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Axial flow positive displacement worm gas generator

An axial flow positive displacement engine has an inlet axially spaced apart and upstream from an outlet. Inner and outer bodies have offset inner and outer axes extend from the inlet to the outlet through first, second, and third sections of a core assembly in serial downstream flow relationship. At least one of the bodies is rotatable about its axis. The inner and outer bodies have intermeshed inner and outer helical blades wound about the inner and outer axes respectively. The inner and outer helical blades extend radially outwardly and inwardly respectively. The helical blades have first, second, and third twist slopes in the first, second, and third sections respectively. The first twist slopes are less than the second twist slopes and the third twist slopes are less than the second twist slopes. A combustor section extends axially downstream through at least a portion of the second section.

Murrow, Kurt David↗

Bridging Empirical and Physical Approaches for Landslide Monitoring and Early Warning

Rainfall-triggered landslides typically occur and are evaluated at local scales, using slope-stability models to calculate coincident changes in driving and resisting forces at the hillslope level in order to anticipate slope failures. Over larger areas, detailed high resolution landslide modeling is often infeasible due to difficulties in quantifying the complex interaction between rainfall infiltration and surface materials as well as the dearth of available in situ soil and rainfall estimates and accurate landslide validation data. This presentation will discuss how satellite precipitation and surface information can be applied within a landslide hazard assessment framework to improve landslide monitoring and early warning by considering two disparate approaches to landslide hazard assessment: an empirical landslide forecasting algorithm and a physical slope-stability model. The goal of this research is to advance near real-time landslide hazard assessment and early warning at larger spatial scales. This is done by employing high resolution surface and precipitation information within a probabilistic framework to provide more physically-based grounding to empirical landslide triggering thresholds. The empirical landslide forecasting tool, running in near real-time at http://trmm.nasa.gov, considers potential landslide activity at the global scale and relies on Tropical Rainfall Measuring Mission (TRMM) precipitation data and surface products to provide a near real-time picture of where landslides may be triggered. The physical approach considers how rainfall infiltration on a hillslope affects the in situ hydro-mechanical processes that may lead to slope failure. Evaluation of these empirical and physical approaches are performed within the Land Information System (LIS), a high performance land surface model processing and data assimilation system developed within the Hydrological Sciences Branch at NASA's Goddard Space Flight Center. LIS provides the capabilities to quantify uncertainty from model inputs and calculate probabilistic estimates for slope failures. Results indicate that remote sensing data can provide many of the spatiotemporal requirements for accurate landslide monitoring and early warning; however, higher resolution precipitation inputs will help to better identify small-scale precipitation forcings that contribute to significant landslide triggering. Future missions, such as the Global Precipitation Measurement (GPM) mission will provide more frequent and extensive estimates of precipitation at the global scale, which will serve as key inputs to significantly advance the accuracy of landslide hazard assessment, particularly over larger spatial scales.

Kirschbaum, Dalia↗

Topographically Induced Thermal Effects on Lunar Hydrogen Distributions: Correlated Observations from the LRO LEND and LOLA Instruments

The question of whether water exists on the Moon's surface has long been an enigma to Lunar researchers. Largely, this was due to the thermally extreme lunar surface environment that would seem to preclude any long term maintenance, manufacture, transport or accumulation of hydrogen (H) volatiles over most of the lunar surface. As a result, for many years the cold permanent shadow regions (PSR) in the bottoms of craters near the lunar poles appeared to provide the basic conditions at least for maintenance of lunar hydrogen. Importantly, recent discoveries indicate that there is some hydrogen at the poles. However, the picture of the lunar hydrogen budget may be more complex than the PSR hypothesis has suggested. This evidence comes from observations by the Lunar Exploration Neutron Detector (LEND) onboard the Lunar Reconnaissance Orbiter (LRO) that inclici1te 1) some H concentrations lie outside PSR and 2) though a few of the larger PSR's have high hydrogen, PSR does not appear to be an independent factor influencing the large-scale suppression of polar epithermals observed by LEND and the Lunar Prospector Neutron Spectrometer. In this research we investigate the possibility that the thermal contrast between pole-facing and equator facing-slopes is a factor influencing the surface distributions of lunar H. We perform this bulk correlated observation and study by developing a thermal proxy from slope data of the Lunar Orbiting Laser Altimeter (LOLA) digital elevation model (DEM) which is registered with the collimated LEND epithermal map. From the LOLA transforms we impose a thermal functional decomposition and systematic statistical analysis of the LEND epithermal map. Our hypothesis testing suggests in most high latitude bands studied> +/- 45 deg: Epithermal rates in pole-facing slopes are significantly lower than epithermal rates in equivalent equator-facing slopes. As a control study, we find that there is no statistically significant difference between equivalent east and west facing slopes. This finding suggests topographic modulation of insolation is a factor influencing the lunar H budget. Importantly, this result is consistent with observations in terrestrial, Martian research.

