Robust elastic impedance inversion using L1-norm misfit function and constraint regularization

The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

Nonstationary sparsity-constrained seismic deconvolution

The Robinson convolution model is mainly restricted by three inappropriate assumptions, i.e., statistically white reflectivity, minimum-phase wavelet, and stationarity. Modern reflectivity inversion methods（e.g., sparsity-constrained deconvolution） generally attempt to suppress the problems associated with the first two assumptions but often ignore that seismic traces are nonstationary signals, which undermines the basic assumption of unchanging wavelet in reflectivity inversion. Through tests on reflectivity series, we confirm the effects of nonstationarity on reflectivity estimation and the loss of significant information, especially in deep layers. To overcome the problems caused by nonstationarity, we propose a nonstationary convolutional model, and then use the attenuation curve in log spectra to detect and correct the influences of nonstationarity. We use Gabor deconvolution to handle nonstationarity and sparsity-constrained deconvolution to separating reflectivity and wavelet. The combination of the two deconvolution methods effectively handles nonstationarity and greatly reduces the problems associated with the unreasonable assumptions regarding reflectivity and wavelet. Using marine seismic data, we show that correcting nonstationarity helps recover subtle reflectivity information and enhances the characterization of details with respect to the geological record.