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NASA NTRS2013

Human and Natural Influences on the Changing Thermal Structure of the Atmosphere

Since the late 1970s, satellite-based instruments have monitored global changes in atmospheric temperature. These measurements reveal multidecadal tropospheric warming and stratospheric cooling, punctuated by short-term volcanic signals of reverse sign. Similar long- and short-term temperature signals occur in model simulations driven by human-caused changes in atmospheric composition and natural variations in volcanic aerosols. Most previous comparisons of modeled and observed atmospheric temperature changes have used results from individual models and individual observational records. In contrast, we rely on a large multimodel archive and multiple observational datasets. We show that a human-caused latitude/altitude pattern of atmospheric temperature change can be identified with high statistical confidence in satellite data. Results are robust to current uncertainties in models and observations. Virtually all previous research in this area has attempted to discriminate an anthropogenic signal from internal variability. Here, we present evidence that a human-caused signal can also be identified relative to the larger "total" natural variability arising from sources internal to the climate system, solar irradiance changes, and volcanic forcing. Consistent signal identification occurs because both internal and total natural variability (as simulated by state-of-the-art models) cannot produce sustained global-scale tropospheric warming and stratospheric cooling. Our results provide clear evidence for a discernible human influence on the thermal structure of the atmosphere.

Santer, Benjamin D.↗

NASA NTRS2022

Ultraviolet Spectropolarimetry Conservative and Nonconservative Mass Transfer in OB Interacting Binaries

The current consensus is that at least half of the OB stars are formed in binary or multiple star systems. The evolution of OB stars is greatly influenced by whether the stars begin as close binaries, and the evolution of the binary systems depend on whether the mass transfer is conservative or nonconservative. FUV/NUV spectropolarimetry is poised to answer the latter question. This paper discusses how the Polstar spectropolarimetry mission can characterize the degree of nonconservative mass transfer that occurs at various stages of binary evolution, from the initial mass reversal to the late Algol phase, and quantify its amount. The proposed instrument combines spectroscopic and polarimetric capabilities, where the spectroscopy can resolve Doppler shifts in UV resonance lines with 10 km/s precision, and polarimetry can resolve linear polarization with 10 −3 precision or better. The spectroscopy will identify absorption by mass streams and other plasmas seen in projection against the stellar disk as a function of orbital phase, as well as scattering from extended splash structures, including jets. The polarimetry tracks the light coming from material not seen against the stellar disk, allowing the geometry of the scattering to be tracked, resolving ambiguities left by the spectroscopy and light-curve information. For example, nonconservative mass streams ejected in the polar direction will produce polarization of the opposite sign from conservative transfer accreting in the orbital plane. Time domain coverage over a range of phases of the binary orbit are well supported by the Polstar observing strategy. Special attention will be given to the epochs of enhanced systemic mass loss that have been identified from IUE observations (pre-mass reversal and tangential gas stream impact). We show how the history of systemic mass and angular momentum loss/gain episodes can be inferred via ensemble evolution through the r–q diagram. Combining the above elements will significantly improve our understanding of the mass transfer process and the amount of mass that can escape from the system, an important channel for changing the final mass and ultimate supernova of a large number of massive stars found in binaries at close enough separation to undergo interaction.

Geraldine J. Peters↗

NASA NTRS1978

Study of turboprop systems reliability and maintenance costs

The overall reliability and maintenance costs (R&MC's) of past and current turboprop systems were examined. Maintenance cost drivers were found to be scheduled overhaul (40%), lack of modularity particularly in the propeller and reduction gearbox, and lack of inherent durability (reliability) of some parts. Comparisons were made between the 501-D13/54H60 turboprop system and the widely used JT8D turbofan. It was found that the total maintenance cost per flight hour of the turboprop was 75% higher than that of the JT8D turbofan. Part of this difference was due to propeller and gearbox costs being higher than those of the fan and reverser, but most of the difference was in the engine core where the older technology turboprop core maintenance costs were nearly 70 percent higher than for the turbofan. The estimated maintenance cost of both the advanced turboprop and advanced turbofan were less than the JT8D. The conclusion was that an advanced turboprop and an advanced turbofan, using similar cores, will have very competitive maintenance costs per flight hour.

