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Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

Ray, Terrill W.

X-ray Micro-Tomography of Ablative Heat Shield Materials

X-ray micro-tomography is a non-destructive characterization technique that allows imaging of materials structures with voxel sizes in the micrometer range. This level of resolution makes the technique very attractive for imaging porous ablators used in hypersonic entry systems. Besides providing a high fidelity description of the material architecture, micro-tomography enables computations of bulk material properties and simulations of micro-scale phenomena. This presentation provides an overview of a collaborative effort between NASA Ames Research Center and Lawrence Berkeley National Laboratory, aimed at developing micro-tomography experiments and simulations for porous ablative materials. Measurements are carried using x-rays from the Advanced Light Source at Berkeley Lab on different classes of ablative materials used in NASA entry systems. Challenges, strengths and limitations of the technique for imaging materials such as lightweight carbon-phenolic systems and woven textiles are discussed. Computational tools developed to perform numerical simulations based on micro-tomography are described. These enable computations of material properties such as permeability, thermal and radiative conductivity, tortuosity and other parameters that are used in ablator response models. Finally, we present the design of environmental cells that enable imaging materials under simulated operational conditions, such as high temperature, mechanical loads and oxidizing atmospheres.Keywords: Micro-tomography, Porous media, Ablation

tomography

Neural networks for calibration tomography

Artificial neural networks are suitable for performing pattern-to-pattern calibrations. These calibrations are potentially useful for facilities operations in aeronautics, the control of optical alignment, and the like. Computed tomography is compared with neural net calibration tomography for estimating density from its x-ray transform. X-ray transforms are measured, for example, in diffuse-illumination, holographic interferometry of fluids. Computed tomography and neural net calibration tomography are shown to have comparable performance for a 10 degree viewing cone and 29 interferograms within that cone. The system of tomography discussed is proposed as a relevant test of neural networks and other parallel processors intended for using flow visualization data.

Decker, Arthur

Database tomography for commercial application

Database tomography is a method for extracting themes and their relationships from text. The algorithms, employed begin with word frequency and word proximity analysis and build upon these results. When the word 'database' is used, think of medical or police records, patents, journals, or papers, etc. (any text information that can be computer stored). Database tomography features a full text, user interactive technique enabling the user to identify areas of interest, establish relationships, and map trends for a deeper understanding of an area of interest. Database tomography concepts and applications have been reported in journals and presented at conferences. One important feature of the database tomography algorithm is that it can be used on a database of any size, and will facilitate the users ability to understand the volume of content therein. While employing the process to identify research opportunities it became obvious that this promising technology has potential applications for business, science, engineering, law, and academe. Examples include evaluating marketing trends, strategies, relationships and associations. Also, the database tomography process would be a powerful component in the area of competitive intelligence, national security intelligence and patent analysis. User interests and involvement cannot be overemphasized.

Kostoff, Ronald N.

Terahertz Computed Tomography of NASA Thermal Protection System Materials

A terahertz axial computed tomography system has been developed that uses time domain measurements in order to form cross-sectional image slices and three-dimensional volume renderings of terahertz-transparent materials. The system can inspect samples as large as 0.0283 cubic meters (1 cubic foot) with no safety concerns as for x-ray computed tomography. In this study, the system is evaluated for its ability to detect and characterize flat bottom holes, drilled holes, and embedded voids in foam materials utilized as thermal protection on the external fuel tanks for the Space Shuttle. X-ray micro-computed tomography was also performed on the samples to compare against the terahertz computed tomography results and better define embedded voids. Limits of detectability based on depth and size for the samples used in this study are loosely defined. Image sharpness and morphology characterization ability for terahertz computed tomography are qualitatively described.

Roth, D. J.

