scholarly journals Full-model wavenumber inversion: An emphasis on the appropriate wavenumber continuation

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. R89-R98 ◽  
Author(s):  
Tariq Alkhalifah
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Initial Model ◽  
Blind Test ◽  
Data Set ◽  
Scattering Angle ◽  
Full Waveform ◽  
The Earth ◽  
Least Squares Fit ◽  
Recorded Data

A model of the earth can be described using a Fourier basis represented by its wavenumber content. In full-waveform inversion (FWI), the wavenumber description of the model is natural because our Born-approximation-based velocity updates are made up of wavefields. Our objective in FWI is to access all the model wavenumbers available in our limited aperture and bandwidth recorded data that are not yet accurately present in the initial velocity model. To invert for those model wavenumbers, we need to locate their imprint in the data. Thus, I review the relation between the model wavenumber buildup and the inversion process. Specifically, I emphasize a focus on the model wavenumber components and identified their individual influence on the data. Missing the energy for a single vertical low-model wavenumber from the residual between the true Marmousi model and some initial linearly increasing velocity model produced a worse least-squares fit to the data than the initial model itself, in which all the residual model wavenumbers were missing. This stern realization validated the importance of wavenumber continuation, specifically starting from the low-model wavenumbers, to higher (resolution) wavenumbers, especially those attained in an order dictated by the scattering angle filter. A numerical Marmousi example determined the important role that the scattering angle filter played in managing the wavenumber continuation from low to high. An application on the SEG2014 blind test data set with frequencies lower than 7 Hz muted out further validated the versatility of the scattering angle filtering.

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 Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Zhendong Zhang ◽  
Tariq Alkhalifah ◽  
Zedong Wu ◽  
Yike Liu ◽  
Bin He ◽  
...  
Keyword(s):  
Field Data ◽  
Extreme Values ◽  
Time Lag ◽  
Waveform Inversion ◽  
Optimal Time ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Full Waveform ◽  
The Earth

Full-waveform inversion (FWI) is an attractive technique due to its ability to build high-resolution velocity models. Conventional amplitude-matching FWI approaches remain challenging because the simplified computational physics used does not fully represent all wave phenomena in the earth. Because the earth is attenuating, a sample-by-sample fitting of the amplitude may not be feasible in practice. We have developed a normalized nonzero-lag crosscorrelataion-based elastic FWI algorithm to maximize the similarity of the calculated and observed data. We use the first-order elastic-wave equation to simulate the propagation of seismic waves in the earth. Our proposed objective function emphasizes the matching of the phases of the events in the calculated and observed data, and thus, it is more immune to inaccuracies in the initial model and the difference between the true and modeled physics. The normalization term can compensate the energy loss in the far offsets because of geometric spreading and avoid a bias in estimation toward extreme values in the observed data. We develop a polynomial-type weighting function and evaluate an approach to determine the optimal time lag. We use a synthetic elastic Marmousi model and the BigSky field data set to verify the effectiveness of the proposed method. To suppress the short-wavelength artifacts in the estimated S-wave velocity and noise in the field data, we apply a Laplacian regularization and a total variation constraint on the synthetic and field data examples, respectively.

scholarly journals Progressive matching optimisation method for FWI

2020 ◽  
Vol 17 (2) ◽  
pp. 357-364
Author(s):  
Francisco A Moura ◽  
Suzane A Silva ◽  
João M de Araújo ◽  
Liacir S Lucena
Keyword(s):  
Waveform Inversion ◽  
Particle Swarm ◽  
Velocity Model ◽  
Two Dimensions ◽  
Distinct Advantage ◽  
Test Case ◽  
Initial Model ◽  
Full Waveform ◽  
Derivative Free ◽  
Particle Swarm Optimisation Algorithm

Abstract To eliminate the dependency on a good initial model of the traditional full waveform inversion (FWI) method, we propose an optimisation method combining a derivative free optimisation method of modified particle swarm with gradient descent search. We worked with the acoustic wave approximation, in two dimensions, with the synthetic Marmousi velocity model as the test case. We were able to obtain a high-precision inversion of this model, comparable to traditional FWI methods, with the distinct advantage of not using an initial model close to the global optimal, as would usually be required. For this result, we used a progressive inversion scheme by consecutive layers, and a modified particle swarm optimisation algorithm where we introduced the gradient of the misfit function as a local search guide, and other regularization terms.

