Starting Velocity Model Research Articles

A collocated inversion of sources and early arrival waveforms for credible tomograms: Synthetic and field data examples

AbstractWaveform inversion is theoretically a powerful tool to reconstruct subsurface structures, but a usually encountered problem is that accurate sources are very rare, causing the computation to be unstable or divergent. This challenging practical problem, although sometimes ignored and even imperceptible, can easily create discrepancies in calculated shot gathers, which will then lead to wrong residuals that will be smeared back to the gradients, hence jeopardizing the inverted tomograms. For any real dataset, every shot gather corresponds to its unique source even if some gathers can be transformed alike after data processing. To resolve this problem, we propose a collocated inversion of sources and early arrival waveforms with the two submodules executing successively. Not only can this method reconstruct a decent source wavelet that approaches the ground truth, but also it can produce credible background tomograms with optimized sources. Part of the cycle skipping problems can also be mitigated because it avoids the trial and error experiments on various sources. Numerical tests on a synthetic and a land dataset validate the effectiveness of this method. Restrictions on initial sources or starting velocity models will be relaxed, and this method can be extended to any other applications for engineering or exploration purposes.

3D frequency-domain acoustic full-waveform inversion using diffraction-angle filtering

The success of seismic imaging techniques such as full-waveform inversion (FWI) depends on using a good starting velocity model or a background velocity model, which can be effectively built by long-wavelength components in the early stages of FWI. This study proposes an optimal strategy for performing 3D frequency-domain FWI with diffraction-angle filtering (DAF). This approach can perform optimized single-frequency FWI with lower computational costs and build a long-wavelength velocity structure by separating low-wavenumber components with DAF. Prior to applying this strategy, we confirm the performance of 3D frequency-domain FWI with DAF in the radiation pattern analysis. DAF effectively separates the diffraction energy of partial derivative wavefields according to the diffraction angle with a negligible increase in computational costs. We then apply our 3D FWI strategy with DAF on synthetic data generated from the 3D SEG/EAGE overthrust model. The wavenumber components are effectively separated, and a long-wavelength velocity model is estimated with DAF compared to conventional FWI. Finally, we apply our strategy to 3D ocean-bottom seismic data from the North Sea. As a result, we observe that 3D FWI with the DAF method successfully reconstructs a long-wavelength velocity structure on the real data using only a single-frequency component.

Borehole acoustic full-waveform inversion

Full-waveform inversion (FWI) is a technique that has the potential for building high-resolution elastic velocity models. We apply this technique to wireline monopole acoustic logging data to image the near-wellbore formation velocity structures, which can be used in a fluid intrusion evaluation. Our FWI workflow is established in cylindrical coordinates instead of Cartesian coordinates to adapt to the borehole geometry. Assuming that the acoustic logging tool is centralized and formation properties are azimuthally invariant, we can simplify the problem to two dimensions in the inversion. Synthetic tests find that the high-resolution P- and S-wave velocity model around the borehole could be successfully inverted using FWI once a reasonable starting velocity model is given. However, borehole FWI differs from seismic FWI in that strong borehole-guided waves exist near the borehole wall due to the elastic effects. The borehole-guided waves have little sensitivity to velocity away from the borehole wall. In addition, it is difficult to simultaneously match the waveform of the body waves and guided waves in synthetic data and field data. Therefore, for field data applications, we propose to obtain the formation velocity structures around the borehole by FWI using only the first arrived P waves. The field data tests find that the proposed method is applicable for inverting the P-wave velocity structure around the borehole with a similar resolution compared with ray-tracing tomography. FWI may achieve higher resolution in field applications in the future with better assumptions made in the forward modeling and using more information in the field data.

Localized adaptive waveform inversion: regularizations for Gabor deconvolution and 3-D field data application

SUMMARYRecently, we have developed a localized adaptive waveform inversion (LAWI) method to tackle the cycle-skipping issue in velocity reconstruction through seismic waveform inversion. The LAWI method employs a local matching filter, computed using Gabor deconvolution, to measure the instantaneous time-shift between observed and calculated data. Unlike the adaptive waveform inversion (AWI) approach, the LAWI method can take the non-stationarity between observed and calculated data into account. In this work, we investigate two types of regularization based on prior information about the expected filter, which could be a minimum-norm filter or a delta-shape filter, with regard to their effects on the robustness and resolution of inversion. We demonstrate on synthetic data the advantages and disadvantages of these two types of prior information, where the delta-type LAWI may handle multiple observed phases not initially predicted by the starting velocity model. Therefore, we apply the delta-type LAWI to a high-quality 3-D field data set in the North Sea, eliminating the need for data-windowing tuning, which can be tedious and time-consuming for 3-D data. Under different workflows with varying reliable initial models and frequency bands of the pressure data considered, we show that the LAWI approach is robust, effective and efficient for reconstructing the P-wave velocity, while other approaches such as AWI and graph-space optimal-transport method may require meticulous data-tuning strategies to converge to the correct model. Well logs and data fits, primarily from early arrivals, give us confidence that this LAWI approach could be applied to various acquisitions and subsurface targets, thanks to its phase-driven principle.

