## Publications

197 results found

Robins TC, Cueto C, Cudeiro J,
et al., 2023, Dual-Probe Transcranial Full-Waveform Inversion: A Brain Phantom Feasibility Study, *ULTRASOUND IN MEDICINE AND BIOLOGY*, Vol: 49, Pages: 2302-2315, ISSN: 0301-5629

Warner M, Nangoo T, Umpleby A,
et al., 2023, Automated salt model building: From compaction trend to final velocity model using waveform inversion, *Leading Edge*, Vol: 42, Pages: 196-206, ISSN: 1070-485X

Conventional seismic velocity model building in complicated salt-affected areas requires the explicit identification of salt boundaries in migrated images and typically involves testing of possible subsurface scenarios through multiple generations. The resulting velocity models are slow to generate and may contain interpreter-driven features that are difficult to verify. We show that it is possible to build a full final velocity model using advanced forms of full-waveform inversion applied directly to raw field data, starting from a model that contains only a simple 1D compaction trend. This approach rapidly generates the final velocity model and migrates processed reflection data at least as accurately as conventionally generated models. We demonstrate this methodology using an ocean-bottom-node data set acquired in deep water over Walker Ridge in the Gulf of Mexico. Our approach does not require exceptionally long offsets or the deployment of special low-frequency sources. We restrict the inversion so it does not use significant energy below 3 Hz or offsets longer than 14 km. We use three advanced forms of waveform inversion to recover the final model. The first is adaptive waveform inversion to proceed from models that begin far from the true model. The second is nonlinear reflection waveform inversion to recover subsalt velocity structure from reflections and their long-period multiples. The third is constrained waveform inversion to produce salt- and sediment-like velocity floods without explicitly identifying salt boundaries or velocities. In combination, these three algorithms successively improve the velocity model so it fully predicts the raw field data and accurately migrates primary reflections, though explicit migration forms no part of the workflow. Thus, model building via waveform inversion is able to proceed from field data to the final model in just a few weeks. It entirely avoids the many cycles of model rebuilding that may otherwise be required.

Yao J, Warner M, Wang Y, 2023, Regularization of anisotropic full waveform inversion with multiple parameters by adversarial neural networks, *Geophysics*, Vol: 88, Pages: R95-R103, ISSN: 0016-8033

The anisotropic full waveform inversion (FWI) is a seismic inverse problem for multiple parameters, that aims to simultaneously reconstruct the vertical velocity and the anisotropic parameters of the Earth's subsurface. This multiparameter inverse problem suffers from two issues. First, the objective function of the data fitting is less sensitive to the anisotropic parameters. Second, the crosstalk effect between the different parameters worsens the model update in the iterative inversion. We proposed to statistically regularize the anisotropic FWI using Wasserstein adversarial networks, which penalize the Wasserstein distance between the distribution of the current model parameters and that of the parameters at the borehole locations. The proposed regularizer can mitigate the problems of anisotropic FWI with multiple parameters. Therefore, the method can also be applied to other inverse problems with multiple parameters.

Chrapkiewicz K, Paulatto M, Heath BA,
et al., 2022, Magma Chamber Detected Beneath an Arc Volcano With Full-Waveform Inversion of Active-Source Seismic Data, *GEOCHEMISTRY GEOPHYSICS GEOSYSTEMS*, Vol: 23

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- Citations: 2

Cudeiro-blanco J, Cueto C, Bates O,
et al., 2022, DESIGN AND CONSTRUCTION OF A LOW-FREQUENCY ULTRASOUND ACQUISITION DEVICE FOR 2-D BRAIN IMAGING USING FULL-WAVEFORM INVERSION, *ULTRASOUND IN MEDICINE AND BIOLOGY*, Vol: 48, Pages: 1995-2008, ISSN: 0301-5629

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- Citations: 6

Debens HA, Knodel D, Mancini F, et al., 2022, Semi-global multi-parameter FWI using public cloud HPC, Pages: 932-936, ISSN: 1052-3812