Imaging of the hip joint. Computed tomography versus magnetic resonance imaging

The authors reviewed the applications and limitations of computed tomography (CT) and magnetic resonance (MR) imaging in the assessment of the most common hip disorders. Magnetic resonance imaging is the most sensitive technique in detecting osteonecrosis of the femoral head. Magnetic resonance reflects the histologic changes associated with osteonecrosis very well, which may ultimately help to improve staging. Computed tomography can more accurately identify subchondral fractures than MR imaging and thus remains important for staging. In congenital dysplasia of the hip, the position of the nonossified femoral head in children less than six months of age can only be inferred by indirect signs on CT. Magnetic resonance imaging demonstrates the cartilaginous femoral head directly without ionizing radiation. Computed tomography remains the imaging modality of choice for evaluating fractures of the hip joint. In some patients, MR imaging demonstrates the fracture even when it is not apparent on radiography. In neoplasm, CT provides better assessment of calcification, ossification, and periosteal reaction than MR imaging. Magnetic resonance imaging, however, represents the most accurate imaging modality for evaluating intramedullary and soft-tissue extent of the tumor and identifying involvement of neurovascular bundles. Magnetic resonance imaging can also be used to monitor response to chemotherapy. In osteoarthrosis and rheumatoid arthritis of the hip, both CT and MR provide more detailed assessment of the severity of disease than conventional radiography because of their tomographic nature. Magnetic resonance imaging is unique in evaluating cartilage degeneration and loss, and in demonstrating soft-tissue alterations such as inflammatory synovial proliferation.

Review

From Tomography to Material Properties of Thermal Protection Systems

The X-ray micro-tomography technique provides non-destructive characterizations of three-dimensional material micro-structures at spatial resolutions from the sub-micron to the centimeter scale. High quality micro-tomography images of NASA Thermal Protection System (TPS) materials are obtained using one of the brightest synchrotron X-ray sources available. Leveraging on NASA supercomputing capabilities, material properties and response are computed from tomography-data. This talk highlights the process and challenges of going from 3D images of actual material structures to simulations of properties and phenomena relevant to TPS material response, such as thermal conductivity, permeability, mass transport and high temperature reactions. The talk is addressed to a broad audience including scientists, engineers, researchers, educators, programmers, managers, and members of the media.

tomography

The Demonstration of a Light Extinction Tomography System at the NASA Glenn Research Center's Icing Research Tunnel

A prototype light extinction tomography system has been developed for acquiring real-time in-situ icing cloud uniformity and density measurements in the NASA Glenn Research Center's Icing Research Tunnel (IRT). These measurements are currently obtained through periodic manual calibrations of the IRT. These calibrations are time consuming and assume that cloud uniformity and density does not greatly vary between the periodic calibrations. It is envisioned that the new light extinction tomography system will provide the means to make these measurements in-situ in real-time and minimize the need for these manual calibrations. This new system uses the principle of light extinction tomography to measure the spray density and distribution in the test section. The prototype system was installed and successfully demonstrated in the Icing Research Tunnel in early 2018. Data sets were acquired for several standard spray and simulated fault conditions to assess system capability and sensitivity. This paper will describe the prototype light extinction system, the theory behind it, and the results of the demonstration test that was conducted in the IRT.

Tomography

Tomography Analysis of Orion Artemis 1 Heatshield Sample

The Orion spacecraft, under NASA's Artemis program, is an integral step in humanity's ambitions of deep space exploration, including our return to the Moon and subsequent mission to Mars. The performance of Orion's heatshield is central to ensuring the safety and success of such missions. This presentation offers a comprehensive overview of the process used in and findings derived from tomography scans of an Artemis 1 heatshield sample executed at the Lawrence Berkeley National Laboratory's Advanced Light Source. These tomography scans captured high-resolution X-Ray images of the heatshield's microstructure, allowing advanced imaging to be employed for 3D image segmentation and visualization of the sample. The Porous Media Analysis (PuMA) software stands central to our analysis, offering robust computational algorithms and methodologies to digitally compute properties of the heatshield material. The presentation discusses the following derived metrics: - Volume fractions, representing the spatial distribution and amounts of various components throughout the heatshield’s depth. - Porosity and crack distributions, offering insights into the void space within the material, critical for understanding the heatshield's structural integrity. - Fiber orientation, detailing the alignment and arrangement of fibers, significant for material orthotropy. - Permeability estimates, quantifying the passage of gas through the material, relevant for re-entry conditions and pyrolysis gasses. One distinctive feature of this study is the comparative evaluation against data obtained from tomography scans of the Exploration Flight Test-1 (EFT-1) heatshield. Such a comparison offers multiple insights, including evaluation of the consistency and repeatability of manufacturing processes as well as understanding of any evolutionary changes in heatshield design or material properties.

