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Global optimization methods for engineering design

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Arora, Jasbir S.↗

New Approach to Diagnosing Properties of Protoplanetary Disks

In this paper we suggest that subjecting the observationally derived properties of protoplanetary disks to the evolutionary interpretation yields new insights into the working of those disks, and offers valuable constraints on their models. We propose that the global properties of individual disks, such as their accretion rates and disk masses, sorted by the mass of the central star, can be indexed by the age of the star to simulate the evolution of a single disk. Using data from published surveys of T Tauri stars, we show that accretion rate data, and disk mass data for the lowest mass stars, form well-defined evolutionary tracks. The higher mass stars show a definitive negative correlation between accretion rates and star ages. We use the time-dependent alpha-disk model of the viscous protoplanetary disk to link the theory to observations. The data are consistent with the standard theoretical paradigm, but not with the layered accretion model. The best fits to the data are obtained for the standard models that start with disks that are about one-third of the mass of the central star and have their angular momenta, j, and alpha-coefficients linked by the relationship j varies as Solar mass(exp 3/2)alpha(exp 1/3). The proportionality constant in this relationship, when derived from the accretion rate data, differs from the constant derived from the disk mass data. We argue that the accretion rate data are more reliable. Taking into account typical values of the specific angular momentum of disk-forming matter, we obtain alpha is greater than or equal to 10(exp -2). A complete time-dependent standard disk model, built on the parameters determined from the best-fit procedure, is presented. Such a model constitutes a good point of departure for various theoretical studies aimed at the issue of formation of planetary systems and the character of protoplanetary disks.

Stepinski, Tomasz F.↗

Trends of Measured Climate Forcing Agents

The growth rate of climate forcing by measured greenhouse gases peaked near 1980 at almost 5 W/sq m per century. This growth rate has since declined to approximately equal to 3 W/sq m per century, largely because of cooperative international actions. We argue that trends can be reduced to the level needed for the moderate "alternative" climate scenario (approximately equal to 2 W/M2 per century for the next 50 years) by means of concerted actions that have other benefits, but the forcing reductions are not automatic "co-benefits" of actions that slow CO2 emissions. Current trends of climate forcings by aerosols remain very uncertain. Nevertheless, practical constraints on changes in emission levels suggest that global warming at a rate + 0.15 +/- 0.05 C per decade will occur over the next several decades.

Hansen, James E.↗

Planetary Transmission Diagnostics

This report presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting algorithm. The lifting scheme, developed by Wim Sweldens of Bell Labs, is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Classic lifting analyzes a given signal using wavelets derived from a single fundamental basis function. A number of researchers have proposed techniques for adding adaptivity to the lifting scheme, allowing the transform to choose from a set of fundamental bases the basis that best fits the signal. This characteristic is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation (synchronous signal-averaging) algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local wave-form changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. The constrained adaptive lifting diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the results are discussed.

Lewicki, David G.↗

A Numerical Optimization Approach for Tuning Fuzzy Logic Controllers

This paper develops a method to tune fuzzy controllers using numerical optimization. The main attribute of this approach is that it allows fuzzy logic controllers to be tuned to achieve global performance requirements. Furthermore, this approach allows design constraints to be implemented during the tuning process. The method tunes the controller by parameterizing the membership functions for error, change-in-error and control output. The resulting parameters form a design vector which is iteratively changed to minimize an objective function. The minimal objective function results in an optimal performance of the system. A spacecraft mounted science instrument line-of-sight pointing control is used to demonstrate results.

Woodard, Stanley E.↗

Towards Time Automata and Multi-Agent Systems

The design of reactive systems must comply with logical correctness (the system does what it is supposed to do) and timeliness (the system has to satisfy a set of temporal constraints) criteria. In this paper, we propose a global approach for the design of adaptive reactive systems, i.e., systems that dynamically adapt their architecture depending on the context. We use the timed automata formalism for the design of the agents' behavior. This allows evaluating beforehand the properties of the system (regarding logical correctness and timeliness), thanks to model-checking and simulation techniques. This model is enhanced with tools that we developed for the automatic generation of code, allowing to produce very quickly a running multi-agent prototype satisfying the properties of the model.

