## Publications

143 results found

Agudo ÒC, Da Silva NV, Warner M,
et al., 2018, Acoustic full-waveform inversion in an elastic world, *Geophysics*, Vol: 83, Pages: R257-R271, ISSN: 0016-8033

© The Authors. Full-waveform inversion (FWI) is a technique used to obtain high-quality velocity models of the subsurface. Despite the elastic nature of the earth, the anisotropic acoustic wave equation is typically used to model wave propagation in FWI. In part, this simplification is essential for being efficient when inverting large 3D data sets, but it has the adverse effect of reducing the accuracy and resolution of the recovered P-wave velocity models, as well as a loss in potential to constrain other physical properties, such as the S-wave velocity given that amplitude information in the observed data set is not fully used. Here, we first apply conventional acoustic FWI to acoustic and elastic data generated using the same velocity model to investigate the effect of neglecting the elastic component in field data and we find that it leads to a loss in resolution and accuracy in the recovered velocity model. Then, we develop a method to mitigate elastic effects in acoustic FWI using matching filters that transform elastic data into acoustic data and find that it is applicable to marine and land data sets. Tests show that our approach is successful: The imprint of elastic effects on the recovered P-wave models is mitigated, leading to better-resolved models than those obtained after conventional acoustic FWI. Our method requires a guess of VP/VSand is marginally more computationally demanding than acoustic FWI, but much less so than elastic FWI.

Roth T, Nangoo T, Shah N, et al., 2018, Improving seismic image with high resolution velocity model from AWI starting with 1D initial model - case study barents sea

© 2017 European Association of Geoscientists and Engineers EAGE. All Rights Reserved. A feasibility study was carried out over a prospective structure in the south western Barents Sea, Norway. The need of a high fidelity velocity model to solve the complex velocity variations in the overburden was the driving mechanism for this test project. A shallow gas anomaly associated with amplitude dimming is causing distortions in imaging and leading to big uncertainty concerning fault identification within and mapping of this interval. Through a special application of FWI, the so-called adaptive waveform inversion (AWI) which allowed starting the inversion with a very simple velocity model, we solved the strong lateral velocity variations in the near surface leading to an improved image, demonstrating the superior quality provided by an AWI based velocity model.

Yao G, da Silva NV, Warner M,
et al., 2018, Separation of Migration and Tomography Modes of Full-Waveform Inversion in the Plane Wave Domain, *Journal of Geophysical Research: Solid Earth*, Vol: 123, Pages: 1486-1501, ISSN: 2169-9313

©2018. American Geophysical Union. All Rights Reserved. Full-waveform inversion (FWI) includes both migration and tomography modes. The migration mode acts like a nonlinear least squares migration to map model interfaces with reflections, while the tomography mode behaves as tomography to build a background velocity model. The migration mode is the main response of inverting reflections, while the tomography mode exists in response to inverting both the reflections and refractions. To emphasize one of the two modes in FWI, especially for inverting reflections, the separation of the two modes in the gradient of FWI is required. Here we present a new method to achieve this separation with an angle-dependent filtering technique in the plane wave domain. We first transform the source and residual wavefields into the plane wave domain with the Fourier transform and then decompose them into the migration and tomography components using the opening angles between the transformed source and residual plane waves. The opening angles close to 180° contribute to the tomography component, while the others correspond to the migration component. We find that this approach is very effective and robust even when the medium is relatively complicated with strong lateral heterogeneities, highly dipping reflectors, and strong anisotropy. This is well demonstrated by theoretical analysis and numerical tests with a synthetic data set and a field data set.

Agudo OC, Da Silva NV, Warner M, et al., 2017, Addressing viscous effects in acoustic full-waveform inversion

Seismic waves are attenuated and dispersed as they travel through the subsurface given that part of the energy is lost into heat. These effects are visible on the recorded seismic data but are commonly ignored when performing acoustic full-waveform inversion (FWI). As a result, the recovered P-wave velocity models are not as well resolved and are quantitatively less accurate. Here we analyse the impact of viscous effects in acoustic FWI of visco-acoustic synthetic data and we propose and apply a method to mitigate attenuation effects while still performing acoustic FWI, which is based on matching filters. We show that only a smooth model of attenuation is required to successfully improve the recovered P-wave velocity model, even when applied to a noisy synthetic dataset.

