True Velocity Model Research Articles

Deep Velocity Generator: A Plug-In Network for FWI Enhancement

Known for its great potential for determining subsurface properties quantitatively, full-waveform inversion (FWI) is a hot topic in the field of exploration seismology. The success of FWI depends significantly on the accuracy of the starting model. Given that both the migration and velocity profiles originate from the same geological structure, the two should be morphologically consistent. Starting from the velocity‐reflector depth trade-off, we propose a deep learning approach with a new training paradigm for building a good starting model. A velocity model and the corresponding migration image are used to form 2-channel inputs, and the Generative Adversarial Network (GAN) is trained to minimize the difference between the output and the true velocity model. After the training, the velocity generator network becomes a plug-in component to enhance the FWI performance. The network can be well generalized to unseen data by training with only the synthetic data. We perform extensive experiments on our test dataset, the Marmousi model, the salt velocity model, and field data to demonstrate the effectiveness of our method. Besides, we briefly give an explanation of why our model produces such outputs in this manuscript, making the proposed method more controllable and credible.

Adaptive Feedback Convolutional‐Neural‐Network‐Based High‐Resolution Reflection‐Waveform Inversion

AbstractFull‐waveform inversion (FWI) applies non‐linear optimization to estimate the velocity model by fitting the observed seismic data. With a smooth starting velocity model, FWI mainly inverts for the shallower background velocity model by fitting the observed direct, diving and refracted data, and updates the interfaces by fitting the observed reflected data. As the deeper parts of background velocity model cannot be effectively updated by fitting the reflected data in FWI, the deeper interfaces are less accurate than the shallower interfaces. To update the deeper background velocity model, many reflection‐waveform inversion (RWI) algorithms were proposed to separate the tomographic and migration components from the reflection‐related gradient. We propose a convolutional‐neural‐network‐based reflection‐waveform inversion (CNN‐RWI) to repeatedly apply the iteratively updated convolutional neural network (CNN) to predict the true velocity model from the smooth starting velocity model (the tomographic components), and the high‐resolution migration image (the migration components). The CNN is iteratively updated by the more representative training data set, which is obtained from the latest CNN‐predicted velocity model by the proposed spatially constrained divisive hierarchical k‐means parcellation method. The more representative the training velocity models are, the more accurate the CNN‐predicted velocity model becomes. Synthetic examples using different portions of the Marmousi2 P‐wave velocity model show that CNN‐RWI inverts for both the shallower and deeper parts of velocity models more accurately than the conjugate‐gradient FWI (CG‐FWI). Both the CNN‐RWI and the CG‐FWI are sensitive to the accuracy of the starting velocity model and the complexity of the unknown true velocity model.

Determination of the time-dependent moment tensor using time reverse imaging

We have developed an approach to determine the time-dependent moment tensor and the origin time in addition to commonly derived locations of seismic events using time reverse imaging (TRI). It is crucial to locate and characterize the occurring microseismicity without making a priori assumptions about the sources to fully understand the subsurface processes inducing seismicity. Low signal-to-noise ratios (S/Ns) often force standard methods to make assumptions about sources or only characterize selected larger magnitude events. In TRI, microearthquakes are located by back propagating the full-recorded time-reversed wavefield through a velocity model until it ideally convergences on the source location. Therefore, it is less affected by low S/Ns and potentially locates and characterizes most of the events. After distinguishing artificial convergence locations from source locations, the quality of the source location and the moment tensors are derived by recording the stress at the determined source locations during the back propagation of the time-reversed wavefield. A robust workflow is derived using synthetic test cases in a realistic scenario with velocity models that only approximate the true velocity model and/or noisy displacement traces. The influence of a rudimentary velocity model on the source-location accuracy and characterization is significant. Our workflow handles these less-than-optimal station distributions and velocity models. Finally, the derived workflow is successfully applied to field data recorded at the geothermal field of Los Humeros, Mexico. Although only a 1D velocity model is currently available, source locations and (time-dependent) moment tensors could be determined for selected events.