Micro-tomography

A Feasibility Study of 4-D Tomography of Soft X-ray Magnetosheath Emissivities Using Multi-Spacecraft Measurements

Upcoming heliophysics missions utilize state-of-the-art wide field-of-view (FOV) imaging technology to measure and investigate the space plasma environment on a global scale. At Earth, remote sensing of soft X-ray emissions, which are generated via the charge exchange interaction between heavy solar wind ions and exospheric neutral atoms, is a promising means to investigate the global magnetosheath structure, its response to varying solar wind conditions, and the spatiotemporal properties of the dayside magnetic reconnection. Data analysis techniques such as optical tomography can provide additional structural and time-varying information from the observed target and thus enhance the mission’s scientific return. In this work, we simulate multiple and simultaneous observations of the dayside magnetosphere using soft X-ray imagers located at long-distance vantage points to reconstruct the time-dependent, three-dimensional (3-D) structure of the magnetosheath using a dynamic tomographic approach. The OpenGCCM MHD model is used to simulate the time-varying response of the magnetosheath to solar wind conditions and, subsequently, generate synthetic soft X-ray images from multiple spacecraft vantage points separated along a common orbit. A detailed analysis is then performed to identify the nominal set of spacecraft that produces the highest fidelity tomographic reconstruction of the magnetopause. This work aims to (i) demonstrate, for the first time, the use of dynamic tomography to retrieve the time-varying magnetosheath structure and (ii) identify a nominal mission design for multi-spacecraft configurations aiming for optical tomography.

3-D/4_d tomography

Measurement of Three-dimensional Density Distributions by Holographic Interferometry and Computer Tomography

The use of holographic interferometry to measure two and threedimensional flows and the interpretation of multiple-view interferograms with computer tomography are discussed. Computational techniques developed for tomography are reviewed. Current research topics are outlined including the development of an automated fringe readout system, optimum reconstruction procedures for when an opaque test model is present in the field, and interferometry and tomography with strongly refracting fields and shocks.

Vest, C. M.

Holographic interferometry and tomography at Ames Research Center

A YAG laser holographic interferometer system and reconstruction laboratory for the Ames 2- by 2-Foot Transonic Wind Tunnel are discussed. This system provides dual plate and double pulse holography for quantitative and qualitative measurements, respectively. Interferometric measurements of two-dimensional airfoils and three-dimensional bodies of revolution for a tomography feasibility study were made. The two-dimensional work included supercritical airfoils, an oscillating airfoil undergoing dynamic stall, and a circulation control airfoil. The tomography experiments centered around hemispherical nose and tangent ogive models. In addition, the tomography work covered the development of a Fourier transform code for the retrieval of the three dimensional density distributions from the interferograms.

Lee, G.

Measuring Weld Profiles By Computer Tomography

Noncontacting, nondestructive computer tomography system determines internal and external contours of welded objects. System makes it unnecessary to take metallurgical sections (destructive technique) or to take silicone impressions of hidden surfaces (technique that contaminates) to inspect them. Measurements of contours via tomography performed 10 times as fast as measurements via impression molds, and tomography does not contaminate inspected parts.

Pascua, Antonio G.

The analysis of a rocket tomography measurement of the N2+3914A emission and N2 ionization rates in an auroral arc

Techniques were developed for recovering two-dimensional distributions of auroral volume emission rates from rocket photometer measurements made in a tomographic spin scan mode. These tomographic inversion procedures are based upon an algebraic reconstruction technique (ART) and utilize two different iterative relaxation techniques for solving the problems associated with noise in the observational data. One of the inversion algorithms is based upon a least squares method and the other on a maximum probability approach. The performance of the inversion algorithms, and the limitations of the rocket tomography technique, were critically assessed using various factors such as (1) statistical and non-statistical noise in the observational data, (2) rocket penetration of the auroral form, (3) background sources of emission, (4) smearing due to the photometer field of view, and (5) temporal variations in the auroral form. These tests show that the inversion procedures may be successfully applied to rocket observations made in medium intensity aurora with standard rocket photometer instruments. The inversion procedures have been used to recover two-dimensional distributions of auroral emission rates and ionization rates from an existing set of N2+3914A rocket photometer measurements which were made in a tomographic spin scan mode during the ARIES auroral campaign. The two-dimensional distributions of the 3914A volume emission rates recoverd from the inversion of the rocket data compare very well with the distributions that were inferred from ground-based measurements using triangulation-tomography techniques and the N2 ionization rates derived from the rocket tomography results are in very good agreement with the in situ particle measurements that were made during the flight. Three pre-prints describing the tomographic inversion techniques and the tomographic analysis of the ARIES rocket data are included as appendices.

