scholarly journals Full-waveform inversion with extrapolated low-frequency data

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R339-R348 ◽  
Author(s):  
Yunyue Elita Li ◽  
Laurent Demanet
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Propagation Model ◽  
Full Waveform Inversion ◽  
Frequency Data ◽  
Local Minima ◽  
Bandwidth Extension ◽  
Low Frequencies ◽  
Full Waveform

The availability of low-frequency data is an important factor in the success of full-waveform inversion (FWI) in the acoustic regime. The low frequencies help determine the kinematically relevant, low-wavenumber components of the velocity model, which are in turn needed to avoid convergence of FWI to spurious local minima. However, acquiring data less than 2 or 3 Hz from the field is a challenging and expensive task. We have explored the possibility of synthesizing the low frequencies computationally from high-frequency data and used the resulting prediction of the missing data to seed the frequency sweep of FWI. As a signal-processing problem, bandwidth extension is a very nonlinear and delicate operation. In all but the simplest of scenarios, it can only be expected to lead to plausible recovery of the low frequencies, rather than their accurate reconstruction. Even so, it still requires a high-level interpretation of band-limited seismic records into individual events, each of which can be extrapolated to a lower (or higher) frequency band from the nondispersive nature of the wave-propagation model. We have used the phase-tracking method for the event separation task. The fidelity of the resulting extrapolation method is typically higher in phase than in amplitude. To demonstrate the reliability of bandwidth extension in the context of FWI, we first used the low frequencies in the extrapolated band as data substitute, to create the low-wavenumber background velocity model, and then we switched to recorded data in the available band for the rest of the iterations. The resulting method, extrapolated FWI, demonstrated surprising robustness to the inaccuracies in the extrapolated low-frequency data. With two synthetic examples calibrated so that regular FWI needs to be initialized at 1 Hz to avoid local minima, we have determined that FWI based on an extrapolated [1, 5] Hz band, itself generated from data available in the [5, 15] Hz band, can produce reasonable estimations of the low-wavenumber velocity models.

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.

Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (6) ◽  
pp. R223-R233 ◽  
Author(s):  
Yong Ma ◽  
Dave Hale
Keyword(s):  
Wave Equation ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Local Minima ◽  
Low Frequencies ◽  
Traveltime Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Dynamic Warping

In reflection seismology, full-waveform inversion (FWI) can generate high-wavenumber subsurface velocity models but often suffers from an objective function with local minima caused mainly by the absence of low frequencies in seismograms. These local minima cause cycle skipping when the low-wavenumber component in the initial velocity model for FWI is far from the true model. To avoid cycle skipping, we discovered a new wave-equation reflection traveltime inversion (WERTI) to update the low-wavenumber component of the velocity model, while using FWI to only update high-wavenumber details of the model. We implemented the low- and high-wavenumber inversions in an alternating way. In WERTI, we used dynamic image warping (DIW) to estimate the time shifts between recorded data and synthetic data. When compared with correlation-based techniques often used in traveltime estimation, DIW can avoid cycle skipping and estimate the time shifts accurately, even when shifts vary rapidly. Hence, by minimizing traveltime shifts estimated by dynamic warping, WERTI reduces errors in reflection traveltime inversion. Then, conventional FWI uses the low-wavenumber component estimated by WERTI as a new initial model and thereby refines the model with high-wavenumber details. The alternating combination of WERTI and FWI mitigates the velocity-depth ambiguity and can recover subsurface velocities using only high-frequency reflection data.

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

Geophysics ◽  
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.

Assisting salt model building with reflection full-waveform inversion

2019 ◽  
Vol 7 (2) ◽  
pp. SB43-SB52 ◽  
Author(s):  
Adriano Gomes ◽  
Joe Peterson ◽  
Serife Bitlis ◽  
Chengliang Fan ◽  
Robert Buehring
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Reflection Data ◽  
Full Waveform ◽  
Velocity Model Building ◽  
Wave Limit ◽  
Rabbit Ears

Inverting for salt geometry using full-waveform inversion (FWI) is a challenging task, mostly due to the lack of extremely low-frequency signal in the seismic data, the limited penetration depth of diving waves using typical acquisition offsets, and the difficulty in correctly modeling the amplitude (and kinematics) of reflection events associated with the salt boundary. However, recent advances in reflection FWI (RFWI) have allowed it to use deep reflection data, beyond the diving-wave limit, by extracting the tomographic term of the FWI reflection update, the so-called rabbit ears. Though lacking the resolution to fully resolve salt geometry, we can use RFWI updates as a guide for refinements in the salt interpretation, adding a partially data-driven element to salt velocity model building. In addition, we can use RFWI to update sediment velocities in complex regions surrounding salt, where ray-based approaches typically struggle. In reality, separating the effects of sediment velocity errors from salt geometry errors is not straightforward in many locations. Therefore, iterations of RFWI plus salt scenario tests may be necessary. Although it is still not the fully automatic method that has been envisioned for FWI, this combined approach can bring significant improvement to the subsalt image, as we examine on field data examples from the Gulf of Mexico.

