Study On The Model-building Of Velocity And Anisotropic Parameters For VTI Media

Firstly, we improved the approximate formula of the phase velocity for qP wave in VTI media proposed by Berryman(2009). By tracking in the current international advances about inhomogeneous viscoelastic waves in anisotropic media, we propose a new perturbation formulas for the phase velocity and the poloarization of inhomogeneous plane wave in dissipative anisotropic media, which are more accurate than that proposed by Cerveny. By numerical analysis and comparison with exact solutions and approximation solution, we found that the accuracy of the new formulas are much higher than that of the original one.Seismic velocity analysis in seismic data processing is a popular technology. We summarizes the approximate formula proposed by predecessors and compares their accuracy by numerical mdeling. We also find that the q1-q2 parameterizaton proposed by Abadd(2009) is the best one. In recent years with the development of an automatic non-hyperbolic velocity analysis techniques, Siliqi(2000) and Abadd introduce the idear of automatic nonhyperoblic velocity analysis. Their method can estimate the moveout velocity and the anellipticity accurately. We combine the latest formulas derived by Alexiso(2009) and the model parameterization of time-distance curves proposed by Abadd(2009), while using the latest technology and the popular Curvelet denoising techniques instead of the Kriging filtering mentioned in Alexiso(2009) and Siliqi(2001). In order to test the performance of this scheme, we applied it to the synthetic data and the field data with large offset, respectively. The final results shows it is satisfactory.Differential semblance velocity inversion is a technology to estimate the velocity from the the objective function of the differential semblance. In the chapter 4 of this thesis, according to the scheme given by Li, and Symes in 2007 for interval velocity inversion based on NMO correction using hyperbolic traveltime formula, we propose the idear of inversion of interval velocity and anellipticity based on NMO correction using the nonhyperbolic one. Through a series of complex mathematical derivation, we show the optimization problem for non-hyperbolic differential semblance inversion, and the derivative of the objective function function with respect to interval velocity and anellipticity. By combining the nonlinear conjugate gradient algorithm with the constrained optimaization frame, we prove the validity of the algorithm using the synthetic data.Seismic tomography based on ray is still an important research topic. In order to realize it for layered VTI media, we firstly need to achieve the parameterization of the underground model and ray tracing in this parameterized model. Many Geophysicsts have proposed so much parameterization methods for ray tracing, in which the simplest one is to sample the underground model by discrete rectangular blocks. The layered underground medium can also be divided into a series of small trapezoidal block. For more complex models, we can discretize it into a series of irregular blocks. In chapter 5 of this thesis, according to the trapezoidal block modeling for isotropic medium by Zelt in 1988, we proposed a new schemes for trapezoidal block modeling.for VTI medium The layered VTI media is divided into a series of trapezoidal blocks, in which each node owns a group of Thomsen parameters. In addition, we also derive the Snell's law for the VTI medium with a tilted interface, which can be used to estimate the phase slowness for reflected or transmitted ray tracing from that of the incident ray. The single-layer model , multi-layered model , and topology multi-layered model is investigated by the proposed scheme, which prove the algorithm's practicality.In addition to computing traveltime by ray tracing in seismic tomography, it is also necessary to calculate Frechet derivative of the raveltime of rays with respect to the model parameters and resolve the inverse problem. In the chapter 6 of this thesis, we discusses the mathematical theory of tomography inverse problem. Moreover, according to the travel perturbation formula proposed by Cerveny, we present the Frechet derivative of the ray traveltime with respect to the model parameters in the trapezoidal blocks. In solving the inverse problem of tomography, according to Bube's mixed l~1/l~2norm inversion theory, we derived a series of regularized and preconditioned mixed l~1/l~2norm inversion method and gives the corresponding algorithm process. Finally, we show a numerical experiment of reflective tomography and compare the results for reflected qP-wave, reflected qPqSV-wave as well as the joint of reflected qP- and reflected qPqSV- wave.