Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inversion methods”

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.

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

At least 613 records · Page 34

STILGAR: Subsurface Models for Graymont Pleasant Gap Mine

The detection, location, and monitoring of underground structures are of great importance to national and global security. Tunnels and voids generate seismic signatures detectable at the surface, but using non-invasive seismic data to image near-surface presents several challenges in real-world applications. In this report, we describe the use of a dense surface seismic deployment to generate subsurface models of the Graymont Pleasant Gap mine - a single-layer mine with a complex structure embedded in a high-velocity P-wave limestone bedrock. Our approach consists of three key methods. We use P-wave arrival times from local blast events to perform a tomography inversion with the tomoTD method, constructing a P-wave velocity model of the subsurface. We model the layer above the mine using Rayleigh wave ellipticity and inversion techniques. We leverage ongoing anthropogenic activities to identify and locate noise sources both on the surface and within the subsurface. With this integrated approach we aim to overcome the challenges and enhance our ability to non-invasively characterize underground structures, contributing to improved seismic monitoring techniques.

58 GEOSCIENCES↗

Securely Aggregated Coded Matrix Inversion

Coded computing is a method for mitigating straggling workers in a centralized computing network, by using erasure-coding techniques. Federated learning is a decentralized model for training data distributed across client devices. In this work we propose approximating the inverse of an aggregated data matrix, where the data is generated by clients; similar to the federated learning paradigm, while also being resilient to stragglers. To do so, we propose a coded computing method based on gradient coding. We modify this method so that the coordinator does not access the local data at any point; while the clients access the aggregated matrix in order to complete their tasks. Here, the network we consider is not centrally administrated, and the communications which take place are secure against potential eavesdroppers.

97 MATHEMATICS AND COMPUTING↗

Uncertainty Quantification of Geophysical Inversion Using Stochastic Partial Differential Equations (LDRD #218329)

This report summarizes work completed under the Laboratory Directed Research and Development (LDRD) project "Uncertainty Quantification of Geophysical Inversion Using Stochastic Differential Equations." Geophysical inversions often require computationally expensive algorithms to find even one solution, let alone propagating uncertainties through to the solution domain. The primary purpose of this project was to find more computationally efficient means to approximate solution uncertainty in geophysical inversions. We found multiple computationally efficient methods of propagating Earth model uncertainty into uncertainties in solutions of full waveform seismic moment tensor inversions. However, the optimum method of approximating the uncertainty in these seismic source solutions was to use the Karhunen-Love theorem with data misfit residuals. This method was orders of magnitude more computationally efficient than traditional Monte Carlo methods and yielded estimates of uncertainty that closely approximated those of Monte Carlo. We will summarize the various methods we evaluated for estimating uncertainty in seismic source inversions as well as work toward this goal in the realm of 3-D seismic tomographic inversion uncertainty.

