SEARCH · Engineering Papers

Results for “Critical Benchmarks”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,729 records · Page 96

All sources NASA NTRS DOE OSTI

DOE OSTI2016

Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: A data-driven, physics-informed Bayesian approach

Despite their well-known limitations, Reynolds-Averaged Navier–Stokes (RANS) models are still the workhorse tools for turbulent flow simulations in today's engineering analysis, design and optimization. While the predictive capability of RANS models depends on many factors, for many practical flows the turbulence models are by far the largest source of uncertainty. As RANS models are used in the design and safety evaluation of many mission-critical systems such as airplanes and nuclear power plants, quantifying their model-form uncertainties has significant implications in enabling risk-informed decision-making. In this work we develop a data-driven, physics-informed Bayesian framework for quantifying model-form uncertainties in RANS simulations. Uncertainties are introduced directly to the Reynolds stresses and are represented with compact parameterization accounting for empirical prior knowledge and physical constraints (e.g., realizability, smoothness, and symmetry). An iterative ensemble Kalman method is used to assimilate the prior knowledge and observation data in a Bayesian framework, and to propagate them to posterior distributions of velocities and other Quantities of Interest (QoIs). We use two representative cases, the flow over periodic hills and the flow in a square duct, to evaluate the performance of the proposed framework. Both cases are challenging for standard RANS turbulence models. Simulation results suggest that, even with very sparse observations, the obtained posterior mean velocities and other QoIs have significantly better agreement with the benchmark data compared to the baseline results. At most locations the posterior distribution adequately captures the true model error within the developed model form uncertainty bounds. The framework is a major improvement over existing black-box, physics-neutral methods for model-form uncertainty quantification, where prior knowledge and details of the models are not exploited. This approach has potential implications in many fields in which the governing equations are well understood but the model uncertainty comes from unresolved physical processes. - Highlights: • Proposed a physics–informed framework to quantify uncertainty in RANS simulations. • Framework incorporates physical prior knowledge and observation data. • Based on a rigorous Bayesian framework yet fully utilizes physical model. • Applicable for many complex physical systems beyond turbulent flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Virtual machine-based simulation platform for mobile ad-hoc network-based cyber infrastructure

In modeling and simulating complex systems such as mobile ad-hoc networks (MANETs) in de-fense communications, it is a major challenge to reconcile multiple important considerations: the rapidity of unavoidable changes to the software (network layers and applications), the difficulty of modeling the critical, implementation-dependent behavioral effects, the need to sustain larger scale scenarios, and the desire for faster simulations. Here we present our approach in success-fully reconciling them using a virtual time-synchronized virtual machine(VM)-based parallel ex-ecution framework that accurately lifts both the devices as well as the network communications to a virtual time plane while retaining full fidelity. At the core of our framework is a scheduling engine that operates at the level of a hypervisor scheduler, offering a unique ability to execute multi-core guest nodes over multi-core host nodes in an accurate, virtual time-synchronized manner. In contrast to other related approaches that suffer from either speed or accuracy issues, our framework provides MANET node-wise scalability, high fidelity of software behaviors, and time-ordering accuracy. The design and development of this framework is presented, and an ac-tual implementation based on the widely used Xen hypervisor system is described. Benchmarks with synthetic and actual applications are used to identify the benefits of our approach. The time inaccuracy of traditional emulation methods is demonstrated, in comparison with the accurate execution of our framework verified by theoretically correct results expected from analytical models of the same scenarios. In the largest high fidelity tests, we are able to perform virtual time-synchronized simulation of 64-node VM-based full-stack, actual software behaviors of MANETs containing a mix of static and mobile (unmanned airborne vehicle) nodes, hosted on a 32-core host, with full fidelity of unmodified ad-hoc routing protocols, unmodified application executables, and user-controllable physical layer effects including inter-device wireless signal strength, reachability, and connectivity.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2013

SystemBurn: Principles of Design and Operation Release 3.1

As high performance computing technology progresses toward the progressively more extreme scales required to address critical computational problems of both national and global interest, power and cooling for these extreme scale systems is becoming a growing concern. A standardized methodology for testing system requirements under maximal system load and validating system environmental capability to meet those requirements is critical to maintaining system stability and minimizing power and cooling risks for high end data centers. Moreover, accurate testing permits the high end data center to avoid issues of under- or over-provisioning power and cooling capacity saving resources and mitigating hazards. Previous approaches to such testing have employed an ad hoc collection of tools, which have been anecdotally perceived to produce a heavy system load. In this report, we present SystemBurn, a software tool engineered to allow a system user to methodically create a maximal system load on large scale systems for the purposes of testing and validation.