Characterising ice slabs in firn using seismic full waveform inversion, a sensitivity study

AbstractThe density structure of firn has implications for hydrological and climate modelling, and ice-shelf stability. The structure of firn can be evaluated from depth models of seismic velocity, widely obtained with Herglotz–Wiechert inversion (HWI), an approach that considers the slowness of refracted seismic arrivals. However, HWI is strictly appropriate only for steady-state firn profiles and the inversion accuracy can be compromised where firn contains ice layers. In these cases, full waveform inversion (FWI) may yield more success than HWI. FWI extends HWI capabilities by considering the full seismic waveform and incorporates reflected arrivals. Using synthetic firn density profiles, assuming both steady- and non-steady-state accumulation, we show that FWI outperforms HWI for detecting ice slab boundaries (5–80 m thick, 5–80 m deep) and velocity anomalies within firn. FWI can detect slabs thicker than one wavelength (here, 20 m, assuming a maximum frequency of 60 Hz) but requires the starting velocity model to be accurate to ±2.5%. We recommend for field practice that the shallowest layers of velocity models are constrained with ground-truth data. Nonetheless, FWI shows advantages over established methods, and should be considered when the characterisation of firn ice slabs is the goal of the seismic survey.

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.

A variational approach for picking optimal surfaces from semblance-like panels

We propose and examine a variational method for determining optimal velocity fields from semblance-like volumes using continuation. The proposed approach finds a minimal-cost surface through a volume, which often corresponds to a velocity field within a semblance scan. This allows picked velocity fields to incorporate information from gathers that are spatially near the midpoint in question. The minimization process amounts to solving a nonlinear elliptic partial differential equation, which is accomplished by changing the elliptic problem to a parabolic one and solving it iteratively until it converges to a critical point which minimizes the cost functional. The continuation approach operates by using a variational framework to iteratively minimize the cost of a velocity surface through successively less-smoothed semblance scans. The method works because a global minimum for the velocity cost functional can only exist when the semblance scan varies smoothly in space and convexly in the parameter being scanned. Using a discretization of the functional with a limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm, we illustrate how the continuation approach is able to avoid local minima that would typically capture the iterative solution of an optimal velocity field determined without continuation by applying the method to seismic processing of a field data set from the Viking Graben. We then use a field data set from the Gulf of Mexico to show how the final velocity model determined by the method using continuation is largely independent of the starting velocity model, producing something resembling a global minimum. Finally, we demonstrate the versatility of the variational picking approach by using it to automatically interpret a seismic horizon from the Heidrun Field.

Joint Traditional and Reflection Envelope Inversion

The envelope inversion (EI) is an effective method to recover low-wavenumber components, which helps to produce a good initial model for full-waveform inversion (FWI). However, when the initial model is not capable of generating reflections, it brings enormous challenges for EI to invert deep low-wavenumber components, especially for short offset data. In contrast, reflection waveform inversion (RWI) uses demigration data to fit the observed reflection, which focuses on the transmission information with short offset seismic data. However, the cycle skipping and high nonlinearity of the RWI misfit still exist when the low-frequency information is absent. In this letter, we develop a joint traditional and reflection envelope inversion (JREI) that utilizes both reflection and transmission waves with envelope low-frequencies to recover low-wavenumber components in the shallow and deep regions simultaneously. We then use the FWI with high-frequency seismic data to obtain the high-wavenumber components. Applications to the modified Marmousi and Overthrust models demonstrate that the JREI can invert a better starting velocity model for the FWI to achieve a high-resolution inversion result.

Two-dimensional Time-domain Full Waveform Inversion of On-ground Common-offset GPR Data Based on Integral Preprocessing

Full waveform inversion (FWI) is an advanced inversion technique for ground penetrating radar (GPR), which could provide quantitative, high-resolution subsurface imaging. FWI has been used widely to process crosshole and on-ground multi-offset GPR data, but its application to on-ground common-offset GPR data is more difficult and being developed. This is mainly because that on-ground common-offset GPR has much less coverage of the subsurface and mainly includes reflective information. The application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Here, we demonstrate a means of achieving this successfully by preprocessing the observed data and the residual fields with an integral algorithm, which could produce a more reasonable gradient and therefore lead to better inversion results. Several cases verify the effectiveness of this method. We achieve the simultaneous inversion of relative permittivity and conductivity for on-ground common-offset GPR, and discuss the trade-off between permittivity and conductivity in details. According to the inversion results of test models, it seems that the inversion result of relative permittivity is more credible in most cases.