Random objective waveform inversion of surface waves

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. EN49-EN61
Author(s):  
Yudi Pan ◽  
Lingli Gao
Keyword(s):  
Objective Function ◽  
Surface Waves ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Initial Model ◽  
S Wave ◽  
Data Set ◽  
Near Surface ◽  
Synthetic Test ◽  
Ground Penetrating

Full-waveform inversion (FWI) of surface waves is becoming increasingly popular among shallow-seismic methods. Due to a huge amount of data and the high nonlinearity of the objective function, FWI usually requires heavy computational costs and may converge toward a local minimum. To mitigate these problems, we have reformulated FWI under a multiobjective framework and adopted a random objective waveform inversion (ROWI) method for surface-wave characterization. Three different measure functions were used, whereas the combination of one measure function with one shot independently provided one of the [Formula: see text] objective functions ([Formula: see text] is the total number of shots). We have randomly chose and optimized one objective function at each iteration. We performed a synthetic test to compare the performance of the ROWI and conventional FWI approaches, which showed that the convergence of ROWI is faster and more robust compared with conventional FWI approaches. We also applied ROWI to a field data set acquired in Rheinstetten, Germany. ROWI successfully reconstructed the main geologic feature, a refilled trench, in the final result. The comparison between the ROWI result and a migrated ground-penetrating radar profile further proved the effectiveness of ROWI in reconstructing the near-surface S-wave velocity model. We also ran the same field example by using a poor initial model. In this case, conventional FWI failed whereas ROWI still reconstructed the subsurface model to a fairly good level, which highlighted the relatively low dependency of ROWI on the initial model.

Application of multiparameter full-waveform inversion in Central Luconia Basin, Sarawak

2016 ◽  
Vol 4 (4) ◽  
pp. SU17-SU24 ◽  
Author(s):  
Vanessa Goh ◽  
Kjetil Halleland ◽  
René-Édouard Plessix ◽  
Alexandre Stopin
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Thin Layers ◽  
Earth Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
Velocity Variations ◽  
Central Luconia

Reducing velocity inaccuracy in complex settings is of paramount importance for limiting structural uncertainties, therefore helping the geologic interpretation and reservoir characterization. Shallow velocity variations due, for instance, to gas accumulations or carbonate reefs, are a common issue offshore Malaysia. These velocity variations are difficult to image through standard reflection-based velocity model building. We have applied full-waveform inversion (FWI) to better characterize the upper part of the earth model for a shallow-water field, located in the Central Luconia Basin offshore Sarawak. We have inverted a narrow-azimuth data set with a maximum inline offset of 4.4 km. Thanks to dedicated broadband preprocessing of the data set, we could enhance the signal-to-noise ratio in the 2.5–10 Hz frequency band. We then applied a multiparameter FWI to estimate the background normal moveout velocity and the [Formula: see text]-parameter. Full-waveform inversion together with broadband data processing has helped to better define the faults and resolve the thin layers in the shallow clastic section. The improvements in the velocity model brought by FWI lead to an improved image of the structural closure and flanks. Moreover, the increased velocity resolution helps in distinguishing between two different geologic interpretations.

High-resolution depth imaging of long-offset 2D data using full-waveform inversion: The Malvinas Basin, Argentina

2019 ◽  
Vol 38 (3) ◽  
pp. 220-225
Author(s):  
Laurence Letki ◽  
Mike Saunders ◽  
Monica Hoppe ◽  
Milos Cvetkovic ◽  
Lewis Goss ◽  
...  
Keyword(s):  
High Resolution ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Depth Imaging ◽  
Additional Information ◽  
Full Waveform ◽  
Seismic Image ◽  
2D Data

The Argentina Austral Malvinas survey comprises 13,784 km of 2D data extending from the shelf to the border with the Falkland Islands. The survey was acquired using a 12,000 m streamer and continuous recording technology and was processed through a comprehensive broadband prestack depth migration workflow focused on producing a high-resolution, high-fidelity data set. Source- and receiver-side deghosting to maximize the bandwidth of the data was an essential ingredient in the preprocessing. Following the broadband processing sequence, a depth-imaging workflow was implemented, with the initial model built using a time tomography approach. Several passes of anisotropic reflection tomography provided a significant improvement in the velocity model prior to full-waveform inversion (FWI). Using long offsets, FWI made use of additional information contained in the recorded wavefield, including the refracted and diving wave energy. FWI resolved more detailed velocity variations both in the shallow and deeper section and culminated in an improved seismic image.

