the true velocity values greatly. The Thomsen parameters are reconstructed very well, except the image of beta(0) is slightly not so good. We can see the inverted and true images of alpha(0), epsilon and delta* are very close to each other. (2) After inversion of the blocky abnormal body model, the velocity image is not reconstructed correctly, because its numerical value and shape differ from the true velocity model greatly. However, the profiles of alpha(0), beta(0) and delta* are reconstructed successfully, except the e parameter. The images of these three inverted parameters are very close to that of the true parameters. Besides, these four numerical experiments all reach satisfactory convergence levels for different anisotropic models. Hence, the simulation results show that traveltime of qP reflection waves can invert anisotropic parameters correctly. The traveltimes of qP reflection waves have been used to invert anisotropic parameters for the layered model and blocky abnormal body model successfully. The images of the reconstructed results are very close to the images of the true anisotropic parameters. The tomographic method proposed here has superior capability in recovering theoretical models compared with the isotropic traveltime tomographic method. The more information is used, the less uncertainty of the inversion results according to the inverse theory. In other words, the inversion results can be improved greatly if the traveltimes of qP, qSV and qSH waves are used in the traveltime inversion. Therefore, joint traveltime inversion of qP, qSV and qSH waves should worth further research.
