Deep learning tutorial for denoising

We herein introduce deep learning to seismic noise attenuation. Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, a deep neural network is trained based on a large training set, where the inputs are the raw datasets and the corresponding outputs are the desired clean data. After the completion of training, the deep learning method achieves adaptive denoising with no requirements of (i) accurate modeling of the signal and noise, and (ii) optimal parameters tuning. We call this intelligent denoising. We use a convolutional neural network as the basic tool for deep learning. The training set is generated with manually added noise in random and linear noise attenuation, and with the wave equation in the multiple attenuation. Stochastic gradient descent is used to solve the optimal parameters for the convolutional neural network. The runtime of deep learning on a graphics processing unit for denoising has the same order as the $f-x$ deconvolutional method. Synthetic and field results show the potential applications of deep learning in the automation of random noise attenuation with unknown variance, linear noise, and multiples.