Hutzler, G.↗

The HYSPIRI Decadal Survey Mission: Update on the Mission Concept and Science Objectives for Global Imaging Spectroscopy and Multi-Spectral Thermal Measurements

The NASA HyspIRI mission is planned to provide global solar reflected energy spectroscopic measurement of the terrestrial and shallow water regions of the Earth every 19 days will all measurements downlinked. In addition, HyspIRI will provide multi-spectral thermal measurements with a single band in the 4 micron region and seven bands in the 8 to 12 micron region with 5 day day/night coverage. A direct broadcast capability for measurement subsets is also planned. This HyspIRI mission is one of those designated in the 2007 National Research Council (NRC) Decadal Survey: Earth Science and Applications from Space. In the Decadal Survey, HyspIRI was recognized as relevant to a range of Earth science and science applications, including climate: "A hyperspectral sensor (e.g., FLORA) combined with a multispectral thermal sensor (e.g., SAVII) in low Earth orbit (LEO) is part of an integrated mission concept [described in Parts I and II] that is relevant to several panels, especially the climate variability panel." The HyspIRI science study group was formed in 2008 to evaluate and refine the mission concept. This group has developed a series of HyspIRI science objectives: (1) Climate: Ecosystem biochemistry, condition & feedback; spectral albedo; carbon/dust on snow/ice; biomass burning; evapotranspiration (2) Ecosystems: Global plant functional types, physiological condition, and biochemistry including agricultural lands (3) Fires: Fuel status, fire frequency, severity, emissions, and patterns of recovery globally (4) Coral reef and coastal habitats: Global composition and status (5) Volcanoes: Eruptions, emissions, regional and global impact (6) Geology and resources: Global distributions of surface mineral resources and improved understanding of geology and related hazards These objectives are achieved with the following measurement capabilities. The HyspIRI imaging spectrometer provides: full spectral coverage from 380 to 2500 at 10 nm sampling; 60 m spatial sampling with a 150 km swath; and fully downlinked coverage of the Earth's terrestrial and shallow water regions every 19 days to provide seasonal cloud-free coverage of the terrestrial surface. The HyspIRI Multi-Spectral Thermal instrument provides: 8 spectral bands from 4 to 12 microns; 60 m spatial sampling with a 600 km swath; and fully downlinked coverage of the Earth's terrestrial shallow water regions every 5 days (day/night) to provide nominally cloud-free monthly coverage. The HyspIRI mission also includes an on-board processing and direct broadcast capability, referred to as the Intelligent Payload Module (IPM), which will allow users with the appropriate antenna to download a subset of the HyspIRI data stream to a local ground station. These science and science application objectives are critical today and uniquely addressed by the combined imaging spectroscopy, thermal infrared measurements, and IPM direct broadcast capability of HyspIRI. Two key objectives are: (1) The global HyspIRI spectroscopic measurements of the terrestrial biosphere including vegetation composition and function to constrain and reduce the uncertainty in climate-carbon interactions and terrestrial biosphere feedback. (2) The global 8 band thermal measurements to provide improved constraint of fire related emissions. In this paper the current HyspIRI mission concept that has been reviewed and refined to its current level of maturity with a Data Products Symposium, Science Workshop and NASA HWorkshop is presented including traceability between the measurements and the science and science application objectives.

Green, Robert O.↗

Revised Thickness of the Lunar Crust from GRAIL Data: Implications for Lunar Bulk Composition

High-resolution gravity data from GRAIL have yielded new estimates of the bulk density and thickness of the lunar crust. The bulk density of the highlands crust is 2550 kg m-3. From a comparison with crustal composition measured remotely, this density implies a mean porosity of 12%. With this bulk density and constraints from the Apollo seismic experiment, the average global crustal thickness is found to lie between 34 and 43 km, a value 10 to 20 km less than several previous estimates. Crustal thickness is a central parameter in estimating bulk lunar composition. Estimates of the concentrations of refractory elements in the Moon from heat flow, remote sensing and sample data, and geophysical data fall into two categories: those with refractory element abundances enriched by 50% or more relative to Earth, and those with abundances the same as Earth. Settling this issue has implications for processes operating during lunar formation. The crustal thickness resulting from analysis of GRAIL data is less than several previous estimates. We show here that a refractory-enriched Moon is not required

