Selective data extension for full-waveform inversion: An efficient solution for cycle skipping

Standard full-waveform inversion (FWI) attempts to minimize the difference between observed and modeled data. However, this difference is obviously sensitive to the amplitude of observed data, which leads to difficulties because we often do not process data in absolute units and because we usually do not consider density variations, elastic effects, or more complicated physical phenomena. Global correlation methods can remove the amplitude influence for each trace and thus can mitigate such difficulties in some sense. However, this approach still suffers from the well-known cycle-skipping problem, leading to a flat objective function when observed and modeled data are not correlated well enough. We optimize based on maximizing not only the zero-lag global correlation but also time or space lags of the modeled data to circumvent the half-cycle limit. We use a weighting function that is maximum value at zero lag and decays away from zero lag to balance the role of the lags. The resulting objective function is less sensitive to the choice of the maximum lag allowed and has a wider region of convergence compared with standard FWI. Furthermore, we develop a selective function, which passes to the gradient calculation only positive correlations, to mitigate cycle skipping. Finally, the resulting algorithm has better convergence behavior than conventional methods. Application to the Marmousi model indicates that this method converges starting with a linearly increasing velocity model, even with data free of frequencies less than 3.5 Hz. Application to the SEG2014 data set demonstrates the potential of our method.

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Tackling cycle skipping in full-waveform inversion with intermediate data

Geophysics ◽

10.1190/geo2018-0096.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. R411-R427 ◽

Cited By ~ 8

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.

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Full-waveform inversion using a nonlinearly smoothed wavefield

Geophysics ◽

10.1190/geo2017-0312.1 ◽

2018 ◽

Vol 83 (2) ◽

pp. R117-R127 ◽

Cited By ~ 13

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.

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From tomography to full-waveform inversion with a single objective function

Geophysics ◽

10.1190/geo2013-0291.1 ◽

2014 ◽

Vol 79 (2) ◽

pp. R55-R61 ◽

Cited By ~ 25

Author(s):

Tariq Alkhalifah ◽

Yunseok Choi

Keyword(s):

Objective Function ◽

Initial Velocity ◽

Waveform Inversion ◽

Synthetic Data ◽

Velocity Model ◽

Full Waveform Inversion ◽

Half Cycle ◽

Velocity Models ◽

Full Waveform ◽

Single Objective

In full-waveform inversion (FWI), a gradient-based update of the velocity model requires an initial velocity that produces synthetic data that are within a half-cycle, everywhere, from the field data. Such initial velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, and are not guaranteed to adhere to the FWI requirements for an initial velocity model. As such, we evaluated an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase-based attribute of the wavefield, along with its phase unwrapping characteristics, provided a frequency-dependent traveltime function that was easy to use and quantify, especially compared to conventional phase representation. With a strong Laplace damping of the modeled, potentially low-frequency, data along the time axis, this attribute admitted a first-arrival traveltime that could be compared with picked ones from the observed data, such as in wave equation tomography (WET). As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped. It, thus, provided a single objective function for a natural transition from WET to FWI. A Marmousi example demonstrated the effectiveness of the approach.

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Local-crosscorrelation elastic full-waveform inversion

Geophysics ◽

10.1190/geo2018-0660.1 ◽

2019 ◽

Vol 84 (6) ◽

pp. R897-R908 ◽

Cited By ~ 3

Author(s):

Zhen-dong Zhang ◽

Tariq Alkhalifah

Keyword(s):

Seismic Data ◽

Weighting Function ◽

Waveform Inversion ◽

Local Similarity ◽

Full Waveform Inversion ◽

Half Cycle ◽

The North ◽

Full Waveform ◽

Global Correlation ◽

The Difference

Full-waveform inversion (FWI) in its classic form is a method based on minimizing the [Formula: see text] norm of the difference between the observed and simulated seismic waveforms at the receiver locations. The objective is to find a subsurface model that reproduces the full waveform including the traveltimes and amplitudes of the observed seismic data. However, the widely used [Formula: see text]-norm-based FWI faces many issues in practice. The point-wise comparison of waveforms fails when the phase difference between the compared waveforms of the predicted and observed data is larger than a half-cycle. In addition, amplitude matching is impractical considering the simplified physics that we often use to describe the medium. To avoid these known problems, we have developed a novel elastic FWI algorithm using the local-similarity attribute. It compares two traces within a predefined local time extension; thus, is not limited by the half-cycle criterion. The algorithm strives to maximize the local similarities of the predicted and observed data by stretching/squeezing the observed data. Phases instead of amplitudes of the seismic data are used in the comparison. The algorithm compares two data sets locally; thus, it performs better than the global correlation in matching multiple arrivals. Instead of picking/calculating one stationary stretching/squeezing curve, we used a weighted integral to find all possible stationary curves. We also introduced a polynomial-type weighting function, which is determined only by the predefined maximum stretching/squeezing and is guaranteed to be smoothly varying within the extension range. Compared with the previously used Gaussian or linear weighting functions, our polynomial one has fewer parameters to play around with. A modified synthetic elastic Marmousi model and the North Sea field data are used to verify the effectiveness of the developed approach and also reveal some of its limitations.

