A blind nonstationary deconvolution method for multichannel seismic data

Deconvolution is essential for high-resolution seismic data processing. Conventional deconvolution methods are either based on a stationary convolution model or under the assumption thatQfactor and the source wavelet are known. However, in reality, seismic wavelet is usually unknown and time-varying during propagation due to attenuation. Thus, we propose a blind nonstationary deconvolution (BND) method which does not require advanceQfactor and source wavelet as inputs and takes into account the lateral continuity of deconvolution results. Firstly, we develop an improved nonstationary convolution model consisting of the time-varying wavelet and reflectivity, which enables us to obtain reflectivity without attenuation estimation. To accommodate the changing frequency spectrum of seismic data, we present a time-varying wavelet estimation method using the frequency spectrum at every sample point and the generalised seismic wavelet function. By incorporating the extracted time-varying wavelet into the improved convolution model, we propose to formulate the objective function for reflectivity inversion as a joint low-rank and sparse inversion convex optimisation problem. It helps deconvolution results keep the sparsity in the vertical direction while maintaining the continuity in the horizontal direction. The performance of BND is evaluated through synthetic examples and a field data example.