Mcdade, Ian C.

The Development of Engineering Tomography for Monolithic and Composite Materials and Components

The research accomplishments under this grant were very extensive in the areas of the development of engineering tomography for monolithic and composite materials and components. Computed tomography was used on graphite composite pins and bushings to find porosity, cracks, and delaminations. It supported the following two programs: Reusable Launch Vehicle (RLV) and Southern Research institute (SRI). Did research using CT and radiography on Nickel based Superalloy dogbones and found density variations and gas shrinkage porosity. Did extensive radiography and CT of PMC composite flywheels and found delamination and non-uniform fiber distribution. This grant supported the Attitude Control Energy Storage Experiment (ACESE) program. Found broken fibers and cracks of outer stainless steel fibers using both radiographic and CT techniques on Pratt and Whitney fuel lines; Supported the Pratt & Whitney and Aging Aircraft engines program. Grant research helped identify and corroborate thickness variations and density differences in a silicon nitride "ROTH" tube using computed tomography.

Hemann, John

Passive Acoustic Tomography Tested for Measuring Gas Temperatures

The requirements of higher performance, better fuel economy, and lower emissions place an increasing premium on knowing the internal operating parameters of jet engines. One of the most important is the gas temperature in the post combustor section of the engine. Typically the gas temperature is measured with a thermocouple probe or by some optical technique such as Rayleigh scattering. Probes, while providing valuable information, have several limitations. The probe signal must be corrected for radiation and conduction losses, probes provide only a point measurement, and probes must be constructed of materials whose melting points are lower than the temperature of the environment into which they are inserted. Some of the disadvantages of probes are overcome by various optical techniques. Nothing needs to be inserted into the flow, and the temperature can be directly related to the signal by known physical laws. However, optical techniques require optical access (i.e., a window) and a light source (such as a laser), and they are very sensitive to the presence of particles in the flow. To overcome these problems, researchers from the NASA Glenn Research Center and The University of Nevada are developing a technique that uses sound instead of light to measure gas temperature. Like optical techniques, it is nonintrusive--no probe need be exposed to the combustion environment--and the temperature is directly related to a measured quantity--the speed of sound, which is proportional to the square root of the absolute temperature. The temperature profile inside the engine is constructed from the differences in arrival time between correlated signals from an array of microphones placed around the circumference of the engine. In much the same way as a complete picture of the inside of your body can be constructed from an array of x-ray photographs taken at different angles, the temperature profile in the engine is constructed from the angular array of microphones. It is tomography by sound waves. Active acoustic tomography, in which a sound pulse is injected into the flow and the time delays between members of an array of microphones are used to construct the temperature field has been used successfully in the stacks of power plants. However, the flow field inside a jet engine is much too noisy for it to be possible to detect an externally injected sound pulse. Instead we are developing passive acoustic tomography, which uses the sound already present in the flow.

Fralick, Gustave C.