This paper explores the potential for hyperscale public cloud high-performance compute (HPC) to enable efficient deployment of a semi-global approach to multi-parameter full-waveform inversion (FWI) over large areas. We introduce several novel aspects to semi-global FWI that improve convergence and suppress crosstalk, while establishing that the algorithm's embarrassingly parallel nature is well suited for public cloud implementation. We describe how various public cloud services can be taken advantage of to reduce the cost of the inversion and provide a reference architecture for the deployment of semi-global FWI to the Amazon Web Services (AWS) platform. Finally, we apply semi-global FWI to raw data from a large-scale legacy surface seismic dataset acquired offshore Australia as part of a re-processing sequence undertaken recently. Our results demonstrate that semi-global FWI can be effectively parallelized across more than one million logical central processing units (CPUs) and is able to recover an anisotropic velocity model in a few hours and in an automated fashion.

Warner M, Armitage J, Umpleby A, et al., 2022, Full-elastic AVA extraction using acoustic FWI, Pages: 907-911, ISSN: 1052-3812

We demonstrate that accurate amplitude-vs-angle parameters can be extracted from raw unprocessed seismic data using purely acoustic full-waveform inversion. The resultant parameters incorporate the full elastic response of the observed data, and it is not necessary to use elastic FWI in order to determine AVA. This approach naturally corrects for a multitude of other amplitude effects including reflector geometry and transmission losses, and it deals correctly with near-critical and post-critical reflections. FWI-based workflows are consequently simpler than conventional workflows, and AVA parameters can normally be generated by FWI within days of raw field data first becoming available.

Yao J, Warner M, Wang Y, 2022, Generating surface-offset common-image gathers with backward wavefield synthesis, *GEOPHYSICS*, Vol: 87, Pages: S129-S135, ISSN: 0016-8033

Warner M, Armitage J, Umpleby A, et al., 2022, AVO DETERMINATION USING ACOUSTIC FWI, Pages: 2054-2058

We demonstrate that purely acoustic FWI, run at true amplitude, can be used to extract accurate AVO parameters using offset-restricted subsets of raw unprocessed seismic data. Rather than producing conventional AVO parameters directly, acoustic FWI instead produces AVO anomalies showing the departure of the input data from the AVO displayed by a purely acoustic model. It is trivial to transform this into conventional AVO. AVO extraction via acoustic FWI applied to elastic synthetic data show that the AVO recovery using acoustic FWI is near perfect. When combined with full-bandwidth FWI, this approach removes any requirement for conventional data processing, model building, explicit migration or Kirchhoff-based AVO extraction. A final depth-migrated reflectivity volume, and accurate AVO parameters, can both be generated purely by acoustic FWI.

Davy R, Frahm L, Bell R,
et al., 2021, Generating high‐fidelity reflection images directly from full‐waveform inversion: Hikurangi Subduction Zone case study, *Geophysical Research Letters*, Vol: 48, Pages: 1-10, ISSN: 0094-8276

Full-waveform inversion (FWI) can resolve subsurface physical properties to high resolutions, yet high-performance computing resources have only recently made it practical to invert for high frequencies. A benefit of high-frequency FWI is that recovered velocity models can be differentiated in space to produce high-quality depth images (FWI images) of a comparable resolution to conventional reflection images.Here, we demonstrate the generation of high-fidelity reflection images directly from the FWI process. We applied FWI up to 38 Hz to seismic data across the Hikurangi subduction margin. The resulting velocity models and FWI images reveal a complex faulting system, sediment deformation, and bottom-simulating reflectors within the shallow accretionary prism. Our FWI images agree with conventional reflection images and better resolve horizons around the Pāpaku thrust fault. Thus, FWI imaging has the potential to replace conventional reflection imaging whilst also providing physical property models that assist geological interpretations.