Arnoux GM, Toomey DR, Hooft EEE,
et al., 2017, Seismic evidence that black smoker heat flux is influenced by localized magma replenishment and associated increases in crustal permeability, *Geophysical Research Letters*, Vol: 44, Pages: 1687-1695, ISSN: 0094-8276

©2017. American Geophysical Union. All Rights Reserved. Hydrothermal circulation at mid-ocean ridges is responsible for ~25% of Earth's heat flux and controls the thermal and chemical evolution of young oceanic crust. The heat flux of black smoker hydrothermal systems is thought to be primarily controlled by localized magma supply and crustal permeability. Nevertheless, magma chamber characteristics and the nature of crustal permeability beneath such systems remain unclear. Here we apply three-dimensional full-waveform inversion to seismic data from the hydrothermally active Endeavour segment of the Juan de Fuca Ridge to image the upper crust in high resolution. We resolve velocity variations directly above the axial magma chamber that correlate with variations in seismicity, black smoker heat flux, and the depth of the axial magmatic system. We conclude that localized magma recharge to the axial magma lens, along with induced seismogenic cracking and increased permeability, influences black smoker heat flux.

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- Citations: 4

Da Silva NV, Yao G, Warner M, et al., 2017, Global visco-acoustic full waveform inversion

Full Waveform Inversion aims to determine parameters of the subsurface by minimising the misfit between the simulated and recorded seismic data. The quality of such fit depends on many different aspects, as for example, the inversion algorithm and the accuracy of the constitutive laws. The latter is particularly important as if there are factors that are not taken into account in the seismic simulation then the inversion algorithm will compensate for their existence in the parameter(s) being estimated. One of such factors is attenuation. Here we introduce an approach that jointly estimates velocity and attenuation using a combination of Quantum Particle Swarm Optimisation with the conventional gradient descent method. This hybrid approach takes advantage of the fact that it is sufficient to estimate smooth models of Q and for this reason these can be represented with a sparse support, thus decreasing substantially the number of weights of the basis functions that have to be estimated and making the use of global algorithms practical. We demonstrate that the proposed method mitigates cross-talk between velocity and attenuation, while allowing the convergence towards accurate models of attenuation and velocity, thus being an effective method for velocity model building and consequently for seismic imaging.

Ravaut C, Maaø FA, Mispel J, et al., 2017, Imaging beneath a gas cloud in the North Sea without conventional tomography

To reduce sensitivity of full-waveform inversion to cycle skipping, new objective functions have been introduced in the last couple of years. We here investigate the capability of adaptive waveform inversion (AWI) based on Wiener coefficients which we apply to a gas cloud field in the North Sea. The objective of this work is to evaluate if AWI can start from a simple 1D like initial velocity model and produce reasonable migrated images. To do so we compare the results from FWI starting from a well-defined reflection tomography model with the results derived from AWI starting from a simple 1D initial model. The quality of the results is evaluated using RMO cubes derived from 3D Kirchhoff PSDM common image gathers. We here demonstrate that, in this gas-cloud context, AWI is able to reconstruct a well resolved velocity in the gas cloud starting from the 1D like model. The quality of the P-wave velocity model is better than the velocity model derived from tomography and similar to the one derived by tomography plus FWI. For this case, we show that AWI could replace tomography for model building thus reducing the project duration.