Time-Domain Terahertz Computed Axial Tomography NDE System

NASA has identified the need for advanced non-destructive evaluation (NDE) methods to characterize aging and durability in aircraft materials to improve the safety of the nation's airline fleet. 3D THz tomography can play a major role in detection and characterization of flaws and degradation in aircraft materials, including Kevlar-based composites and Kevlar and Zylon fabric covers for soft-shell fan containment where aging and durability issues are critical. A prototype computed tomography (CT) time-domain (TD) THz imaging system has been used to generate 3D images of several test objects including a TUFI tile (a thermal protection system tile used on the Space Shuttle and possibly the Orion or similar capsules). This TUFI tile had simulated impact damage that was located and the depth of damage determined. The CT motion control gan try was designed and constructed, and then integrated with a T-Ray 4000 control unit and motion controller to create a complete CT TD-THz imaging system prototype. A data collection software script was developed that takes multiple z-axis slices in sequence and saves the data for batch processing. The data collection software was integrated with the ability to batch process the slice data with the CT TD-THz image reconstruction software. The time required to take a single CT slice was decreased from six minutes to approximately one minute by replacing the 320 ps, 100-Hz waveform acquisition system with an 80 ps, 1,000-Hz waveform acquisition system. The TD-THZ computed tomography system was built from pre-existing commercial off-the-shelf subsystems. A CT motion control gantry was constructed from COTS components that can handle larger samples. The motion control gantry allows inspection of sample sizes of up to approximately one cubic foot (.0.03 cubic meters). The system reduced to practice a CT-TDTHz system incorporating a COTS 80- ps/l-kHz waveform scanner. The incorporation of this scanner in the system allows acquisition of 3D slice data with better signal-to-noise using a COTS scanner rather than the gchirped h scanner. The system also reduced to practice a prototype for commercial CT systems for insulating materials where safety concerns cannot accommodate x-ray. A software script was written to automate the COTS software to collect and process TD-THz CT data.

Zimdars, David

3D Observation of GEMS by Electron Tomography

Amorphous silicates in chondritic porous interplanetary dust particles (CP-IDPs) coming from comets are dominated by glass with embedded metal and sulfides (GEMS). GEMS grains are submicron-sized rounded objects (typically 100-500) nm in diameter) with anaometer-sized (10-50 nm) Fe-Ni metal and sulfide grains embedded in an amorphous silicate matrix. Several formation processes for GEMS grains have been proposed so far, but these models are still being debated [2-5]. Bradley et al. proposed that GEMS grains are interstellar silicate dust that survived various metamorphism or alteration processes in the protoplanetary disk and that they are amorphiation products of crystalline silicates in the interstellar medium by sputter-deposition of cosmic ray irradiation, similar to space weathering [2,4]. This consideration is based on the observation of nano-sized crystals (approximately 10 nm) called relict grains in GEMS grains and their shapes are pseudomorphs to the host GEMS grains. On the other hand, Keller and Messenger proposed that most GEMS formed in the protoplanetary disk as condensates from high temperature gas [3,5]. This model is based on the fact that most GEMS grains have solar isotopic compositions and have extremely heterogeneous and non-solar elemental compositions. Keller and Messenger (2011) also reported that amorphous silicates in GEMS grains are surrounded by sulfide grains, which formed as sulfidization of metallic iron grains located on the GEMS surface. The previous studies were performed with 2D observation by using transmission electron microscopy (TEM) or scanning TEM (STEM). In order to understand the structure of GEMS grains described above more clearly, we observed 3D structure of GEMS grains by electron tomography using a TEM/STEM (JEM-2100F, JEOL) at Kyoto University. Electron tomography gives not only 3D structures but also gives higher spatial resolution (approximately a few nm) than that in conventional 2D image, which is restricted by sample thickness ) approx. or greater than 50 nm). Three cluster IDPs (L2036AA5 cluster4, L2009L8 cluster 13 and W726A2) were used for the observations. ID W726A2 was collected without silicon oil, which is ordinary used to collect IDPs, so this sample has no possibility of contaminations caused by silicon oil or solvent to rinse it [6]. The samples were embedded in epoxy risin and sliced into ultrathin sections (50-300 nm) using an ultramicotome. The sections were observed by BF-TEM and HAADF-STEM (high angle annular dark field-scanning TEM) modes. Images were obtained by rotating the sample tilt angle over a range of +/- 65 deg in 1 deg steps. The obtained images were reconstructed to slice images. Mineral phases in the slice images were estimated by comparing with a 2D elemental map obtained by an EDS (energy dispersive X-ray spectroscopy) system equipped in the TEM/STEM. Careful examination of the slice images confirmed that iron grains are embedded in the amorphous silicate matrix of the GEMS grains, but sulfide grains were mainly present on the surface of the amorphous silicate. These results are consistent with the model that GEMS grains formed as condensates [3,5], although more data are needed to conclude the origin of GEMS grains. The present study is the first successful example adapting the electron tomography to the IDPs. This type of analysis will be important for planetary material sciences in the future.

Matsuno, Junya