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

Interpretation ◽

10.1190/int-2016-0038.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. SU17-SU24 ◽

Cited By ~ 3

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.

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

The Leading Edge ◽

10.1190/tle38030220.1 ◽

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.

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

Geophysics ◽

10.1190/geo2012-0161.1 ◽

2013 ◽

Vol 78 (2) ◽

pp. R37-R46 ◽

Cited By ~ 11

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.

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Anisotropic 3D full-waveform inversion

Geophysics ◽

10.1190/geo2012-0338.1 ◽

2013 ◽

Vol 78 (2) ◽

pp. R59-R80 ◽

Cited By ~ 233

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.

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MULTISCALES FULL WAVEFORM INVERSION USING A FILTERING APPROACH AND GRADIENT PRECONDITIONING

Brazilian Journal of Geophysics ◽

10.22564/rbgf.v35i4.899 ◽

2018 ◽

Vol 35 (4) ◽

pp. 247

Author(s):

Rafael Abreu Cristo ◽

Milton Porsani

Keyword(s):

Objective Function ◽

High Frequency ◽

Waveform Inversion ◽

Wiener Filter ◽

Velocity Model ◽

Multiscale Approach ◽

Full Waveform Inversion ◽

Model Choice ◽

Geometrical Spreading ◽

Full Waveform

ABSTRACT. The FWI multiscale approach in data domain produces better results because the problem gets closer to the overall minimum avoiding the local minima. The method works in different scales, avoiding the initial velocity model choice as well as the cycle skipping. Regarding to multiscale approach, it was done choosing frequencies band performed by Wiener filter and a SVD filter trace by trace both in data domain. The trace by trace SVD filter works taking each trace of the gradient and assembles on the shifted matrix traces and do the decomposition from low to high frequency. In addition this multiscale approach in data domain was compared to another multiscale approach using damping filters on the objective function (MDFOF). Due to the problem of geometrical spreading, during the propagation of the wave field, the deeper regions of the model are not well illuminated, hence the preconditioning of the objective function gradient was done in order to eliminate this problem and allow the deeper regions to be compared. Keywords: SVD filter; Full waveform inversion; Gradient preconditioning; Pseudo Hessian diagonal. RESUMO. A abordagem multiescala no problema da FWI, produz melhores resultados pois o problema consegue convergir para o mínimo global, evitando o problema do mínimo local. O método funciona em diferentes escalas, evitando o problema da escolha no modelo inicial de velocidade bem como o problema de salto de ciclo. Em relação à abordagem multiescala, o mesmo foi realizado escolhendo bandas de frequências usando o filtro de Wiener e o filtro SVD traço a traço. O filtro SVD traço a traço funciona tomando cada traço do gradiente e da matriz de traços deslocados a faz a decomposição das baixas às altas frequências. Além dessa, abordagem multiescala no domínio do dado, outra abordagem multiescala usando filtros atenuantes foi comparada com a abordagem multiescala no domínio do dado. Devido ao problema de divergência esférica, durante a propagação da onda, as regiões mais profundas do modelo não são corretamente imageadas, portanto faz-se necessário o precondicionamento do gradiente foi feito com intuito de eliminar esse problema e permitir a comparação das duas abordagens nas regiões mais profundas do modelo. Palavras-chave: Filtro SVD; Inversion complete da forma de onda; Precondicionamento do gradiente; Diagonal da Pseudo Hessiana.

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An application of full-waveform inversion to land data using the pseudo-Hessian matrix

Interpretation ◽

10.1190/int-2015-0214.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T627-T635

Author(s):

Yikang Zheng ◽

Wei Zhang ◽

Yibo Wang ◽

Qingfeng Xue ◽

Xu Chang

Keyword(s):

Hessian Matrix ◽

Waveform Inversion ◽

Computational Cost ◽

Velocity Model ◽

Surface Velocity ◽

Full Waveform Inversion ◽

Data Set ◽

Near Surface ◽

Full Waveform ◽

The Time Domain

Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

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