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DOE OSTI2022

BayesMT: A Probabilistic Bayesian Framework for the Seismic Moment Tensor

Moment tensors (MTs) have long been used in earthquake and explosion source analysis, and there has been a renewed interest in how they can inform us about the seismic source, particularly in the geophysical monitoring community due to its application in event identification and yield analysis. However, parameter uncertainties in seismic MT inversion are rarely available. The inverse procedure often does not quantify MT model errors such as event location, data noise and Earth model that are essential for estimating solution robustness. To address this need, we propose to adopt the Bayesian probabilistic framework to incorporate uncertainties in MT inversions. In this study, we present the theoretical background of a probabilistic Bayesian framework for MT inversion accounting for model and measurements errors and illustrate the implementation of the method using a synthetic example.

58 GEOSCIENCES↗

DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗

NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Efficient computation of natural frequencies and associated free vibration modes of spinning flexible structures is required to accurately determine the nature of interaction between the flexible structure and the attitude control system, which is vital in relating control torques to attitude angles. While structural discretization is effected by the finite element method, the resulting eigenvalue problem is solved by a combined Sturm sequence and inverse iteration procedure that yields a few specified roots and associated vectors. An eigenvalue procedure, based on a simultaneous iteration technique, provides efficient computation of the first few roots and vectors; a modal synthesis procedure proves to be useful for eigenproblem solutions of unusual structures such as spacecraft.

Gupta, K. K.↗

NASA NTRS1976

Free vibration analysis of spinning flexible space structures

Gupta, K. K.↗

NASA NTRS1976

Limb-brightening observations from the OSO-7 satellite. II - Comparison of Abel-inverted intensities of Fe XIV and Fe XIII EUV emission lines with predictions

Intensities of Fe XIV and Fe XIII EUV emission lines obtained at coronal locations beyond the limb by the Goddard spectroheliograph on the OSO 7 satellite have been corrected for the wavelength dependence of the instrument's sensitivity and have been Abel-inverted to provide a valid comparison with theoretical predictions for each ion. Details of the Abel-inversion procedure are given, including explicit formulas for application of Bracewell's (1956) method. The intensity ratios of pairs of lines originating from a common level are compared with expected theoretical transition probability ratios over a range of heliocentric distance; deviations in some cases yield information about adjacent unclassified lines. Comparison of the observations with predictions for Fe XIV and Fe XIII shows generally good agreement, with a few interesting discrepancies that may imply a corresponding need for more accurate collisional excitation cross sections. The same comparison yields the variation of electron density with heliocentric radius for each ion separately; the two density functions are found to agree within a factor of three.

Kastner, S. O.↗

NASA NTRS1977

Numerical analysis of free vibrations of damped rotating structures

This paper is concerned with the efficient numerical solution of damped and undamped free vibration problems of rotating structures. While structural discretization is achieved by the finite element method, the associated eigenproblem solution is effected by a combined Sturm sequence and inverse iteration technique that enables the computation of a few required roots only without having to compute any other. For structures of complex configurations, a modal synthesis technique is also presented, which is based on appropriate combinations of eigenproblem solution of various structural components. Such numerical procedures are general in nature, which fully exploit matrix sparsity inherent in finite element discretizations, and prove to be most efficient for the vibration analysis of any damped rotating structure, such as rotating machineries, helicopter and turbine blades, spinning space stations, among others.

Gupta, K. K.↗

NASA NTRS1978

Stochastic inverse problem in the radiation of noise

The reported investigation is concerned with a stochastic inverse radiation problem in a uniform medium. The problem is illustrated with the aid of a simple model consisting of an array of point sources. The entropy functional is chosen to be the structural functional in determining the source distribution. A general theory for the stochastic inverse problem is introduced. It is shown that the general procedure yields the methods of the Lagrangian multiplier, when the structural and residual functionals are specialized. Tihonov's regularization and a method related to generalized or pseudoinverses are also obtained. Examples considered for purposes of illustration are related to a continuous source with the least noise intensity, a continuous source with a potential, and an axisymmetric line source.