Source-domain full-waveform inversions

Conventional full-waveform inversion (FWI) updates a velocity model by minimizing the data residuals between the predicted and observed data at the receiver positions. We have developed a new FWI to update the velocity model by minimizing virtual source artifacts at the receiver positions in the source-domain FWI (SFWI). Virtual source artifacts are created by replacing the propagating source wavefield by the forward-time observed data at the receiver positions as a data-residual constraint. Therefore, no matter whether the velocity model is correct or not, the data residuals at the receiver positions always are forced to be zero. If the velocity model is correct, this data-residual constraint has no effect on the wavefield because the predicted data are the same as the observed data. However, if the estimated velocity model is incorrect, the mismatch between the replaced forward-time observed data and the incorrect predicted upgoing waves (e.g., the reflected waves) at the receiver positions will produce downgoing artifact waves. Thus, the data-residual constraint behaves as a virtual source to create artifact wavefields. By minimizing the virtual source artifacts (equivalent to producing the artifact wavefield), the velocity model can be iteratively updated toward the true velocity model. Similar to conventional FWI, SFWI can be implemented in either the frequency or time domain, which is unlike previous source-domain solutions which have to be implemented only in the frequency domain to solve the normal equations. SFWI does more overfitting of noisy observed data than conventional FWI does because noise is amplified by the differential operators when calculating the virtual source artifacts. Tests on synthetic data indicate that SFWI inverts for the velocity model more accurately than conventional FWI for noise-free or low-noise data.

Measuring PmP travel times using teleseismic S-wave waveform data*

Joint inversion for crustal velocity structure using only surface wave dispersion and receiver function data often suffers the non-unique solution problem due to lack of P wave velocity constraint in the data. Here we developed a method for measuring PmP travel time using teleseismic S wave waveform. The major improvement by this method over the previous one-layer-crust search method is its use of a more realistic multi-layer-crust (MLC) velocity model in the study region based on available information. Numerical tests show that compared with the previous search method the MLC search method is faster and more reliable and accurate. One limit of the MLC search method is the requirement of a multi-layer background model, thus this method might not be applicable in regions where the velocity structure is unknown. Nevertheless, our numerical tests show that the MLC search method is robust in the sense that small deviations of the background model from the true velocity model do not influence the results severely. We applied the MLC search method to data from a temporary linear array across the Wabash Valley Seismic Zone in the central USA. We obtained 157 PmP travel-time measurements that show lateral crustal structure variation in the region. The measurements provide additional constraints in joint inversion for crustal velocity structure in this seismically active region.

Velocity estimation performance of GNSS online services (APPS and AUSPOS)

Before now, the various studies that have been undertaken to investigate the positioning performance of GNSS Online Services have been limited with regard to both time and number of sessions. Within the scope of this study, the accuracy of the velocity models estimated by APPS and AUSPOS are analysed using a wider period. Local ISKI CORS Network stations are used as the subject. To generate true values for an accurate comparison, 129 sessions with BERNESE (v5.2) software were conducted between 2008 and 2019. A linear trend was determined by using least-squares adjustment to obtain true velocity values. To test the reliability of the true velocity values, seasonal, semi-annual and annual oscillation movements have been examined. Additionally, the coherence of the velocity model with the sample data and compliance with the tectonic plate has been investigated. For GNSS Online Services, 34 sessions were carried out over the same timescale, and the velocity model was estimated. A Z-test with a 0.05 significance level was used to examine the performance of APPS and AUSPOS velocity values. As a result, the estimated true velocity model shows high compliance with sample data and the tectonic plate; no seasonal, semi-annual or annual oscillation movements were identified. According to the study’s statistical test, the velocity model of APPS solutions performs slightly better than that of AUSPOS. However, both services show high performance in the velocity determination. In summary, the usability of GNSS Online Services in determining velocity has been shown with this study.