Warner M, Nangoo T, Umpleby A, et al., 2021, Adaptive reflection waveform inversion: Faster, tighter, deeper, smarter, Pages: 582-586, ISSN: 1052-3812

We demonstrate that an appropriate combination of adaptive waveform inversion (AWI) (Guasch et al., 2019), kinematic reflection waveform inversion (RWI) (Warner et al., 2018), and quantum particle-swarm global optimization (qPSO) (Debens et al., 2015), is able to generate accurate well-resolved velocity models from unprocessed raw field data. We begin from simple one-dimensional starting models, we use minimal human intervention, and we recover velocity models, that are both kinematically accurate and highly resolved in space, to depths that lie well below the deepest penetration of refracted arrivals. Using this approach, refractions, reflections and multiples all contribute to the quality of the final velocity model. We demonstrate the efficacy of this approach using a realistic blind synthetic dataset in 2D, and using the corresponding reflection-dominated narrow-azimuth 3D field dataset that served, in part, as the motivation and archetype for the synthetic. For the field data, we demonstrate a close match to a blind well that penetrates below the refracted arrivals. This approach can build final velocity models in a small fraction of the time required for conventional depth velocity-model building. We show three types of inversion: (1) simple vanilla FWI which evolves towards local minima, leading to mis-convergence when starting far from the true answer, (2) AWI which increase the region of convexity that surrounds the global minimum, and (3) AWI-RWI which targets residual timing errors and that has explicit sensitivity to reflection moveout and so is able to recover deep macro-model velocity reflection updates.

Nangoo T, Shah N, Lin T, et al., 2021, Accurate velocities and reduced cycle times from cloud-enabled full waveform inversion using XWI (AWI and RWI)

The central objective of advanced Full Waveform Inversion is to enable rapid turnaround of accurate velocities directly from raw seismic data. AWI with its convolutional filter-based residual represents a fundamental change in the way FWI is normally run, as an 'add on' to time-consuming velocity- model building performed on preprocessed data, where its role is to finesse a tomography starting model. Here we show the combined solution of AWI and RWI known collectively as XWI serves as a predictor for unseen drilling logs. The inversion is run on raw data from NW Australia (6 sailline validation test) demonstrating convergence to essentially the same result from two simple 1D starting models. It is able to predict deviations in a sonic log from a starting position over 1000 m/s away from the measured value. The cloud environment where XWI ingests traces directly from blob storage consists of a dynamic pool of interruptible compute instances. This allows for cost-effective frequency sweeps through the iterations and scalable hyperparameter scans. It also is configured for interfacing XWI with interactive processing software for seamless trace preparation and project start up.

Guasch L, Calderon Agudo O, Tang M-X,
et al., 2020, Full-waveform inversion imaging of the human brain, *npj Digital Medicine*, Vol: 3, Pages: 1-12, ISSN: 2398-6352

Magnetic resonance imaging and X-ray computed tomography provide the two principal methods available for imaging the brain at high spatial resolution, but these methods are not easily portable and cannot be applied safely to all patients. Ultrasound imaging is portable and universally safe, but existing modalities cannot image usefully inside the adult human skull. We use in silico simulations to demonstrate that full-waveform inversion, a computational technique originally developed in geophysics, is able to generate accurate three-dimensional images of the brain with sub-millimetre resolution. This approach overcomes the familiar problems of conventional ultrasound neuroimaging by using the following: transcranial ultrasound that is not obscured by strong reflections from the skull, low frequencies that are readily transmitted with good signal-to-noise ratio, an accurate wave equation that properly accounts for the physics of wave propagation, and adaptive waveform inversion that is able to create an accurate model of the skull that then compensates properly for wavefront distortion. Laboratory ultrasound data, using ex vivo human skulls and in vivo transcranial signals, demonstrate that our computational experiments mimic the penetration and signal-to-noise ratios expected in clinical applications. This form of non-invasive neuroimaging has the potential for the rapid diagnosis of stroke and head trauma, and for the provision of routine monitoring of a wide range of neurological conditions.