Chow, P. L.↗

NASA NTRS1993

Computation of nonequilibrium radiating shock layers

A computational technique of coupling radiative transfer to fluid motion is developed for axisymmetric blunt body shock layer flows in a thermochemical nonequilibrium environment. The coupled formulation of radiation and flowfield leads to a governing set of integro-differential equations. This equation set is solved using a modified Gauss-Seidel line relaxation techniques which incorporates the inversion of full block matrix associated with radiative transfer using a block iteration method. The thermodynamic state of the gas is described by three temperatures: translational, rotational, and vibrational-electronic. Radiation phenomenon is assumed to be governed by the vibrational-electronic temperature. The radiative properties are described by a spectrally detailed model. The computations are presented for two cases, including the Fire II flight experiment. It is shown that the method converges and the calculated spectra qualitatively agree with the experimental data for the two test cases. The calculated total radiative flux underestimates the measured values owing to the low vibrational-electronic temperature predicted in the flowfield calculation.

Gokcen, Tahir↗

NASA NTRS1993

Boundary layer stratus clouds - Inferred from satellite infrared spectral measurements over oceans

A method to remotely sense marine stratus clouds, that are underneath the boundary layer inversion produced by strong subsidence, is developed with the help of the measurements made by the Infrared Interferometer Spectrometer (IRIS) on board the Nimbus 4 satellite. These measurements, which had a spectral resolution of 2.8/cm and a field view of about 100 km in the region 870-980/cm, allow one to compare the weak absorption due to water vapor lines with that of the weak nu3-nu1 band of CO2. From such a comparison it is possible to sense the presence of these boundary layer stratus clouds. Maps of these clouds over subsidence regions of the tropical and subtropical oceans deduced from IRIS data show the usefulness of the technique to climatological studies.

Prabhakara, C.↗

DOE OSTI2022

The weathered bedrock vadose zone: A hidden control on water availability in the western United States (Final Technical Report)

This report summarizes the research completed during the project entitled "The weathered bedrock vadose zone: A hidden control on water availability in the western United States" (Award: DE-SC0018039). The report covers work completed between 9/15/17 and 9/14/20. The objective of the exploratory project work was to evaluate the overarching hypothesis that the subsurface underlying actively eroding landscapes is systematically structured as a result of a balance between weathering and erosion and that this structure leads to dynamic moisture storage within weathered rock. To accomplish project objectives, we characterized hillslope weathering profile structure and conducted subsurface moisture monitoring across four study sites with comparable bedrock types but differing erosion rate and hydroclimate: The Angelo Coast Range Reserve (ACRR), Sagehorn-Russell Ranch (SRR), Antelope Valley Ranch (AVR), and the LBNL Watershed Function Scientific Focus Area (SFA). New characterization and monitoring infrastructure at the AVR and SFA sites was established through this project and enables long-term monitoring of hydrologic and carbon fluxes at the sites for comparison with long-term monitoring in other sites. Deep drilling, downhole logging, and characterization of chemistry and porosity of rock recovered from drilling reveals two weathering fronts across the sites. A shallower front is marked by the extent of pervasive fracturing and oxidation of pyrite and organic carbon. A deeper weathering front is marked by the appearance of open fractures and discoloration. At the AVR site, multiple ridge tops of different hillslope length were investigated to establish the relationship between the weathering front and topography. Drilling reveals that the fraction of the hillslope relief that is weathered scales with hillslope length, consistent with the theoretical framework that guided the project relating groundwater drainage with landscape evolution. With the establishment of new boreholes, we have documented significant water storage in weathered bedrock using low-field borehole nuclear magnetic resonance (NMR) across all four sites. In the upper 4 m of bedrock, the average water contents at ACRR, AVR, SRR, and SFA are approximately 25%, 16%, 25%, 23% respectively. At the ACRR site, where long-term monitoring via neutron probe surveys and time-domain transmission sensors are available, we have demonstrated that NMR reliably records moisture content and importantly, moisture content dynamics in weathered bedrock. Across all sites, our NMR monitoring has also revealed that a considerable fraction of the water storage occurs in fractures or pores that are significantly larger than the fine-grained bedrock matrix of the parent rock. To identify the proportion of water storage occurring in fractures and large pores, we analyzed the NMR signal by evaluating both the sum of echoes and an inversion of the NMR signal for a distribution of T2 relaxation times. Both methods reveal that at least 20% of the water storage occurs in fractures and larger pores across all sites. To constrain the interpretation of the in-situ field-scale NMR measurements, we compare the NMR response in the field to independent pore-structure information obtained via helium pycnometry. Results support the inference that dynamic seasonal water storage is dominantly restricted to the fracture network, which can reach 7% of the total volume. This dynamic range in water content is comparable to that of some soils, underscoring the need to understand how this region of the Earth System is structured, and functions as a hydrologic reservoir.

