[Paper Review] Deep learning for low frequency extrapolation of multicomponent data in elastic full waveform inversion

Hongyu Sun, Laurent Demanet|arXiv (Cornell University)|Dec 31, 2020

Seismic Imaging and Inversion Techniques45 references5 citations

TL;DR

This paper proposes a deep learning approach to extrapolate low-frequency components from band-limited multicomponent elastic seismic data to improve starting models for elastic full waveform inversion (FWI). Using a convolutional neural network (CNN) with a large receptive field, trained separately on vertical and horizontal particle velocity components, the method synthesizes 2–4 Hz low-frequency data that enables successful inversion of P- and S-wave velocities, significantly reducing cycle-skipping issues in elastic FWI on the Marmousi2 model.

ABSTRACT

Full waveform inversion (FWI) strongly depends on an accurate starting model to succeed. This is particularly true in the elastic regime: The cycle-skipping phenomenon is more severe in elastic FWI compared to acoustic FWI, due to the short S-wave wavelength. In this paper, we extend our work on extrapolated FWI (EFWI) by proposing to synthesize the low frequencies of multi-component elastic seismic records, and use those "artificial" low frequencies to seed the frequency sweep of elastic FWI. Our solution involves deep learning: we separately train the same convolutional neural network (CNN) on two training datasets, one with vertical components and one with horizontal components of particle velocities, to extrapolate the low frequencies of elastic data. The architecture of this CNN is designed with a large receptive field, by either large convolutional kernels or dilated convolution. Numerical examples on the Marmousi2 model show that the 2-4Hz low frequency data extrapolated from band-limited data above 4Hz provide good starting models for elastic FWI of P-wave and S-wave velocities. Additionally, we study the generalization ability of the proposed neural network over different physical models. For elastic test data, collecting the training dataset by elastic simulation shows better extrapolation accuracy than acoustic simulation, i.e., a smaller generalization gap.

Motivation & Objective

• To address the severe cycle-skipping problem in elastic full waveform inversion (FWI), which is exacerbated by short S-wave wavelengths and poor starting model dependency.
• To develop a computationally efficient method for generating synthetic low-frequency components from band-limited multicomponent seismic data to seed the frequency sweep of elastic FWI.
• To evaluate the generalization capability of deep learning models trained on acoustic vs. elastic synthetic data for low-frequency extrapolation.
• To assess the performance of extrapolated low frequencies in enabling accurate inversion of P-wave and S-wave velocities in elastic FWI.

Proposed method

• A deep convolutional neural network (CNN) is trained to extrapolate low frequencies from band-limited multicomponent seismic data using two separate training datasets: one for vertical particle velocity and one for horizontal particle velocity.
• The CNN architecture employs either large convolutional kernels or dilated convolutions to achieve a large receptive field, enabling long-range spatial dependencies crucial for low-frequency extrapolation.
• The model is trained on synthetic elastic wavefields generated via the stress-velocity formulation with an eighth-order finite-difference scheme, using both acoustic and elastic training data for comparison.
• Low-frequency data are synthesized in the 0–5 Hz range and used to initialize elastic FWI, with inversion performance compared against true low-frequency data.
• The method leverages the redundancy in wavefield data and the physical consistency of wave propagation to extrapolate missing low-frequency energy.

Experimental results

Research questions

• RQ1 Can deep learning effectively extrapolate low-frequency components from band-limited multicomponent elastic seismic data to improve elastic FWI starting models?
• RQ2 How does the performance of a CNN trained on acoustic data compare to one trained on elastic data when generalizing to elastic test data?
• RQ3 To what extent do extrapolated low frequencies (2–4 Hz) enable successful elastic FWI of P-wave and S-wave velocities when starting from 4 Hz data?
• RQ4 What is the impact of training data physics (acoustic vs. elastic) on the generalization gap of the deep learning model?

Key findings

• The CNN with a large receptive field successfully extrapolated 0–5 Hz low-frequency components from band-limited data, showing strong agreement with true low-frequency data on the Marmousi2 model.
• Elastic FWI initialized with 2–4 Hz extrapolated data achieved inversion results comparable to those using true low-frequency data, demonstrating effectiveness in mitigating cycle-skipping.
• The neural network trained on elastic training data showed significantly better generalization to elastic test data than the one trained on acoustic data, indicating a smaller generalization gap.
• Extrapolated low-frequency data from 2–4 Hz were sufficient to generate accurate low-wavenumber starting models for P- and S-wave velocity inversion, even when the original data were band-limited above 4 Hz.
• The study confirms that realistic elastic training data are essential for robust low-frequency extrapolation, as acoustic training data lead to higher prediction errors on elastic test data.