Agudo OC, da Silva NV, Stronge G,
et al., 2020, Mitigating elastic effects in marine 3-D full-waveform inversion, *GEOPHYSICAL JOURNAL INTERNATIONAL*, Vol: 220, Pages: 2089-2104, ISSN: 0956-540X

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- Citations: 7

Guasch L, Agudo OC, Tang MX, et al., 2020, Full-waveform inversion of transmitted ultrasound to image the human brain, Pages: 3517-3521, ISSN: 1052-3812

We demonstrate that acoustic full-waveform inversion (FWI), using transmitted ultrasound, is able to reconstruct accurate high-resolution images of the human brain in three dimensions in a way that would be entirely familiar to most geophysicists. Imaging the brain through the bones of the skull has close analogies to imaging sedimentary sequences beneath complex salt bodies. Here we use adaptive waveform inversion to build the skull, and use conventional FWI to recover the brain, a similar approach to that used for sub-salt imaging. This new form of non-invasive neuroimaging has the potential for rapid diagnosis of stroke and head trauma, and for the routine monitoring of a wide range of neurological conditions.

Heath BA, Hooft EEE, Toomey DR,
et al., 2019, Tectonism and Its Relation to Magmatism Around Santorini Volcano From Upper Crustal <i>P</i> Wave Velocity, *JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH*, Vol: 124, Pages: 10610-10629, ISSN: 2169-9313

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- Citations: 19

da Silva NV, Yao G, Agudo ÒC, et al., 2019, 3D elastic semi-global waveform inversion – estimation of Vp to Vs ratio, Pages: 1440-1444, ISSN: 1052-3812

Elastic FWI depends upon an accurate estimate of a constraining Vp to Vs ratio. Such a relation can be obtained empirically from rock-physics relations or from the analysis of the seismic data. The first is case-dependent and the second requires intense human intervention. Herein, we report a new method for a semi-automatic estimation of Vp to Vs ratios from seismic data requiring only a waveform inversion algorithm and minimal data intervention. We show synthetic examples and a real-data case study.

Debens HA, Nangoo T, Mancini F, et al., 2019, Penetrating below the diving waves with RWI, AWI, and FWI: A NWS Australia case study

© 81st EAGE Conference and Exhibition 2019. All rights reserved. FWI has become a standard in velocity model building, however standalone FWI has not. To address this, FWI is brought into the model building sequence earlier by alternating RWI and AWI to recover the long-wavelength acoustic velocity model that is usually built by ray-based tomography. The corresponding long-wavelength anisotropy model is extracted using semi-global FWI. Least-squares FWI then has an adequate starting point to commence introducing the full range of length scales into the final model. The outcome is a high-resolution velocity model bypassing tomography, which penetrates over a kilometre deeper than the turning point of the deepest diving waves.

Debens HA, Nangoo T, Mancini F, et al., 2019, Penetrating below the diving waves with RWI, AWI, and FWI: A NWS Australia case study

FWI has become a standard in velocity model building, however standalone FWI has not. To address this, FWI is brought into the model building sequence earlier by alternating RWI and AWI to recover the long-wavelength acoustic velocity model that is usually built by ray-based tomography. The corresponding long-wavelength anisotropy model is extracted using semi-global FWI. Least-squares FWI then has an adequate starting point to commence introducing the full range of length scales into the final model. The outcome is a high-resolution velocity model bypassing tomography, which penetrates over a kilometre deeper than the turning point of the deepest diving waves.