McClanahan, T. P.↗

Satellite Remote Sensing Estimation of River Discharge: Application to the Yukon River Alaska

A methodology based on general hydraulic relations for rivers has been developed to estimate the discharge (flow rate) of rivers using satellite remote sensing observations. The estimates of discharge, flow depth, and flow velocity are derived from remotely observed water surface area, water surface slope, and water surface height, and demonstrated for two reaches of the Yukon River in Alaska, at Eagle (reach length 34.7 km) and near Stevens Village (reach length 38.3 km). The method is based on fundamental equations of hydraulic flow resistance in rivers, including the Manning equation and the Prandtl-von Karman universal velocity distribution equation. The method employs some new hydraulic relations to help define flow resistance and height of the zero flow boundary in the channel. Estimates are made both with and without calibration. The water surface area of the river reach is measured by using a provisional version of the U.S. Geological Survey (USGS) Landsat based product named Dynamic Surface Water Extent (DSWE). The water surface height and slope measurements require a self-consistent datum, and are derived from observations from the Jason-2 satellite altimeter mission. At both reach locations, the Jason-2 radar altimeter non-winter heights consistently tracked the stage recorded at USGS streamgages with a standard deviation of differences (error) during the non-winter periods of less than 7%. Part of the error may be due to differences in the gage and altimeter crossing locations with respect to the range of stage change and the response to changes in discharge at the upstream and downstream locations. For the non-winter periods, the radar derived slope estimates (mean = 0.0003) were constant over the mission lifetime, and in agreement with previously measured USGS water surface slopes and slopes determined from USGS topographic maps. The accuracy of the mean of the uncalibrated daily estimates of discharge varied between reaches, ranging from 13% near Stevens Village (N = 90) to −21% at Eagle (N = 246) based on the absolute error, and 5% to −6% based on the error of the log of the estimates. Calibrating to the mean of USGS daily discharge estimates from the streamflow rating for the same period of record at each streamgage resulted in mean absolute errors ranging from 1% to 2%, and log errors ranging from 1% or less. The error pattern of the estimates shows that without calibration, even though the mean is well simulated, the high and low end values over the range of estimates may have significant bias.