Taylor, G. Jeffrey↗

A Decade of Volcanic Observations from Aura and the A-Train

Aura observations have made many seminal contributions to volcanology. Prior to the Aura launch, satellite observations of volcanic degassing (e.g., from TOMS) were mostly restricted to large eruptions. However, the vast majority of volcanic gases are released during quiescent 'passive' degassing between eruptions. The improved sensitivity of Aura OMI permitted the first daily, space-borne measurements of passive volcanic SO2 degassing, providing improved constraints on the source locations and magnitude of global SO2 emissions for input to atmospheric chemistry and climate models. As a result of this unique sensitivity to volcanic activity, OMI data were also the first satellite SO2 measurements to be routinely used for volcano monitoring at several volcano observatories worldwide. Furthermore, the Aura OMI SO2 data also offer unprecedented sensitivity to volcanic clouds in the UTLS, elucidating the transport, fate and lifetime of volcanic SO2 and providing critical input to aviation hazard mitigation efforts. Another major advance has been the improved vertical resolution of volcanic clouds made possible by synergy between Aura and other A-Train instruments (e.g., AIRS, CALIPSO, CloudSat), advanced UV SO2 altitude retrievals, and inverse trajectory modeling of detailed SO2 cloud maps. This altitude information is crucial for climate models and aviation hazards. We will review some of the highlights of a decade of Aura observations of volcanic activity and look ahead to the future of volcanic observations from space.

Aura↗

Coronal Diagnostic Experiment (CODEX)

Understanding solar wind sources and acceleration mechanisms is an overarching solar physics goal. Current models are highly under-constrained due to the limitations of the existing data, particularly in the ~3-10 Rs range. COronal Diagnostic Experiment (CODEX) is designed to deliver the first global, comprehensive data sets that will impose crucial constraints and answer targeted essential questions, including: Are there signatures of hot plasma released into the solar wind from previously closed fields? What are the velocities and temperatures of the density structures that are observed so ubiquitously within streamers and coronal holes? To provide these crucial measurements, NASA’s Goddard Space Flight Center, in collaboration with the Korea Astronomy and Space Science Institute, and Italian National Institute for Astrophysics (INAF) will develop a next-generation coronagraph for the International Space Station. This imaging coronagraph uses multiple filters to obtain simultaneous measurements of electron density, temperature, and velocity within a single instrument. This will be the first time all three have been measured simultaneously for this critical field-of-view, and CODEX achieves these measurements multiple times a day.

Jeff Newmark↗

Neurocomputing strategies in decomposition based structural design

The present paper explores the applicability of neurocomputing strategies in decomposition based structural optimization problems. It is shown that the modeling capability of a backpropagation neural network can be used to detect weak couplings in a system, and to effectively decompose it into smaller, more tractable, subsystems. When such partitioning of a design space is possible, parallel optimization can be performed in each subsystem, with a penalty term added to its objective function to account for constraint violations in all other subsystems. Dependencies among subsystems are represented in terms of global design variables, and a neural network is used to map the relations between these variables and all subsystem constraints. A vector quantization technique, referred to as a z-Network, can effectively be used for this purpose. The approach is illustrated with applications to minimum weight sizing of truss structures with multiple design constraints.

Szewczyk, Z.↗

Cosmological constraints on pseudo-Nambu-Goldstone bosons

Particle physics models with pseudo-Nambu-Goldstone bosons (PNGBs) are characterized by two mass scales: a global spontaneous symmetry breaking scale, f, and a soft (explicit) symmetry breaking scale, Lambda. General model insensitive constraints were studied on this 2-D parameter space arising from the cosmological and astrophysical effects of PNGBs. In particular, constraints were studied arising from vacuum misalignment and thermal production of PNGBs, topological defects, and the cosmological effects of PNGB decay products, as well as astrophysical constraints from stellar PNGB emission. Bounds on the Peccei-Quinn axion scale, 10(exp 10) GeV approx. = or less than f sub pq approx. = or less than 10(exp 10) to 10(exp 12) GeV, emerge as a special case, where the soft breaking scale is fixed at Lambda sub QCD approx. = 100 MeV.

Frieman, Joshua A.↗

Attitude Representations for Kalman Filtering

The four-component quaternion has the lowest dimensionality possible for a globally nonsingular attitude representation, it represents the attitude matrix as a homogeneous quadratic function, and its dynamic propagation equation is bilinear in the quaternion and the angular velocity. The quaternion is required to obey a unit norm constraint, though, so Kalman filters often employ a quaternion for the global attitude estimate and a three-component representation for small errors about the estimate. We consider these mixed attitude representations for both a first-order Extended Kalman filter and a second-order filter, as well for quaternion-norm-preserving attitude propagation.