Debens HA, Nangoo T, Mancini F, et al., 2019, Penetrating below the diving waves with RWI, AWI, and FWI: A NWS Australia case study

© 81st EAGE Conference and Exhibition 2019. All rights reserved. FWI has become a standard in velocity model building, however standalone FWI has not. To address this, FWI is brought into the model building sequence earlier by alternating RWI and AWI to recover the long-wavelength acoustic velocity model that is usually built by ray-based tomography. The corresponding long-wavelength anisotropy model is extracted using semi-global FWI. Least-squares FWI then has an adequate starting point to commence introducing the full range of length scales into the final model. The outcome is a high-resolution velocity model bypassing tomography, which penetrates over a kilometre deeper than the turning point of the deepest diving waves.

Yao J, Guasch L, Warner M, et al., 2019, Removing elastic effects in FWI using supervised cycled generative adversarial networks

© 81st EAGE Conference and Exhibition 2019 Workshop Programme. All rights reserved. We use a CycleGAN to map acoustic synthetic data to elastic data, and to map elastic field data to acoustic data, and use the resulting data to perform acoustic FWI on a 3D field dataset that shows strong elastic effects at top chalk. Using machine learning to change the effective physics of field data has many other potential applications.

Warner M, Nangoo T, Pavlov A, et al., 2019, Extending the velocity resolution of waveform inversion below the diving waves using AWI

© 81st EAGE Conference and Exhibition 2019. All rights reserved. The combination of conventional FWI and adaptive waveform inversion is used to invert a broad-band narrow azimuth shallow-water towed-streamer dataset, recovering an accurate velocity model, to 20 Hz, above, within and below high velocity chalk to a total depth of around 5000 m. FWI alone cannot achieve this depth of penetration from this dataset.

Hooft EEE, Heath BA, Toomey DR,
et al., 2019, Corrigendum to “Seismic imaging of Santorini: Subsurface constraints on caldera collapse and present-day magma recharge” [Earth Planet. Sci. Lett. 514 (2019) 48–61], *Earth and Planetary Science Letters*, Vol: 515, Pages: 291-291, ISSN: 0012-821X

Hooft EEE, Heath BA, Toomey DR,
et al., 2019, Seismic imaging of Santorini: subsurface constraints on caldera collapse and present-day magma recharge, *Earth and Planetary Science Letters*, Vol: 514, Pages: 48-61, ISSN: 0012-821X

Volcanic calderas are surface depressions formed by roof collapse following evacuation of magma from an underlying reservoir. The mechanisms of caldera formation are debated and predict differences in the evolution of the caldera floor and distinct styles of magma recharge. Here we use a dense, active source, seismic tomography study to reveal the sub-surface physical properties of the Santorini caldera in order to understand caldera formation. We find a ∼3-km-wide, cylindrical low-velocity anomaly in the upper 3 km beneath the north-central portion of the caldera, that lies directly above the pressure source of the 2011-2012 inflation. We interpret this anomaly as a low-density volume caused by excess porosities of between 4% and 28%, with pore spaces filled with hot seawater. Vents that were formed during the first three phases of the 3.6 ka Late Bronze Age (LBA) eruption are located close to the edge of the imaged structure. The correlation between older volcanic vents and the low-velocity anomaly suggests that this feature may be long-lived. We infer that collapse of a limited area of the caldera floor resulted in a high-porosity, low-density cylindrical volume, which formed by either chaotic collapse along reverse faults, wholesale subsidence and infilling with tuffs and ignimbrites, phreatomagmatic fracturing, or a combination of these processes. Phase 4 eruptive vents are located along the margins of the topographic caldera and the velocity structure indicates that coherent down-drop of the wider topographic caldera followed the more limited collapse in the northern caldera. This progressive collapse sequence is consistent with models for multi-stage formation of nested calderas along conjugate reverse and normal faults. The upper crustal density differences inferred from the seismic velocity model predict differences in subsurface gravitational loading that correlate with the location of 2011-2012 edifice inflation. This result supports the hypothesis th

Guasch L, Warner M, Ravaut C, 2019, Adaptive waveform inversion: practice, *Geophysics*, Vol: 84, Pages: R447-R461, ISSN: 0016-8033