Bjerklie, David M.↗

Understanding the Space Weathering of Mercury Through Laboratory Experiments

Introduction: Airless surfaces across the solar system are continually modified by energetic particles from solar wind and micrometeoroid bombardment [1,2]. This process is known as space weathering, and it alters the chemical, microstructural, and optical properties of surface regoliths on airless bodies, including Mercury. On the Moon and S-type asteroids, the reflectance spectral signatures of space weathering include reddening (increasing reflectance with increasing wavelength), darkening (lowering of reflectance), and the attenuation of characteristic absorption bands [2]. Such spectral changes are driven by the production of Fe-bearing nanoparticles(npFe) through both solar wind irradiation and micrometeoroid bombardment. While our understanding of space weathering for the Moon and near-Earth S-types asteroids is advanced, insight into how these processes operate on other planetary bodies is limited. In particular, Mercury experiences a uniquely intense space weathering environment than planetary counterparts at 1 AU, including a moreintense solar wind flux and higher velocity micrometeoroid impacts [4]. Additionally, Mercury has a surface composition unique in the inner solar system, including regions of the surface with very low albedo known as the low reflectance material (LRM), which is enriched in carbon, likely graphite, up to 4wt.% [5].In addition, the concentration of Fe across Mercury’s surface islow (<2 wt.%) compared to the Moonor S-type asteroids asteroids[6]. Our understanding of the effects of space weathering on C-rich and Fe-poor phases is limited. Since Fe plays a critical role inthe development of space weathering characteristicson other airless surfaces(e.g., npFe), its limited availability may significantly affect the development of space weathering features in Mercury surface materials. We can simulate space weathering processes in the laboratory to explore their effects on the microstructural, chemical, and spectral characteristics of Mercury surface materials[7]. Here we used pulsed laser irradiation to simulate the short duration, high-temperature events associated with micrometeoroid impacts. We performed coordinated analyses including reflectance spectroscopy and electron microscopy to investigate the spectral, chemical, and microstructural changes in these mercurian analog samples. Methods: For these experiments, we usedforsteritic olivine with varying FeOcontents, a mineral phase proposed to be abundant on the surface of Mercury. We mixed each sample with graphite to simulate LRM regions of the surface. Wesynthesized the olivinesamplesat 1-bar at NASA’s Johnson Space Centerand prepared pressed powder pellets for laser irradiation [8].We prepared three samples, each with a base layer of olivineto maintain structural integrity and topped witha surface layer containing the graphite-olivine mixture: 1) Sample SC-001 San Carlos olivine(Fo90.91),2)Sample F-S-002 with0.05 wt.% FeO olivine, and 3) F-T-004 with 0.53 wt.% FeO olivine. Each sample was mixed with 5 wt.% powdered graphite and had grain sizes ranging from 45to 125μm. We irradiated each sample usinga pulsed Nd-YAG laser, (l=1064 nm, ~6 ns pulse duration, energy of 48 mJ/pulse) while undervacuumat Northern Arizona University. The laser was rastered1x and then 5x over the surfaceof each sample to simulate progressive space weathering. We collected in situreflectance spectra from the samples after each laser pulse witha Nicolet IS50 Fourier-Transform Infrared spectrometer (lfrom 0.65-2.5 μm). We used an FEI Nova NanoSEM200scanning electron microscope (SEM) and a Hitachi TM4000 Plus benchtop SEM at Purdue University to image the surface morphology and topography of the samples. We extracted thin sections for analysis in the transmission electron microscope(TEM)using the FEI Helios NanoLab 660 focused ion beam (FIB) SEM at the University of Arizona.We performed analysis of the microstructural and chemical characteristics of the samples using the 200 keV JEOL 2500 scanning TEM at Johnson Space Center. Reflectance Spectroscopy Results:Reflectance spectra for each sample are shown in Fig. 1.SC-001:The spectrum of the unirradiated sample exhibits a weak 1.0 μm absorption feature, associated with Fe2+in the olivine,and low overall reflectance (Fig. 1a). Thereflectance and the depth of the absorption band increases after 1x laser raster but are at their lowest after 5x laser rasters.F-T-004:The unirradiated sample has a blue-sloped spectrum with low reflectance without identifiable absorption features (Fig. 1b). With progressive laser irradiation, the sample reflectance increases and becomes strongly red-sloped.F-S-002:The unirradiated sample exhibits a dark, blue-slopedspectrum. The brightness of the sample increases significantly from <0.2average reflectance over >0.8 reflectance in the most irradiated sampleand thespectral slope also becomesslightly reddened (Fig. 1c). Microstructural and Chemical Analysis: Two primary alteration textures were observed in the samples exposed to simulated space weathering: 1) fluffy C-rich,and 2) vesiculated melt. The fluffy C-rich texture is composed oflow-densitydeposits distributed across the surface of the sample(Fig. 2A). Analysis of a FIB section extracted from a low-density C-rich region in sample SC-001 reveals multiple globule-type deposits, discrete from stacked graphite, likely produced via melting from the laser irradiation [9].The vesiculated melt textureis smooth and uniformly distributed across isolated regions of the sample surface. The vesicles measure up to 100s of nmin diameter. Analysis of a FIB section from this texture was extracted from sample F-T-004 reveals a layer of amorphous melt material, close to 100 nm thick and uniform across the FIB section (Fig. 2B). Isolated regions of this melt layer contain small nanoparticles, <5 nm in diameter. Chemical analysis through energy dispersive X-ray spectroscopy reveals the composition of this layer is enriched in Si and depleted in Mg and O compared to the underlying sample. Implications for Space Weathering on Mercury: Previous experiments simulating space weathering of Mercury have showndarkening and reddening of spectra[7,10].However, our use of low-Fe materials and graphite to create a sample set more analogous to the mercurian surface. Our results indicate that sample composition plays a significant and important role in the space weathering of Mercury. In particular, our spectral data demonstrates a strong correlation between spectral slope, Fe content, and simulated space weathering. While the variation in FeO content between samples F-S-002 and F-T-004 is <0.6 wt.%, the spectra deviate from flat to strongly red-sloped(F-T-004). This reddeningmay be linked to the presence of very small nanoparticles observed in the melt textures extracted from sample F-T-004. For the SC-001 sample, the fluffy C-rich textures may be developed by the amalgamation of small graphite particles into these unique morphologies. Such observations indicate that space weathering on Mercury may result in both familiar and new microstructural and chemical characteristics. References: [1]Hapke B. (2001) J. Geophys. Res.-Planet.,106,10039–10073. [2]Pieters C.M. and Noble S.K. (2016) J. Geophys. Res-Planet., 121, 1865–1884. [3] Lucey P.G., and Riner, M.A. (2011) Icarus,212, 451-462.[4]CintalaM.J.(1992)J. Geophys. Res.-Planet.,97,947–973.[5]Klima R.L.et al.(2018)Geophys.Res.Letters, 45, 2945–2953. [6]Nittler L.R., et al. (2011) Science 333, 1847-1850.[7]Sasaki S. and Kurahashi E. (2004) Space weathering on Mercury, Adv.Space Res., 33, 2152-2155.[8] Vander KaadenK.E., et al. (2018) LPSCXLIX, Abstract 1230. [9] McGlaun M.L. et al. (2019) LPSCL, Abstract 2019. [10] TrangD.et al. (2018)LPSCXLIX,Abstract2083

