Waveform inversion using a logarithmic wavefield

Although waveform inversion has been studied extensively since its beginning [Formula: see text] ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology- or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our wave form inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noise-free synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below [Formula: see text] are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

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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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Random objective waveform inversion of surface waves

Geophysics ◽

10.1190/geo2019-0613.1 ◽

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.

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Structurally constrained impedance inversion

Interpretation ◽

10.1190/int-2016-0049.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T577-T589 ◽

Cited By ~ 8

Author(s):

Haitham Hamid ◽

Adam Pidlisecky

Keyword(s):

Objective Function ◽

Seismic Data ◽

Field Data ◽

A Priori ◽

Structural Constraints ◽

Inversion Algorithm ◽

Data Set ◽

Impedance Inversion ◽

Single Trace ◽

Complex Geology

In complex geology, the presence of highly dipping structures can complicate impedance inversion. We have developed a structurally constrained inversion in which a computationally well-behaved objective function is minimized subject to structural constraints. This approach allows the objective function to incorporate structural orientation in the form of dips into our inversion algorithm. Our method involves a multitrace impedance inversion and a rotation of an orthogonal system of derivative operators. Local dips used to constrain the derivative operators were estimated from migrated seismic data. In addition to imposing structural constraints on the inversion model, this algorithm allows for the inclusion of a priori knowledge from boreholes. We investigated this algorithm on a complex synthetic 2D model as well as a seismic field data set. We compared the result obtained with this approach with the results from single trace-based inversion and laterally constrained inversion. The inversion carried out using dip information produces a model that has higher resolution that is more geologically realistic compared with other methods.

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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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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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Crosshole seismic tomography

Geophysics ◽

10.1190/1.1442644 ◽

1989 ◽

Vol 54 (2) ◽

pp. 200-215 ◽

Cited By ~ 130

Author(s):

N. D. Bregman ◽

R. C. Bailey ◽

C. H. Chapman

Keyword(s):

Ray Tracing ◽

Field Data ◽

Velocity Structure ◽

Least Squares Method ◽

Current Model ◽

Velocity Model ◽

Crystalline Rock ◽

Inversion Method ◽

Data Set ◽

Waveform Data

Many tomographic interpretations of crosshole seismic traveltimes have approximated the raypaths with straight lines connecting the source and receiver. This approximation is valid where the velocity does not vary greatly, but in many regions of interest velocity variations of 10–20 percent or more are observed, causing significant ray curvature. Other work has taken this nonlinear effect into account, but there do not appear to be many cases of demonstrated success in its application to the crosshole seismic problem. We present here an iterative inversion scheme based on two‐dimensional ray tracing and its successful application to field data. The interpretation method iteratively ray traces and then updates the velocity model. Within each iteration, the differences between the data and the current model traveltimes obtained by ray tracing are related to the unknown velocity perturbations through a system of linear equations. A damped least‐squares method solves for the velocity perturbations which update the model. The iterations continue until the synthetic traveltimes fit the data to within the data error or until no improvement in the fit of the traveltimes is observed. The method is demonstrated on a small synthetic data set, where convergence to the correct solution is achieved in a few iterations. The method is then applied to field data from a crosshole experiment in crystalline rock. The frequency range of the seismograms is 1 to 6.6 kHz, allowing resolution of velocity structure on a scale of several meters. The resulting velocity image shows good agreement with other geologic and geophysical data. Synthetic Maslov seismograms calculated for the derived velocity model agree well with the waveform data, providing an independent test of the validity of the inversion method.

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Mitigating elastic effects in marine 3-D full-waveform inversion

Geophysical Journal International ◽

10.1093/gji/ggz569 ◽

2019 ◽

Vol 220 (3) ◽

pp. 2089-2104

Author(s):

Òscar Calderón Agudo ◽

Nuno Vieira da Silva ◽

George Stronge ◽

Michael Warner

Keyword(s):

Wave Equation ◽

Field Data ◽

Waveform Inversion ◽

Velocity Model ◽

P Wave ◽

Data Sets ◽

Acoustic Wave Equation ◽

Data Set ◽

Velocity Models ◽

Full Waveform

SUMMARY The potential of full-waveform inversion (FWI) to recover high-resolution velocity models of the subsurface has been demonstrated in the last decades with its application to field data. But in certain geological scenarios, conventional FWI using the acoustic wave equation fails in recovering accurate models due to the presence of strong elastic effects, as the acoustic wave equation only accounts for compressional waves. This becomes more critical when dealing with land data sets, in which elastic effects are generated at the source and recorded directly by the receivers. In marine settings, in which sources and receivers are typically within the water layer, elastic effects are weaker but can be observed most easily as double mode conversions and through their effect on P-wave amplitudes. Ignoring these elastic effects can have a detrimental impact on the accuracy of the recovered velocity models, even in marine data sets. Ideally, the elastic wave equation should be used to model wave propagation, and FWI should aim to recover anisotropic models of velocity for P waves (vp) and S waves (vs). However, routine three-dimensional elastic FWI is still commercially impractical due to the elevated computational cost of modelling elastic wave propagation in regions with low S-wave velocity near the seabed. Moreover, elastic FWI using local optimization methods suffers from cross-talk between different inverted parameters. This generally leads to incorrect estimation of subsurface models, requiring an estimate of vp/vs that is rarely known beforehand. Here we illustrate how neglecting elasticity during FWI for a marine field data set that contains especially strong elastic heterogeneities can lead to an incorrect estimation of the P-wave velocity model. We then demonstrate a practical approach to mitigate elastic effects in 3-D yielding improved estimates, consisting of using a global inversion algorithm to estimate a model of vp/vs, employing matching filters to remove elastic effects from the field data, and performing acoustic FWI of the resulting data set. The quality of the recovered models is assessed by exploring the continuity of the events in the migrated sections and the fit of the latter with the recovered velocity model.