Frequency-domain reflection-based full waveform inversion for short-offset seismic data

The full waveform inversion (FWI) is a high-resolution algorithm used to invert accurate subsurface velocity models. However, inverting accurate velocity models from field data using the conventional FWI without an accurate long-wavelength starting velocity model is difficult. This difficulty occurs because of the band-limited frequency of the field seismic data and the acquisition geometry of the field seismic exploration. The low-frequency components and long-offset seismic data are essential for the inversion of the long-wavelength velocity model using the FWI. However, low-frequency signals are difficult to record from the field seismic exploration, and the maximum offset of the streamer is usually not sufficient in length. Therefore, the conventional FWI cannot easily invert the long-wavelength velocity from field seismic data but can invert the migration-like short-wavelength velocity, and it is subject to the problem of severe local minima. To invert the long-wavelength velocity from reflection-dominant, short-offset field seismic data, reflection-based full waveform inversion (RFWI) which decomposes the FWI gradient into high- and low-wavenumber components, is suggested. However, the conventional RFWI also contains high-wavenumber components, which obstruct long-wavelength velocity updates in the deep part of the model. Moreover, true amplitude migration and preprocessing to extract reflection signals from observed data are necessary for the conventional RFWI. In this study, a new frequency-domain RFWI algorithm, which uses wavefield separation and a two-step approach, is proposed. The wavefield separation divides the wavefield into up/down-going waves to remove the high-wavenumber component of the gradient and the two-step approach alternately updates the short- and long-wavelength velocities to reduce the computational cost. The effectiveness of the proposed algorithm is verified using the reflection-dominant, short-offset Marmousi synthetic seismic data and Tonga field seismic data.

Ambient Rayleigh wave field imaging of the critical zone in a weathered granite terrane

A 200 m wide square array of 400 vertical-component geophones was deployed three times to record the ambient seismic field at a 500 Hz sampling frequency. A geophone spacing of 10 m was used to target the near surface velocity structure and each array recorded for 3–4 days. Cross-correlation of the ambient seismic field produced cross-correlation functions from which fundamental-mode Rayleigh wave group delay times where picked in 59 narrow-bands from 14 to 130 Hz. The group delay times were inverted to make a set of 59 group velocity maps from 14 to 130 Hz. From the group velocity maps, dispersion curves were interpolated at 400 10 m spaced grid points to make data for 400 one-dimensional shear-velocity inversions. To find a best starting velocity model for the inversions, both linear gradient and half-space velocity models were explored. Our conclusion was that the half-space velocity models were the least prejudicial to the inverted form of our shear-velocity models. To find the best half-space velocity at each array inversion point, shear-velocity inversions were performed for a range of regularization values and half-space velocities from 500 to 2000 m/s. Joint inspection of the model-norm versus data-residual norm curves (‘L-curves’) and the shear-velocity models was performed to find smooth monotonically increasing velocity models that also have sharp L-curve corners. The resulting shear-velocity volumes find about 400 m/s near-surface velocities increasing to 700–800 m/s at 30 m depth which is our maximum depth of good resolution. Critical zone research generally defines the near-surface using three layers: the saprolite that includes the soil layer, the fractured bedrock, and the non-permeable bedrock also called the protolith. This work was able to image the base of the saprolite layer but not the base of the fractured bedrock layer. The saprolite thickness varies from 5–20 m and is generally thicker along the ridge with respect to the valleys. In summary, this work shows that high-frequency fundamental mode Rayleigh waves can be extracted from multi-day ambient seismic field recording to make images of near-surface shear-wave velocity.