58 GEOSCIENCES↗

The Global Methane Budget 2000–2017

Understanding and quantifying the global methane (CH4) budget is important for assessing realistic pathways to mitigate climate change. Atmospheric emissions and concentrations of CH4 continue to increase, making CH4 the second most important human-influenced greenhouse gas in terms of climate forcing, after carbon dioxide (CO2). The relative importance of CH4 compared to CO2 depends on its shorter atmospheric lifetime, stronger warming potential, and variations in atmospheric growth rate over the past decade, the causes of which are still debated. Two major challenges in reducing uncertainties in the atmospheric growth rate arise from the variety of geographically overlapping CH4 sources and from the destruction of CH4 by short-lived hydroxyl radicals (OH). To address these challenges, we have established a consortium of multidisciplinary scientists under the umbrella of the Global Carbon Project to synthesize and stimulate new research aimed at improving and regularly updating the global methane budget. Following Saunois et al. (2016), we present here the second version of the living review paper dedicated to the decadal methane budget, integrating results of top-down studies (atmospheric observations within an atmospheric inverse-modelling framework) and bottom-up estimates (including process-based models for estimating land surface emissions and atmospheric chemistry, inventories of anthropogenic emissions, and data-driven extrapolations). For the 2008–2017 decade, global methane emissions are estimated by atmospheric inversions (a top-down approach) to be 576 Tg CH4/yr (range 550–594, corresponding to the minimum and maximum estimates of the model ensemble). Of this total, 359 Tg CH4/yr or ∼ 60 % is attributed to anthropogenic sources, that is emissions caused by direct human activity (i.e. anthropogenic emissions; range 336–376 Tg CH4/yr or 50 %–65 %). The mean annual total emission for the new decade (2008–2017) is 29 Tg CH4/yr larger than our estimate for the previous decade (2000–2009), and 24 Tg CH4/yr larger than the one reported in the previous budget for 2003–2012 (Saunois et al., 2016). Since 2012, global CH4 emissions have been tracking the warmest scenarios assessed by the Intergovernmental Panel on Climate Change. Bottom-up methods suggest almost 30 % larger global emissions (737 Tg CH4/yr, range 594–881) than top-down inversion methods. Indeed, bottom-up estimates for natural sources such as natural wetlands, other inland water systems, and geological sources are higher than top-down estimates. The atmospheric constraints on the top-down budget suggest that at least some of these bottom-up emissions are overestimated. The latitudinal distribution of atmospheric observation-based emissions indicates a predominance of tropical emissions (∼ 65 % of the global budget, < 30° N) compared to mid-latitudes (∼ 30 %, 30–60° N) and high northern latitudes (∼ 4 %, 60–90° N). The most important source of uncertainty in the methane budget is attributable to natural emissions, especially those from wetlands and other inland waters. Some of our global source estimates are smaller than those in previously published budgets (Saunois et al., 2016; Kirschke et al., 2013). In particular wetland emissions are about 35 Tg CH4/yr lower due to improved partition wetlands and other inland waters. Emissions from geological sources and wild animals are also found to be smaller by 7 Tg CH4/yr by 8 Tg CH4/yr, respectively. However, the overall discrepancy between bottom-up and top-down estimates has been reduced by only 5 % compared to Saunois et al. (2016), due to a higher estimate of emissions from inland waters, highlighting the need for more detailed research on emissions factors. Priorities for improving the methane budget include (i) a global, high-resolution map of water-saturated soils and inundated areas emitting methane based on a robust classification of different types of emitting habitats; (ii) further development of process-based models for inland-water emissions; (iii) intensification of methane observations at local scales (e.g., FLUXNET-CH4 measurements) and urban-scale monitoring to constrain bottom-up land surface models, and at regional scales (surface networks and satellites) to constrain atmospheric inversions; (iv) improvements of transport models and the representation of photochemical sinks in top-down inversions; and (v) development of a 3D variational inversion system using isotopic and/or co-emitted species such as ethane to improve source partitioning.

methane budget↗

An FFT-based approach for Bloch wave analysis: application to polycrystals

A method based on the Fast Fourier Transform is proposed to obtain the dispersion relation of acoustic waves in heterogeneous periodic media with arbitrary microstructures. The microstructure is explicitly considered using a voxelized Representative Volume Element (RVE). The dispersion diagram is obtained solving an eigenvalue problem for Bloch waves in Fourier space. To this aim, two linear operators representing stiffness and mass are defined through the use of differential operators in Fourier space. The smallest eigenvalues are obtained using the implicitly restarted Lanczos and the subspace iteration methods, and the required inverse of the stiffness operator is done using the conjugate gradient with a preconditioner. The method is used to study the propagation of acoustic waves in elastic polycrystals, showing the strong effect of crystal anistropy and polycrystaline texture on the propagation. It is shown that the method combines the simplicity of classical Fourier series analysis with the versatility of Finite Elements to account for complex geometries proving an efficient and general approach which allows the use of large RVEs in 3D.

