InversionNet: A real-time and accurate full waveform inversion with convolutional neural network

2018 ◽  
Vol 144 (3) ◽  
pp. 1683-1683 ◽  
Author(s):  
Youzuo Lin ◽  
Yue Wu
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Real Time ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform

Parametric convolutional neural network-domain full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R881-R896 ◽  
Author(s):  
Yulang Wu ◽  
George A. McMechan
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Initial Velocity ◽  
Prior Information ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Model Errors ◽  
Initial Model ◽  
Full Waveform

Most current full-waveform inversion (FWI) algorithms minimize the data residuals to estimate a velocity model based on the assumption that the updated model is the sum of a background model and an estimated model perturbation. We have performed reparameterization of the initial velocity model, by the weights in a convolutional neural network (CNN), to automatically capture the salient features in the initial model, as a priori information. The prior information in CNN weights is iteratively updated as regularization to constrain the CNN-domain inversion to refine the features captured in CNN pretraining by reducing the data misfit. Synthetic examples using a 1D increasing velocity function v(z) and a 2D smoothed version of the correct Marmousi2 model as initial models indicate that the performance of the CNN-domain FWI depends on the existence and accuracy of the prior information in the initial velocity model (i.e., whether features whose positions, shapes, and values are present in the correct model are approximately included in the initial model). Forty different sets of randomly initialized CNN weights are used to parameterize and test CNN-domain FWI, using a 2D smoothed Sigsbee model as the initial velocity model. All 40 sets invert for the Sigsbee salt body more accurately (with a smaller standard deviation of the final rms model errors), by CNN-domain FWI, than FWI does. Features that are not represented within the CNN hidden layers in the initial velocity model, and so cannot be recovered by CNN-domain FWI, can be recovered using the final CNN-domain FWI velocity model as the starting model in a subsequent conventional FWI.

scholarly journals ML-descent: An optimization algorithm for full-waveform inversion using machine learning

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R477-R492 ◽  
Author(s):  
Bingbing Sun ◽  
Tariq Alkhalifah
Keyword(s):  
Neural Network ◽  
Machine Learning ◽  
Inverse Problem ◽  
Optimization Algorithm ◽  
Waveform Inversion ◽  
Slight Modification ◽  
Descent Method ◽  
Quadratic Functions ◽  
Full Waveform Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) is a nonlinear optimization problem, and a typical optimization algorithm such as the nonlinear conjugate gradient or limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) would iteratively update the model mainly along the gradient-descent direction of the misfit function or a slight modification of it. Based on the concept of meta-learning, rather than using a hand-designed optimization algorithm, we have trained the machine (represented by a neural network) to learn an optimization algorithm, entitled the “ML-descent,” and apply it in FWI. Using a recurrent neural network (RNN), we use the gradient of the misfit function as the input, and the hidden states in the RNN incorporate the history information of the gradient similar to an LBFGS algorithm. However, unlike the fixed form of the LBFGS algorithm, the machine-learning (ML) version evolves in response to the gradient. The loss function for training is formulated as a weighted summation of the L2 norm of the data residuals in the original inverse problem. As with any well-defined nonlinear inverse problem, the optimization can be locally approximated by a linear convex problem; thus, to accelerate the training, we train the neural network by minimizing randomly generated quadratic functions instead of performing time-consuming FWIs. To further improve the accuracy and robustness, we use a variational autoencoder that projects and represents the model in latent space. We use the Marmousi and the overthrust examples to demonstrate that the ML-descent method shows faster convergence and outperforms conventional optimization algorithms. The energy in the deeper part of the models can be recovered by the ML-descent even when the pseudoinverse of the Hessian is not incorporated in the FWI update.

scholarly journals Extrapolated full-waveform inversion with deep learning

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R275-R288 ◽  
Author(s):  
Hongyu Sun ◽  
Laurent Demanet
Keyword(s):  
Neural Network ◽  
Numerical Experiments ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Bandwidth Extension ◽  
Low Frequencies ◽  
Full Waveform ◽  
The Neural Network ◽  
Band Limited

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 have adopted an architecture of convolutional neural network (CNN) to automatically extrapolate the missing low frequencies. The band-limited 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, 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 band-limited data. The introduced 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 random noise, a poorly known source wavelet, and a different finite-difference scheme in the forward modeling operator. Finally, this approach is not subject to strong assumptions on signals or velocity models of other methods for bandwidth extension and seems to offer a tantalizing solution to the problem of properly initializing FWI.

Towards real-time monitoring: data assimilated time-lapse full waveform inversion for seismic velocity and uncertainty estimation

2020 ◽  
Vol 223 (2) ◽  
pp. 811-824
Author(s):  
Chao Huang ◽  
Tieyuan Zhu
Keyword(s):  
Kalman Filter ◽  
Real Time ◽  
Waveform Inversion ◽  
Time Lapse ◽  
Uncertainty Estimation ◽  
Covariance Matrices ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Velocity Changes ◽  
Over Time

SUMMARY Rapid development of time-lapse seismic monitoring instrumentations has made it possible to collect dense time-lapse data for tomographically retrieving time-lapse (even continuous) images of subsurface changes. While traditional time-lapse full waveform inversion (TLFWI) algorithms are designed for sparse time-lapse surveys, they lack of effective temporal constraint on time-lapse data, and, more importantly, lack of the uncertainty estimation of the TLFWI results that is critical for further interpretation. Here, we propose a new data assimilation TLFWI method, using hierarchical matrix powered extended Kalman filter (HiEKF) to quantify the image uncertainty. Compared to existing Kalman filter algorithms, HiEKF allows to store and update a data-sparse representation of the cross-covariance matrices and propagate model errors without expensive operations involving covariance matrices. Hence, HiEKF is computationally efficient and applicable to 3-D TLFWI problems. Then, we reformulate TLFWI in the framework of HiEKF (termed hereafter as TLFWI-HiEKF) to predict time-lapse images of subsurface spatiotemporal velocity changes and simultaneously quantify the uncertainty of the inverted velocity changes over time. We demonstrate the validity and applicability of TLFWI–HiEKF with two realistic CO2 monitoring models derived from Frio-II and Cranfield CO2 injection sites, respectively. In both 2-D and 3-D examples, the inverted high-resolution time-lapse velocity results clearly reveal a continuous velocity reduction due to the injection of CO2. Moreover, the accuracy of the model is increasing over time by assimilating more time-lapse data while the standard deviation is decreasing over lapsed time. We expect TLFWI-HiEKF to be equipped with real-time seismic monitoring systems for continuously imaging the distribution of subsurface gas and fluids in the future large-scale CO2 sequestration experiments and reservoir management.

scholarly journals A Physics-Based Neural-Network Way to Perform Seismic Full Waveform Inversion

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 112266-112277 ◽  
Author(s):  
Yuxiao Ren ◽  
Xinji Xu ◽  
Senlin Yang ◽  
Lichao Nie ◽  
Yangkang Chen
Keyword(s):  
Neural Network ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform
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