Two robust imaging methodologies for challenging environments: Wave-equation dispersion inversion of surface waves and guided waves and supervirtual interferometry + tomography for far-offset refractions

Two robust imaging technologies are reviewed that provide subsurface geologic information in challenging environments. The first one is wave-equation dispersion (WD) inversion of surface waves and guided waves (GW) for the shear-velocity (S-wave) and compressional-velocity (P-wave) models, respectively. The other method is traveltime inversion for the velocity model, in which supervirtual refraction interferometry (SVI) is used to enhance the signal-to-noise ratio of far-offset refractions. We have determined the benefits and liabilities of both methods with synthetic seismograms and field data. The benefits of WD are that (1) there is no layered-medium assumption, as there is in conventional inversion of dispersion curves. This means that 2D or 3D velocity models can be accurately estimated from data recorded by seismic surveys over rugged topography, and (2) WD mostly avoids getting stuck in local minima. The liability is that WD for surface waves is almost as expensive as full-waveform inversion (FWI) and, for Rayleigh waves, only recovers the S-velocity distribution to a depth no deeper than approximately 1/2 to 1/3 wavelength of the lowest-frequency surface wave. The limitation for GW is that, for now, it can estimate the P-velocity model by inverting the dispersion curves from GW propagating in near-surface low-velocity zones. Also, WD often requires user intervention to pick reliable dispersion curves. For SVI, the offset of usable refractions can be more than doubled, so that traveltime tomography can be used to estimate a much deeper model of the P-velocity distribution. This can provide a more effective starting velocity model for FWI. The liability is that SVI assumes head-wave first arrivals, not those from strong diving waves.

Full waveform inversion with angle-dependent gradient preconditioning using wavefield decomposition

The main objective of the full waveform inversion (FWI) is to deliver a velocity model which produces accurate and high resolution depth images. An integral part of FWI is the iterative optimization process aiming at minimizing an objective function describing the misfit between the observed and modelled data with respect to the velocity model parameters. However, FWI commonly suffers from local minima due to errors in data fitting and the starting velocity model. In this study, we develop a methodology to enhance convergence and mitigate the risk of having solutions falling into local minima. We employ optical flow to decompose the source and residual receiver wavefields and map them into the subsurface angle domain. Having evaluated the propagation vectors of the respective cleaner wavefields, subsurface reflection and azimuth angles can be robustly computed. Using such information we can apply angle-dependent preconditioning within the inversion algorithm. During a conventional FWI workflow, larger angles (i.e., transmission wavepaths) are mainly responsible for long wavelength velocity anomalies whereas narrow angles (i.e., reflection wavepaths) influence short wavelength velocity anomalies. In the proposed FWI methodology, we apply an optimized weighting function based on these estimated subsurface reflection angles in order to weight certain angle directions needed for gradient estimation using in parameter updating. Following a hierarchical approach, allowing for larger angles at the early stage of the FWI application, we initially solve for the smooth and longer wavelength velocity updates. Relaxing the opening angle from large to mid to narrow, the gradient direction will first estimate long wavelength velocity model updates (transmission-based wavepaths), following by short wavelength velocity model updates (reflection-based wavepaths). Moreover, angle-dependent-based gradient preconditioning can reduce cycle skips and improve convergence during FWI iterations.

Application of full waveform inversion algorithms to seismic data lacking low-frequency information from a simple starting model

Full waveform inversion (FWI) is a method that is used to reconstruct velocity models of the subsurface. However, this approach suffers from the local minimum problem during optimisation procedures. The local minimum problem is caused by several issues (e.g. lack of low-frequency information and an inaccurate starting model), which can create obstacles to the practical application of FWI with real field data. We applied a 4-phase FWI in a sequential manner to obtain the correct velocity model when a dataset lacks low-frequency information and the starting velocity model is inaccurate. The first phase is Laplace-domain FWI, which inverts the large-scale velocity model. The second phase is Laplace-Fourier-domain FWI, which generates a large- to mid-scale velocity model. The third phase is a frequency-domain FWI that uses a logarithmic wavefield; the inverted velocity becomes more accurate during this step. The fourth phase is a conventional frequency-domain FWI, which generates an improved velocity model with correct values. The detailed methods of applying each FWI phase are explained, and the proposed method is validated via numerical tests with a SEG/EAGE salt synthetic dataset and Gulf of Mexico field dataset. The numerical tests show that the 4-phase FWI inverts the velocity correctly despite the lack of low-frequency information and an inaccurate starting velocity model both in synthetic data and field data.

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

Reflection full waveform inversion

Because of the combination of optimization algorithms and full wave equations, full-waveform inversion (FWI) has become the frontier of the study of seismic exploration and is gradually becoming one of the essential tools for obtaining the Earth interior information. However, the application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Compared to other types of seismic waves, reflections carry the information of the deep part of the subsurface. Reflection FWI, therefore, is able to improve the accuracy of imaging the Earth interior further. Here, we demonstrate a means of achieving this successfully by interleaving least-squares RTM with a version of reflection FWI in which the tomographic gradient that is required to update the background macro-model is separated from the reflectivity gradient using the Born approximation during forward modeling. This provides a good update to the macro-model. This approach is then followed by conventional FWI to obtain a final high-fidelity high-resolution result from a poor starting model using only reflection data. Further analysis reveals the high-resolution result is achieved due to a deconvolution imaging condition implicitly used by FWI.