97 MATHEMATICS AND COMPUTING↗

Proxy-based Bayesian inversion of strain tensor data measured during well tests

Recent instrument developments have made it possible to measure the strain tensor caused by injecting or pumping fluid from aquifers or reservoirs, but the full value of these data is limited because the long runtimes of poroelastic forward models makes it impractical to use many inversion schemes. This limits the interpretation of strain data for managing the recovery of resources or storage of wastes in the subsurface. This paper describes a method of inverting deformation data using a poroelastic numerical simulator so the results can be used to manage reservoirs or aquifers. We developed a workflow designed to reduce the number of simulations sufficiently to make it feasible to use DREAMzs, an advanced Bayesian inversion method that translates the uncertainties from different sources into unbiased posterior parameter distributions and uncertainty envelopes around the field data. Using a KNN proxy model for the poroelastic simulator is key to reducing the overall computations, and the workflow includes a strategy for ensuring the proxy model results converge on the results from the simulator. The workflow is tested using an idealized example that verifies the ability to correctly identify parameters and characterize noise used to perturb the data. Field data from an injection test at an oil reservoir near Tulsa, Oklahoma, are also used to evaluate the efficacy of the workflow with a real dataset. The workflow identified 265 history matching solutions out of 1240 total simulation runs (21% acceptance ratio), where the results were used to characterize posterior parameter distribution and evaluate the prediction uncertainty. Furthermore, this workflow is significant because it enables strain tensor, or other geomechanical measurements to be interpreted to guide decision-making during energy and environmental processes in the subsurface.

42 ENGINEERING↗

Correcting for digital image correlation speckle inversion at high temperature using color cameras

Digital image correlation (DIC) is a popular, noncontacting technique to measure full-field deformation by using cameras to track the motion of an applied surface pattern. Because it is noncontacting, DIC can be performed for extreme temperature applications (e.g., hot-fire rocket testing of carbon composite rocket nozzles) under harsh conditions during which bonded gauges are damaged. Speckle pattern inversion is a phenomenon that sometimes occurs while performing high-temperature DIC. During speckle pattern inversion, portions of the surface pattern that were initially darker at room temperature (e.g., graphite) may emit more light due to blackbody radiation than the portions that were initially paler, thereby producing images in which the pattern appears inverted at high temperature relative to the initial pattern at room temperature. This phenomenon can prevent the correlation algorithm from being able to resolve the displacements between images. This work compares three methods to mitigate speckle pattern inversion: (A) the subtraction method, a recently-published technique in which two high-temperature images are subtracted to remove unwanted light; (B) the filtering method, a popular technique in which optical bandpass filters screen out unwanted light; and (C) the histogram rescaling method, a proposed new method that pairs a color camera with a blue light source and uses information from the green sensor of the camera to correct against inversion in the blue sensor through postprocessing. The histogram rescaling method is shown to successfully eliminate speckle pattern inversion and has the added advantages that it does not require quasi-static loading to be able to compensate for speckle pattern inversion, nor does it impose thick-glass distortions caused by the optical filter.

Rowley, Lindsey J.↗

Polynomial Compensation, Inversion, And Approximation

New criterion introduced for design of discrete-time compensator. Method devised for polynomial compensation, inversion, and approximation of discrete-time linear systems. Involves quadratic measure of difference between response of compensated system and desired response. Impulse response of compensated system improves as degree of polynomial increases. Compensator emphasizes matching of large initial response. Compensators used in variety of applications, including navigation systems for spacecraft, aircraft, ships, and automated manufacturing equipment.

Baram, Yoram↗

A direct application of the non-linear inverse transformation flight control system design on a STOVL aircraft

The nonlinear inverse transformation flight control system design method is applied to the Lockheed Ft. Worth Company's E-7D short takeoff and vertical land (STOVL) supersonic fighter/attack aircraft design with a modified General Electric F110 engine which has augmented propulsive lift capability. The system is fully augmented to provide flight path control and velocity control, and rate command attitude hold for angular axes during the transition and hover operations. In cruise mode, the flight control system is configured to provide direct thrust command, rate command attitude hold for pitch and roll axes, and sideslip command with turn coordination. A control selector based on the nonlinear inverse transformation method is designed specifically to be compatible with the propulsion system's physical configuration which has a two dimensional convergent-divergent aft nozzle, a vectorable ventral nozzle, and a thrust augmented ejector. The nonlinear inverse transformation is used to determine the propulsive forces and nozzle deflections, which in combination with the aerodynamic forces and moments (including propulsive induced contributions), and gravitational force, are required to achieve the longitudinal and vertical acceleration commands. The longitudinal control axes are fully decoupled within the propulsion system's performance envelope. A piloted motion-base flight simulation was conducted on the Vertical Motion Simulator (VMS) at NASA Ames Research Center to examine the handling qualities of this design. Based on results of the simulation, refinements to the control system have been made and will also be covered in the report.