scholarly journals Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R77-R88 ◽  
Author(s):  
Yunseok Choi ◽  
Tariq Alkhalifah
Keyword(s):  
Objective Function ◽  
Frequency Band ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
Full Waveform ◽  
Adjoint State ◽  
Recorded Data ◽  
Adjoint State Method

Full-waveform inversion (FWI) suffers from the cycle-skipping problem when the available frequency-band of data is not low enough. We have applied an exponential damping to the data to generate artificial low frequencies, which helps FWI to avoid cycle skipping. In this case, the least-squares misfit function does not properly deal with the exponentially damped wavefield in FWI because the amplitude of traces decays almost exponentially with increasing offset in a damped wavefield. Thus, we use a deconvolution-based objective function for FWI of the exponentially damped wavefield. The deconvolution filter includes inherently a normalization between the modeled and observed data; thus, it can address the unbalanced amplitude of a damped wavefield. We specifically normalize the modeled data with the observed data in the frequency-domain to estimate the deconvolution filter and selectively choose a frequency-band for normalization that mainly includes the artificial low frequencies. We calculate the gradient of the objective function using the adjoint-state method. The synthetic and benchmark data examples indicate that our FWI algorithm generates a convergent long-wavelength structure without low-frequency information in the recorded data.

scholarly journals Full-waveform inversion using a nonlinearly smoothed wavefield

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. R117-R127 ◽  
Author(s):  
Yuanyuan Li ◽  
Yunseok Choi ◽  
Tariq Alkhalifah ◽  
Zhenchun Li ◽  
Kai Zhang
Keyword(s):  
Objective Function ◽  
Global Minimum ◽  
Waveform Inversion ◽  
Gradient Methods ◽  
Low Frequency ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Low Frequencies ◽  
Full Waveform ◽  
Global Correlation

Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

Constrained full-waveform inversion by model reparameterization

Geophysics ◽  
2012 ◽  
Vol 77 (2) ◽  
pp. R117-R127 ◽  
Author(s):  
Antoine Guitton ◽  
Gboyega Ayeni ◽  
Esteban Díaz
Keyword(s):  
Waveform Inversion ◽  
Model Space ◽  
Real Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Coherent Noise ◽  
Low Frequencies ◽  
Full Waveform ◽  
Geological Information ◽  
Ill Posed

The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D synthetic and field data examples how preconditioning with nonstationary directional Laplacian filters outperforms traditional waveform inversion when sparse data are inverted and when sharp velocity contrasts are present. Adding geological information with preconditioning could benefit full-waveform inversion of real data whenever irregular geometry, coherent noise and lack of low frequencies are present.

scholarly journals Elastic envelope inversion using multicomponent seismic data without low frequency

2014 ◽  
Vol 1 (2) ◽  
pp. 1757-1802
Author(s):  
C. Huang ◽  
L. Dong ◽  
Y. Liu ◽  
B. Chi
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Low Frequency ◽  
Velocity Model ◽  
Inversion Method ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Full Waveform ◽  
Multicomponent Data

Abstract. Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the benefit of such low frequency information, we use elastic envelope of multicomponent data to construct the objective function and present an elastic envelope inversion method to recover the long-wavelength components of the subsurface model, especially for the S-wave velocity model. Numerical tests using synthetic data for the Marmousi-II model prove the effectiveness of the proposed elastic envelope inversion method, especially when low frequency is missing in multicomponent data and when initial model is far from the true model. The elastic envelope can reduce the nonlinearity of inversion and can provide an excellent starting model.

scholarly journals Resolving high frequency anomalies of gas cloud using full waveform inversion

2016 ◽  
Vol 59 (1) ◽  
Author(s):  
Srichand Prajapati ◽  
Deva Ghosh
Keyword(s):  
High Resolution ◽  
Physical Properties ◽  
Cloud Model ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Low Frequencies ◽  
High Frequencies ◽  
Full Waveform ◽  
Gas Cloud

<p>High resolution models with structurally improved results significant to the physical properties of rocks in geologically complex areas require advance modeling methodologies. Low frequencies are required to understand the geological properties of the rocks while high frequencies is needed to address the structural challenges. Recent industry success in inversion have shown the accurate and robust results for the low frequencies. In this work, we provide a strategy to resolve geologically complex area such as gas cloud (at high frequencies) using full waveform inversion (FWI) based on 2D wave equation. Our contribution here, is the improvement in FWI imaging by: (i) solving the wave field equation to recover high resolution inversion results which is consistence to physical properties and shows structural enhancements; (ii) estimating the distribution of local minima which is largely affected by initial velocity model. To validate our approach, we demonstrate algorithms on synthetic gas cloud model.</p>

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