M S Thompson↗

Passive imaging based multi-cue hazard detection spacecraft safe landing

Accurate assessment of potentially damaging ground hazards during the spacecraft EDL (Entry, Descent and Landing) phase is crucial to insure a high probability of safe landing. A lander that encounters a large rock, falls off a cliff, or tips over on a steep slope can sustain mission ending damage. Guided entry is expected to shrink landing ellipses from 100-300 km to -10 km radius for the second generation landers as early as 2009. Regardless of size and location, however, landing ellipses will almost always contain hazards such as craters, discontinuities, steep slopes, and large rocks. It is estimated that an MSL (Mars Science Laboratory)-sized lander should detect and avoid 16- 150m diameter craters, vertical drops similar to the edges of 16m or 3.75m diameter crater, for high and low altitude HAD (Hazard Detection and Avoidance) respectively. It should also be able to detect slopes 20' or steeper, and rocks 0.75m or taller. In this paper we will present a passive imaging based, multi-cue hazard detection and avoidance (HDA) system suitable for Martian and other lander missions. This is the first passively imaged HDA system that seamlessly integrates multiple algorithm-crater detection, slope estimation, rock detection and texture analysis, and multicues- crater morphology, rock distribution, to detect these hazards in real time.

hazard detection↗

Derivation of formulas for root-mean-square errors in location, orientation, and shape in triangulation solution of an elongated object in space

Formulas are derived for the root-mean-square (rms) displacement, slope, and curvature errors in an azimuth-elevation image trace of an elongated object in space, as functions of the number and spacing of the input data points and the rms elevation error in the individual input data points from a single observation station. Also, formulas are derived for the total rms displacement, slope, and curvature error vectors in the triangulation solution of an elongated object in space due to the rms displacement, slope, and curvature errors, respectively, in the azimuth-elevation image traces from different observation stations. The total rms displacement, slope, and curvature error vectors provide useful measure numbers for determining the relative merits of two or more different triangulation procedures applicable to elongated objects in space.

Long, S. A. T.↗

The Hubble relation for nonstandard candles and the origin of the redshift of quasars

It is shown that the magnitude-log (redshift) relation for brightest quasars can have a slope different from the value expected for standard candles. The value of this slope depends on the luminosity function and its evolution. Therefore the difference of this slope from the expected value cannot be used as evidence against the cosmological origin of the redshift of the quasars. It is shown that the observed variation of the luminosity of the brightest objects with redshift is consistent with the cosmological hypothesis and that it agrees with (and perhaps could be used to complement) the luminosity function obtained from V/Vm analysis. It is also shown that the nonzero slope of the magnitude-log (redshift) relation rules out the local quasar hypothesis, where it is assumed that the sources are nearby (less than 500 Mpc), that the bulk of their redshift is intrinsic, and that there is no dependence on distance of the intrinsic properties of the sources.

