High-frequency localized elastic full waveform inversion for time-lapse seismic surveys

Seismic full waveform inversion is a powerful method to estimate the elastic properties of the subsurface. To mitigate the non-linearity and cycle-skipping problems, in a hierarchical manner, one inverts first low-frequency contents to determine long- and medium-wavelength structures and then increases the frequency contents to obtain detailed information. However, the inversion of higher frequencies can be computationally very expensive, especially when the target of interest, such as oil/gas reservoirs and axial melt lens, is at a great depth, far away from source and receiver arrays. To address this problem, we present a localized full waveform inversion algorithm where iterative modeling is performed locally, allowing us to extend inversions for higher frequencies with little computation effort. Our method is particularly useful for time-lapse seismic, where the changes in elastic parameters are local due to fluid extraction and injection in the subsurface. In our method, both sources and receivers are extrapolated to a region close to the target area, allowing forward modeling and inversion to be performed locally after low-frequency full-model inversion for the background model, which by nature only represents long- to medium-wavelength features. Numerical tests show that the inversion of low-frequency data for the overburden is sufficient to provide an accurate high-frequency estimation of elastic parameters of the target region.

Download Full-text

Denoising for full-waveform inversion with expanded prediction-error filters

Geophysics ◽

10.1190/geo2020-0573.1 ◽

2021 ◽

pp. 1-54

Author(s):

Milad Bader ◽

Robert G. Clapp ◽

Biondo Biondi

Keyword(s):

High Frequency ◽

Prediction Error ◽

Signal To Noise Ratio ◽

Waveform Inversion ◽

Low Frequency ◽

Full Waveform Inversion ◽

Frequency Data ◽

Signal To Noise ◽

Frequency Signal ◽

Full Waveform

Low-frequency data below 5 Hz are essential to the convergence of full-waveform inversion towards a useful solution. They help build the velocity model low wavenumbers and reduce the risk of cycle-skipping. In marine environments, low-frequency data are characterized by a low signal-to-noise ratio and can lead to erroneous models when inverted, especially if the noise contains coherent components. Often field data are high-pass filtered before any processing step, sacrificing weak but essential signal for full-waveform inversion. We propose to denoise the low-frequency data using prediction-error filters that we estimate from a high-frequency component with a high signal-to-noise ratio. The constructed filter captures the multi-dimensional spectrum of the high-frequency signal. We expand the filter's axes in the time-space domain to compress its spectrum towards the low frequencies and wavenumbers. The expanded filter becomes a predictor of the target low-frequency signal, and we incorporate it in a minimization scheme to attenuate noise. To account for data non-stationarity while retaining the simplicity of stationary filters, we divide the data into non-overlapping patches and linearly interpolate stationary filters at each data sample. We apply our method to synthetic stationary and non-stationary data, and we show it improves the full-waveform inversion results initialized at 2.5 Hz using the Marmousi model. We also demonstrate that the denoising attenuates non-stationary shear energy recorded by the vertical component of ocean-bottom nodes.

Download Full-text

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

Geophysics ◽

10.1190/geo2020-0159.1 ◽

2020 ◽

Vol 85 (6) ◽

pp. A37-A43

Author(s):

Jinwei Fang ◽

Hui Zhou ◽

Yunyue Elita Li ◽

Qingchen Zhang ◽

Lingqian Wang ◽

...

Keyword(s):

Deep Learning ◽

Seismic Data ◽

High Frequency ◽

Waveform Inversion ◽

Low Frequency ◽

Data Driven ◽

Full Waveform Inversion ◽

Frequency Data ◽

Recovery Method ◽

Full Waveform

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 have developed a data-driven low-frequency recovery method based on deep learning from high-frequency signals. In our method, we develop the idea of using a basic data patch of seismic data to build a local data-driven mapping in low-frequency recovery. Energy balancing and data patches are used 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 then can be used to predict low-frequency data from high-frequency data. Our 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 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 our approach can reliably recover the low-frequency data.

Download Full-text

Acoustic 2D full waveform inversion to solve gas cloud challenges

Annals of Geophysics ◽

10.4401/ag-6720 ◽

2015 ◽

Vol 58 (4) ◽

Author(s):

Srichand Prajapati ◽

Deva Ghosh

Keyword(s):

Cloud Model ◽

Hessian Matrix ◽

Waveform Inversion ◽

Low Frequency ◽

Full Waveform Inversion ◽

Inversion Algorithm ◽

Frequency Model ◽

Full Waveform ◽

Minimum Number ◽

Gas Cloud

<p>The existing conventional inversion algorithm does not provide satisfactory results due to the complexity of propagated wavefield though the gas cloud. Acoustic full waveform inversion has been developed and applied to a realistic synthetic offshore shallow gas cloud feature with Student-t approach, with and without simultaneous sources encoding. As a modeling operator, we implemented the grid based finite-difference method in frequency domain using second order elastic wave equation. Jacobin operator and its adjoint provide a necessary platform for solving full waveform inversion problem in a reduced Hessian matrix. We invert gas cloud model in 5 frequency band selected from 1 to 12 Hz, each band contains 3 frequencies. The inversion results are highly sensitive to the misfit. The model allows better convergence and recovery of amplitude losses. This approach gives better resolution then the existing least-squares approach. In this paper, we implement the full waveform inversion for low frequency model with minimum number of iteration providing a better resolution of inversion results.</p>