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Simultaneous reverse time migration of primaries and free-surface related multiples without multiple prediction

Geophysics ◽

10.1190/geo2012-0450.1 ◽

2014 ◽

Vol 79 (1) ◽

pp. S1-S9 ◽

Cited By ~ 23

Author(s):

Yibo Wang ◽

Xu Chang ◽

Hao Hu

Keyword(s):

Free Surface ◽

Field Data ◽

Synthetic Data ◽

Velocity Model ◽

Reverse Time ◽

Reverse Time Migration ◽

Data Set ◽

Imaging Condition ◽

Time Migration ◽

Multiple Prediction

Prestack reverse time migration (RTM) is usually regarded as an accurate imaging tool and has been widely used in exploration. Conventional RTM only uses primaries and treats free-surface related multiples as noise; however, free-surface related multiples can sometimes provide extra illumination of the subsurface, and this information could be used in migration procedures. There are many migration methods using free-surface related multiples, but most approaches need to predict multiples, which is time consuming and prone to error. We discovered a new RTM approach that uses the primaries and the free-surface related multiples simultaneously. Compared with migration methods that only use free-surface related multiples, the proposed approach can provide comparable migration results and does not need multiple predictions. In our approach, the source function in conventional RTM was replaced with recorded field data including primaries and free-surface related multiples, together with a synthetic wavelet; the back-propagated primaries in the conventional RTM were replaced with complete recorded field data. The imaging condition of the proposed approach was the same as the crosscorrelation imaging condition of conventional RTM. A three-layer velocity model with scatterers and the Sigsbee 2B synthetic data set were used for numerical experiments. The numerical results showed that the proposed approach can cover a wider range of the subsurface and provide better illumination compared with conventional RTM. The proposed approach was easy to implement and avoided tedious multiple prediction; it might be significant for general complex subsurface imaging.

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Localizing microseismic events on field data using a U-Net based convolutional neural network trained on synthetic data

Geophysics ◽

10.1190/geo2020-0868.1 ◽

2021 ◽

pp. 1-47

Author(s):

N. A. Vinard ◽

G. G. Drijkoningen ◽

D. J. Verschuur

Keyword(s):

Hydraulic Fracturing ◽

Field Data ◽

Synthetic Data ◽

Region Of Interest ◽

Velocity Model ◽

Mitigation Measures ◽

Large Field ◽

Data Sets ◽

Data Set ◽

Full Waveforms

Hydraulic fracturing plays an important role when it comes to the extraction of resources in unconventional reservoirs. The microseismic activity arising during hydraulic fracturing operations needs to be monitored to both improve productivity and to make decisions about mitigation measures. Recently, deep learning methods have been investigated to localize earthquakes given field-data waveforms as input. For optimal results, these methods require large field data sets that cover the entire region of interest. In practice, such data sets are often scarce. To overcome this shortcoming, we propose initially to use a (large) synthetic data set with full waveforms to train a U-Net that reconstructs the source location as a 3D Gaussian distribution. As field data set for our study we use data recorded during hydraulic fracturing operations in Texas. Synthetic waveforms were modelled using a velocity model from the site that was also used for a conventional diffraction-stacking (DS) approach. To increase the U-Nets ability to localize seismic events, we augmented the synthetic data with different techniques, including the addition of field noise. We select the best performing U-Net using 22 events that have previously been identified to be confidently localized by DS and apply that U-Net to all 1245 events. We compare our predicted locations to DS and the DS locations refined by a relative location (DSRL) method. The U-Net based locations are better constrained in depth compared to DS and the mean hypocenter difference with respect to DSRL locations is 163 meters. This shows potential for the use of synthetic data to complement or replace field data for training. Furthermore, after training, the method returns the source locations in near real-time given the full waveforms, alleviating the need to pick arrival times.

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

Geophysics ◽

10.1190/geo2016-0649.1 ◽

2018 ◽

Vol 83 (3) ◽

pp. R201-R211 ◽

Cited By ~ 6

Author(s):

Zedong Wu ◽

Tariq Alkhalifah

Keyword(s):

Objective Function ◽

Weighting Function ◽

Waveform Inversion ◽

Velocity Model ◽

Full Waveform Inversion ◽

Half Cycle ◽

Process Data ◽

Data Set ◽

Full Waveform ◽

Global Correlation

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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