Yao G, Da Silva N, Warner M, et al., 2017, Improved FWI convergence using efficient receiver-side Spatial preconditioning employing ray theory

Spatial preconditioning can improve the convergence of full-waveform inversion (FWI) significantly. An accurate spatial preconditioning consists of the contribution of both the source and receivers. Prohibited by the unfordable computational cost of directly forming the receiver spatial preconditioning, source-only spatial preconditioning using the energy of the incident source wavefield is typically used to precondition the gradient of FWI. Although this is an efficient means of spatial preconditioning, the quality of the inversion result is still compromised. To improve the quality of spatial preconditioning, we here approximate the receiver spatial preconditioning using ray theory since ray tracing is much faster than numerically solving the two-way wave equation directly. In order to maintain the same time cycle as the inversion without receiver spatial preconditioning, we use an additional compute node to calculate the receiver spatial preconditioning in parallel with other compute nodes used for the usual gradient computation. The effectiveness is demonstrated by applying this technique to the Marmousi model.

Yao J, Guasch L, Warner M, 2017, Convergence regions for AWI and FWI

Cycle-skipping is the most significant local minimum FWI suffers in practice, while adaptive waveform inversion (AWI) provides a new waveform-inversion scheme which is robust against cycle-skipping. In this paper, we present an extensive test exploring the convergence properties of both FWI and AWI against cycle-skipping. A set of 1300 initial models are designed by progressively smoothing the Marmousi model and by bulk shifting its mean slowness. The convergence regions of FWI and AWI are mapped based on the recovered models of both approaches. AWI shows a convergence region broader than FWI. It succeeds refining the initial models to the global minimum which FWI cannot.

Agudo OC, da Silva NV, Warner M, et al., 2016, Acoustic full-waveform inversion in an elastic world, Pages: 1058-1062, ISSN: 1052-3812

© 2016 SEG. Despite the elastic nature of the earth, wave propagation in the subsurface is normally modeled using the acoustic anisotropic wave equation, in part due to the requirement to be efficient when dealing with large 3D datasets. This simplification has a negative effect on the quality of recovered P-wave models, as it means that amplitude information in the observed data cannot be fully utilized when applying full-waveform inversion (FWI) (Warner et al., 2013). We examine the consequences of using an acoustic wave propagator in two synthetic examples, and we propose a method to mitigate elastic effects in acoustic FWI based on matching filters. We find that our proposed approach is successful: the recovered P-wave models are better resolved than those obtained using conventional acoustic FWI.

Esser E, Guasch L, Herrmann FJ,
et al., 2016, Constrained waveform inversion for automatic salt flooding, *Leading Edge*, Vol: 35, Pages: 235-239, ISSN: 1070-485X

© 2016 by The Society of Exploration Geophysicists. Given appropriate data acquisition, processing to remove nonprimary arrivals, and use of an accurate migration algorithm, it is the quality of the subsurface velocity model that typically controls the quality of imaging that can be obtained from salt-affected seismic data. Full-waveform inversion has the potential to improve the accuracy, resolution, repeatability, and speed with which such velocity models can be generated, but, in the absence of an accurate starting model, that potential is difficult to realize in practice. Presented are successful inversion results, obtained from synthetic subsalt models, using a robust full-waveform inversion code that includes constraints upon the set of allowable earth models. These constraints include limitations on the total variation of the velocity of the model and, most significantly, on the asymmetric variation of velocity with depth such that negative velocity excursions are limited. During the iteration, these constraints are relaxed progressively so that the final model is driven principally by the seismic data, but the constraints act to steer the inversion path away from local minima in its early stages. This methodology is applied to portions of the 2004 BP benchmark and Phase I SEAM salt models, recovering an accurate model of the salt body, including its base and flanks, and an accurate model of the subsalt velocity structure, starting from one-dimensional velocity models that are severely cycle skipped. This approach removes entirely the requirement to pick salt boundaries from migrated seismic data, and acts as a form of automatic salt and sediment flooding during full-waveform inversion.

