Extrapolated full waveform inversion with deep learning (1909.11536v2)

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.

Extrapolated Full Waveform Inversion with Deep Learning

The paper "Extrapolated full waveform inversion with deep learning" by Hongyu Sun and Laurent Demanet addresses a crucial challenge in full waveform inversion (FWI): the lack of low-frequency seismic data, which can lead to convergence issues such as cycle skipping. Traditional seismic data acquisition often misses these low frequencies due to technical limitations, leaving a significant gap that complicates the inversion process.

The authors propose leveraging convolutional neural networks (CNNs) to tackle bandwidth extension as a regression problem. They demonstrate a methodology where bandlimited seismic recordings serve as inputs to a neural network designed to extrapolate the missing low frequencies automatically, thus bypassing traditional pre-processing and post-processing steps. This method involves training CNNs on synthetic P-wave data, enabling them to predict low-frequency seismogram components accurately. This innovation aligns with the increasing recognition of machine learning's effectiveness in addressing complex geophysical challenges.

A striking aspect of their research is the capability of CNNs to achieve satisfactory generalization performances. Even under conditions of noise, unknown wavelet effects, and different forward modeling operators, the neural network maintains robust predictive abilities. In their experimental setup, the authors train the network using submodels of the Marmousi model, preparing it to extrapolate for the BP 2004 benchmark model successfully. The network demonstrated strong capabilities in handling uncertainties, illustrating a notable degree of resilience against common sources of error in seismic data.

The proposed approach offers promising implications for the field of seismic imaging. By improving the initialization step of FWI, the authors' method reduces the risk of cycle skipping, facilitating a more accurate low-wavenumber model essential for successful inversion. Additionally, the approach demonstrates potential for application on other complex geological models, suggesting a pathway towards improved FWI solutions that could adapt to various subsurface structures.

The findings of this paper could have significant ramifications for both theoretical advancements and practical applications in geophysical exploration. The integration of deep learning with seismic inversion processes represents a forward step, potentially enabling more efficient workflows, reducing computational costs, and increasing the detail and accuracy of subsurface models.

However, the work does highlight some inherent limitations. The neural network's success hinges substantially on the diversity and comprehensiveness of the training dataset. The requirement for a vast amount of representative samples underscores challenges concerning overfitting and extended training durations. Furthermore, improvements in multi-trace extrapolation could enhance the coherence of predicted low frequencies, thus advancing the overall methodology's utility.

Looking ahead, future research can explore diversifying training datasets, refining network architectures, and examining the application of this method to real field data. Such efforts could enhance the generalizability of CNN-based extrapolation approaches, further solidifying their role in advancing seismic imaging techniques. In summary, this paper introduces a sophisticated, machine-learning-driven approach to overcoming long-standing challenges in seismic data inversion, paving the way for significant improvements in geophysical exploration methodologies.