Extrapolated full-waveform inversion with deep learning

Abstract

The lack of low frequency information and a good initial model can seriously affect the success of full waveform inversion (FWI), due to the inherent cycle skipping problem. Computational low frequency extrapolation is in principle the most direct way to address this issue. By considering bandwidth extension as a regression problem in machine learning, we propose an architecture of convolutional neural network (CNN) to automatically extrapolate the missing low frequencies without preprocessing and post-processing steps. The bandlimited recordings are the inputs of the CNN and, in our numerical experiments, a neural network trained from enough samples can predict a reasonable approximation to the seismograms in the unobserved low frequency band, both in phase and in amplitude. The numerical experiments considered are set up on simulated P-wave data. In extrapolated FWI (EFWI), the low-wavenumber components of the model are determined from the extrapolated low frequencies, before proceeding with a frequency sweep of the bandlimited data. The proposed deep-learning method of low-frequency extrapolation shows adequate generalizability for the initialization step of EFWI. Numerical examples show that the neural network trained on several submodels of the Marmousi model is able to predict the low frequencies for the BP 2004 benchmark model. Additionally, the neural network can robustly process seismic data with uncertainties due to the existence of noise, poorly-known source wavelet, and different finite-difference scheme in the forward modeling operator. Finally, this approach is not subject to the structural limitations of other methods for bandwidth extension, and seems to offer a tantalizing solution to the problem of properly initializing FWI.

Deep-Learning-Driven Full-Waveform Inversion for Ultrasound Breast Imaging

“…Here, we discuss the methodology used for training and testing the bandwidth extension CNN solutions for the low-frequency extrapolation of band-limited USCT data. These include PyTorch implementations of both our proposed U-Net based 2D CNN solution and the 1D CNN model described by Sun et al [ 17 ]. Both CNNs were run on a GTX 2080 Ti GPU (Nvidia, Santa Clara, CA, US) using the same training and testing datasets, allowing for the performance of both bandwidth-extension methods to be compared.…”

“…For this application, this DNN would be used to approximate an operation that directly extrapolates the true low-frequency signal phase and amplitude values from band-limited signal data. This was demonstrated for geophysical applications by Sun et al using a 1D convolutional neural network (CNN) that was trained to perform this task using synthetic data of a signal transmitted through acoustic subsurface models [ 17 ].…”

Machine learning and fault rupture: a review

“…A different and interesting application aimed at recovering seismic signal hidden in noise was proposed by Sun [128]. The authors rely on a convolu- tional neural network to extrapolate missing low frequencies in synthetic seismic records.…”

Cross-equalization of time-lapse seismic data using recurrent neural networks

“…Recently, deep learning (DL) models have been utilized in many geophysical applications such as seismic data pre-processing (e.g., Ovcharenko et al, 2017Ovcharenko et al, , 2019Kazei et al, 2019a;Sun and Demanet, 2019), and inversion (e.g., Araya-Polo et al, 2018;Sun and Alkhalifah, 2019;Plotnitskii et al, 2019;Kazei et al, 2019bKazei et al, , 2020Sun and Alkhalifah, 2020a,b). In the context of time-lapse, Yuan et al (2020) used a convolution neural network (CNN) to image the velocity changes in different vintages.…”