Study On Impedance Inversion

This thesis uses a parameterization method of underground model based on truncated Fourier series.The FFT forward transform is used to calculate the coefficients of the truncated Fourier series,and the FFT is used to calculate the reverse coefficients of the truncated Fourier coefficients to reconstruct the parameterized model.The calculation efficiency of the traditional direct calculation method using DFT and the FFT based method in coefficient estimation and model reconstruction is compared.The forward and inverse FFT transforms are used to evaluate the Fourier series coefficients and the reconstruction model respectively.Compared with the DFT method,the calculation efficiency is improved by 2-3 orders of magnitude.This thesis applies the model parameterization method based on truncated Fourier coefficients to wave impedance inversion.Unlike traditional impedance inversion methods,the impedance inversion based on truncated Fourier coefficient model parameterization iteratively inverts the FFT parameterized coefficients instead of directly inverting impedance.Based on the second-order acoustic equation,this thesis reformulates the conventional wave equation containing density and velocity parameters as an acoustic equation defined solely by impedance parameters,and then applies the equation to impedance inversion based on truncated Fourier coefficient model parameterization.Under the periodic condition of the Fourier series,the number of retained series when increasing the truncated coefficients is increased to better invert the short-wavelength components of the model,thereby significantly improving the inversion accuracy.In addition,this thesis introduces a viscoelastic factor to consider the attenuation effect in the wave equation and derives an impedance form of the acoustic equation with attenuation.Through numerical simulations,the study investigates the influence of the value on the wavelet in the time and frequency domains,and finally,the multi-parameter inversion of the low-order Fourier coefficients for impedance and viscoelastic factors is implemented using the Newton method.