Data-driven low-frequency signal recovery using deep-learning predictions in full-waveform inversion

Abstract

The lack of low-frequency signals in seismic data makes the full-waveform inversion (FWI) procedure easily fall into local minima leading to unreliable results. To reconstruct the missing low-frequency signals more accurately and effectively, we propose a data-driven low-frequency recovery method based on deep learning from the high-frequency signals. In the proposed method, we introduce the idea of employing a basic data patch of seismic data to build a local data-driven mapping in low-frequency recovery. Energy balancing and data patches are employed to prepare high- and low-frequency data for training a convolutional neural network (CNN) to establish the relationship between the high-and-low-frequency data pairs. The trained CNN can then be utilized to predict low-frequency data from high-frequency data. The proposed CNN was trained on the Marmousi model and tested on the Overthrust model, as well as field data. The synthetic experimental results reveal that the predicted low-frequency data match the true low-frequency data very well both in the time and frequency domains, and the field results show the successfully extended low-frequency spectra. Furthermore, two FWI tests using the predicted data demonstrate that the proposed approach can reliably recover the low-frequency data.

Multi-Task Learning for Low-Frequency Extrapolation and Elastic Model Building From Seismic Data

“…The approach is suitable for elastic waveform inversion in marine survey layout. Fang et al [42] and Ovcharenko et al [43] extrapolated low frequencies by training convolutional networks on AGC-balanced patches of time-domain seismic data in marine and land setups, respectively. Aharchaou and Baumstein [44] avoided using synthetic data and trained a UNet neural network to translate knowledge of low-frequency data from OBN surveys to band-limited shallow streamer data.…”

Deep Learning for Geophysics: Current and Future Trends

“…To make DL-based imaging applicable to large scale inputs, more works aim to collaborate with traditional methods and solve one of the mentioned bottlenecks, such as extrapolating the frequency range of seismic data from high to low frequencies for FWI (Fang, Zhou, et al, 2020;Ovcharenko et al, 2019), and adding constraints to FWI (Zhang & Alkhalifah, 2019). To mitigate the "curse of dimensionality" problem of global optimization in FWI, CAE is used to reduce the dimension of FWI by optimizing in the latent space (Gao et al, 2019).…”

Coupling Deep Learning with Full Waveform Inversion

“…We start with the most challenging scenario where we train the neural network to approximate the inverse operator for the velocity model (20) with randomly generated Fourier coefficients without any decay requirement on the coefficients, that is, we set the decay rate α = 0 in (22). This is an extremely challenging case because the effective parameter space of this class of velocity models grows exponentially with respect to the number of Fourier models we have in the model.…”

“…This is what we observed in our numerical experiments. In this section, we show some training-validation results for the velocity model (20) with decaying Fourier coefficients following the pattern we imposed in (22). We present results from two different cases: the slow decay case with α = 1/2 and the fast decay case with α = 1.…”

“…In recent years, there are great interest in the FWI community to use deep learning techniques, based on neural networks, to replace the classical least-squares based inversion methods [1,4,16,22,23,28,31,32,36,39,49,54,55,56,57,63,65,66,67,68]. Assume that we are given a set of sampled data…”