Download Full-text

Progressive transfer learning for low-frequency data prediction in full waveform inversion

Geophysics ◽

10.1190/geo2020-0598.1 ◽

2021 ◽

pp. 1-82

Author(s):

Wenyi Hu ◽

Yuchen Jin ◽

Xuqing Wu ◽

Jiefu Chen

Keyword(s):

Transfer Learning ◽

High Frequency ◽

Waveform Inversion ◽

Low Frequency ◽

High Frequency Data ◽

Training Dataset ◽

Full Waveform Inversion ◽

Frequency Data ◽

Velocity Models ◽

Full Waveform

To effectively overcome the cycle-skipping issue in full waveform inversion (FWI), we developed a deep neural network (DNN) approach to predict the absent low-frequency components by exploiting the hidden physical relation connecting the low- and the high-frequency data. To efficiently solve this challenging nonlinear regression problem, two novel strategies were proposed to design the DNN architecture and to optimize the learning process: (1) dual data feed structure; (2) progressive transfer learning. With the dual data feed structure, not only the high-frequency data, but also the corresponding beat tone data are fed into the DNN to relieve the burden of feature extraction. The second strategy, progressive transfer learning, enables us to train the DNN using a single evolving training dataset. Within the framework of the progressive transfer learning, the training dataset continuously evolves in an iterative manner by gradually retrieving the subsurface information through the physics-based inversion module, progressively enhancing the prediction accuracy of the DNN and propelling the inversion process out of the local minima. The synthetic numerical experiments suggest that, without any a priori geological information, the low-frequency data predicted by the progressive transfer learning are sufficiently accurate for an FWI engine to produce reliable subsurface velocity models free of cycle-skipping artifacts.

Download Full-text

Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Symmetry ◽

10.3390/sym13020260 ◽

2021 ◽

Vol 13 (2) ◽

pp. 260

Author(s):

Meng Suo ◽

Dong Zhang ◽

Yan Yang

Keyword(s):

Nonlinear Equations ◽

Waveform Inversion ◽

Optimal Solution ◽

Inversion Method ◽

Full Waveform Inversion ◽

Inversion Algorithm ◽

Elastic Wave Equation ◽

Full Waveform ◽

Ultrasonic Propagation ◽

Joint Velocity

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Download Full-text

Multi-scale time-frequency domain full waveform inversion with a weighted local correlation-phase misfit function

Journal of Geophysics and Engineering ◽

10.1093/jge/gxz062 ◽

2019 ◽

Vol 16 (6) ◽

pp. 1017-1031 ◽

Cited By ~ 5

Author(s):

Yong Hu ◽

Liguo Han ◽

Rushan Wu ◽

Yongzhong Xu

Keyword(s):

Frequency Domain ◽

Seismic Data ◽

Waveform Inversion ◽

Low Frequency ◽

Full Waveform Inversion ◽

Local Correlation ◽

Time Frequency ◽

Model Dependence ◽

Full Waveform ◽

Frequency Components

Abstract Full Waveform Inversion (FWI) is based on the least squares algorithm to minimize the difference between the synthetic and observed data, which is a promising technique for high-resolution velocity inversion. However, the FWI method is characterized by strong model dependence, because the ultra-low-frequency components in the field seismic data are usually not available. In this work, to reduce the model dependence of the FWI method, we introduce a Weighted Local Correlation-phase based FWI method (WLCFWI), which emphasizes the correlation phase between the synthetic and observed data in the time-frequency domain. The local correlation-phase misfit function combines the advantages of phase and normalized correlation function, and has an enormous potential for reducing the model dependence and improving FWI results. Besides, in the correlation-phase misfit function, the amplitude information is treated as a weighting factor, which emphasizes the phase similarity between synthetic and observed data. Numerical examples and the analysis of the misfit function show that the WLCFWI method has a strong ability to reduce model dependence, even if the seismic data are devoid of low-frequency components and contain strong Gaussian noise.

Download Full-text

Application of the variable projection scheme for frequency-domain full-waveform inversion

Geophysics ◽

10.1190/geo2012-0351.1 ◽

2013 ◽

Vol 78 (6) ◽

pp. R249-R257 ◽

Cited By ~ 20

Author(s):

Maokun Li ◽

James Rickett ◽

Aria Abubakar

Keyword(s):

Frequency Domain ◽

Waveform Inversion ◽

Simulated Data ◽

Calibration Procedure ◽

Full Waveform Inversion ◽

Inversion Algorithm ◽

Unknown Parameters ◽

Variable Projection ◽

Full Waveform ◽

Data Calibration

We found a data calibration scheme for frequency-domain full-waveform inversion (FWI). The scheme is based on the variable projection technique. With this scheme, the FWI algorithm can incorporate the data calibration procedure into the inversion process without introducing additional unknown parameters. The calibration variable for each frequency is computed using a minimum norm solution between the measured and simulated data. This process is directly included in the data misfit cost function. Therefore, the inversion algorithm becomes source independent. Moreover, because all the data points are considered in the calibration process, this scheme increases the robustness of the algorithm. Numerical tests determined that the FWI algorithm can reconstruct velocity distributions accurately without the source waveform information.

Download Full-text