Elastic Full Waveform Inversion For VTI Media

Elastic full waveform inversion takes advantage of the recorded seismic waveform to obtain the physical parameters which close to the real model through the minimization processing of target function,and can provide high precision velocity model.As the wave equation which describes transmission laws of seismic wave in complex medium becomes more and more complex,and it is increasing that the number of physical parameters contained in the equation.The full waveform inversion of multi-parameter in anisotropic media can provide more and more accurate physical parameters to describing the characteristics of underground geologic structure.However,FWI has been extended to anisotropic media,litimited to acoustic approximations,it is often influenced by the coupling effect of parameters and the restriction of the inputed data type,caused that the inversion results of some parameters are less than ideal.Therefore,in this paper,on the basis of predecessors' research,performing the transmission data for elastic full waveform inversion in 2D VTI?Vertical Transversely Isotropic,VTI?media through a chosen set of VTI parameters.And studied the sensitivity of the objective function to the model parameters.This paper studies the method of time domain elastic FWI in VTI media.First,considering the complexity of anisotropic medium,made a comprehensive analysis of the anisotropic medium,and established the elastic wave equation of VTI medium.The difference scheme of vector wave in VTI medium is deduced based on the high finite difference method with staggered grid.On the premise of introducing the basic theory of inversion methods,we obtain the gradient expression of the objective function to the stiffness coefficient and the parameters come from different parameterizations by using the adjoint-state method.The Thomsen parameters that representing the anisotropy are set into two means of parameterization to study the radiation modes of the disturbed parameters that come from different wave fields.Finally,Using multiple models to perform multi-component transmission data in a homogeneous VTI background model and applying the radiation pattern of the disturbed parameters to analyze the sensitivity of the objective function to the inversion parameters of different parameterizations.And it turns out that:when the background model is given,and in the case of the receivers record P-wave and S-wave energy near the vicinity of the symmetry axis,FWI of transmission data inverted with the first parameterization?VP0,VS0,Vnmo,Vhor?can effectively resolve the parameters of speed V_P0and V_S0.Under the condition of the model that receiving the scattered wave energy perpendicular to the axis of symmetry in VTI media,the application of the first parameterization can effectively recovereand V_S0.The main advantage of the second parameterization(ln(1/V²_P0)?ln(1/V²_S0)?1+2e?1+2d)is to improve the inversion effect of parameter V_P00 in the structural model that perpendicular to the axis of symmetry in VTI media.By separating the wave field into P-wave or S-wave,the precision of inversion can be improved by filtering base on the scattering angle for certain parameter.Through the comprehensive analysis of parameter sensitivity and coupling relation can help to improve the precision of multiple parameter full waveform inversion for different structural models.