Source record↗

NASA NTRS2002

Analysis of Carbon Nanotube Metal-Semiconductor Diode Device

We study recently reported drain current Id-drain voltage Vd characteristics of a carbon nanotube metal semiconductor diode device with the gate voltage Vg applied to modulate the carrier density in the nanotube. The diode was kink-shaped at the metal-semiconductor interface. It was shown that (1) larger negative Vg blocked Id more effectively in the negative Vd region, resulting in the rectifying Id-Vd characteristics, and that (2) positive Vg allowed Id in the both Vd polarities, resulting in the non-rectifying characteristics. The negative Vd was the Schottky reverse direction, judging from the negligible Id behavior for a wide region of -4 V less than Vd less than 0 V, with Vg = -4 V. Such negative Vg would attract positive charges from the metallic electrodes (charge reservoir) to the nanotube and lower the nanotube Fermi energy (EF). With larger negative Vg, the experiment showed that the Schottky forward direction (Vd greater than 0) had a smaller turn-on voltage and the Schottky reverse direction (Vd less than 0) was more resistant to the tunneling breakdown. Therefore, the majority carriers in the transport would be electrons since they can see a lower tunneling barrier (shallower built-in potential) in the forward direction when EF is lowered, and a thicker tunneling barrier (Schottky barrier) in the reverse direction due to the reduction in the electron density when EF is lowered.

Yamada, Toshishige↗

NASA NTRS2002

Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory

This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.

Dukeman, Greg A.↗

NASA NTRS2011

Temperature-Sensitive Coating Sensor Based on Hematite

A temperature-sensitive coating, based on hematite (iron III oxide), has been developed to measure surface temperature using spectral techniques. The hematite powder is added to a binder that allows the mixture to be painted on the surface of a test specimen. The coating dynamically changes its relative spectral makeup or color with changes in temperature. The color changes from a reddish-brown appearance at room temperature (25 C) to a black-gray appearance at temperatures around 600 C. The color change is reversible and repeatable with temperature cycling from low to high and back to low temperatures. Detection of the spectral changes can be recorded by different sensors, including spectrometers, photodiodes, and cameras. Using a-priori information obtained through calibration experiments in known thermal environments, the color change can then be calibrated to yield accurate quantitative temperature information. Temperature information can be obtained at a point, or over an entire surface, depending on the type of equipment used for data acquisition. Because this innovation uses spectrophotometry principles of operation, rather than the current methods, which use photoluminescence principles, white light can be used for illumination rather than high-intensity short wavelength excitation. The generation of high-intensity white (or potentially filtered long wavelength light) is much easier, and is used more prevalently for photography and video technologies. In outdoor tests, the Sun can be used for short durations as an illumination source as long as the amplitude remains relatively constant. The reflected light is also much higher in intensity than the emitted light from the inefficient current methods. Having a much brighter surface allows a wider array of detection schemes and devices. Because color change is the principle of operation, the development of high-quality, lower-cost digital cameras can be used for detection, as opposed to the high-cost imagers needed for intensity measurements with the current methods. Alternative methods of detection are possible to increase the measurement sensitivity. For example, a monochrome camera can be used with an appropriate filter and a radiometric measurement of normalized intensity change that is proportional to the change coating temperature. Using different spectral regions yields different sensitivities and calibration curves for converting intensity change to temperature units. Alternatively, using a color camera, a ratio of the standard red, green, and blue outputs can be used as a self-referenced change. The blue region (less than 500 nm) does not change nearly as much as the red region (greater than 575 nm), so a ratio of color intensities will yield a calibrated temperature image. The new temperature sensor coating is easy to apply, is inexpensive, can contour complex shape surfaces, and can be a global surface measurement system based on spectrophotometry. The color change, or relative intensity change, at different colors makes the optical detection under white light illumination, and associated interpretation, much easier to measure and interpret than in the detection systems of the current methods.