Benchmark↗

DOE OSTI2026

IER-620 CED-3b: Experiment Execution Summary for the Pulsed-Neutron Die-Away Experiments (PNDA) with Propylene Glycol and Mobilmet 423

There is a strong need for new benchmarks to validate neutron thermal scattering laws (TSLs). Lawrence Livermore National Laboratory (LLNL) has designed a Pulsed-Neutron Die Away (PNDA) testbed for this purpose. The experiment has a deuterium-tritium (D-T) neutron generator that impinges a 10 -4 s, mono-energetic pulse of 14.1 MeV neutrons on a target sample. After the pulse, the neutron population moderates and establishes a thermal equilibrium within the sample, with a fundamental spatial mode and characteristic decay-time eigenvalue, ⍺. The ⍺ eigenvalue can be extracted from the experimental measurements of the time-dependent neutron flux coming off the surface of the sample and can then be used as an integral parameter (similar to k eff ) to validate nuclear data involved with neutron migration, thermalization, and absorption. For moderating materials and geometric configurations, the ⍺ eigenvalue is heavily dependent on thermal neutron scattering of the target material. For that reason, a PNDA experiment can have a higher sensitivity to TSLs than is commonly available with the k eff parameter in critical experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Concentration and Recovery of Rare Earth Elements from Eastern US Coal Refuse

Recent studies funded by the US Department of energy have shown that coal and coal byproducts contain elevated contents of Rare Earth Elements (REEs), making them a potential resource for these critical materials. The approach employed in this research focused on the concentration and extraction of REEs from fine coal refuse derived from various preparation plants in the Appalachian coal basin of the United States. Initial efforts in this research focused on the identification and characterization of REEs in various fine coal refuse streams from nine distinct industrial preparation plants in Appalachia. The average REE content in these materials was determined to be approximately 200 ppm, but the REE content showed a strong correlation to the aluminum content, suggesting that the REEs are closely associated with the clay minerals present in the refuse. Given the relatively low REE concentrations, initial efforts sought to concentrate the REEs through decarbonization and dispersive liberation steps. In these tests, high-shear agitation in the presence of a polyelectrolyte, followed by sedimentation was able to isolate the REE-enriched fine clay particles from siliceous gangue minerals. Following the dispersive liberation step, all samples were found to have an REE content greater than 300 ppm, a benchmark used for many initial exploratory studies. In one case, the REE content was increased by more than 125%. Subsequent extraction tests initially utilized a direct ion-exchange leaching approach with ammonium sulfate as lixiviant. In all cases, the simple ion-exchange leaching process failed to recover significant quantities of rare earth elements, ultimately suggesting that the REEs in fine coal waste may be passivated or bound in a colloidal phase. To access this colloidal phase, several alternative approaches were evaluated, including leaching with alternative ion-exchange lixiviants, reductive leaching, gas-purged leaching, and others. The approach that showed the most promise was strong alkaline pretreatment, followed by ion-exchange leaching with ammonium sulfate at pH 4. A combination of strong alkali and high-temperatures treatment successfully liberated the REEs, converting them to a form amenable to ion-exchange leaching. The highest REE recovery achieved with this method was determined to be 39%. Lastly, bench-scale solvent extraction tests were used to further concentrate REEs in the leach solution and demonstrate that mixed rare earth concentrates can be successfully produced from fine coal refuse.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2015

Locally-Adaptive, Spatially-Explicit Projection of U.S. Population for 2030 and 2050

Localized adverse events, including natural hazards, epidemiological events, and human conflict, underscore the criticality of quantifying and mapping current population. Moreover, knowing the spatial distribution of future population allows for increased preparation in the event of an emergency. Building on the spatial interpolation technique previously developed for high resolution population distribution data (LandScan Global and LandScan USA), we have constructed an empirically-informed spatial distribution of the projected population of the contiguous U.S. for 2030 and 2050. Whereas most current large-scale, spatially explicit population projections typically rely on a population gravity model to determine areas of future growth, our projection model departs from these by accounting for multiple components that affect population distribution. Modelled variables, which included land cover, slope, distances to larger cities, and a moving average of current population, were locally adaptive and geographically varying. The resulting weighted surface was used to determine which areas had the greatest likelihood for future population change. Population projections of county level numbers were developed using a modified version of the U.S. Census s projection methodology with the U.S. Census s official projection as the benchmark. Applications of our model include, but are not limited to, suitability modelling, service area planning for governmental agencies, consequence assessment, mitigation planning and implementation, and assessment of spatially vulnerable populations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