Markley, F. Landis↗

An Optimization Approach to Support Science Decision Making for Lunar Surface Exploration

Introduction: Scientific exploration is one of the three pillars of NASA’s Moon2Mars architecture, with crew surface extra vehicular activities (EVA) serving a critical enabling function. Development of surface EVA operational planning and execution, specifically integrating science and flight control teams (FCT), is currently being explored through analog scenarios. This integration, exercised, for example, through the Joint EVA and Hu-man Surface Mobility Test Team (JETT), allows for science input on EVA activities in near real-time through a Science Evaluation Room (SER), or Arte-mis science backroom, which integrates with the broader FCT through the Science Officer. The SER works within the FCT to support dynamic EVA planning in response to changes in operational constraints as well as science opportunities and re-prioritization, increasing the mission science return and accelerating the accomplishment of the Moon2Mars science objectives. The SER works within the FCT to provide recommendations to traverse execution in near real-time. One challenge is the requirement to deliver SER inputs to the FCT on operationally relevant timelines. Failure to do so may result in suboptimal execution of science exploration EVAs or even loss of key science objectives. To close this gap, we present a network optimization tool to allow the SER to provide rapid input to the FCT in response to changes in operational constraints or science opportunities. Inputs are predicated on approved science objectives, and clear rationale must be provided to the FCT for any requested change. Accordingly, this tool incorporates the Science Traceability Matrix (STM), SER prioritization scheme, and station characterization and action planning with operational constraints such as duration, traverse speed, and distance to maximize science objectives based on SER priorities, consistent with FCT operational requirements. Method: As a proof of concept, we used an existing linear programing software package used to simulate optimal routes through cellular metabolism. We built a Demonstrative Model with three STM objectives and four stations on a region of the Moon. The objectives were given an arbitrary prioritization and mapped to the stations through four possible crew actions. (Figs. 1 and 2). This station to STM mapping is consistent with the method used by the JETT5 Science Team to develop analog surface EVA science planning. We used a grid system with the landing site at the origin and the four stations placed across the positive x,y quadrant. Actions were assigned to each station and the accomplishment of those actions resulted in a numerical “reward” based on the ability of that action to achieve science objectives. The aggregate reward from each individual STM objective contributes to a global score (Science Yield), weighted by its priority. Operational constraints included a requirement to start and end at the landing site, 5 minutes each for initial station characterization and “clean up,” and variable total EVA time, traverse rate (fixed to 0.5 meters per second in our example), and time to perform each action (10, 5, 7, and 15 min for actions 1, 2, 3, and 4, respectively). Additional constraints and variables will be added in the future (e.g., sample mass, number of stations, traverse route constraints, illumination). Optimization. We converted the connections (arcs) between these stations (nodes) into a mixed integer linear programming optimization problem (arcs = constraints, nodes = variables) with the objective to maximize Science Yield. For any action, the Science Yield is equal to the relevance of that action to an STM objective [3, 2, and 1 point(s) for High, Med., and Low relevance, respectively], multiplied by the STM Objective Priority [3, 2, and 1 point(s) for High, Med., and Low priority, respectively]. This resulted in a model that computes the optimal station and action combination to maximize the Science Yield. These weightings can be adjusted by the SER as desired. Results: We explored three test cases for the Demonstrative Model. First, we set the maximum EVA duration to 120 minutes and computed the optimal route (Fig. 3A). The model suggested per-forming Actions 1 and 2 at Station P01, followed by Actions 1 and 2 at Station P02, and finally Actions 1 and 3 at Station P04 before returning to the Landing Site. Second, we adjusted the STM Objective Priori-ty order and computed the new optimal route (Fig. 3B). Under this situation, the model suggested per-forming all Actions at Station P02 followed by all Actions at Station P03. The previous test cases were relevant to SER planning activities. Next, we explored providing mid-EVA replanning input to the FCT. Scenario: While executing the Route in Fig. 3A the crew finishes at Station P01 and FCT decides that the EVA needs to finish in 45 minutes back at the Landing Site. FCT asks SER to recommend changes to the plan to accommodate this operation-al change. Using the model and incorporating these new constraints (start at Station P01, max. time of 45 min), the model suggested performing Actions 2 and 4 at Station P03 (Fig. 4), requiring 41 minutes to complete and return to the Landing Site. Interestingly, Station 3 was not part of the original route. Using the model, we determined the EVA would need 66 minutes, instead of 45, in order for the original Station P04 to yield a larger Science Yield than Station P03. The parametrization and simulation was per-formed in less than a minute, demonstrating the operational relevance of the approach. Future Efforts: The results from the Demonstrative Model suggest this tool can accelerate SER decision making on operationally relevant timelines. Use in analog activities, such as JETT5 or follow-ons, which have over a dozen stations for a crew to explore and over a dozen actions per station, will provide needed validation of the utility of this tool for planning EVAs, replanning mid-EVA, or planning follow-on EVAs based on previous results. Further integration with FCT execution monitoring tools may provide additional efficiency gains, al-lowing rapid and iterative exploration of operation-al and science decision space by the FCT and SER.

