A Reflectivity Inversion Method Based On The Data-driven Time-varying Wavelet Extraction

Reflectivity inversion is essential for high-resolution seismic data processing.Conventional reflectivity inversion methods are either based on a stationary convolution model or under the assumption that seismic data are stationary in each time window,which ignores the nonstationarity of seismic data due to attenuation processes.According to the convolution model,a seismic trace is the convolution result of a seismic wavelet with the reflectivity.In reality,considering the anelastic attenuation,noise,and other physical processes,the seismic wavelet is unknown and of time-varying characteristic during propagation.Therefore,reflectivity inversion from known seismic data is nonstationary and blind.We propose a blind deconvolution method based on the data-driven time-varying wavelet extraction,which does not require source wavelet as inputs and avoids intrinsic instability associated with inverse Q filtering when used to compensate the nonstationary seismic data.Due to the fact that field seismic data whose frequency spectrum generally changes from shallow to deep formations are always nonstationary,we present a data-driven method for time-varying wavelet extraction（DTWE）.Firstly,we transform the seismogram into the time-frequency domain by using a spectral decomposition technique to produce the frequency spectrum at each sample point of the seismic trace.In order to better present the changing frequency spectrum,we establish the analytical relationship between the theoretical parameters and the statistical properties of the frequency spectrum.Thus,time-varying wavelets are generated according to the local frequency spectrum at every instant.On the one side,this method estimates the time-varying wavelet along the time axis instead of a constant wavelet for the whole seismic trace;on the other side,because the estimation of parameters for wavelet extraction is fully data-driven,the results of the proposed method are more accurate and suitable for the nonstationary nature of actual seismic data.we present the improved nonstationary convolution expression as a result of the time-varying wavelet matrix in which each column is the propagating wavelet for the travel time of the column and the reflectivity.By incorporating the extracted time-varying wavelets and ₁l norm into the cost function,we achieve blind deconvolution from nonstationary seismic data,which does not require advance Q factor and source wavelet as inputs.Taking into account the lateral continuity of deconvolution results,we formulate the objective function for reflectivity inversion as a joint low-rank and sparse inversion convex optimization problem.It helps deconvolution results keep the sparsity in the vertical direction while maintaining the continuity in the horizontal direction,especially under noise contamination.