Multiparameter Full-waveform Inversion For Acoustic VTI Medium Based On Inexact Full Newton Algorithm

Seismic inversion is an effective mean to research the structure and distribution of the subsurface medium,which uses the information carried by seismic waves to obtain the physical parameters of underground medium.As the further research of underground medium,how to obtain higher accuracy physical parameters of underground medium has become one of the main problems of geophysical inversion,and the traditional method of seismic inversion can no longer be the needs of seismic exploration.In recent years,full waveform inversion as a new type of seismic data inversion method which is widely favored by the geophysicist,because it can be fully used in all kinds of useful information in order to get higher accuracy of medium parameters.It becomes one of the major research focuses in current seismic explorationConventional full waveform inversion research mainly based on the theory of isotropic medium,and in an actual underground medium,the rock as a result of the stress induced,directional arrangement of fractures and other factors,makes the distribution of the wide range of anisotropic medium.So the FWI based on the theory of anisotropic will be able to provide more accurate,higher resolution of the subsurface medium as a result,which helps to describe the physical parameters of underground medium,accurately.So the research of FWI in anisotropic medium is particularly important.The forward numerical modeling is very important for FWI.The traditional numerical simulation is based on elastic wave equation of motion can be a very good description of seismic wave propagation in the underground medium but exist in the process of simulation parameters,the problem such as large amount ofcalculation,time-consuming,would increase the amount of calculation and calculation of FWI memory.By comparison,using the acoustic wave equation to do numerical simulation,which has advantages of less parameters,less amount of calculation and it's easy to be implement.The numerical results can approximate well with elastic wave numerical results.So it can avoid the increases of complexity in multi parameter FWI.Base on the acoustic approximation assumption,we applied the acoustic wave equation instead of a numerical simulation of the elastic wave equation,and we have deduced the acoustic equation in VTI(transverse isotropic medium),and calculating the forward modeling in frequency domain.In addition,we introduced the basic theory of full waveform inversion and the setting of the objective function,the calculation of updated model parameters,and the selection of optimization algorithm and common problems in FWI,respectively.In addition,due to the large amount of calculation in the work of FWI caused problems for a longer time.We use the mixed source sampling instead of the traditional single source,to promote the efficiency of FWI.But there is crosstalk noise caused by mixed source.We introduced a new kind of source coding technology,which on the basis of the experimental results show that the inversion accuracy.It can improve the efficiency effectively of the inversion calculation.In anisotropic medium FWI,we to invert multiple physical parameters of underground medium.Firstly,we have discusses the parameterization in VTI FWI.Different kinds of parameterizations can affect the inversion with different parameters.We use the radiation pattern to analysis the sensitivity of the parameters,and according to the results of numerical simulation,we give the parameterization strategies.At the same time,we use the analysis of Hessian matrix characteristic to explain the coupling effect between different parameters,and how it affects the inversion results.It can reduce the coupling effect between different parameters by using the accurately Hessian matrix.We introduced a kind of inexact full Newton method to calculate the Hessianmatrix inverse operator,and compared with L-BFGS method,the experimental results show that inverse operator of the Hessian matrix is more accurate by using the inexact full Newton algorithm and the inversion results precision is higher.But this kind of optimization algorithm is also less than L-BFGS method.Because it need more numbers of forward modeling in each iteration which will reduce the speed of convergence which is acceptable.