Science Operations↗

Workshop on the Growth of Continental Crust

Constraints and observations were discussed on a fundamental unsolved problem of global scale relating to the growth of planetary crusts. All of the terrestrial planets were considered, but emphasis was placed on the Earth's continental crust. The title of each session is: (1) Extraterrestrial crustal growth and destruction; (2) Constraints for observations and measurements of terrestrial rocks; (3) Models of crustal growth and destruction; and (4) Process of crustal growth and destruction.

Ashwal, Lewis D.↗

Behavior of Spinning Space Vehicles with Onboard Liquids, 2nd Edition, Technical Report B8030

Although the fundamental principles of spin stabilization are well established, uncertainty regarding the potential for rapid nutation growth caused by onboard liquids is a continuing concern. NASA and other organizations regularly encounter the issue of rapid nutation growth due to energy dissipation by liquids on spinning vehicles. Of concern is the stability of spinning upper stages and of spacecraft that spin for part or all of their missions. Several missions have required last-minute hardware or operational changes to deal with rapid nutation divergences that were identified late in the program. In some instances, major schedule slips were barely averted. In at least two cases, it was determined that a spinning upper stage was not a viable option. Historically, the "slosh" issue has been addressed by each space vehicle project individually, if it has been addressed at all. Due to budgetary and programmatic constraints, individual projects are unable to address the problem globally. Hence, there has been little effort to collect available test and flight data and use that data to make a coherent, unified picture of the "slosh" effect and how to deal with it. To some extent, each project has had to "reinvent the wheel", which can be both costly and risky. This study is a step toward correcting the situation. Specifically, the goal was to identify and collect available flight and test data for spinning vehicles with onboard liquid propellants. A total of 149 flight data points and 1,692 test points were collected as part of this study. This data was analyzed, correlated, and is presented here in a normalized form. In most cases, the normalization involves a dimensionless nutation time constant that can be used to predict performance of other vehicles with the same type of tank. For some configurations, it was also possible to identify conditions that can lead to resonance between nutational motion and liquid modes. Gaps in the knowledge base are identified and approaches to filling those gaps are outlined. The data presented here has two different but related uses. First, it can be applied directly to current and future spacecraft programs. Second, it can provide truth models for testing analytical techniques. Experience has shown that purely analytical models of the liquid "slosh" effect on spinning vehicles are unreliable unless they are validated against flight or test data. To the author's knowledge, this report contains the most extensive and varied data set available. As such, it should be a good resource for anyone seeking to develop and validate improved analytical techniques. All of the original digital data sets have been archived on disk, with copies provided to NASA/KSC. With some restrictions, many of these data sets can be made available to researchers within the United States. Whenever possible, spacecraft are identified by name in this report. However, several organizations provided access to data with the explicit proviso that their programs not be identified and that parameters be presented only in normalized form. These constraints have been respected.

