Initial Model Incorporation for Deep Learning FWI: Pretraining or Denormalization?

Subsurface property neural network reparameterized full waveform inversion (FWI) has emerged as an effective unsupervised learning framework, which can invert stably with an inaccurate starting model. It updates the trainable neural network parameters instead of fine-tuning on the subsurface model directly. There are primarily two ways to embed the prior knowledge of the initial model into neural networks, that is, pretraining and denormalization. Pretraining first regulates the neural networks' parameters by fitting the initial velocity model; Denormalization directly adds the outputs of the network into the initial models without pretraining. In this letter, we systematically investigate the influence of the two ways of initial model incorporation for the neural network reparameterized FWI. We demonstrate that pretraining requires inverting the model perturbation based on a constant velocity value (mean) with a two-stage implementation. It leads to a complex workflow and inconsistency of objective functions in the two-stage process, causing the network parameters to become inactive and lose plasticity. Experimental results demonstrate that denormalization can simplify workflows, accelerate convergence, and enhance inversion accuracy compared with pretraining.

S2S-WTV: Seismic Data Noise Attenuation Using Weighted Total Variation Regularized Self-Supervised Learning

Seismic data often undergoes severe noise due to environmental factors, which seriously affects subsequent applications. Traditional hand-crafted denoisers such as filters and regularizations utilize interpretable domain knowledge to design generalizable denoising techniques, while their representation capacities may be inferior to deep learning denoisers, which can learn complex and representative denoising mappings from abundant training pairs. However, due to the scarcity of high-quality training pairs, deep learning denoisers may sustain some generalization issues over various scenarios. In this work, we propose a self-supervised method that combines the capacities of deep denoiser and the generalization abilities of hand-crafted regularization for seismic data random noise attenuation. Specifically, we leverage the Self2Self (S2S) learning framework with a trace-wise masking strategy for seismic data denoising by solely using the observed noisy data. Parallelly, we suggest the weighted total variation (WTV) to further capture the horizontal local smooth structure of seismic data. Our method, dubbed as S2S-WTV, enjoys both high representation abilities brought from the self-supervised deep network and good generalization abilities of the hand-crafted WTV regularizer and the self-supervised nature. Therefore, our method can more effectively and stably remove the random noise and preserve the details and edges of the clean signal. To tackle the S2S-WTV optimization model, we introduce an alternating direction multiplier method (ADMM)-based algorithm. Extensive experiments on synthetic and field noisy seismic data demonstrate the effectiveness of our method as compared with state-of-the-art traditional and deep learning-based seismic data denoising methods.