Chung, W. W.↗

Time dependent computation of the Euler equations for designing 2-D cascades, including the case of transonic shock free design

A numerical method to solve the inverse problem for airfoil cascades is described. The case of compressible, inviscid flow is considered. The proposed method is based on the finite difference approximation of the time-dependent Euler equations. Numerical examples show the capability of the method to design subsonic or transonic shockless blades.

Zannetti, L.↗

Global Methane Budget 2000–2020

Abstract. Understanding and quantifying the global methane (CH4) budget is important for assessing realistic pathways to mitigate climate change. CH4 is the second most important human-influenced greenhouse gas in terms of climate forcing after carbon dioxide (CO2), and both emissions and atmospheric concentrations of CH4 have continued to increase since 2007 after a temporary pause. The relative importance of CH4 emissions compared to those of CO2 for temperature change is related to its shorter atmospheric lifetime, stronger radiative effect, and acceleration in atmospheric growth rate over the past decade, the causes of which are still debated. Two major challenges in quantifying the factors responsible for the observed atmospheric growth rate arise from diverse, geographically overlapping CH4 sources and from the uncertain magnitude and temporal change in the destruction of CH4 by short-lived and highly variable hydroxyl radicals (OH). To address these challenges, we have established a consortium of multidisciplinary scientists under the umbrella of the Global Carbon Project to improve, synthesise, and update the global CH4 budget regularly and to stimulate new research on the methane cycle. Following Saunois et al. (2016, 2020), we present here the third version of the living review paper dedicated to the decadal CH4 budget, integrating results of top-down CH4 emission estimates (based on in situ and Greenhouse Gases Observing SATellite (GOSAT) atmospheric observations and an ensemble of atmospheric inverse-model results) and bottom-up estimates (based on process-based models for estimating land surface emissions and atmospheric chemistry, inventories of anthropogenic emissions, and data-driven extrapolations). We present a budget for the most recent 2010–2019 calendar decade (the latest period for which full data sets are available), for the previous decade of 2000–2009 and for the year 2020. The revision of the bottom-up budget in this 2025 edition benefits from important progress in estimating inland freshwater emissions, with better counting of emissions from lakes and ponds, reservoirs, and streams and rivers. This budget also reduces double counting across freshwater and wetland emissions and, for the first time, includes an estimate of the potential double counting that may exist (average of 23 Tg CH4 yr−1). Bottom-up approaches show that the combined wetland and inland freshwater emissions average 248 [159–369] Tg CH4 yr−1 for the 2010–2019 decade. Natural fluxes are perturbed by human activities through climate, eutrophication, and land use. In this budget, we also estimate, for the first time, this anthropogenic component contributing to wetland and inland freshwater emissions. Newly available gridded products also allowed us to derive an almost complete latitudinal and regional budget based on bottom-up approaches. For the 2010–2019 decade, global CH4 emissions are estimated by atmospheric inversions (top-down) to be 575 Tg CH4 yr−1 (range 553–586, corresponding to the minimum and maximum estimates of the model ensemble). Of this amount, 369 Tg CH4 yr−1 or ∼ 65 % is attributed to direct anthropogenic sources in the fossil, agriculture, and waste and anthropogenic biomass burning (range 350–391 Tg CH4 yr−1 or 63 %–68 %). For the 2000–2009 period, the atmospheric inversions give a slightly lower total emission than for 2010–2019, by 32 Tg CH4 yr−1 (range 9–40). The 2020 emission rate is the highest of the period and reaches 