Research On Wave Equation Forward Modeling And Envelope Full Waveform Inversion

Full waveform inversion has become a research hotspot in recent years because of its high precision and high resolution inversion. It has a great application prospect in the field of oil and gas exploration. However, the effect of full waveform inversion is severely constrained by the inaccurate initial model and the missing low frequency data.In this paper,the envelope full waveform inversion method is studied. The main contents of this paper are as follows:(1) The high-order finite difference method for the numerical simulation of wave equation is studied, and the numerical dispersion and adaptability of the high-order finite difference method are analyzed.(2) The absorbing boundary condition of the two order paraxial approximation absorbing boundary condition and the attenuation boundary condition is studied. In the absorption boundary, the mixed absorbing boundary conditions are obtained by combining the two order paraxial approximation boundary condition and the attenuation boundary condition can not only absorb the boundary reflection but also save the memory.(3) Envelope full waveform inversion method is studied. By means of the Hilbert transform to extract the signal envelope. The envelope function of the envelope of the observed wave field and the envelope of the simulated wave field is established. Envelope inversion is realized by back propagation algorithm. The results of the envelope inversion are taken as the initial model of the traditional full waveform inversion. It can suppress the traditional full waveform inversion to fall into the local minimum due to the lack of low frequency data.Numerical results show that: The high-order finite difference method can effectively suppress the numerical dispersion and has strong adaptability to the incident wave at different angles. The mixed absorbing boundary condition can not only absorb boundary reflection but also save memory. Envelope inversion can get more low frequency information and get a smooth background velocity model, but it has poor performance in detail. In the absence of low frequency data, the envelope inversion model is used as the initial model of the traditional full waveform inversion to obtain the accurate inversion results.