A Physics-Based Neural-Network Way to Perform Seismic Full Waveform Inversion

Seismic full waveform inversion is a common technique that is used in the investigation of subsurface geology. Its classic implementation involves forward modeling of seismic wavefield based on a certain type of wave equation, which reflects the physics nature of subsurface seismic wavefield propagation. However, obtaining a good inversion result using traditional seismic waveform inversion methods usually comes with a high computational cost. Recently, with the emerging popularity of deep learning techniques in various computer vision tasks, deep neural network (DNN) has demonstrated an impressive ability in dealing with complex nonlinear problems, including seismic velocity inversion. Now, extensive efforts have been made in developing a DNN architecture to tackle the problem of seismic velocity inversion, and promising results have been achieved. However, due to the dependence of a labeled dataset, i.e., the barely accessible true velocity model corresponding to real seismic data, the current supervised deep learning inversion framework may suffer from limitations on generalization. One possible solution to mitigate this issue is to impose the governing physics into this kind of purely data-driven method. Thus, following the procedures of traditional seismic full waveform inversion, we propose a seismic waveform inversion network, namely SWINet, based on wave-equation-based forward modeling network cells. By treating the single-shot observation data and its corresponding shot position as training data pairs, the inverted velocity model can be obtained as the trainable network parameters. Moreover, since the proposed seismic waveform inversion method is performed in a neural-network way, its implementation and inversion effect could benefit from some built-in tools in Pytorch, such as automatic differentiation, Adam optimizer and mini-batch strategy, etc. Numerical examples indicate that the SWINet method may possess great potential in resulting a good velocity inversion effect with relatively fast convergence and lower computation cost.

Improving the least-squares image by using angle information to avoid cycle skipping

In the past few decades, the least-squares reverse time migration (LSRTM) algorithm has been widely used to enhance images of complex subsurface structures by minimizing the data misfit function between the predicted and observed seismic data. However, this algorithm is sensitive to the accuracy of the migration velocity model, which, in the case of real data applications (generally obtained via tomography), always deviates from the true velocity model. Therefore, conventional LSRTM faces a cycle-skipping problem caused by a smeared image when using an inaccurate migration velocity model. To address the cycle-skipping problem, we have introduced an angle-domain LSRTM algorithm. Unlike the conventional LSRTM algorithm, our method updates the common source-propagation angle image gathers rather than the stacked image. An extended Born modeling operator in the common source-propagation angle domain is was derived, which reproduced kinematically accurate data in the presence of velocity errors. Our method can provide more focused images with high resolution as well as angle-domain common-image gathers (ADCIGs) with enhanced resolution and balanced amplitudes. However, because the velocity model is not updated, the provided image can have errors in depth. Synthetic and field examples are used to verify that our method can robustly improve the quality of the ADCIGs and the finally stacked images with affordable computational costs in the presence of velocity errors.

A simple inversion algorithm to estimate a linearly increasing velocity model for microseismic monitoring

Microseismic monitoring is used to optimise shale gas production or enhanced geothermal stimulation. The technical tools for microseismic monitoring, which is a passive seismic method, are similar to those used in earthquake detection, but differ in that the target area is much smaller than areas affected by earthquakes. Therefore, it is important to use an accurate velocity model. However, such models require conducting an additional survey, which can be both expensive and time-consuming. Many microseismic monitoring studies have used an approximated velocity model constructed from well logging data to reduce these additional costs. In this study, we used a simple approximated model in which velocity increases linearly with depth and creates an accurate velocity model, eliminating the need for an additional survey. We analytically derived formulas for seismic ray traveltime and inverted the velocity gradient using the Gauss–Newton method. Using a numerical example, we verified that the proposed algorithm accurately describes the long-wavelength trend of the true velocity model in a negligibly short time. We performed a Monte Carlo simulation to evaluate the effects of traveltime picking errors. The simulation results indicated that the proposed algorithm provides a reasonable solution under the probable uncertainty of traveltime picking. Finally, we verified that our algorithm was not sensitive to the initial velocity gradient through inversion tests using various initial values. Thus, the numerical example and analysis confirm that the proposed algorithm is efficient and robust.

