Deep decomposition learning for reflectivity inversion

Abstract

We report a combination of classical regularization theory with a null space neural network approach based on deep decomposition learning, paying particular attention to the solution of one ubiquitous problem in seismic exploration: the recovery of full‐band reflectivity from band‐limited seismic traces. The method extends the popular post‐processing approach by learning how to improve an initial reconstruction with estimated missing components from the null space of the forward operator, which in our case, are the missing frequency components of the reflectivity. We integrate the null space element prediction to act in conjunction with convolutional neural network based denoising and a data‐consistent algorithm. The proposed framework honours the input measurements while enforcing generalization. Numerical experiments on synthetic and real datasets show that the proposed method naturally enforces a high‐resolution prediction consistent with the low‐resolution input seismic traces. We compare its performance with state‐of‐the‐art thin‐bed reflectivity estimation methods.