3-D Seismic Inversion by Model Parameterization With Fourier Coefficients

In seismic inversion, the subsurface model can be parameterized by a truncated Fourier series, and then, the inversion problem is the inversion of the Fourier coefficients. To improve the efficiency of the evaluation of the Fourier coefficients and the reconstruction of the model from the inverted coefficients, we propose to use the efficient implementation of the fast Fourier transform (FFT) to speed up these two calculations. By using the FFT pair, the computation time for 3-D subsurface models with realistic size could be reduced by two-three orders of magnitude compared to conventional methods. When this model parameterization scheme is applied to seismic impedance inversion, we have proposed two strategies to further improve the efficiency. One is to invert the Fourier coefficients from small-valued numbers to large-valued numbers, and the other is to divide the seismic data into subgroups and use part of them for the inversion of the Fourier coefficients. Both strategies are helpful for efficient inversion of the Fourier coefficients from the seismic data. Moreover, thanks to this model parameterization scheme, the Fourier coefficients are inverted in a multitrace manner, and the impedance model reconstructed from the inverted Fourier coefficients has a good spatial continuity. The scheme can generate stable and continuous impedance models from the inversion of seismic data with missing traces, with affordable computation times.