Ray-tracing traveltime tomography versus wave-equation traveltime inversion for near-surface seismic land data

Full-waveform inversion of land seismic data tends to get stuck in a local minimum associated with the waveform misfit function. This problem can be partly mitigated by using an initial velocity model that is close to the true velocity model. This initial starting model can be obtained by inverting traveltimes with ray-tracing traveltime tomography (RT) or wave-equation traveltime (WT) inversion. We have found that WT can provide a more accurate tomogram than RT by inverting the first-arrival traveltimes, and empirical tests suggest that RT is more sensitive to the additive noise in the input data than WT. We present two examples of applying WT and RT to land seismic data acquired in western Saudi Arabia. One of the seismic experiments investigated the water-table depth, and the other one attempted to detect the location of a buried fault. The seismic land data were inverted by WT and RT to generate the P-velocity tomograms, from which we can clearly identify the water table depth along the seismic survey line in the first example and the fault location in the second example.

The Garden Banks model experience

To better understand deepwater imaging challenges in the Gulf of Mexico, we constructed a large 3D model based on the complex salt geology of the Garden Banks protraction area. We simulated a regional wide-azimuth (WAZ) streamer survey with offsets of ±8 km inline and ±4 km crossline over this model. Using the true velocity model, reverse time migration of this data set produced a usable subsalt image nearly everywhere. The same synthetic seismic data set was passed to interpreters and geophysicists to process and image as if it were real field data. They did not get to see the true velocity model. Instead they performed conventional “migrate, pick, and flood” top-down velocity-model building, followed by final imaging through their interpreted velocity model. Where the salt was relatively simple, we found that the interpreted velocity model was reasonably accurate. Reverse time migration of the seismic data through these parts of the velocity model produced an image that was imperfect, but still usable for exploration-scale, structural interpretation. Where the salt structure was complex, however, it was sometimes grossly misinterpreted. The ensuing large-scale errors in the interpreted velocity model resulted in an unusable, shattered subsalt image. We next simulated a low-frequency, ocean-bottom-node (OBN) acquisition, with offsets up to 30 km in all azimuths. We started with the imperfect model produced by the interpreters and investigated what it would take for full-waveform inversion (FWI) to successfully find and fix the gross interpretation errors. Initial results suggest this “interpretation followed by FWI” methodology could produce a velocity model capable of generating an adequate subsalt image, but it may require ultrawide offsets (30 km), ultralow frequencies (below 2 Hz), and improved FWI algorithms to do so.

Application of frequency-domain waveform inversion method in Marmousi shots data

Frequency-domain waveform seismic tomography includes modeling of wave propagation and full waveform inversion of correcting the initial velocity model. In the forward modeling, we use direct solution based on sparse matrix factorization, combined with nine-point finite-difference for the linear system of equations. In the waveform inversion, we use preconditioned gradient method where the preconditioner is provided by the diagonal of the approximate Hessian matrix. We successfully applied waveform inversion method from low to high frequency in two sets of Marmousi data. One is the data set generated by frequency-domain finite-difference modeling, and the other is the original Marmousi shots data set. The former result is very close to the true velocity model. In the original shots data set inversion, we replace the prior source with estimated source; the result is also acceptable, and consistent with the true model.

Non-uniqueness of waveform inversions in the Laplace domain

The non-uniqueness of the solution is one of the major obstacles for a successful full waveform inversion. This paper shows that there are at least two solutions for waveform inversions in the Laplace domain: the true velocity model; the long-wavelength background velocity model. The Laplace domain inversion can recover the true velocity model if provided with an accurate initial model, but it will instead result in a smooth long-wavelength velocity model if the initial model is inaccurate and smooth. In this case, the inverted long-wavelength velocity model can still be used for either migration or as an initial velocity model for frequency domain waveform inversion.