Efficient Laplace-domain full waveform inversion using a cyclic shot subsampling method

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. R37-R46 ◽  
Author(s):  
Wansoo Ha ◽  
Changsoo Shin
Keyword(s):  
Waveform Inversion ◽  
Computation Time ◽  
Velocity Model ◽  
Divide And Conquer ◽  
Iteration Step ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Laplace Domain ◽  
Full Waveform ◽  
Subsampling Method

Full waveform inversion is a method used to recover subsurface parameters, and it requires heavy computational resources. We present a cyclic shot subsampling method to make the full waveform inversion efficient while maintaining the quality of the inversion results. The cyclic method subsamples the shots at a regular interval and changes the shot subset at each iteration step. Using this method, we can suppress the aliasing noise present in regular-interval subsampling. We compared the cyclic method with divide-and-conquer, random, and random-in-each-subgroup subsampling methods using the Laplace-domain full waveform inversion. We found examples of a 2D marine field data set from the Gulf of Mexico and a 3D synthetic salt velocity model. In the inversion examples using the subsampling methods, we could reduce the computation time and obtain results comparable to that without a subsampling technique. The cyclic method and two random subsampling methods yielded similar results; however, the cyclic method generated the best results, especially when the number of shot subsamples was small, as expected. We also examined the effect of subsample updating frequency. The updating frequency does not have a significant effect on the results when the number of subsamples is large. In contrast, frequent subsample updating becomes important when the number of subsamples is small. The random-in-each-subgroup scheme showed the best results if we did not update the subsamples frequently, while the cyclic method suffers from aliasing. The results suggested that the cyclic subsampling scheme can be an alternative to the random schemes and the distributed subsampling schemes with a frequently changing subset are better than lumped subsampling schemes.

scholarly journals Full waveform inversion in time and frequency domain of velocity modeling in seismic imaging: FWISIMAT a Matlab code

2018 ◽  
Vol 22 (4) ◽  
pp. 291-300
Author(s):  
Sagar Singh ◽  
Ali Ismet Kanli ◽  
Sagarika Mukhopadhyay
Keyword(s):  
Frequency Domain ◽  
Seismic Imaging ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Initial Model ◽  
Final Model ◽  
Full Waveform ◽  
True Model ◽  
Starting Model

This paper investigates the capability of acoustic Full Waveform Inversion (FWI) in building Marmousi velocity model, in time and frequency domain. FWI is an iterative minimization of misfit between observed and calculated data which is generally solved in three segments: forward modeling, which numerically solves the wave equation with an initial model, gradient computation of the objective function, and updating the model parameters, with a valid optimization method. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented using the Marmousi velocity model as the true model. An initial model is obtained by smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive on the starting model. The final model is compared with the true model to review the number of recovered velocities. FWI codes developed in MATLAB herein FWISIMAT (Full Waveform Inversion in Seismic Imaging using MATLAB) are successfully implemented usingMarmousi velocity model astrue model. An initial model is derived from smoothing the true model to initiate FWI procedure. Smoothing ensures an adequate starting model for FWI, as the FWI procedure is known to be sensitive onstarting model. The final model is compared with the true model to review theamount of recovered velocities. 

Anisotropic 3D full-waveform inversion

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. R59-R80 ◽  
Author(s):  
Michael Warner ◽  
Andrew Ratcliffe ◽  
Tenice Nangoo ◽  
Joanna Morgan ◽  
Adrian Umpleby ◽  
...  
Keyword(s):  
High Velocity ◽  
Field Data ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Low Velocity ◽  
Data Set ◽  
Reflection Data ◽  
Full Waveform ◽  
Gas Cloud