Petrosian, V.↗

Measured noise reductions resulting from modified approach procedures for business jet aircraft

Five business jet airplanes were flown to determine the noise reductions that result from the use of modified approach procedures. The airplanes tested were a Gulfstream 2, JetStar, Hawker Siddeley 125-400, Sabreliner-60 and LearJet-24. Noise measurements were made 3, 5, and 7 nautical miles from the touchdown point. In addition to a standard 3 deg glide slope approach, a 4 deg glide slope approach, a 3 deg glide slope approach in a low-drag configuration, and a two-segment approach were flown. It was found that the 4 deg approach was about 4 EPNdB quieter than the standard 3 deg approach. Noise reductions for the low-drag 3 deg approach varied widely among the airplanes tested, with an average of 8.5 EPNdB on a fleet-weighted basis. The two-segment approach resulted in noise reductions of 7 to 8 EPNdB at 3 and 5 nautical miles from touchdown, but only 3 EPNdB at 7 nautical miles from touchdown when the airplanes were still in level flight prior to glide slope intercept. Pilot ratings showed progressively increasing workload for the 4 deg, low-drag 3 deg, and two-segment approaches.

Burcham, F. W., Jr.↗

Possible evidence for latitude-dependent cosmic-ray modulation

It is suggested that the slope of the modulated proton spectrum at low energies (less than 250 MeV) is not well accounted for in a steady state spherically symmetrical cosmic-ray modulation model and therefore may contain information on the effects of latitude variations. Under quasi-steady interplanetary conditions, slopes steeper than unity have been observed for low-energy protons. It is shown that the slope of unity or a steeper slope may be a natural consequence of having a region of enhanced modulation lying immediately above or below the solar equatorial plane and therefore may be due to the variation of interplanetary conditions with heliocentric latitude.

Fisk, L. A.↗

The morphological evolution of mare-highland contacts - A potential measure of relative mare surface age

The uniform breaks in slopes along many mare-highland contacts may be debris aprons transported primarily by impact erosion at relatively slow rates. Other suggestions, such as the 'high lava mark' hypothesis, appear inadequate to explain all of the unique characteristics of these widespread features. There is a reasonable correlation of overall slope form (profile) and apron distribution with established mare age provinces. Distinctive debris aprons in the younger maria could represent the initial stages of lunar slope degradation produced mainly by the postmare impact flux. The growth of debris aprons must be qualitatively related to the impact flux recorded on adjacent mare surfaces and could provide an approximate means of extrapolating relative mare ages to highland scarps and crater walls. By combining detailed measurements of lunar slopes with development of a realistic model for impact modification of these features, approximate limits for the cumulative lunar flux distribution through time might be derived.

Young, R. A.↗

Modeling of terrain gradient for stochastically spaced rows of a measurement matrix

Terrain gradients are employed to evaluate passable regions for unmanned martian roving vehicle. Range data matrix is displaced randomly row wise at the shallow elevation angles near the skyline. The magnitude of the measurement noise in the elevation angles can approach that of the spacing of the same angle. By using a variable incremental data spacing scanning scheme, one can estimate this signal noise ratio. It is found that the error in slope estimate at far distance becomes large for a given elevation angle error. Evaluation of the in-path slopes can be expressed in terms of the inverse of the range slopes. This is because of the fact that the elevation angle is considered as a random variable while the range data are relatively less noisy. An error analysis is performed and it is found that the change of slope is a nonlinear function of the error in elevation angle.

Mediavilla, R.↗

Achievable flatness in a large microwave power transmitting antenna

A dual reference SPS system with pseudoisotropic graphite composite as a representative dimensionally stable composite was studied. The loads, accelerations, thermal environments, temperatures and distortions were calculated for a variety of operational SPS conditions along with statistical considerations of material properties, manufacturing tolerances, measurement accuracy and the resulting loss of sight (LOS) and local slope distributions. A LOS error and a subarray rms slope error of two arc minutes can be achieved with a passive system. Results show that existing materials measurement, manufacturing, assembly and alignment techniques can be used to build the microwave power transmission system antenna structure. Manufacturing tolerance can be critical to rms slope error. The slope error budget can be met with a passive system. Structural joints without free play are essential in the assembly of the large truss structure. Variations in material properties, particularly for coefficient of thermal expansion from part to part, is more significant than actual value.