Local Angle Domain Target Oriented Illumination Analysis and Imaging Using Beamlets

AbstractPrestack depth migration has been widely used for seismic imaging recently. However, the imaging of sub‐salt structure is still a hard issue even in true velocity model. Here, we use local angle domain target oriented illumination analysis to study how the acquisition geometry affects the image quality, especially for some reflectors with certain dip angle in the sub‐salt area. Numerical tests based on 2D SEG/EAGE salt model help us to better understand the capability of prestack migration under the given acquisition system. This analysis can also provide us an easy and efficient way to do target‐oriented migration for the given reflector.

Migration velocity analysis using the common image cube (CIC)

Migration velocity analysis (MVA) is commonly performed in the image domain in conjunction with ray-based tomography to update the velocity model. This approach can be challenging in the presence of large velocity errors as it may require many MVA iterations before converging to a model that can focus the events in the image domain. We introduced a downward continuation-based domain for carrying out MVA that is more flexible than conventional domains. This approach consists of two steps: (1) forming the common image cube (CIC) and (2) modeling the Green’s functions. In the first step, the cross-correlation imaging condition is relaxed to produce more than the zero lag common image gather (CIG). Slicing these data at different lags forms a series of CIGs, whereas a conventional CIG can be obtained by slicing the cube at the zero lag. When the velocity model used for the migration differs from the true velocity model, properly flattened events may occur in CIGs other than the zero lag. In the second step, for each event on the CIG, we picked the cross-correlation lag and depth at which it flattens best. For each event, we modeled a Green’s function by seeding a source at the focusing depth using one-way wave-equation modeling. This process is then repeated for other events at different lateral positions. The result is a set of Green’s functions whose wavefield approximates the ones that would have been generated if the correct velocity model was used to simulate these gathers. The updated Green functions are easier to work with than the raw data as they have less noise. Wavefield tomography can then be applied on these data-driven, modeled Green’s functions to build the final velocity model. Tests on synthetic and real 2D data confirm the method’s effectiveness in building velocity models in complex structural areas with large lateral velocity variations.

Two-dimensional Laplace-domain waveform inversion using adaptive meshes: an experience of the 2004 BP velocity-analysis benchmark data set

SUMMARY To delineate the Earth's structure precisely by time- or frequency-domain waveform inversions, an appropriate initial model that contains long-wavelength structures of the true model is essential. A Laplace-domain waveform inversion, which can provide a smooth velocity model that is equivalent to a long-wavelength velocity model from scratch, was recently proposed. The Laplace-domain waveform inversion can be used for obtaining a good initial model for full-waveform inversions. To improve the applicability of the 2-D Laplace-domain waveform inversion to field data, we adopted the adaptive finite element not only to deal with sources and receivers at shallow depths but also to reduce the computational burden using larger elements below the sources and receivers. For the boundary condition on the bounded domain for the Laplace-domain modelling and inversion, the unique property of the Laplace-domain wavefield, which was damped rapidly from a source, was taken into account. The computational domain was extended further from a source and then the Dirichlet boundary condition was applied to the outer edges of the extended model. With these two adaptations, our Laplace-domain waveform inversion could then be tested on a very large 2004 BP velocity-analysis benchmark data set. Numerical tests of the BP model, which contains three salt domes of high-velocity contrast, were conducted on a self-made synthetic data set by Laplace-domain modelling and a time-domain original data set. For the two data sets, a Laplace-domain waveform inversion using the adaptive mesh successfully provided a smooth velocity model that contained long-wavelength structures of the true velocity model. The smooth velocity model obtained by the Laplace-domain waveform inversion was used as a good initial model for the frequency-domain waveform inversion of the original BP data set. The resulting frequency-domain inversion recovered almost every feature of the salt domes except for some subsalt structures.