We have developed and implemented a robust and practical scheme for anisotropic 3D acoustic full-waveform inversion (FWI). We demonstrate this scheme on a field data set, applying it to a 4C ocean-bottom survey over the Tommeliten Alpha field in the North Sea. This shallow-water data set provides good azimuthal coverage to offsets of 7 km, with reduced coverage to a maximum offset of about 11 km. The reservoir lies at the crest of a high-velocity antiformal chalk section, overlain by about 3000 m of clastics within which a low-velocity gas cloud produces a seismic obscured area. We inverted only the hydrophone data, and we retained free-surface multiples and ghosts within the field data. We invert in six narrow frequency bands, in the range 3 to 6.5 Hz. At each iteration, we selected only a subset of sources, using a different subset at each iteration; this strategy is more efficient than inverting all the data every iteration. Our starting velocity model was obtained using standard PSDM model building including anisotropic reflection tomography, and contained epsilon values as high as 20%. The final FWI velocity model shows a network of shallow high-velocity channels that match similar features in the reflection data. Deeper in the section, the FWI velocity model reveals a sharper and more-intense low-velocity region associated with the gas cloud in which low-velocity fingers match the location of gas-filled faults visible in the reflection data. The resulting velocity model provides a better match to well logs, and better flattens common-image gathers, than does the starting model. Reverse-time migration, using the FWI velocity model, provides significant uplift to the migrated image, simplifying the planform of the reservoir section at depth. The workflows, inversion strategy, and algorithms that we have used have broad application to invert a wide-range of analogous data sets.

Relaxing the initial model constraint for crustal-scale full-waveform inversion with graph-space optimal transport misfit function

2020 ◽  
Author(s):  
Andrzej Górszczyk ◽  
Ludovic Métivier ◽  
Romain Brossier
Keyword(s):  
Seismic Data ◽  
Optimal Transport ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Wide Angle ◽  
Initial Model ◽  
Full Waveform ◽  
Long Offset ◽  
Obs Data

<p>Investigations of the deep lithosphere aiming at the reconstruction of the geological models remain one of the key sources of the knowledge about the processes shaping the outer shell of our planet. Among different methods, the active seismic Ocean-Bottom Seismometer (OBS) experiments conducted in wide-angle configuration are routinely employed to better understand these processes. Indeed, long-offset seismic data, combined with computationally efficient travetime tomographic methods, have a great potential to constrain the macro-scale subsurface velocity models at large depths. </p><p>On the other hand, decades of development of acquisition systems, more and more efficient algorithms and high-performance computing resources make it now feasible to move beyond the regional raytracing-based traveltime tomography. In particular, the waveform inversion methods, such as Full-Waveform Inversion (FWI), are able to exhaustively exploit the rich information collected along the long-offset diving and refraction wavepaths, additionally enriched with the wide-angle reflection arrivals. So far however, only a few attempts have been conducted in the academic community to combine wide-angle seismic data with FWI for high-resolution crustal-scale velocity model reconstruction. This is partially due to the non-convexity of FWI misfit function, which increases with the complexity of the geological setting reflected by the seismograms. </p><p>In its classical form FWI is a nonlinear least-squares problem, which is solved through the local optimization techniques. This imposes the strong constraint on the accuracy of the starting FWI model. To avoid cycle-skipping problem the initial model must predict synthetic data within the maximum error of half-period time-shift with respect to the observed data. The criterion is difficult to fulfil when facing the crustal-scale FWI, because the long-offset acquisition translates to the long time of wavefront propagation and therefore accumulation of the traveltime error along the wavepath simulated in the initial model. This in turns increases the possibility of the cycle-skipping taking into account large number of propagated wavelengths.</p><p>Searching to mitigate this difficulty, here we investigate FWI with a Graph-Space Optimal Transport (GSOT) misfit function. Comparing to the classical least-squares norm, GSOT is convex with respect to the patterns in the waveform which can be shifted in time for more than half-period. Therefore, with proper data selection strategy GSOT misfit-function has potential to reduce the risk of cycle-skipping. We demonstrate the robustness of this novel approach using 2D wide-angle OBS data-set generated in a GO_3D_OBS synthetic model of subduction zone (30 km x 175 km). We show that using GSOT cost-function combined with the multiscale FWI strategy, we reconstruct in details the highly complex geological structure starting from a simple 1D velocity model. We believe that further developments of OT-based misfit functions can significantly reduce the constraints on the starting model accuracy and reduce the overall risk of cycle-skipping during FWI of wide-angle OBS data.</p>

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