58 GEOSCIENCES↗

NASA NTRS2000

A New Neural Network Approach Including First-Guess for Retrieval of Atmospheric Water Vapor, Cloud Liquid Water Path, Surface Temperature and Emissivities Over Land From Satellite Microwave Observations

The analysis of microwave observations over land to determine atmospheric and surface parameters is still limited due to the complexity of the inverse problem. Neural network techniques have already proved successful as the basis of efficient retrieval methods for non-linear cases, however, first-guess estimates, which are used in variational methods to avoid problems of solution non-uniqueness or other forms of solution irregularity, have up to now not been used with neural network methods. In this study, a neural network approach is developed that uses a first-guess. Conceptual bridges are established between the neural network and variational methods. The new neural method retrieves the surface skin temperature, the integrated water vapor content, the cloud liquid water path and the microwave surface emissivities between 19 and 85 GHz over land from SSM/I observations. The retrieval, in parallel, of all these quantities improves the results for consistency reasons. A data base to train the neural network is calculated with a radiative transfer model and a a global collection of coincident surface and atmospheric parameters extracted from the National Center for Environmental Prediction reanalysis, from the International Satellite Cloud Climatology Project data and from microwave emissivity atlases previously calculated. The results of the neural network inversion are very encouraging. The r.m.s. error of the surface temperature retrieval over the globe is 1.3 K in clear sky conditions and 1.6 K in cloudy scenes. Water vapor is retrieved with a r.m.s. error of 3.8 kg/sq m in clear conditions and 4.9 kg/sq m in cloudy situations. The r.m.s. error in cloud liquid water path is 0.08 kg/sq m . The surface emissivities are retrieved with an accuracy of better than 0.008 in clear conditions and 0.010 in cloudy conditions. Microwave land surface temperature retrieval presents a very attractive complement to the infrared estimates in cloudy areas: time record of land surface temperature will be produced.

Aires, F.↗

DOE OSTI2020

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Tao, Xuecheng↗

DOE OSTI2025

Applying Gaussian Process Machine Learning and Modern Probabilistic Programming to Satellite Data to Infer CO 2 Emissions

Satellite data provides essential insights into the spatiotemporal distribution of CO 2 concentrations. However, many atmospheric inverse models fail to adequately incorporate the spatial and temporal correlations inherent in satellite observations and often lack rigorous methods for estimating parameters like spatial length scales. We introduce an inference model that processes the spatiotemporal covariance in satellite data and estimates hyperparameters such as covariance length scales. Our approach uses the Gaussian process (GP) machine learning (ML) and modern probabilistic programming languages (PPLs) to perform atmospheric inversions of emissions from satellite data. We develop a GP ML inversion system based on modern PPLs and the GEOS-Chem chemical transport model, simulating atmospheric CO 2 concentrations corresponding to the Orbiting Carbon Observatory-2/3 (OCO-2/3) data for July 2020. In our supervised learning framework, we treat the GEOS-Chem simulated data set as the target, with predictors derived by scaling the target with sector-specific factors hidden from the GP machine. Our results show that the GP model, combined with GPU-enabled PPLs, effectively retrieves true emission scaling factors and infers noise levels concealed within the data. This suggests that our method could be applied over larger areas with more complex covariance structures, enabling comprehensive analysis of the spatiotemporal patterns observed in OCO-2/3 and similar satellite data sets.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Search for magnetically-induced signatures in the arrival directions of ultra-high-energy cosmic rays measured at the Pierre Auger Observatory