608 Tg CH4 yr−1 (range 581–627), which is 12 % higher than the average emissions in the 2000s. Since 2012, global direct anthropogenic CH4 emission trends have been tracking scenarios that assume no or minimal climate mitigation policies proposed by the Intergovernmental Panel on Climate Change (shared socio-economic pathways SSP5 and SSP3). Bottom-up methods suggest 16 % (94 Tg CH4 yr−1) larger global emissions (669 Tg CH4 yr−1, range 512–849) than top-down inversion methods for the 2010–2019 period. The discrepancy between the bottom-up and the top-down budgets has been greatly reduced compared to the previous differences (167 and 156 Tg CH4 yr−1 in Saunois et al. (2016, 2020) respectively), and for the first time uncertainties in bottom-up and top-down budgets overlap. Although differences have been reduced between inversions and bottom-up, the most important source of uncertainty in the global CH4 budget is still attributable to natural emissions, especially those from wetlands and inland freshwaters. The tropospheric loss of methane, as the main contributor to methane lifetime, has been estimated at 563 [510–663] Tg CH4 yr−1 based on chemistry–climate models. These values are slightly larger than for 2000–2009 due to the impact of the rise in atmospheric methane and remaining large uncertainty (∼ 25 %). The total sink of CH4 is estimated at 633 [507–796] Tg CH4 yr−1 by the bottom-up approaches and at 554 [550–567] Tg CH4 yr−1 by top-down approaches. However, most of the top-down models use the same OH distribution, which introduces less uncertainty to the global budget than is likely justified. For 2010–2019, agriculture and waste contributed an estimated 228 [213–242] Tg CH4 yr−1 in the top-down budget and 211 [195–231] Tg CH4 yr−1 in the bottom-up budget. Fossil fuel emissions contributed 115 [100–124] Tg CH4 yr−1 in the top-down budget and 120 [117–125] Tg CH4 yr−1 in the bottom-up budget. Biomass and biofuel burning contributed 27 [26–27] Tg CH4 yr−1 in the top-down budget and 28 [21–39] Tg CH4 yr−1 in the bottom-up budget. We identify five major priorities for improving the CH4 budget: (i) producing a global, high-resolution map of water-saturated soils and inundated areas emitting CH4 based on a robust classification of different types of emitting ecosystems; (ii) further development of process-based models for inland-water emissions; (iii) intensification of CH4 observations at local (e.g. FLUXNET-CH4 measurements, urban-scale monitoring, satellite imagery with pointing capabilities) to regional scales (surface networks and global remote sensing measurements from satellites) to constrain both bottom-up models and atmospheric inversions; (iv) improvements of transport models and the representation of photochemical sinks in top-down inversions; and (v) integration of 3D variational inversion systems using isotopic and/or co-emitted species such as ethane as well as information in the bottom-up inventories on anthropogenic super-emitters detected by remote sensing (mainly oil and gas sector but also coal, agriculture, and landfills) to improve source partitioning. The data presented here can be downloaded from https://doi.org/10.18160/GKQ9-2RHT (Martinez et al., 2024).

54 ENVIRONMENTAL SCIENCES↗

Extremal inversion of lunar travel time data

The tau method, developed by Bessonova et al. (1974), of inversion of travel times is applied to lunar P-wave travel time data to find limits on the velocity structure of the moon. Tau is the singular solution to the Clairaut equation. Models with low-velocity zones, with low-velocity zones at differing depths, and without low-velocity zones, were found to be consistent with data and within the determined limits. Models with and without a discontinuity at about 25-km depth have been found which agree with all travel time data to within two standard deviations. In other words, the existence of the discontinuity and its size and location have not been uniquely resolved. Models with low-velocity channels are also possible.

