Nonstationary seismic reflectivity inversion based on prior-engaged semisupervised deep learning method

Reflectivity inversion methods based on a stationary convo-lution model are essential for seismic data processing. They compress the seismic wavelet, and by broadening the bandwidth of seismic data, they assist the interpretation of seismic sections. Unfortunately, they do not apply to realistic nonstationary de -convolution cases in which the seismic wavelet varies as it prop-agates in the subsurface. Deep learning techniques have been proposed to solve inverse problems in which networks can be-have as the regularizer of the inverse problem. Our goal is to adopt a semisupervised deep learning approach to invert reflec-tivity when the propagating wavelet is considered unknown and time-variant. To this end, we have designed a prior-engaged neural network by unrolling an alternating iterative optimization algorithm, in which convolutional neural networks are used to solve two subproblems. One is to invert the reflectivity, and the other is to estimate the time-varying wavelets. In general, it is well known that, when working with geophysical inverse prob-lems such as ours, one has limited access to labeled data for training the network. We circumvent the problem by training the network via a data-consistency cost function in which seis-mic traces are honored. Reflectivity estimates also are honored at spatial coordinates in which true reflectivity series derived from borehole data are available. The cost function also penal-izes time-varying wavelets from varying abruptly along the spatial direction. Experiments are conducted to find the effec-tiveness of our method. We also compare our approach to a non -stationary blind deconvolution algorithm based on regularized inversion. Our findings reveal that the developed method im-proves the vertical resolution of seismic sections with noticeable correlation coefficient improvements over the nonstationary blind deconvolution. In addition, our method is less sensitive to initial estimates of nonstationary wavelets. Moreover, it needs less human intervention when setting parameters than regular-ized inversion.