Migration velocity analysis by double path-integral migration

The idea of path-integral imaging is to sum over the migrated images obtained for a set of migration velocity models. Velocities where common-image gathers align horizontally are stationary, thus favoring these images in the overall stack. The overall image forms with no knowledge of the true velocity model. However, the velocity information associated with the final image can be determined in the process. By executing the path-integral imaging twice and weighting one of the stacks with the velocity value, the stationary velocities that produce the final image can then be extracted by a division of the two images. The velocity extraction, interpola-tion, and smoothing can be done fully automatically, without the need for human interpretation or other intervention. A numerical example demonstrated that quantitative information about the migration velocity model can be determined by double path-integral migration. The so-obtained velocity model can then be used as a starting model for subsequent velocity analysis tools like migration velocity analysis or tomographic methods.

Crosshole seismic tomography: working solutions to issues in real data travel time inversion

In travel time inversion of crosshole seismic tomography, when dealing with real data, the following three issues need to be addressed: how to suppress the effect of data errors, how to balance the data contribution and reference model, and how to properly set the geological constraints (well logs) in an inversion. Signal-to-noise ratios of travel time data picked from real crosshole seismic surveys likely depend on the vertical offset between a source and a receiver, since the overall attenuation will typically be greater for a longer ray path. Therefore, to suppress the effect of data errors in a least-squares solution, a data confidence matrix is used in practice where the weighting is set logically based on the vertical offset. When a model constraint is adopted in the inversion to seek a solution with least deviation from some prescribed background that is most likely to have no spurious structure, a trade-off parameter is used to explicitly balance the dependence of the inversion solution to the data contribution and the reference model. The latter is built by combining sonic logging information, which is hard geological evidence at the vicinity of wells, and an initial estimate from the travel time back-projection, a preliminary solution of the travel time tomography. Geological constraints are set so that the inversion solution should have the least deviation from the hard geological evidence, and more deviation for the remaining part of the survey region, since the true velocity model might differ from such an initial estimate and the true ray paths might deviate from the initial ray paths.

Tau migration and velocity analysis: Theory and synthetic examples

Prestack migration velocity analysis in the time domain reduces the velocity‐depth ambiguity usually hampering the performance of prestack depth‐migration velocity analysis. In prestack τ migration velocity analysis, we keep the interval velocity model and the output images in vertical time. This allows us to avoid placing reflectors at erroneous depths during the velocity analysis process and, thus, avoid slowing down its convergence to the true velocity model. Using a 1D velocity update scheme, the prestack τ migration velocity analysis performed well on synthetic data from a model with a complex near‐surface velocity. Accurate velocity information and images were obtained using this time‐domain method. Problems occurred only in resolving a thin layer where the low resolution and fold of the synthetic data made it practically impossible to estimate velocity accurately in this layer. This 1D approach also provided us reasonable results for synthetic data from the Marmousi model. Despite the complexity of this model, the τ domain implementation of the prestack migration velocity analysis converged to a generally reasonable result, which includes properly imaging the elusive top‐of‐the‐reservoir layer.

Automatic cross‐well tomography by semblance and differential semblance optimization: theory and gradient computation

A technique for automatic cross‐well tomography based on semblance and differential semblance optimization is presented. Given a background velocity, the recorded seismic data traces are back‐propagated towards the source, i.e. shifted towards time zero using the modelled traveltime between the source and the receiver and corrected for the geometrical spreading. Therefore each back‐propagated trace should be a pulse, close to time zero. The mismatches between the back‐propagated traces indicate an error in the velocity model. This error can be measured by stacking the back‐propagated traces (semblance optimization) or by computing the norm of the difference between adjacent traces (differential semblance optimization).It is known from surface seismic reflection tomography that both the semblance and differential semblance functional have good convexity properties, although the differential semblance functional is believed to have a larger basin of attraction (region of convergence) around the true velocity model. In the case of the cross‐well transmission tomography described in this paper, similar properties are found for these functionals.The implementation of this automatic method for cross‐well tomography is based on the high‐frequency approximation to wave propagation. The wavefronts are constructed using a ray‐tracing algorithm. The gradient of the cost function is computed by the adjoint‐state technique, which has the same complexity as the computation of the functional. This provides an efficient algorithm to invert cross‐well data. The method is applied to a synthetic data set to demonstrate its efficacy.