Guasch L, Warner M, Herrmann FJ, 2016, Constrained waveform inversion - Automatic salt flooding with inclusions

The quality of the subsurface velocity model is most often the limiting factor in salt-affected seismic imaging. FWI can potentially improve the accuracy and resolution of such models, but realising this can be difficult in practice. Here we present constrained FWI results, using data from synthetic sub-salt models. We include constraints upon the set of allowable earth models; these include limitations upon the total variation norm of the velocity of the model, and upon the variation of velocity with depth such that negative velocity excursions are controlled. These constraints are progressively relaxed during iteration so that the final results are dominated by the data mismatch. The constraints act to steer the inversion towards geologically realistic models. We have applied this approach to a modified version of the SEAM salt model where we have introduced salt inclusions and a re-entrant structure at top salt. We are able to recover an accurate model of the dirty salt body starting from a one-dimensional velocity model.

Irabor K, Warner M, 2016, Reflection FWI, Pages: 1136-1140, ISSN: 1052-3812

© 2016 SEG. We demonstrate that FWI can successfully recover all wavelengths within a velocity model using as input only raw, multiple-contaminated, short-offset, reflection data. To do this, we isolate the tomographic and migration aspects of FWI based upon the direction of travel of the forward and residual wavefields, we alternate migrationlike and tomography-like FWI iterations, and we do not retain the migration component between iterations. We follow this alternating scheme by conventional reflection FWI to recover the full-bandwidth velocity model.

Morgan J, Warner M, Arnoux G,
et al., 2016, Next-generation seismic experiments - II: wide-angle, multi-azimuth, 3-D, full-waveform inversion of sparse field data, *GEOPHYSICAL JOURNAL INTERNATIONAL*, Vol: 204, Pages: 1342-1363, ISSN: 0956-540X

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Silverton A, Warner M, Morgan J,
et al., 2016, Offset-variable density improves acoustic full-waveform inversion: a shallow marine case study, *GEOPHYSICAL PROSPECTING*, Vol: 64, Pages: 1201-1214, ISSN: 0016-8025

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Warner M, Guasch L, 2016, Adaptive waveform inversion: Theory, *GEOPHYSICS*, Vol: 81, Pages: R429-R445, ISSN: 0016-8033

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- Citations: 11

Burgess T, Warner M, 2015, Preconditioning FWI with approximate receiver Green's functions, Pages: 1116-1121, ISSN: 1052-3812

© 2015 SEG. Preconditioning of full-waveform inversion (FWI) using approximations to the inverse Hessian is well established. Different approximations to the Hessian give different rates of convergence and therefore, given that the iteration count is typically limited by available compute resources, different levels of quality in the final results. In this paper, we demonstrate a low-cost, general-purpose, diagonal Hessian approximation which includes factors related to the receiver Green's functions and provides significant uplift in image quality compared to approximations not including these factors.

Debens HA, Warner M, Umpleby A, et al., 2015, Global anisotropic 3D FWI, Pages: 1193-1197, ISSN: 1052-3812

© 2015 SEG. Seismic anisotropy influences both the kinematics and dynamics of seismic waveforms. If anisotropy is not adequately taken into account during full-waveform seismic inversion (FWI), then inadequacies in the anisotropy model are likely to manifest as significant error in the recovered P-wave velocity model. Conventionally, anisotropic FWI uses either a fixed anisotropy model derived from tomography or such, or it uses a local inversion scheme to recover the anisotropy as part of the FWI; both of these methods can be problematic. In this paper, we show that global rather than local FWI can be used to recover the long-wavelength anisotropy model, and that this can then be followed by more-conventional local FWI to recover the detailed model. We demonstrate this approach on a full 3D field dataset, and show that it avoids problems associated to cross-talk that can bedevil local inversion schemes. Although our method provides a global inversion of anisotropy, it is nonetheless affordable and practical for 3D field data.