Automatic early arrival traveltime tomography and its applications

We have developed a method of macrovelocity inversion that does not require explicit picking of either common-image point gathers or first breaks. The method uses head waves, diving waves, and wide-angle reflections in seismic data (collectively early arrival energies) for accurate estimation of velocity and anisotropy parameters. In this method, seismic data are first decomposed into Gaussian packets. Packets associated with early arrival energies are selected and used as input to a tomography solver. The outputs of the solver are velocity and Thomsen’s anisotropy parameters, or any of their combinations. Using information contained in the packets, we can correctly model the early arrival energies (first breaks and/or other refractions). The workflow is fully automatic and can be used in a batch processing environment with minimum human intervention. We have tested the method on synthetic and field data sets. In one synthetic test, we were able to reduce traveltime residuals of diving waves from 400 to 5 ms and recover anisotropic model parameters that are sensitive to early arrival traveltimes. In another synthetic test, we were able to recover a large shallow low-velocity anomaly with a very simple starting velocity model. The first field data set was for a shallow marine seismic data project. We were able to obtain a better shallow velocity model using our method than when using a legacy approach. In the second field data test, we applied our method on a deepwater data set from a dual-coil acquisition, with full-azimuth and long-offset coverage. Our method can correctly model early arrival energies recorded at long offsets and use them in the iterative inversion such that better estimation of velocities and anisotropy parameters in shallow sediments can be achieved. We have tested different starting models for the inversion. We are able to get very similar results, suggesting that our method is not sensitive to the accuracy of a starting model.

FWI for model updates in large-contrast media

We describe a new solution for recovering the long-wavelength features of a velocity model in gradient-based full-waveform inversion (FWI). The method uses reflected and transmitted wave modes to recover high-resolution velocity models. The new FWI gradient enables reliable velocity updates deeper than the maximum penetration depth of diving waves and reduces the FWI dependency on recording ultralong offsets. We also discuss a new FWI regularization scheme that overcomes the limitations of the inversion in the presence of high-contrast geobodies and cycle skipping. The solution utilizes a priori information about the earth model in the regularization as an extra term in the objective function. The implementation makes use of the split Bregman method, making it efficient and accurate. Results from applying the new FWI gradient to field data show that we can combine both transmitted and reflected energy in a global FWI scheme to obtain high-resolution velocity models without imprint of the reflectivity on the velocity updates. We illustrate the new regularization method's potential on the BP 2004 velocity benchmark model where our regularized FWI solution is capable of using a simple starting velocity model to deliver a high-quality reconstruction of salt bodies.

P and S wave tomography of Japan subduction zone from joint inversions of local and teleseismic travel times and surface-wave data

We determined P and S wave velocity tomography of the Japan subduction zone down to a depth of 700km by conducting joint inversions of a large number of high-quality arrival-time data of local earthquakes and teleseismic events which are newly collected for this study. We also determined 2-D phase-velocity images of fundamental mode Rayleigh waves at periods of 20–150s beneath Japan and the surrounding oceanic regions using amplitude and phase data of teleseismic Rayleigh waves. A detailed 3-D S-wave tomography of the study region is obtained by jointly inverting S-wave arrival times of local and teleseismic events and the Rayleigh-wave phase-velocity data. Our inversion results reveal the subducting Pacific and Philippine Sea slabs clearly as dipping high-velocity zones from a 1-D starting velocity model. Prominent low-velocity (low-V) anomalies are revealed in the mantle wedge above the slabs and in the mantle below the Pacific slab. The distinct velocity contrasts between the subducting slabs and the surrounding mantle reflect significant lateral variations in temperature as well as water content and/or the degree of partial melting. The low-V anomalies in the mantle wedge are attributed to slab dehydration and corner flows in the mantle wedge. A sheet-like low-V zone is revealed under the Pacific slab beneath NE Japan, which may reflect hot upwelling from the deeper mantle and subduction of a plume-fed asthenosphere as well. Our present results indicate that joint inversions of different seismic data are very effective and important for obtaining robust tomographic images of the crust and mantle.

Do we really need a very accurate starting velocity model for Full Waveform Inversion?

SUMMARY Full Waveform Inversion (FWI) has recently emerged as one of the most exciting new techniques in the seismic industry, with the potential to deliver incredibly detailed velocity models. We applied FWI to 2D lines from the Exmouth basin, Western Australia. Results showed that FWI can produce excellent high resolution velocity models even if the starting velocity model is far from perfect providing that the input data is rich in low frequencies