Adaptive waveform inversion (AWI) reformulates the misfit function used to perform full-waveform inversion (FWI), so that it no longer contains local minima related to cycle skipping. It does this by finding a model that drives the ratio of the predicted and observed data sets to unity rather than driving the difference between these two data sets to zero as is the case for conventional FWI. We apply AWI to a 3D field data set acquired over a pervasive gas cloud in the North Sea, comparing its performance with that of conventional FWI in a variety of circumstances. When starting inversion from 3 Hz, and using a good starting model obtained from reflection tomography, FWI and AWI generate similar models although the FWI result contains edge artifacts that are not produced by AWI. However, when the starting frequency is increased to approximately 6 Hz, or when the starting model is less accurate, FWI fails to recover a good model whereas AWI continues to converge. When both of these conditions apply, FWI fails comprehensively, leading to a model that is significantly worse than the starting model, whereas the AWI result remains largely unaffected. We applied Kirchhoff depth migration to the fully-processed data using the FWI result obtained following reflection tomography, and using the AWI result obtained from a simple one-dimensional starting model. We use the resulting migrated volumes, together with measures of residual moveout throughout the volume, to show that the AWI result from a simple starting model is at least as good as the FWI result obtained following tomography. We conclude that AWI is robust in the presence of cycle skipping on this 3D field data set, and can proceed successfully from a less-accurate starting model, and from a higher starting frequency, in circumstances in which FWI fails completely.

Yao G, da Silva NV, Warner M,
et al., 2019, Tackling cycle skipping in full-waveform inversion with intermediate data, *GEOPHYSICS*, Vol: 84, Pages: R411-R427, ISSN: 0016-8033

Da Silva NV, Yao G, Warner M, 2019, Semiglobal viscoacoustic full-waveform inversion, *Geophysics*, Vol: 84, Pages: R271-R293, ISSN: 0016-8033

© The Authors. Full-waveform inversion deals with estimating physical properties of the earth's subsurface by matching simulated to recorded seismic data. Intrinsic attenuation in the medium leads to the dispersion of propagating waves and the absorption of energy - media with this type of rheology are not perfectly elastic. Accounting for that effect is necessary to simulate wave propagation in realistic geologic media, leading to the need to estimate intrinsic attenuation from the seismic data. That increases the complexity of the constitutive laws leading to additional issues related to the ill-posed nature of the inverse problem. In particular, the joint estimation of several physical properties increases the null space of the parameter space, leading to a larger domain of ambiguity and increasing the number of different models that can equally well explain the data. We have evaluated a method for the joint inversion of velocity and intrinsic attenuation using semiglobal inversion; this combines quantum particle-swarm optimization for the estimation of the intrinsic attenuation with nested gradient-descent iterations for the estimation of the P-wave velocity. This approach takes advantage of the fact that some physical properties, and in particular the intrinsic attenuation, can be represented using a reduced basis, substantially decreasing the dimension of the search space. We determine the feasibility of the method and its robustness to ambiguity with 2D synthetic examples. The 3D inversion of a field data set for a geologic medium with transversely isotropic anisotropy in velocity indicates the feasibility of the method for inverting large-scale real seismic data and improving the data fitting. The principal benefits of the semiglobal multiparameter inversion are the recovery of the intrinsic attenuation from the data and the recovery of the true undispersed infinite-frequency P-wave velocity, while mitigating ambiguity between the estimated parameters.