Burkhard, N.↗

Early and Late Chromosome Damages in Human Lymphocytes Induced by Gamma Rays and Fe Ions

Chromosomal translocations and inversions are considered stable, and cells containing these types of chromosome aberrations can survive multiple cell divisions. An efficient method to detect an inversion is multi-color banding fluorescent in situ hybridization (mBAND) which allows identification of both inter- and intrachromosome aberrations simultaneously. Post irradiation, chromosome aberrations may also arise after multiple cell divisions as a result of genomic instability. To investigate the stable or late-arising chromosome aberrations induced after radiation exposure, we exposed human lymphocytes to gamma rays and Fe ions ex vivo, and cultured the cells for multiple generations. Chromosome aberrations were analyzed in cells collected at first mitosis and at several time intervals during the culture period post irradiation. With gamma irradiation, about half of the damages observed at first mitosis remained after 7 day- and 14 day- culture, suggesting the transmissibility of damages to the surviving progeny. Detailed analysis of chromosome break ends participating in exchanges revealed a greater fraction of break ends involved in intrachromosome aberrations in the 7- and 14-day samples in comparison to the fraction at first mitosis. In particular, simple inversions were found at 7 and 14 days, but not at the first mitosis, suggesting that some of the aberrations might be formed days post irradiation. In contrast, at the doses that produced similar frequencies of gamma-induced chromosome aberrations as observed at first mitosis, a significantly lower yield of aberrations remained at the same population doublings after Fe ion exposure. At these equitoxic doses, more complex type aberrations were observed for Fe ions, indicating that Fe ion-induced initial chromosome damages are more severe and may lead to cell death. Comparison between low and high doses of Fe ion irradiation in the induction of late damages will also be discussed.

Sunagawa, Mayumi↗

mBAND Analysis of Late Chromosome Aberrations in Human Lymphocytes Induced by Gamma Rays and Fe Ions

Chromosomal translocations and inversions are considered stable, and cells containing these types of chromosome aberrations can survive multiple cell divisions. An efficient method to detect an inversion is multi-color banding fluorescent in situ hybridization (mBAND) which allows identification of both inter- and intrachromosome aberrations simultaneously. Post irradiation, chromosome aberrations may also arise after multiple cell divisions as a result of genomic instability. To investigate the stable or late-arising chromosome aberrations induced after radiation exposure, we exposed human lymphocytes to gamma rays and Fe ions ex vivo, and cultured the cells for multiple generations. Chromosome aberrations were analyzed in cells collected at first mitosis and at several time intervals during the culture period post irradiation. With gamma irradiation, about half of the damages observed at first mitosis remained after 7 day- and 14 day- culture, suggesting the transmissibility of damages to the surviving progeny. Detailed analysis of chromosome break ends participating in exchanges revealed a greater fraction of break ends involved in intrachromosome aberrations in the 7- and 14-day samples in comparison to the fraction at first mitosis. In particular, simple inversions were found at 7 and 14 days, but not at the first mitosis, suggesting that some of the aberrations might be formed days post irradiation. In contrast, at the doses that produced similar frequencies of gamma-induced chromosome aberrations as observed at first mitosis, a significantly lower yield of aberrations remained at the same population doublings after Fe ion exposure. At these equitoxic doses, more complex type aberrations were observed for Fe ions, indicating that Fe ion-induced initial chromosome damages are more severe and may lead to cell death. Comparison between low and high doses of Fe ion irradiation in the induction of late damages will also be discussed.