A Subgrid Approach for Modeling Microtopography Effects on Overland Flow

Microtopography, or heterogeneities in the elevation across scales much smaller than the domain of interest, plays a critical role in surface water retention, surface/subsurface interactions, and runoff. Resolving microtopographic influences on flow requires high–resolution simulations, which are computationally demanding even when considering the surface system in isolation and even more so when surface flow is one component in integrated simulations that couple surface flow with unsaturated subsurface flow. There is thus significant motivation for models that allow the effects of subgrid microtopography to be better represented. Subgrid models modify coarsened models to capture the microtopography–induced nonlinear effects on hydrologic processes. We present a subgrid model that alters the water storage and flow terms in the diffusion wave equation for surface flow. Stochastically generated microtopography with strongly contrasting spatial structure, high–resolution digital elevation maps from a polygonal tundra site on the North Slope of Alaska and a hummocky microtopography from a field site in Northern Minnesota are used to assess the accuracy and applicability of the subgrid model to disparate landscapes. Approaches for determining subgrid model parameters are tested and simulation results using the subgrid model are compared to benchmark fine–scale simulations and to coarse simulations that ignore microtopography. Our findings confirm that a properly parameterized subgrid model greatly improves the coarse–scale representation of hydrographs and total water content in the system. Furthermore, using the polygonal tundra example, we propose and test a strategy for moving to application–relevant spatial scales by combining microtopography classification and a few fine–scale simulations on small subdomains.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are critical for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study introduces one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Time-resolved electrical potential pump – X-ray photoelectron spectroscopy probe developments for investigating dynamic processes occurring at electrochemical interfaces

Electrode–electrolyte interfaces are of critical importance in several fields, including renewable energy, corrosion, and environmental chemistry. However, investigating these interfaces under operational conditions poses considerable challenges due to the limitations of the instrumentation employed. While recent advancements in in situ and operando techniques have enhanced our comprehension of the steady-state properties of solid-liquid interfaces, the dynamic behaviors of these systems remain inadequately explored. This study introduces a time-resolved X-ray photoelectron spectroscopy (XPS) technique designed to capture transient reaction intermediates and charging dynamics at electrified interfaces. The presented proof-of-principle study demonstrates that electrochemical processes, represented by an equivalent electrical circuit (EEC) model, can be probed and understood using square wave voltage pulses of a potentiostat synchronized to the modified data acquisition of an XPS setup. This method offers a valuable alternative to traditional pump–probe techniques, facilitating the investigation of a broader range of electrochemical systems. A dedicated software package for analyzing time- and energy-resolved XPS with a focus on extracting parameters of the EEC is geared towards benchmarking different EECs in future real-world electrochemical experiments.

Electrochemistry↗

DOE OSTI2023

Bipolar Membrane Capacitive Deionization for pH-Assisted Ionic Separations

Selective ionic separations represent an increasingly important technical area for the strategic interests of the U.S. economy–for example, securing critical minerals and materials and circular economy aspirations that include recovering organic acids from processed biomass. This work disseminates bipolar membrane (BPM) capacitive deionization for selective ionic separations from multicomponent, ionic species mixtures. The selective separations are guided by the Pourbaix diagram and acid–base equilibria principles. BPM capacitive deionization was demonstrated to generate alkaline or acidic process streams depending upon the location of the BPM in the electrochemical cell. The role of system operating parameters, such as the cell voltage, residence time, and feed concentration on effluent stream pH was studied. It was observed that the pH adjustment in BPM-CDI/MCDI (MCDI, membrane capacitive deionization) was more sensitive to the cell voltage when compared to the process stream residence time and salt feed concentration. The BPM-MCDI gave over 6 times higher percentage of copper(II) removal when compared to sodium ion removal from brine mixtures. Lastly, BPM-MCDI demonstrated over 40% greater removal for copper ions from brine mixtures and fivefold higher removal for itaconic acid from brine mixtures when benchmarked against a traditional flow-by-MCDI setup.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

Prospects for detecting UF6 hydrolysis intermediates by mass spectrometry, resonance Raman, and NQR spectroscopy

