Small-angle AVO Analysis Of PS-wave In Tilted TI Media

In seismic exploration , amplitude variation with offset (AVO) and amplitude variation with azimuth (AVAZ) analyses are frequently-used and perfect useful methords for recognizing the lithology and inversing the stratum parameters . The traditional AVO theory is on the assumption that the underground medium is isotropic, but along with the more and more higher exploration precision, all the seismic exploration works should comsider the fact that the underground media is anisotropic . The AVO analysis in anisotropic media a very rapidness improving.In this articale , first , we introduced the the basic theory of anistropic media especially the TI (transversely isotropic) media which containing elasticity coefficients, anisotropic Thomsen parameters and the phase velocity and group velocity in anisotropic media.All of these parameters are the necessarily condition of getting the reflection coefficients in anisotropic media. Recently, the methords of getting the reflection and transmission coefficients are based on the first order perturbation theory in the approximately of weak contrast and weak anisotropic. In this article ,this theory is introduced briefly.Based on, we analysis and summarize the reflection coefficients of PP wave and PS wave in anisotropic media. First, the VTI ( transversely isotropic with a vertical symmetry ) media and HTI(transversely isotropic with a horizontal symmetry) media are the special cases of orthorhombic anisotropic media, then the existing reflection coefficients expressions of orthorhombic anisotropic media can be applicable in VTI and HTI media. There is a corresponding relationship between the anisotropic parameters in orthorhombic anisotropic media and in the VTI or HTI media. From this on we can get new reflection coefficients expressions which are suitable for VTI and HTI media.For the orthorhombic anisotropic, VTI and HTI media ,we can get the reflection coefficients on the interface which comparting any two medias we talked about before. At the same time,because the incidence angle are normaly minum or commonly in the AVO analysis of factly seismic data, so in the reflection coefficients expressions the third order terms of the incidence angle's sine value are be close to zero.At this moment the eave out of these terms should not take too much errors of reflection coefficients.On the other hand this predigestion makes the work of AVO anylysis and inverse more practicality and easely.In the former reflection coefficients expressions of PP wave in anisotropic media, we can not find a direct relationship between the reflection coefficients and the Thomsen anisotropic parameters. In this article ,we first get the VTI media's elasticity coefficients matrix through the relationship of Thomsen anisotropin patameters and elasticity coefficients. When we have confirm azimuth and dip angles of the symmetry in TTI media the elasticity coefficients in TTI meida can be confirmed by the rotating of reference frame.Finally we get the reflection coefficients in TTI media through the common expressions of reflection coefficients in weak anisotropic media.When one of the two medias around the interface is TTI media, a very complex phenomena appears for the PS wave. In the first order perturbation we can get a conclusion that a PS reflection wave appearing by a vertical incidence P wave when the A34 and A35 in the elasticity coefficients matrix are nonzero. We know that in the isotropic,VTI or HTI media,all the two elasticity coefficients are zero, but if one of the two medias is TTI, the vertical incidence P wave makes a reflection PS wave.The reflection coefficients can even be as high as 0.1 although the media is a moderate anisotropic media. In this article we summarize the express of the phase velocity previously, this exact phase velocity make it possible to get the exact reflection coefficients of the PS wave which appearance because of the P wave's normal incidence on the ISO/TTI or a TTI/TTI interface. Finally, systematical analysis the PS wave's ormal incidence reflection coefficients and the AVO gradient varing with the wave velocity in the urper and lower layer,the density and the anisotropic parameters.Finally,the nonlinear inverse methords are introduced into the process of the inverse from the AVO information to anisotropic parameters in anisotropic media. In this article, there's a inverse processing from synthetic seismic recoder to anisotropic parameters in anistropic media using genetic algorithm. It is well know that the genetic algorithm is a heuristics monte-carlo inverse algorithm, it simulates the process of life evolution in nature, so lots of large scal and multivariable nonlinear inverse problem can be resolverd through the genetic algorithm. In this article, we get the exactly PP and PS wave reflection coefficients, build a objective fuction, make a optimization inverse, the finally result is close to the theoretical value. In a word we get the target that inverse the anisotropic parameters using the reflection coefficients.We can get a conclusion that the inverse result from PP wave reflection is a little worse than the result from PS wave although they're all using the genetic algorithm. Through a careful observation we can get a reasonable explaination. In the results of PS wave we can find that the result of dip angle is more accurately than the azimuth angle of the symmetry in TTI media. By analysising the forward data we find the reason why the phenomenon occur.From the wave equation semic record getted by pseudo-spectral methord we met a terrible problem to get the exact reflection coefficients. Because the anisotropic parameters are very sensitiveble to the varing of reflection coefficients, even a less erros can make the inverse processing failed. However, the error of reflection would not effect the qualitative analysis. The line consisted by the plots of relative amplitude and the sine of incidence angle is correlated with the AVO gradient. The slop of the line is proportional to the AVO gradient.