We search for signals of magnetically-induced effects in the arrival directions of ultra-high-energy cosmic rays detected at the Pierre Auger Observatory. We apply two different methods. One is a search for sets of events that show a correlation between their arrival direction and the inverse of their energy, which would be expected if they come from the same point-like source, they have the same electric charge and their deflection is relatively small and coherent. We refer to these sets of events as “multiplets”. The second method, called “thrust”, is a principal axis analysis aimed to detect the elongated patterns in a region of interest. We study the sensitivity of both methods using a benchmark simulation and we apply them to data in two different searches. The first search is done assuming as source candidates a list of nearby active galactic nuclei and starburst galaxies. The second is an all-sky blind search. We report the results and we find no statistically significant features. We discuss the compatibility of these results with the indications on the mass composition inferred from data of the Pierre Auger Observatory.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress–strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three-dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Extraction of mechanical properties of materials through deep learning from instrumented indentation

Instrumented indentation has been developed and widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials. This method is particularly desirable for those applications where it is difficult to experimentally determine the mechanical properties using stress–strain data obtained from coupon specimens. Such applications include material processing and manufacturing of small and large engineering components and structures involving the following: three dimensional (3D) printing, thin-film and multilayered structures, and integrated manufacturing of materials for coupled mechanical and functional properties. Here, we utilize the latest developments in neural networks, including a multifidelity approach whereby deep-learning algorithms are trained to extract elastoplastic properties of metals an d alloys from instrumented indentation results using multiple datasets for desired levels of improved accuracy. We have established algorithms for solving inverse problems by recourse to single, dual, and multiple indentation and demonstrate that these algorithms significantly outperform traditional brute force computations and function-fitting methods. Moreover, we present several multifidelity approaches specifically for solving the inverse indentation problem which 1) significantly reduce the number of high-fidelity datasets required to achieve a given level of accuracy, 2) utilize known physical and scaling laws to improve training efficiency and accuracy, and 3) integrate simulation and experimental data for training disparate datasets to learn and minimize systematic errors. The predictive capabilities and advantages of these multifidelity methods have been assessed by direct comparisons with experimental results for indentation for different commercial alloys, including two wrought aluminum alloys and several 3D printed titanium alloys.

3D printed materials, stress-strain behavior, mult↗

DOE OSTI2023

Real-space inversion and super-resolution of ultrafast scattering

Ultrafast scattering using x-rays or electrons is an emerging method to obtain structure dynamics at the atomic lengthscales and timescales. However, directly resolving in real-space atomic motions is inherently limited by the finite detector range and the probe energy. So, as a result, the time-resolved signal interpretation is mostly done in reciprocal space and relies on modeling and simulations of specific structures and processes. Here, we introduce a model-free approach to directly resolve scattering signals in real space, surpassing the diffraction limit, using scattering kernels and signal priors that naturally arise from the measurement constraints. We demonstrate the approach on simulated and experimental data, recover multiple atomic motions at sub-angstrom resolutions, and discuss the recovery accuracy and resolution limits versus signal fidelity. The approach offers a robust path to obtain high-resolution real-space information of atomic-scale structure dynamics using current time-resolved x-ray or electron scattering sources.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Extension of the flux fit method for estimating power deposition profiles

The flux fit method is used to self-consistently estimate the power deposition profile and heat transport profiles from temperature measurements originating from perturbative experiments with a modulated source. Furthermore, this letter improves on this method by addressing the limitations and assumptions. The most crucial improvement is the additional freedom in the source deposition profile. Allowing for a variable central deposition location and height and including a skewness parameter produces deposition profiles more consistent with the measurement data, but still wider than equilibrium ray tracing in two different DIII-D discharges. Moreover, we show that the quality of the estimated deposition profile is key to the accuracy of diffusivity and connectivity estimates, but inversely, the estimated transport parameters hardly affect the quality of the power deposition estimate. Using this method, we show that the power deposition profile estimate is broadened with respect to ray-tracing by about 1.7-1.8 times in two DIII-D discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