Debens HA, Warner MR, Umpleby A, 2015, Global anisotropic FWI, Pages: 4052-4056

Seismic anisotropy influences both the kinematics and dynamics of seismic waveforms. As such, if not taken into account properly during multi-parameter full-waveform seismic inversion (FWI), the anisotropy can manifest itself as significant error in the recovered P-wave velocity model. With this in mind we demonstrate a hybrid local-global inversion scheme to extract the low-wavenumber component of the anisotropy in combination with a high-resolution P-wave velocity model. This can then be followed by conventional local inversion for one or both parameters. Our results demonstrate that this technique suppresses the cross-talk between anisotropy and velocity, whilst producing more accurate final models for both parameters.

Esser E, Herrmann F, Guasch L, et al., 2015, Constrained waveform inversion in salt-affected datasets, Pages: 1086-1090, ISSN: 1052-3812

© 2015 SEG. We have developed an accurate and robust methodology that is capable of inverting seismic data in salt-affected environments, to obtain a highly resolved velocity model, without the use of travel-time tomography or explicit salt flooding, in circumstances where conventional full-waveform inversion (FWI) and similar approaches fail. A reflection-driven inversion, in combination with total variation (TV) constraints applied to the adaptive waveform inversion (AWI) objective function, provides the building blocks required to recover both long and short-wavelength velocity models in such environments.

Guasch L, Burgess T, Warner M, 2015, Optimised adaptive waveform inversion - Improved convergence via conjugate gradients and superior step-length calculation, Pages: 4062-4066

The insensitivity of Adaptive Waveform Inversion (AWI) to cycle-skipped local minima in the solution space makes it a robust alternative to conventional full waveform inversion when neither good starting models nor low frequencies are available. Despite the absence of such local minima in AWI, steepestdescent optimisation methods used with simple line searches, converge slowly as a result of non-linearity between residuals and model parameters. In this paper, we show that an improved step-length calculation, and use of conjugate gradients, generate shorter paths that require fewer iterations to reach the vicinity of the global minimum, reaching the desired solution much more rapidly, and opening opportunities to apply this technique to raw field data with little prior knowledge of the velocity structure.

Warner M, Guasch L, 2015, Adaptive waveform inversion using incomplete physics, imperfect data, and an incorrect source, Pages: 4057-4061

Adaptive waveform inversion (AWI) provides a means of performing full-waveform inversion (FWI) that appears to be immune to the effects of cycle skipping. However, the form of the AWI algorithm suggests that it could have increased sensitivity to errors in the assumed source wavelet, to noise in the field data, and to inadequacies in the physics used to simulate wave propagation. We examine each of these for a synthetic model. We show that AWI is in fact less sensitive than FWI to errors in the source wavelet, and is no more sensitive to errors in the data and in the modelling than is FWI. It appears likely that the immunity that AWI displays to cycle skipping also contributes to its reduced sensitivity to errors in the assumed source wavelet.

Warner M, Guasch L, 2015, Robust adaptive waveform inversion, Pages: 1059-1063, ISSN: 1052-3812

© 2015 SEG. Adaptive Waveform Inversion (AWI) was introduced by Warner & Guasch (2014) as a means to avoid cycle skipping during full-waveform inversion. Here we demonstrate the robustness of this new method by applying it to three challenging problems: a 3D field dataset without an accurate velocity model to start the inversion; a highly realistic blind synthetic dataset that contains elastic effects, attenuation, an unknown density model and ambient noise; and a simple synthetic dataset where the inversion proceeds using the wrong source wavelet. AWI outperforms conventional FWI in each of these applications, and remains stable and accurate throughout.

Yao G, Debens HA, Umpleby A, et al., 2015, Adaptive Finite Difference for Seismic Wavefield Modelling, 77th EAGE Conference and Exhibition 2015

Yao G, Debens HA, Umpleby A, et al., 2015, Adaptive finite difference for seismic wavefield modelling, Pages: 650-654

We present an alternative scheme for calculating finite difference coefficients in seismic wavefield modelling. This novel technique seeks to minimise the difference between the accurate value of spatial derivatives and the value calculated by the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method maximises the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods whilst comparable to Zhang's optimised finite difference method.