Sunagawa, Mayumi↗

LA17-V-InverseRadTransportProblem-PD2Kb. Final Project Report

In the inverse radiation transport problem, a radiation signal emanating from an unknown object is used to reconstruct geometric and material parameters of the object , e.g., the mass of special nuclear material (SNM), the isotopic composition of the SNM (e.g., the enrichment of 235U), the thickness of shielding, etc. The inverse radiation transport problem is one of the most fundamental and important in the emergency response mission, and has been addressed in previous NA-22 and NA-42/84 investments by using derivative-free optimization methods. Our project was aimed at (i) consolidating previous work by applying polynomial chaos expansion (PCE) for reducing significantly the number of forward model simulations required by derivative-free optimization methods; (ii) developing a general-purpose framework and stand-alone software for solving the inverse radiation transport problem by applying a new “predictive modeling” methodology (predictive modeling of coupled multi-physics systems, PM_CMPS) which enables the fusing of experimental and computational information; and (iii) developing several benchmarks (for unscattered gamma rays) for demonstrating the quantification of non-Gaussian features (e.g., skewness and kurtosis, which characterize asymmetries and long tails) of response distributions by deterministically and efficiently propagating parameter uncertainties (covariances and higher-order moments, where available) using high-order sensitivities computed by the recently developed comprehensive adjoint sensitivity analysis methodology (C-ASAM). With regard to (i), application of PCE, the most significant accomplishment of this project was an implementation of PCE into INVERSE that significantly reduced computation time for the DiffeRential Evolution Adaptive Metropolis (DREAM) and Differential Evolution (DE) methods. For inverse transport problems with measurements of neutron leakage, neutron multiplication, and neutron-induced gamma-rays, the solution times for the DREAM and DE methods were reduced by factors of 30-300, reducing run times from hours to minutes while maintaining the same accuracy as the standard (non-PCE) DREAM and DE. Speedups were further improved by exploring sparse grid quadrature sets using the Toolkit for Adaptive Stochastic Modeling and Non-Intrusive ApproximatioN (Tasmanian) toolset. An initial exploration of sparse grids indicated that further speedups factors of 5-10 are obtainable. The implementation of PCE in INVERSE is not in a form that users can easily access. With regard to (ii), solving the inverse problem using a predictive modeling paradigm, the most significant accomplishment of this project were the derivation and implementation of adjoint-based second derivatives in neutron and photon transport theory. There are two codes that compute these derivatives. SENSPG computes them for uncollided gamma rays and SENSMG computes them for neutron leakage. SENSMG is open-source code available on github. Other significant accomplishments included a stand-alone code, MULTI-PRED, that implements the predictive modeling paradigm, along with a detailed manual. The code was implemented in the existing INVERSE code for inverse problems, but a head-to-head comparison of inverse methods was not achieved. We also derived and implemented the capability to compute sensitivities for multiplicity measurements into the SENSMG code, and this capability was used in a data assimilation application, but it was not used for solving inverse problems. With regard to (iii), developing benchmarks to demonstrate the importance of high-order sensitivity and uncertainty analysis, the most significant accomplishment of this project were two test problems that showed how important second-order sensitivities are.

07 ISOTOPE AND RADIATION SOURCES↗

A fast and accurate radiance algorithm for application to inversion of limb measurements

A method is devised to accurately calculate broad band limb radiance based on a precalculated data base consisting of homogeneous path emissivity as a function of mass path data for various temperatures and pressures. Accurately estimating limb radiance by splicing together interpolated information from the emissivity curves requires no temperature or pressure weighting, and only two interpolations per layer path. The emissivity growth approximation (EGA) technique is applied in a simulated inversion study to the inference of O3, H2O, NO2 and HNO3, and it is found to have comparable accuracies to more sophisticated many-degree band models. The EGA technique is also found to be two orders of magnitude faster, while requiring one second per inversion for one constituent at one-km resolution, allowing a completely nonlinear relaxation time inversion to be done at linear speeds. The technique is also expected to work well for nadir calculations, and prove adequate for estimating occultation radiances.

Gordley, L. L.↗

Simultaneous stochastic inversion for geomagnetic main field and secular variation. II - 1820-1980

With the aim of producing readable time-dependent maps of the geomagnetic field at the core-mantle boundary, the method of simultaneous stochastic inversion for the geomagnetic main field and secular variation, described by Bloxham (1987), was applied to survey data from the period 1820-1980 to yield two time-dependent geomagnetic-field models, one for the period 1900-1980 and the other for 1820-1900. Particular consideration was given to the effect of crustal fields on observations. It was found that the existing methods of accounting for these fields as sources of random noise are inadequate in two circumstances: (1) when sequences of measurements are made at one particular site, and (2) for measurements made at satellite altitude. The present model shows many of the features in the earth's magnetic field at the core-mantle boundary described by Bloxham and Gubbins (1985) and supports many of their earlier conclusions.

Bloxham, Jeremy↗