Ried, R. C.↗

The topographic effect on spectral response from nadir-pointing sensors

It is difficult to interpret multispectral Landsat earth resources data in areas of rugged and mountainous terrain because of the topographic effect on the sensor response. The objectives of this study were to examine and quantify the topographic effect on the sensor response from a uniform sand surface, to assess a simple theoretical incidence model for modeling the radiance from the surface, and to simulate Landsat sensor response due to the topographic effect. A field experiment was designed to collect data from a large range of slope angles and aspects at a range of solar elevations, using a hand-held radiometer. Analysis of these data showed that the magnitude of the topographic effect varied as a function of the solar elevation, the azimuthal orientation of the slope, and the slope inclination. The field measured variations in spectral response were found to have generally strong correlations with the theoretical model, and it was shown that the applicability of the Lambertian assumption varied within and between data sets. It is concluded that if slope angle, aspect, and solar zenith angle and azimuth are known, a technique incorporating a model to reduce the topographic effect prior to multispectral classification may be developed.

Holben, B. N.↗

A data base approach for prediction of deforestation-induced mass wasting events

A major topic of concern in timber management is determining the impact of clear-cutting on slope stability. Deforestation treatments on steep mountain slopes have often resulted in a high frequency of major mass wasting events. The Geographic Information System (GIS) is a potentially useful tool for predicting the location of mass wasting sites. With a raster-based GIS, digitally encoded maps of slide hazard parameters can be overlayed and modeled to produce new maps depicting high probability slide areas. The present investigation has the objective to examine the raster-based information system as a tool for predicting the location of the clear-cut mountain slopes which are most likely to experience shallow soil debris avalanches. A literature overview is conducted, taking into account vegetation, roads, precipitation, soil type, slope-angle and aspect, and models predicting mass soil movements. Attention is given to a data base approach and aspects of slide prediction.

Logan, T. L.↗

Investigation of the equatorial orographic-dynamic mechanism applying the bounded derivative method

A system of equations which describe the motion of a barotropic fluid in the presence of bottom topography are presented. The mathematical expression for orography is developed and the bounded derivative initialization method is applied to suppress gravitational oscillations. A stationary orographic trough is simulated. The geopotential and zonal motion have maximum deviation from the mean state at the top of the mountain. Regarding meridional speed, outflow occurs on the windward slope and inflow on the leeward slope. Divergence of order (10(-6)s(-1) is found on the windward slope while convergence of the same order of magnitude resides on the leeward slope. This outcome may have interesting implications regarding real climatology occurring over the equatorial regions of continental land masses.

Semazzi, F. H. M.↗

A New Technique for System-to-system Transfer of Surface Data

The purpose is to describe a recently developed technique aimed at providing a universal interface between surface types. In brief, a software package was developed which functions a common denominator of CAD/CAM surface types. This software enable one to convert from any given surface representation to any other target representation. The tiles maintain the same slope continuity as the target surface gram, bicubic patches are used since they allow one to match point, slope, and twist vectors to the target surface. Thus, slopes can be continuous or discontinuous as they are on the target surface. The patches can be of lower order if desired. For example, if only point information is available, the patches produced will be bilinear; however, the number of patches required is likely to increase correspondingly. The patches can be of higher order although many systems will not accept patches of more than order four. The final result of the program is a rectangular grid of bicubic patches. The patches fit the target surface exactly at their corners. Also, the patch corners have the same tangent and twist vectors. Adjacent patches will have slope continuity, unless a discontinuity was indicated by the target surface.

Sterling, M. W.↗

The spatial structure of terrain - A process signal in satellite digital images

Pattern recognition procedures applied to Landsat imagery carry an implicit assumption that the digital data are independently distributed. That assumption is incorrect over virtually any terrain. Deviations from independence occur because slopes follow a systematic pattern of variation arising from the slope-forming processes. That pattern can be identified using the stochastic process methodology of Box and Jenkins.Angles of adjacent slopes are autocorrelated and the bidirectional reflectance function transfers these systematic slope changes to the sensor. Imagery becomes autocorrelated through this transfer. Autocorrelation in the imagery can be removed through direct calculation from a digital elevation model or by use of stochastic process methodology. The latter has the advantage that the residuals are white noise; and it is applicable in any area, even where a D.E.M. is unavailable. The stochastic process signal can be used to study terrain processes.

Craig, R. G.↗