Yao G, Warner M, 2015, Bootstrapped waveform inversion: Longwavelength velocities from pure reflection data, Pages: 4067-4071

Conventional FWI cannot successfully invert pure reflection data to recover the long-wavelength velocity model. We present an FWI methodology that can solve this problem, and demonstrate its success inverting data from a simple but difficult-to-invert synthetic model. The method proceeds by modifying the FWI objective function, and by interleaving a migration-like form of FWI with a tomography-like form. Starting from a constant-velocity, this FWI approach produces a full-bandwidth velocity model that accurately depth migrates the reflection data.

Guasch L, Warner M, 2014, Adaptive waveform inversion -FWI without cycle skipping -Applications, Pages: 3970-3974

Conventional FWI suffers from cycle skipping if the starting model is inadequate at the lowest frequencies present in a dataset. The newly developed technique of adaptive FWI overcomes cycle skipping, and is able to invert normal bandwidth data beginning from an inaccurate velocity model. Here we apply the method to data extracted from a 3D field model, and show that the new method outperforms conventional FWI when starting at higher frequencies than have previously been used to invert this field dataset. We also apply the new methodology to a synthetic dataset that is not cycle skipped, but that is dominated by reflected rather than refracted arrivals. In this case, we show that adaptive FWI also produces a superior result because it has enhanced sensitivity to reflection data, and is able to update the velocity macro-model successfully using reflection-only data.

Silverton A, Warner M, Umpleby A, et al., 2014, Non-physical water density as a proxy to improve data fit during acoustic FWI, Pages: 4135-4139

Major uplift in imaging is evident when migration is performed with a FWI velocity model for a North Sea hydrocarbon field. However, a small but significant, systematic mismatch in travel-time remains between the field data and synthetic data predicted using the final FWI model. However we perturb the model, the source, the number of iterations, the end result invariably returns to give the same final mismatch in which the predicted data are late. We know that both the synthetic and field data contain strong water-bottom multiples, and these affect the duration, bandwidth and amplitude decay of the coda. However, the finitedifference representation of the velocity model does not contain the seabed explicitly. We propose changing the assumed density of the water layer, which changes the seabed reflection amplitudes without affecting other aspects of the data, thereby properly modelling the seabed reflectivity. The wave-train is in reality an interference pattern between several arrivals, and as the relative strength of those arrivals changes, the interference pattern changes, thereby better fitting the travel-times. We find that decreasing the density of seawater improves the fit to the field data, and that we have to reduce the density by a greater factor as offset increases.

Warner M, Guasch L, 2014, Adaptive waveform inversion: Theory, Pages: 1089-1093, ISSN: 1052-3812

© 2014 SEG. We present a new method for performing full-waveform inversion that appears to be immune to the effects of cycle skipping - Adaptive Waveform Inversion (AWI). The method uses Wiener filters to match observed and predicted data. The inversion is formulated so that the model is updated in the direction that drives these Wiener filters towards delta functions at zero lag, at which point the true model has been recovered. The method is computationally efficient, it appears to be universally applicable, and it recovers the correct model when conventional FWI fails entirely.

Warner M, Guasch L, 2014, Adaptive waveform inversion -FWI without cycle skipping -Theory, Pages: 3965-3969

Conventional FWI minimises the direct differences between observed and predicted seismic datasets. Because seismic data are oscillatory, this approach will suffer from the detrimental effects of cycle skipping if the starting model is inaccurate. We reformulate FWI so that it instead adapts the predicted data to the observed data using Wiener filters, and then iterates to improve the model by forcing the Wiener filters towards zero-lag delta functions. This adaptive FWI scheme is demonstrated on synthetic data where it is shown to be immune to cycle skipping, and is able to invert successfully data for which conventional FWI fails entirely. The new method does not require low frequencies or a highly accurate starting model to be successful. Adaptive FWI has some features in common with wave-equation migration velocity analysis, but it works for all types of arrivals including multiples and refractions, and it does not have the high computational costs of WEMVA in 3D.

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