Bencic, Timothy J.↗

NASA NTRS1977

Static performance of vectoring/reversing non-axisymmetric nozzles

An experimental program sponsored by the Air Force Flight Dynamics Laboratory is currently in progress to determine the internal and installed performance characteristics of five different thrust vectoring/reversing non-axisymmetric nozzle concepts for tactical fighter aircraft applications. Internal performance characteristics for the five non-axisymmetric nozzles and an advanced technology axisymmetric baseline nozzle were determined in static tests conducted in January 1977 at the NASA-Langley Research Center. The non-axisymmetric nozzle models were tested at thrust deflection angles of up to 30 degrees from horizontal at throat areas associated with both dry and afterburning power. In addition, dry power reverse thrust geometries were tested for three of the concepts. The best designs demonstrated internal performance levels essentially equivalent to the baseline axisymmetric nozzle at unvectored conditions. The best designs also gave minimum performance losses due to vectoring, and reverse thrust levels up to 50% of maximum dry power forward thrust. The installed performance characteristics will be established based on wind tunnel testing to be conducted at Arnold Engineering Development Center in the fall of 1977.

Willard, C. M.↗

NASA NTRS1998

Evaluation of 3D Inverse Code Using Rotor 67 as Test Case

A design modification of Rotor 67 is carried out with a full 3D inverse method. The blade camber surface is modified to produce a prescribed pressure loading distribution, with the blade tangential thickness distribution and the blade stacking line at midchord kept the same as the original Rotor 67 design. Because of the inviscid-flow assumption used in the current version of the method, Rotor 67 geometry is modified for use at a design point different from the original design value. A parametric study with the prescribed pressure loading distribution yields the following results. In the subsonic section, smooth pressure loading shapes generally produce blades with well-behaved blade surface pressure distributions. In the supersonic section, the study shows that the strength and position of the passage shock correlate with the characteristics of the blade pressure loading shape. In general, "smooth" prescribed blade pressure loading distributions generate blade designs with reverse cambers which have the effect of weakening the passage shock.

Dang, T.↗

NASA NTRS1998

Assessment of Uncertainty in the Determination of Activation Energy for Polymeric Materials

An assessment of the experimental uncertainty in obtaining the kinetic activation energy from thermogravimetric analysis (TGA) data is presented. A neat phenolic resin, Borden SC1O08, was heated at three heating rates to obtain weight loss vs temperature data. Activation energy was calculated by two methods: the traditional Flynn and Wall method based on the slope of log(q) versus 1/T, and a modification of this method where the ordinate and abscissa are reversed in the linear regression. The modified method produced a more accurate curve fit of the data, was more sensitive to data nonlinearity, and gave a value of activation energy 75 percent greater than the original method. An uncertainty analysis using the modified method yielded a 60 percent uncertainty in the average activation energy. Based on this result, the activation energy for a carbon-phenolic material was doubled and used to calculate the ablation rate In a typical solid rocket environment. Doubling the activation energy increased surface recession by 3 percent. Current TGA data reduction techniques that use the traditional Flynn and Wall approach to calculate activation energy should be changed to the modified method.

