scholarly journals Full-intensity waveform inversion

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R649-R658 ◽  
Author(s):  
Yike Liu ◽  
Bin He ◽  
Huiyi Lu ◽  
Zhendong Zhang ◽  
Xiao-Bi Xie ◽  
...  
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Low Frequencies ◽  
Full Waveform ◽  
Seismic Waveform ◽  
Using Data ◽  
Full Intensity ◽  
Starting Model

Many full-waveform inversion schemes are based on the iterative perturbation theory to fit the observed waveforms. When the observed waveforms lack low frequencies, those schemes may encounter convergence problems due to cycle skipping when the initial velocity model is far from the true model. To mitigate this difficulty, we have developed a new objective function that fits the seismic-waveform intensity, so the dependence of the starting model can be reduced. The waveform intensity is proportional to the square of its amplitude. Forming the intensity using the waveform is a nonlinear operation, which separates the original waveform spectrum into an ultra-low-frequency part and a higher frequency part, even for data that originally do not have low-frequency contents. Therefore, conducting multiscale inversions starting from ultra-low-frequency intensity data can largely avoid the cycle-skipping problem. We formulate the intensity objective function, the minimization process, and the gradient. Using numerical examples, we determine that the proposed method was very promising and could invert for the model using data lacking low-frequency information.

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 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 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.

scholarly journals Adaptive waveform inversion: Theory

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R429-R445 ◽  
Author(s):  
Michael Warner ◽  
Lluís Guasch
Keyword(s):  
Waveform Inversion ◽  
Computational Cost ◽  
Synthetic Data ◽  
Velocity Model ◽  
Seismic Inversion ◽  
New Method ◽  
Low Frequencies ◽  
Full Waveform ◽  
True Model ◽  
Starting Model

Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.

scholarly journals Waveform inversion based on wavefield decomposition

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. R457-R470 ◽  
Author(s):  
Fang Wang ◽  
Daniela Donno ◽  
Hervé Chauris ◽  
Henri Calandra ◽  
François Audebert
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Velocity Model ◽  
Model Parameters ◽  
Data Set ◽  
Low Frequencies ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
Gradient Based ◽  
Wavefield Decomposition

Full-waveform inversion (FWI) is a technique for determining the optimal model parameters by minimizing the seismic data misfit between observed and modeled data. The objective function may be highly nonlinear if the model is complex and low-frequency data are missing. If a data set mainly contains reflections, this problem particularly prevents the gradient-based methods from recovering the long wavelengths of the velocity model. Several authors observed that nonlinearity could be reduced by progressively introducing higher wavenumbers to the model. We have developed a new inversion workflow to solve this problem by breaking down the FWI gradient formula into four terms after wavefield decomposition and then selecting proper terms to invert for the short- and long-wavelength components of the velocity model alternately. Numerical tests applied on a 2D synthetic model indicate that this method is efficient at recovering the long wavelengths of the velocity model using mainly offset-limited reflection events. The source does not need to contain low frequencies. The initial velocity model may have large errors that would otherwise prevent convergence for conventional FWI.

Full-waveform inversion with borehole constraints for elastic VTI media

Geophysics ◽  
2020 ◽  
Vol 85 (6) ◽  
pp. R553-R563
Author(s):  
Sagar Singh ◽  
Ilya Tsvankin ◽  
Ehsan Zabihi Naeini
Keyword(s):  
Objective Function ◽  
Reservoir Characterization ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Rock Physics ◽  
Anisotropic Media ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Trade Offs ◽  
Vti Media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.

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.

Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. R411-R427 ◽  
Author(s):  
Gang Yao ◽  
Nuno V. da Silva ◽  
Michael Warner ◽  
Di Wu ◽  
Chenhao Yang
Keyword(s):  
Objective Function ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Intermediate Data ◽  
Full Waveform ◽  
L2 Norm ◽  
Recorded Data

Full-waveform inversion (FWI) is a promising technique for recovering the earth models for exploration geophysics and global seismology. FWI is generally formulated as the minimization of an objective function, defined as the L2-norm of the data residuals. The nonconvex nature of this objective function is one of the main obstacles for the successful application of FWI. A key manifestation of this nonconvexity is cycle skipping, which happens if the predicted data are more than half a cycle away from the recorded data. We have developed the concept of intermediate data for tackling cycle skipping. This intermediate data set is created to sit between predicted and recorded data, and it is less than half a cycle away from the predicted data. Inverting the intermediate data rather than the cycle-skipped recorded data can then circumvent cycle skipping. We applied this concept to invert cycle-skipped first arrivals. First, we picked up the first breaks of the predicted data and the recorded data. Second, we linearly scaled down the time difference between the two first breaks of each shot into a series of time shifts, the maximum of which was less than half a cycle, for each trace in this shot. Third, we moved the predicted data with the corresponding time shifts to create the intermediate data. Finally, we inverted the intermediate data rather than the recorded data. Because the intermediate data are not cycle-skipped and contain the traveltime information of the recorded data, FWI with intermediate data updates the background velocity model in the correct direction. Thus, it produces a background velocity model accurate enough for carrying out conventional FWI to rebuild the intermediate- and short-wavelength components of the velocity model. Our numerical examples using synthetic data validate the intermediate-data concept for tackling cycle skipping and demonstrate its effectiveness for the application to first arrivals.

scholarly journals Deep learning for low-frequency extrapolation from multioffset seismic data

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R989-R1001 ◽  
Author(s):  
Oleg Ovcharenko ◽  
Vladimir Kazei ◽  
Mahesh Kalita ◽  
Daniel Peter ◽  
Tariq Alkhalifah
Keyword(s):  
Deep Learning ◽  
Seismic Data ◽  
Signal To Noise Ratio ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Low Frequencies ◽  
Seismic Surveys ◽  
Full Waveform ◽  
Frequency Components ◽  
Marine Seismic

Low-frequency seismic data are crucial for convergence of full-waveform inversion (FWI) to reliable subsurface properties. However, it is challenging to acquire field data with an appropriate signal-to-noise ratio in the low-frequency part of the spectrum. We have extrapolated low-frequency data from the respective higher frequency components of the seismic wavefield by using deep learning. Through wavenumber analysis, we find that extrapolation per shot gather has broader applicability than per-trace extrapolation. We numerically simulate marine seismic surveys for random subsurface models and train a deep convolutional neural network to derive a mapping between high and low frequencies. The trained network is then tested on sections from the BP and SEAM Phase I benchmark models. Our results indicate that we are able to recover 0.25 Hz data from the 2 to 4.5 Hz frequencies. We also determine that the extrapolated data are accurate enough for FWI application.

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