Publications
197 results found
Yao G, Da Silva NV, Warner M, et al., 2018, Extraction of tomography mode for full-waveform inversion with non-stationary smoothing, 2018 SEG International Exposition and Annual Meeting, Pages: 1364-1368
© 2018 SEG. Full-waveform inversion (FWI) includes both migration and tomography modes. The tomographic component of the gradient from reflections usually is much weaker than the migration component. In order to use the tomography mode of FWI, it is necessary to extract the tomographic component from the gradient. We analyze the characteristics of wavenumbers of the migration and tomographic components, and then introduce a new method to extract the tomographic component based upon non-stationary smoothing. We demonstrate the effectiveness of the proposed method for enhancing the tomographic mode of FWI throughout theoretical analysis and numerical examples.
Calderon Agudo O, Vieira Da Silva N, Warner M, et al., 2018, Acoustic full-waveform inversion in an elastic world, Geophysics, Vol: 83, Pages: R257-R271, ISSN: 1942-2156
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/VS and is marginally more computationally demanding than acoustic FWI, but much less so than elastic FWI.Read More: https://library.seg.org/doi/10.1190/geo2017-0063.1
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.
Yao G, Shah N, Umpleby A, et al., 2018, High-resolution reflection FWI
We demonstrate reflection FWI on a less-than-ideal 3D narrow-azimuth towed-streamer dataset that contains little refracted energy and that is deficit in low frequencies. We begin from a very simple starting model built rapidly from stacking velocities. We fist use an FWI scheme that alternates between a migration-like and a tomography-like stage, showing that this can both recover the background velocity model and generate high vertical resolution. We follow this by using global inversion to build the long-wavelength anisotropy model. Finally, we use more-conventional reflection-based FWI to introduce the full range of wavelengths into the recovered velocity model, and show that this both migrates the reflection data and is structurally conformable with the reflections.
Yao G, Shah N, Umpleby A, et al., 2018, High-resolution reflection FWI
© 2018 Society of Petroleum Engineers. All rights reserved. We demonstrate reflection FWI on a less-than-ideal 3D narrow-azimuth towed-streamer dataset that contains little refracted energy and that is deficit in low frequencies. We begin from a very simple starting model built rapidly from stacking velocities. We fist use an FWI scheme that alternates between a migration-like and a tomography-like stage, showing that this can both recover the background velocity model and generate high vertical resolution. We follow this by using global inversion to build the long-wavelength anisotropy model. Finally, we use more-conventional reflection-based FWI to introduce the full range of wavelengths into the recovered velocity model, and show that this both migrates the reflection data and is structurally conformable with the reflections.
Jones I, Singh J, Cox P, et al., 2018, The evolution of tomography and FWI: An example of high resolution velocity estimation using refraction and reflection FWI
© 2018 80th EAGE Conference and Exhibition 2018 Workshop Programme. The primary objective of this project was to improve the understanding of the internal structure of the Viscata and Fortuna reservoirs, and this objective was met via clearer internal imaging of these reservoir intervals and the overlying gas-charged sediments. The underlying geophysical challenge was the presence of extensive, but small-scale low-velocity gas pockets, which gave rise to significant and cumulative image distortion at target level. This distortion had not been resolved in a vintage 2013 broadband preSDM project, as the velocity model was not sufficiently well resolved. But in the initial commercial phase of this project, high-resolution non-parametric tomography using improved broadband deghosted data enabled us to achieve the stated objectives. The follow-on work, considered here, deals with the use of full waveform inversion, to see if we could further delineate small-scale velocity anomalies, associated with the highly compartmentalized reservoir units.
Warner M, da Silva N, Kalinicheva T, et al., 2018, Separation of migration and tomography modes of full-waveform inversion in the plane-wave domain
© 2018 Society of Petroleum Engineers. All rights reserved. Full-waveform inversion (FWI) includes both migration and tomography modes. The migration mode acts like a non-linear least-squares migration, mapping model interfaces with reflections, while the tomography mode builds the 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 scattering angles between the transformed source and residual plane waves. Scattering angles close to 180° contribute to the tomography component, while the others correspond to the migration component. We found that this approach is very effective and robust even when the medium is relatively complicated with strong lateral heterogeneities, steeply dipping reflectors, and strong seismic anisotropy. This is well demonstrated by theoretical analysis, and numerical tests with synthetic and field datasets.
Guasch L, Lin T, Herrmann F, et al., 2018, Automated salt-model building using constrained FWI
© 2018 Society of Petroleum Engineers. All rights reserved. We apply full-waveform inversion to the full-scale 3D SEAM sub-salt dataset to recover the velocity model starting from a poor approximation to the true model. We use adaptive waveform inversion to provide robustness against cycle skipping, and constrain the model using both total variation and asymmetric hinge-loss total variation applied vertically. These constraints are gradually relaxed as the inversion proceeds. We are able to recover the salt model accurately to a depth of about 5000 m, including the rugose top of salt, salt welds and inclusions, salt flanks and over-hangs, and a slightly lower-velocity carapace lying immediately above the salt; we successfully recover migrated interfaces below base salt to depths of around 10,000m. The inversion uses frequencies between 2 and 7 Hz, includes surface multiples and ghosts in the input data, and does not commit inversion crime.