Simulations are performed to consider several spectrometric and spectroscopic candidates for elucidating the mechanism of the hydrolysis of uranium hexafluoride (UF6). This study is among the first to benchmark the def-mTZVP basis sets for actinide-containing molecules, and it is shown to be a suitable basis set for surveying geometrical structures and vibrational spectra when used in conjunction with density functional theory. An experiment is proposed coupling mass spectrometric ion selection with vibrational spectroscopy, and supporting infrared and Raman spectral simulations demonstrate that ionization blue-shifts bands and can change their qualitative features. Ultraviolet resonance Raman is shown to have good prospects for discriminating U–O–U bridged intermediates, evidence for which was observed recently [L. E. McNamara et al., J. Phys. Chem. A 130, 775–786 (2026)]. As a more speculative approach, we also consider the prospect of addressing 233U or 235U nuclei by quadrupole resonance (NQR) spectroscopy for assigning early stage intermediate complexes. In doing so, we provide a first order-of-magnitude estimate for the collision-induced NQR signal for the UF6 dimer, which is of interest for the interpretation of a fast decoherence time observed in liquid-phase nuclear magnetic resonance. Having provided critical insights into the formation and stability of UF6 hydrolysis intermediates in previous studies, this computational spectroscopy survey is expected to help guide and expedite future laboratory campaigns.

Lutz, Jesse J. [Center for Computing Research, San↗

NASA NTRS2004

Effect of Random Thermal Spikes on Stirling Convertor Heater Head Reliability

Onboard radioisotope power systems being developed to support future NASA exploration missions require reliable design lifetimes of up to 14 yr and beyond. The structurally critical heater head of the high-efficiency developmental Stirling power convertor has undergone extensive computational analysis of operating temperatures (up to 650 C), stresses, and creep resistance of the thin-walled Inconel 718 bill of material. Additionally, assessment of the effect of uncertainties in the creep behavior of the thin-walled heater head, the variation in the manufactured thickness, variation in control temperature, and variation in pressure on the durability and reliability were performed. However, it is possible for the heater head to experience rare incidences of random temperature spikes (excursions) of short duration. These incidences could occur randomly with random magnitude and duration during the desired mission life. These rare incidences could affect the creep strain rate and therefore the life. The paper accounts for these uncertainties and includes the effect of such rare incidences, random in nature, on the reliability. The sensitivities of variables affecting the reliability are quantified and guidelines developed to improve the reliability are outlined. Furthermore, the quantified reliability is being verified with test data from the accelerated benchmark tests being conducted at the NASA Glenn Research Center.

Shah, Ashwin R.↗

NASA NTRS2004

Effect of Random Thermal Spikes on Stirling Convertor Heater Head Reliability

Onboard radioisotope power systems being developed to support future NASA exploration missions require reliable design lifetimes of up to 14 yr and beyond. The structurally critical heater head of the high-efficiency developmental Stirling power converter has undergone extensive computational analysis of operating temperatures (up to 650 C), stresses, and creep resistance of the thin-walled Inconel 718 bill of material. Additionally assessment of the effect of uncertainties in the creep behavior of the thin-walled heater head, the variation in the manufactured thickness, variation in control temperature, and variation in pressure on the durability and reliability were performed. However, it is possible for the heater head to experience rare incidences of random temperature spikes (excursions) of short duration. These incidences could occur randomly with random magnitude and duration during the desired mission life. These rare incidences could affect the creep strain rate and therefore the life. The paper accounts for these uncertainties and includes the effect of such rare incidences, random in nature, on the reliability. The sensitivities of variables affecting the reliability are quantified and guidelines developed to improve the reliability are outlined. Furthermore, the quantified reliability is being verified with test data from the accelerated benchmark tests being conducted at the NASA Glenn Research Center.

Shah, Ashwin R.↗

DOE OSTI2026

Optical nanofiber testbeds for benchmarking membrane-waveguide photonic integrated circuit platforms toward on-chip quantum inertial sensing