Da Silva NV, Yao G, Warner M, 2019, Wave modeling in viscoacoustic media with transverse isotropy, *Geophysics*, Vol: 84, Pages: C41-C56, ISSN: 0016-8033

© 2019 Society of Exploration Geophysicists. We have developed a derivation of a system of equations for acoustic waves in a medium with transverse isotropy (TI) in velocity and attenuation. The equations are derived from Cauchy's equation of motion, and the constitutive law is Hooke's generalized law. The anisotropic anelasticity is introduced by combining Thomsen's parameters with standard linear solids. The convolutional term in the constitutive law is eliminated by the method of memory variables. The resulting system of partial differential equations is second order in time for the pseudopressure fields and for the memory variables. We determine the numerical implementation of this system with the finite-difference method, with second-order accuracy in time and fourth-order accuracy in space. Comparison with analytical solutions, and modeling examples, demonstrates that our modeling approach is capable of capturing TI effects in intrinsic attenuation. We compared our modeling approach against an alternative method that implements the constitutive law of an anisotropic visco-acoustic medium, with vertical symmetry, in the frequency domain. Modeling examples using the two methods indicate a good agreement between both implementations, demonstrating a good accuracy of the method introduced herein. We develop a modeling example with realistic geologic complexity demonstrating the usefulness of this system of equations for applications in seismic imaging and inversion.

Agudo ÓC, Vieira Da Silva N, Warner M,
et al., 2018, Addressing viscous effects in acoustic full-waveform inversion, *Geophysics*, Vol: 83, Pages: R611-R628, ISSN: 0016-8033

In conventional full-waveform inversion (FWI), viscous effects are typically neglected, and this is likely to adversely affect the recovery of P-wave velocity. We have developed a strategy to mitigate viscous effects based on the use of matching filters with the aim of improving the performance of acoustic FWI. The approach requires an approximate estimate of the intrinsic attenuation model, and it is one to three times more expensive than conventional acoustic FWI. First, we perform 2D synthetic tests to study the impact of viscoacoustic effects on the recorded wavefield and analyze how that affects the recovered velocity models after acoustic FWI. Then, we apply the current method on the generated data and determine that it mitigates viscous effects successfully even in the presence of noise. We find that having an approximate estimate for intrinsic attenuation, even when these effects are strong, leads to improvements in resolution and a more accurate recovery of the P-wave velocity. Then, we implement and develop our method on a 2D field data set using Gabor transforms to obtain an approximate intrinsic attenuation model and inversion frequencies of up to 24 Hz. The analysis of the results indicates that there is an improvement in terms of resolution and continuity of the layers on the recovered P-wave velocity model, leading to an improved flattening of gathers and a closer match of the inverted velocity model with the migrated seismic data.

Da Silva NV, Yao G, Warner M, 2018, Semi-global inversion of v<inf>p</inf> to v<inf>s</inf> ratio for elastic wavefield inversion, *Inverse Problems*, Vol: 34, ISSN: 0266-5611

© 2018 IOP Publishing Ltd. We introduce an approach to estimate the ratio between P- and S-wave velocities, v p/v s, in the scope of elastic full waveform inversion (FWI). Elastic FWI is generally implemented with local optimization methods relying on initial estimates of the long wavelengths of P- and S-wave models. However, successful inversions can be hindered if an accurate enough relation between v p and v s velocities is not used as a constraint. This relation can be estimated from empirical relations. Herein, we introduce an alternative approach based upon a semi-global inversion scheme. We observe that for a large number of cases, and particularly in the context of FWI, v p/v s can be represented on a sparse basis. This sparse basis has a much smaller dimension than that of the typical model space in elastic FWI. This creates the possibility of using global optimization methods. The optimal estimate of v p/v s is obtained with quantum particle swarm optimization (QPSO). This method probes a population of possible models. The assessment of each model of v p/v s in the population is obtained with nested local iterations updating for v p only. Conventional elastic FWI is then carried out for jointly estimating high-resolution models of v p and v s. We demonstrate with synthetic examples that the estimates of v p are relatively robust to errors in the estimated v p/v s, and that effectively a sparse representation of the model of v p/v s is feasible for the reconstruction of a model of v s. We also demonstrate that the proposed approach performs better than constraining elastic FWI with an empirical relation between v p and v s, leading to improved estimates of models of v p and v s from seismic data.

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