Jones IF, Singh J, Cox P, et al., 2018, High resolution velocity estimation using refraction and reflection fwi - the fortuna region, offshore Equatorial Guinea
The primary objective of this project was to improve the understanding of the internal structure of the Viscata and Fortuna reservoirs, and this objective was met via clearer internal imaging of these reservoir intervals and the overlying gas-charged sediments. The underlying geophysical challenge was the presence of extensive, but small-scale low-velocity gas pockets, which gave rise to significant and cumulative image distortion at target level. This distortion had not been resolved in a vintage 2013 broadband preSDM project, as the velocity model was not sufficiently well resolved. But in the initial commercial phase of this project, high-resolution non-parametric tomography using improved broadband deghosted data enabled us to achieve the stated objectives. The follow-on work, considered here, deals with the use of full waveform inversion, to see if we could further delineate small-scale velocity anomalies, associated with the highly compartmentalized reservoir units.
Cooke A, Selvage J, Jones I, et al., 2018, First EAGE/PESGB workshop on velocities
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
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.
Warner M, Stekl I, Umpleby A, 2018, 3D wavefield tomography: Synthetic and field data examples, Pages: 3330-3334
Full wavefield tomography has become well established in two dimensions, but its extension into 3D for realistically sized problems is computationally daunting. In this paper, we present one of the first studies to apply 3D wavefield tomography to field data, and demonstrate that the method can solve useful exploration problems that that are not tractable by other methods.
Kalinicheva T, Warner M, Ashley J, et al., 2017, Two- vs three-dimensional full-waveform inversion in a 3D world, SEG Technical Program Expanded Abstracts 2017, Publisher: Society of Exploration Geophysicists
Arnoux G, Toomey D, Hooft E, 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: 1944-8007
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 remains 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.
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., 2017, Addressing viscous effects in acoustic full-waveform inversion, Publisher: SOC EXPLORATION GEOPHYSICISTS, Pages: R611-R628, ISSN: 0016-8033
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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.
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.
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.
Warner M, Guasch L, 2016, Adaptive waveform inversion: theory, Geophysics, Vol: 81, Pages: R429-R445, ISSN: 0016-8033
Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.
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
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.
Morgan JV, Warner MR, 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: 1365-246X
3-D full-waveform inversion (FWI) is an advanced seismic imaging technique that has been widely adopted by the oil and gas industry to obtain high-fidelity models of P-wave velocity that lead to improvements in migrated images of the reservoir. Most industrial applications of 3-D FWI model the acoustic wavefield, often account for the kinematic effect of anisotropy, and focus on matching the low-frequency component of the early arriving refractions that are most sensitive to P-wave velocity structure. Here, we have adopted the same approach in an application of 3-D acoustic, anisotropic FWI to an ocean-bottom-seismometer (OBS) field data set acquired across the Endeavour oceanic spreading centre in the northeastern Pacific. Starting models for P-wave velocity and anisotropy were obtained from traveltime tomography; during FWI, velocity is updated whereas anisotropy is kept fixed. We demonstrate that, for the Endeavour field data set, 3-D FWI is able to recover fine-scale velocity structure with a resolution that is 2–4 times better than conventional traveltime tomography. Quality assurance procedures have been employed to monitor each step of the workflow; these are time consuming but critical to the development of a successful inversion strategy. Finally, a suite of checkerboard tests has been performed which shows that the full potential resolution of FWI can be obtained if we acquire a 3-D survey with a slightly denser shot and receiver spacing than is usual for an academic experiment. We anticipate that this exciting development will encourage future seismic investigations of earth science targets that would benefit from the superior resolution offered by 3-D FWI.
Agudo OC, da Silva NV, Warner M, et al., 2016, Acoustic full-waveform inversion in an elastic world, Pages: 1058-1062, ISSN: 1052-3812
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.
Irabor K, Warner M, 2016, Reflection FWI, Pages: 1136-1140, ISSN: 1052-3812
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.
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.
Silverton A, Warner M, Morgan J, et al., 2015, Offset-variable density improves acoustic full-waveform inversion: a shallow marine case study, Geophysical Prospecting, Vol: 64, Pages: 1201-1214, ISSN: 0016-8025
We have previously applied three-dimensional acoustic, anisotropic, full-waveform inversion to a shallow-water, wide-angle, ocean-bottom-cable dataset to obtain a high-resolution velocity model. This velocity model produced: an improved match between synthetic and field data, better flattening of common-image gathers, a closer fit to well logs, and an improvement in the pre-stack depth-migrated image. Nevertheless, close examination reveals that there is a systematic mismatch between the observed and predicted datafrom this full-waveform inversion model, with the predicted data being consistently delayed in time. We demonstrate that this mismatch cannot be produced by systematic errors in the starting model, by errors in the assumed source wavelet, by incomplete convergence, or by the use of an insufficiently fine finite-difference mesh. Throughout these tests, the mismatch is remarkably robustwith the significant exception that we do not see an analogous mismatch when inverting synthetic acoustic data. We suspect therefore that the mismatch arises because of inadequacies in the physics that are used during inversion. For ocean-bottom-cabledata in shallow water at low frequency, apparent observed arrival times, in wide-angle turning-ray data, result from the characteristics of the detailed interference pattern between primary refractions, surface ghosts, and a large suite of wide-angle multiple reflected and/or multiple refracted arrivals. In these circumstances, the dynamics of individual arrivals can strongly influence the apparent arrival times of the resultant compound waveforms. In acoustic full-waveform inversion, we do not normally know the density of the seabed, and we do not properly account for finite shear velocity, finite attenuation, and fine-scale anisotropy variation, all of which can influence the relative amplitudes of different interfering arrivals, which in their turn influence the apparent kinematics. Here, wedemonstrate that the introduction of
Yao G, Debens HA, Umpleby A, et al., 2015, Adaptive Finite Difference for Seismic Wavefield Modelling, 77th EAGE Conference and Exhibition 2015
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.
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.
Burgess T, Warner M, 2015, Preconditioning FWI with approximate receiver Green's functions, Pages: 1116-1121, ISSN: 1052-3812
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.
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