Darby, Stephania P.↗

NASA NTRS2014

Cost Analysis In A Multi-Mission Operations Environment

Spacecraft control centers have evolved from dedicated, single-mission or single missiontype support to multi-mission, service-oriented support for operating a variety of mission types. At the same time, available money for projects is shrinking and competition for new missions is increasing. These factors drive the need for an accurate and flexible model to support estimating service costs for new or extended missions; the cost model in turn drives the need for an accurate and efficient approach to service cost analysis. The National Aeronautics and Space Administration (NASA) Huntsville Operations Support Center (HOSC) at Marshall Space Flight Center (MSFC) provides operations services to a variety of customers around the world. HOSC customers range from launch vehicle test flights; to International Space Station (ISS) payloads; to small, short duration missions; and has included long duration flagship missions. The HOSC recently completed a detailed analysis of service costs as part of the development of a complete service cost model. The cost analysis process required the team to address a number of issues. One of the primary issues involves the difficulty of reverse engineering individual mission costs in a highly efficient multimission environment, along with a related issue of the value of detailed metrics or data to the cost model versus the cost of obtaining accurate data. Another concern is the difficulty of balancing costs between missions of different types and size and extrapolating costs to different mission types. The cost analysis also had to address issues relating to providing shared, cloud-like services in a government environment, and then assigning an uncertainty or risk factor to cost estimates that are based on current technology, but will be executed using future technology. Finally the cost analysis needed to consider how to validate the resulting cost models taking into account the non-homogeneous nature of the available cost data and the decreasing flight rate. This paper presents the issues encountered during the HOSC cost analysis process, and the associated lessons learned. These lessons can be used when planning for a new multi-mission operations center or in the transformation from a dedicated control center to multi-center operations, as an aid in defining processes that support future cost analysis and estimation. The lessons can also be used by mature serviceoriented, multi-mission control centers to streamline or refine their cost analysis process.

Newhouse, M.↗

NASA NTRS1996

Increased Efficiency LED

In a semiconductor light emitting diode (LED) a large proportion of the light produced will be internally reflected when it strikes the end face of the LED at a semiconductor-air interface. This is due to the high index of refraction of most LED semiconductor materials. This problem may be partially overcome by modification of the shape of the LED by a reverse taper of the sides of the LED. Light is redirected by the taper to strike the interface at an angle closer to normal. This allows light to exit the LED that would be totally internally reflected in an untapered LED. The novelty of the present invention lies in the tapering of the sides of the LED for increased through transmission of light. Prior art devices have made use surface modifications such as roughening, addition of guiding layers, use of index matching materials and hemispherical shaping of the emitting end of the LED. Current technology LEDs have a transmission efficiency of only a few percent. An increase in this efficiency would be of great value to any technology that makes use of LEDs for light generation. The present invention is related to LAR 1 5050-SB, Collection of Light from Optical Fibers of NA greater than 1.

Egalon, Claudio Oliviera↗

NASA NTRS1990

Flux flow and flux dynamics in high-T(sub c) superconductors

Because high temperature superconductors, including BYCO and BSCCO, are type 2 superconductors with relatively low H(sub c 1) values and high H(sub c 2) values, they will be in a critical state for many of their applications. In the critical state, with the applied field between H(sub c 1) and H(sub c 2), flux lines have penetrated the material and can form a flux lattice and can be pinned by structural defects, chemical inhomogeneities, and impurities. A detailed knowledge of how flux penetrates the material and its behavior under the influence of applied fields and current flow, and the effect of material processing on these properties, is required in order to apply, and to improve the properties of, these superconductors. When the applied field is changed rapidly, the time dependence of flux change can be divided into three regions, an initial region which occurs very rapidly, a second region in which the magnetization has a 1n(t) behavior, and a saturation region at very long times. A critical field is defined for depinning, H(sub c,p) as that field at which the hysteresis loop changes from irreversible to reversible. As a function of temperature it is found that H(sub c,p) is well described by a power law with an exponent between 1.5 and 2.5. The behavior of H(sub c,p) for various materials and its relationship to flux flow and flux dynamics are discussed.