Recent advances in cold atom interferometry with optical and magnetic atom guides have set the stage for quantum inertial sensors capable of operating in dynamic environments. In this work, we present three key innovations—evanescent-field (EF) atom guides, optical nanofiber testbeds, and membrane-waveguide photonic integrated circuit (PIC) platforms—to advance EF-guided atom interferometry. First, we demonstrate EF atom guides on optical nanofiber testbeds, which serve as performance benchmarks for our membrane-waveguide PIC platforms. Second, we achieve low-power (⁠ ~ 5 mW) guiding of freely moving, laser-cooled 133 Cs atoms in two-color, traveling-wave EF optical dipole traps at the novel, heat-efficient magic wavelengths of 793 and 937 nm (i.e., “793/937-nm EF atom guides”). Concurrently, we design and fabricate membrane-waveguide PIC platforms for these EF atom guides; in our prior work, we showed that these structures safely accommodate 4–6 times the required optical trap power under vacuum and enable dense cold atom generation via magneto-optical trapping in the vicinity of the optical wavguide for efficient loading. Third, we verify preserved atomic coherence via microwave fields and EF-coupled Doppler-free Raman beams; to our knowledge, this is the first report of coherence fringes driven by co-propagating EF-coupled Raman beams with only 150 nW of total optical power. By providing a direct comparison between optical nanofiber testbeds and membrane-waveguide PIC platforms, our results lay critical groundwork for the on-chip realization of EF-guided atom interferometry and the development of fully integrated, compact, lightweight, and low-power quantum accelerometers and gyroscopes.

Orozco, Adrian [Sandia National Laboratories (SNL-↗

DOE OSTI2022

Optimization of particle tracking methods for stochastic media

Random media emerge in several applications involving particle transport, encompassing e.g. photon propagation through Rayleigh-Taylor instabilities in fuel pellets for inertial confinement fusion, or neutron multiplication problems related to the assessment of re-criticality risk following severe accidents with fuel degradation. Reference calculations in such material configurations by means of Monte Carlo transport codes are particularly challenging, since high-density stochastic media might involve several hundreds of thousands of volumes and thus make particle tracking routines extremely cumbersome. In order to cope with these issues, two distinct strategies have been proposed so far: the use of neighbor maps, or the use of delta tracking. In this work we will compare these methods and illustrate their specific merits and drawbacks, as taken both alone and in combination with each other. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2010

Experimental Creep Life Assessment for the Advanced Stirling Convertor Heater Head

The United States Department of Energy is planning to develop the Advanced Stirling Radioisotope Generator (ASRG) for the National Aeronautics and Space Administration (NASA) for potential use on future space missions. The ASRG provides substantial efficiency and specific power improvements over radioisotope power systems of heritage designs. The ASRG would use General Purpose Heat Source modules as energy sources and the free-piston Advanced Stirling Convertor (ASC) to convert heat into electrical energy. Lockheed Martin Corporation of Valley Forge, Pennsylvania, is integrating the ASRG systems, and Sunpower, Inc., of Athens, Ohio, is designing and building the ASC. NASA Glenn Research Center of Cleveland, Ohio, manages the Sunpower contract and provides technology development in several areas for the ASC. One area is reliability assessment for the ASC heater head, a critical pressure vessel within which heat is converted into mechanical oscillation of a displacer piston. For high system efficiency, the ASC heater head operates at very high temperature (850 C) and therefore is fabricated from an advanced heat-resistant nickel-based superalloy Microcast MarM-247. Since use of MarM-247 in a thin-walled pressure vessel is atypical, much effort is required to assure that the system will operate reliably for its design life of 17 years. One life-limiting structural response for this application is creep; creep deformation is the accumulation of time-dependent inelastic strain under sustained loading over time. If allowed to progress, the deformation eventually results in creep rupture. Since creep material properties are not available in the open literature, a detailed creep life assessment of the ASC heater head effort is underway. This paper presents an overview of that creep life assessment approach, including the reliability-based creep criteria developed from coupon testing, and the associated heater head deterministic and probabilistic analyses. The approach also includes direct benchmark experimental creep assessment. This element provides high-fidelity creep testing of prototypical heater head test articles to investigate the relevant material issues and multiaxial stress state. Benchmark testing provides required data to evaluate the complex life assessment methodology and to validate that analysis. Results from current benchmark heater head tests and newly developed experimental methods are presented. In the concluding remarks, the test results are shown to compare favorably with the creep strain predictions and are the first experimental evidence for a robust ASC heater head creep life.

Krause, David L.↗

DOE OSTI2018

Frequency-domain full-waveform inversion with non-linear descent directions

Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. In this study, we examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss–Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s 0 is, in our scheme, proportional to at most (Δs/s 0 ) 3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss–Newton FWI update is proportional to (Δs/s 0 ) 2 . For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. Lastly, the inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a benchmark FWI approach involving the standard gradient.

58 GEOSCIENCES↗