Hubert, Carl↗

Global Geochemical Variation on the Lunar Surface: A Three-Element Approach

We present a method for displaying the relative abundances of three important elements (Th, Fe, and Ti) on the same map projection of the lunar surface. Using Th-, Fe-, and Ti-elemental abundances from orbital geochemical data and assigning each element a primary color, a false-color map of the lunar surface was created. This approach is similar to the ternary diagram approach presented by Davis and Spudis with some important differences, discussed later. For the present maps, Th abundances were measured by the Lunar Prospector (LP) Gamma-Ray Spectrometer(GRS).The new LPGRS low-altitude dataset was used in this analysis. Iron and Ti weight percentages were based on Clementine spectral reflectance data smoothed to the LP low altitude footprint. This method of presentation was designed to aid in the location and recognition of three principal lunar compositions: ferroan anorthosite (FAN), mare basalts (MB), and the Mg suite/ KREEP-rich rocks on the lunar surface, with special emphasis on the highlands and specific impact basins. In addition to the recognition of these endmember rock compositions, this method is an attempt to examine the relationship between elemental compositions that do not conform readily to previously accepted or observed endmember rocks in various specific regions of interest, including eastern highlands regions centered on 150 deg longitude, and a northern highlands Th-rich region observed. The LP low-altitude data has full width at half-maximum spatial resolution of about 40 km. The Clementine spectral reflectance datasets were adapted using an equal-area, gaussian smoothing routine to this footprint. In addition, these datasets, reported in weight percent of FeO and of Ti02, were adjusted to Fe and Ti weight percentages. Each dataset was then assigned one of the three primary colors: blue for Th, red for Fe, and green for Ti. For each element, the data range was normalized to represent the ratio of each point to the maximum in the dataset. (To view the color table, go to http://cass.jsc.nasa.gov/meetings/moon99/pdf/8033.pdf.) The full range of lunar longitudes is represented, but due to the lack of coverage of the Clementine data for latitudes > 70 deg and <-70 deg, the data for these regions is excluded. The differences between this approach and the ternary diagram approach of Davis and Spudis eliminate some of the uncertainty and ambiguity of the ternary diagram approach. Rather than using a ratio of Th to Ti normalized to CI chondritic ratios, and a ternary diagram with ternary apexes located at specific endmember compositional values, elemental compositions were used independently, eliminating the errors resulting from dividing numbers that can have high uncertainties, especially at low concentration. The three elements used in this method of presentation were chosen for several reasons. One reason for the inclusion of Th in this study is that it is an accurate indicator of KREEP. Iron and Ti concentrations are both low in highland regolith, causing any small fluctuations in Th to stand out very well. In addition, Fe and Ti are good compositional indicators of different mare basalts. Mixed with red for Fe, the green for Ti produces a yellow signal in high-Ti basalts. While universally high in Fe relative to the surrounding highlands, mare basalts have a diverse range of Ti values, making Ti concentration a valuable asset to the classification and identification of different basalt types. Finally, an important constraint in element selection is the availability of the global data, both from LP and Clementine results. Data for Th, Fe, and Ti are among the highest quality of existing lunar remote-sensing data. In addition, LP data for Fe and Ti will become available, enabling these data to be incorporated into the analysis. Using upper-limit values for end member rock compositions calculated from Korotev et al., attempts were made to locate the different endmember compositions of terranes on this diagram. Most strikingly, ferroan anorthosite (Th < and = 0.37 micro g/g; Fe (wt%)< and =2.29; Ti (wt%) < and = 0.22), which should appear as an almost black, reddish color, does not appear on the diagram at any noticeable frequency. Based on this analysis, the suggestion of extensive FAN regions on the lunar surface is not strong, especially at the presently accepted values for Fe and Th. However, to make sure this effect is not due to systematic errors, a thorough investigation of the precision, accuracy, and uncertainties of the Fe, Ti, and Th abundances needs to be carried out, especially at low concentrations. A particular region of interest is an area of high Th concentrations relative to Fe and Ti content north and east of Humboldtianum Crater. First observed by Lawrence et al., this region does not coincide with any visible impact structure and comprises one of the closest approximations to pure blue (high Th, very low Ti and Fe) on the lunar surface. Such an elemental composition does not lend itself readily to classification, and presents something of an anomaly. More detailed analysis of this region is needed to understand its structure and origin. There seems to be a longitudinal asymmetry in the Th concentrations of the highlands regolith. High-Th, low-Ti, and Fe regions are located between 135 deg and 180 deg longitude and between -30 deg and +30 deg latitude. While the Th levels are not high enough to attract attention in a single elemental display, the variation in the abundance of Th relative to Fe and Ti abundances can be clearly seen. The composition that these data suggest is not well represented in the sample return suite. In addition, these regions were largely missed by the Apollo orbital ground tracks, which only covered the outer edge of the areas of interest. The LP orbital Th data represent the first information about the Th concentrations in these regions of the highlands. Additional information contained in original.

Thomsen, D. R.↗