Bennett, L. H.↗

NASA NTRS1991

Flux flow and flux dynamics in high-Tc superconductors

Because high temperature superconductors, including BYCO and BSSCO, are type 2 superconductors with relatively low H(sub c 1) values and high H(sub c 2) values, they will be in a critical state for many of their applications. In the critical state, with the applied field between H(sub c 1) and H(sub c 2), flux lines have penetrated the material and can form a flux lattice and can be pinned by structural defects, chemical inhomogeneities, and impurities. A detailed knowledge of how flux penetrates the material and its behavior under the influence of applied fields and current flow, and the effect of material processing on these properties, is required in order to apply, and to improve the properties of these superconductors. When the applied field is changed rapidly, the time dependence of flux change can be divided into three regions, an initial region which occurs very rapidly, a second region in which the magnetization has a 1n(t) behavior, and a saturation region at very long times. A critical field is defined for depinning, H(sub c,p) as that field at which the hysteresis loop changes from irreversible to reversible. As a function of temperature, it is found that H(sub c,p) is well described by a power law with an exponent between 1.5 and 2.5. The behavior of H(sub c,p) for various materials and its relationship to flux flow and flux dynamics are discussed.

Bennett, L. H.↗

NASA NTRS2014

Cost Analysis in a Multi-Mission Operations Environment

Spacecraft control centers have evolved from dedicated, single-mission or single mission-type support to multi-mission, service-oriented support for operating a variety of mission types. At the same time, available money for projects is shrinking and competition for new missions is increasing. These factors drive the need for an accurate and flexible model to support estimating service costs for new or extended missions; the cost model in turn drives the need for an accurate and efficient approach to service cost analysis. The National Aeronautics and Space Administration (NASA) Huntsville Operations Support Center (HOSC) at Marshall Space Flight Center (MSFC) provides operations services to a variety of customers around the world. HOSC customers range from launch vehicle test flights; to International Space Station (ISS) payloads; to small, short duration missions; and has included long duration flagship missions. The HOSC recently completed a detailed analysis of service costs as part of the development of a complete service cost model. The cost analysis process required the team to address a number of issues. One of the primary issues involves the difficulty of reverse engineering individual mission costs in a highly efficient multi-mission environment, along with a related issue of the value of detailed metrics or data to the cost model versus the cost of obtaining accurate data. Another concern is the difficulty of balancing costs between missions of different types and size and extrapolating costs to different mission types. The cost analysis also had to address issues relating to providing shared, cloud-like services in a government environment, and then assigning an uncertainty or risk factor to cost estimates that are based on current technology, but will be executed using future technology. Finally the cost analysis needed to consider how to validate the resulting cost models taking into account the non-homogeneous nature of the available cost data and the decreasing flight rate. This paper presents the issues encountered during the HOSC cost analysis process, and the associated lessons learned. These lessons can be used when planning for a new multi-mission operations center or in the transformation from a dedicated control center to multi-center operations, as an aid in defining processes that support future cost analysis and estimation. The lessons can also be used by mature service-oriented, multi-mission control centers to streamline or refine their cost analysis process.

Felton, Larry↗

NASA NTRS2001

A Model for Formation of Dust, Soil and Rock Coatings on Mars: Physical and Chemical Processes on the Martian Surface

This model is one of many possible scenarios to explain the generation of the current surface material on Mars using chemical, magnetic and spectroscopic data From Mars and geologic analogs from terrestrial sites. One basic premise of this model is that the dust/soil units are not derived exclusively from local rocks, but are rather a product of global, and possibly remote, weathering processes. Another assumption in this model is that there are physical and chemical interactions of the atmospheric dust particles and that these two processes create distinctly different results on the surface. Physical processes distribute dust particles on rocks and drift units, forming physically-aggregated layers; these are reversible processes. Chemical reactions of the dust/soil particles create alteration rinds on rock surfaces and cohesive, crusted surface units between rocks, both of which are relatively permanent materials. According to this model the dominant components of the dust/soil particles are derived from alteration of volcanic ash and tephra, and contain primarily nanophase and poorly crystalline ferric oxides/oxyhydroxide phases as well as silicates. These phases are the alteration products that formed in a low moisture environment. These dust/soil particles also contain a smaller amount of material that was exposed to more water and contains crystalline ferric oxides/oxyhydroxides, sulfates and clay silicates. These components could have formed through hydrothermal alteration at steam vents or fumeroles, thermal fluids, or through evaporite deposits. Wet/dry cycling experiments are presented here on mixtures containing poorly crystalline and crystalline ferric oxides/oxyhydroxides, sulfates and silicates that range in size from nanophase to 1-2 pm diameter particles. Cemented products of these soil mixtures are formed in these experiments and variation in the surface texture was observed for samples containing smectites, non-hydrated silicates or sulfates. Reflectance spectra were measured of the initial particulate mixtures, the cemented products and ground versions of the cemented material. The spectral contrast in the visible/near-infrared and mid-infrared regions is significantly reduced for the cemented material compared to the initial soil, and somewhat reduced for the ground, cemented soil compared to the initial soil. The results of this study suggest that diurnal and seasonal cycling on Mars will have a profound effect on the texture and spectral properties of the dust/soil particles on the surface. The model developed in this study provides an explanation for the generation of cemented or crusted soil units and rock coatings on Mars and may explain albedo variations on the surface observed near large rocks or crater rims.

Bishop, Janice↗

NASA NTRS2006

Optimum Design of a Compound Helicopter

A design and aeromechanics investigation was conducted for a 100,000-lb compound helicopter with a single main rotor, which is to cruise at 250 knots at 4000 ft/95 deg F condition. Performance, stability, and control analyses were conducted with the comprehensive rotorcraft analysis CAMRAD II. Wind tunnel test measurements of the performance of the H-34 and UH-1D rotors at high advance ratio were compared with calculations to assess the accuracy of the analysis for the design of a high speed helicopter. In general, good correlation was obtained when an increase of drag coefficients in the reverse flow region was implemented. An assessment of various design parameters (disk loading, blade loading, wing loading) on the performance of the compound helicopter was conducted. Lower wing loading (larger wing area) and higher blade loading (smaller blade chord) increased aircraft lift-to-drag ratio. However, disk loading has a small influence on aircraft lift-to-drag ratio. A rotor parametric study showed that most of the benefit of slowing the rotor occurred at the initial 20 to 30% reduction of the advancing blade tip Mach number. No stability issues were observed with the current design. Control derivatives did not change significantly with speed, but the did exhibit significant coupling.

Yeo, Hyeonsoo↗

NASA NTRS2006

The Distant Magnetotail Under Long Duration, Very Northward IMF Conditions: October 22-24, 2003

A unique 32 hour interval of very northward Interplanetary Magnetic Field (IMF) on October 22-24, 2003 created a exceptionally thick cold dense magnetotail plasma sheet, a small polar cap and accompanying small tail lobe. These features were detected by the Cluster DMSP and FAST spacecraft and modeled by a global simulation as described in papers by Oieroset et al. (2005) and Li et al. (2005). During the same interval the Wind spacecraft was passing through the center of the magnetotail about 130 Re downstream of Earth. Wind results will be described that reveal a very unusual magnetotail characterized by (1) continual tailward flow of 200-400 km/s with densities in the range 0.2-3/cc, both of whch are clearly less than those expected in the magnetosheath, (2) a mostly northward Bz but with a predominant Bx field component with sign reversals indicating crossings between the two hemispheres of the tail, and (3) velocity waves superposed on the downstream flow with peak-to-peak amplitudes of 100 to 200 km/s, periods of 10 to 20 minutes and clockwise polarization. Low altitude DMSP and Fast measurements reveal an auroral oval with enhanced latitudinal thickness and a small polar cap filled with structured precipitzting electrons and few ions. A new global MHD simulation of the event exhibits a highly elliptical tail of diminished cross-section at 130 Re with major axis aligned with the northward IMF. The tail current sheet also tends to be aligned in a north-south direction with the two tail hemispheres to the east and west with their polarities depending on prior history of the IMF. The simulation appears to be consistent with many, but not all, of the observations. High latitude cusp reconnection and subsequent downtail flow of closed field lines may explain the tail structure, but the waves are more likely due to the Kelvin-Helmholtz instability often thought to occur during northward IMF conditions.

Fairfield, Donald H.↗

NASA NTRS1998

Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field

The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.

Voorhies, C.↗