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All sourcesNASA NTRSDOE OSTI
NASA NTRS1977

A local earthquake coda magnitude and its relation to duration, moment M sub O, and local Richter magnitude M sub L

A relationship was found between the seismic moment, M sub O, of shallow local earthquakes and the total duration of the signal, t, in seconds, measured from the earthquakes origin time, assuming that the end of the coda is composed of backscattering surface waves due to lateral heterogenity in the shallow crust following Aki. Using the linear relationship between the logarithm of M sub O and the local Richter magnitude M sub L, a relationship between M sub L and t, was found. This relationship was used to calculate a coda magnitude M sub C which was compared to M sub L for Southern California earthquakes which occurred during the period from 1972 to 1975.

Suteau, A. M.↗
NASA NTRS2017

Determination of the Limiting Magnitude

The limiting magnitude of an optical camera system is an important property to understand since it is used to find the completeness limit of observations. Limiting magnitude depends on the hardware and software of the system, current weather conditions, and the angular speed of the objects observed. If an object exhibits a substantial angular rate during the exposure, its light spreads out over more pixels than the stationary stars. This spreading causes the limiting magnitude to be brighter when compared to the stellar limiting magnitude. The effect, which begins to become important when the object moves a full width at half max during a single exposure or video frame. For targets with high angular speeds or camera systems with narrow field of view or long exposures, this correction can be significant, up to several magnitudes. The stars in an image are often used to measure the limiting magnitude since they are stationary, have known brightness, and are present in large numbers, making the determination of the limiting magnitude fairly simple. In order to transform stellar limiting magnitude to object limiting magnitude, a correction must be applied accounting for the angular velocity. This technique is adopted in meteor and other fast-moving object observations, as the lack of a statistically significant sample of targets makes it virtually impossible to determine the limiting magnitude before the weather conditions change. While the weather is the dominant factor in observing satellites, the limiting magnitude for meteors also changes throughout the night due to the motion of a meteor shower or sporadic source radiant across the sky. This paper presents methods for determining the limiting stellar magnitude and the conversion to the target limiting magnitude.

Kingery, Aaron↗
NASA NTRS2017

Determination of the Meteor Limiting Magnitude

We present our method to calculate the meteor limiting magnitude. The limiting meteor magnitude defines the faintest magnitude at which all meteors are still detected by a given system. An accurate measurement of the limiting magnitude is important in order to calculate the meteoroid flux from a meteor shower or sporadic source. Since meteor brightness is linked to meteor mass, the limiting magnitude is needed to calculate the limiting mass of the meteor flux measurement. The mass distribution of meteoroids is thought to follow a power law, thus being slightly off in the limiting magnitude can have a significant effect on the measured flux. Sky conditions can change on fairly short timescales; therefore one must monitor the meteor limiting magnitude at regular intervals throughout the night, rather than just measuring it once. We use the stellar limiting magnitude as a proxy of the meteor limiting magnitude. Our method for determining the stellar limiting magnitude and how we transform it into the meteor limiting magnitude is presented. These methods are currently applied to NASA's wide-field meteor camera network to determine nightly fluxes, but are applicable to other camera networks.

A Kingery↗
NASA NTRS2023

Recent Changes in Cyanobacteria Algal Bloom Magnitude in Large Lakes Across the Contiguous United States

Cyanobacterial blooms in inland lakes produce large quantities of biomass that impact drinking water systems, recreation, and tourism and may produce toxins that can adversely affect public health. This study analyzed nine years of satellite-derived bloom records and compared how the bloom magnitude has changed from 2008-2011 to 2016-2020 in 1881 of the largest lakes across the contiguous United States (CONUS). We determined bloom magnitude each year as the spatio-temporal mean cyanobacteria biomass from May to October and in concentrations of chlorophyll-a. We found that bloom magnitude decreased in 465 (25%) lakes in the 2016-2020 23 period. Conversely, there was an increase in bloom magnitude in only 81 lakes (4%). Bloom magnitude either didn’t change, or the observed change was in the uncertainty range in the majority of the lakes (n=1335, 71%). Above-normal wetness and normal or below-normal maximum temperature over the warm season may have caused the decrease in bloom magnitude in the eastern part of the CONUS in recent years. On the other hand, a hotter and dryer warm season in the western CONUS may have created an environment for increased algal biomass. While more lakes saw a decrease in bloom magnitude, the pattern was not monotonic over the CONUS. The variations in temporal changes in bloom magnitude within and across climatic regions depend on the interactions between land use land cover (LULC) and physical factors such as temperature and precipitation. Despite expectations suggested by recent global studies, bloom magnitude has not increased in larger US lakes over this time period.

remote sensing↗
NASA NTRS1981

Stability of individual loudness functions obtained by magnitude estimation and production

A correlational analysis of individual magnitude estimation and production exponents at the same frequency is performed, as is an analysis of individual exponents produced in different sessions by the same procedure across frequency (250, 1000, and 3000 Hz). Taken as a whole, the results show that individual exponent differences do not decrease by counterbalancing magnitude estimation with magnitude production and that individual exponent differences remain stable over time despite changes in stimulus frequency. Further results show that although individual magnitude estimation and production exponents do not necessarily obey the .6 power law, it is possible to predict the slope of an equal-sensation function averaged for a group of listeners from individual magnitude estimation and production data. On the assumption that individual listeners with sensorineural hearing also produce stable and reliable magnitude functions, it is also shown that the slope of the loudness-recruitment function measured by magnitude estimation and production can be predicted for individuals with bilateral losses of long duration. Results obtained in normal and pathological ears thus suggest that individual listeners can produce loudness judgements that reveal, although indirectly, the input-output characteristic of the auditory system.

Hellman, R. P.↗
NASA NTRS1979

Self-motion magnitude estimation during linear oscillation - Changes with head orientation and following fatigue

Two types of experiments concerning the estimated magnitude of self-motion during exposure to linear oscillation on a parallel swing are described in this paper. Experiment I examined changes in magnitude estimation as a function of variation of the subject's head orientation, and Experiments II a, II b, and II c assessed changes in magnitude estimation performance following exposure to sustained, 'intense' linear oscillation (fatigue-inducting stimulation). The subjects' performance was summarized employing Stevens' power law R = k x S to the nth, where R is perceived self-motion magnitude, k is a constant, S is amplitude of linear oscillation, and n is an exponent). The results of Experiment I indicated that the exponents, n, for the magnitude estimation functions varied with head orientation and were greatest when the head was oriented 135 deg off the vertical. In Experiments II a-c, the magnitude estimation function exponents were increased following fatigue. Both types of experiments suggest ways in which the vestibular system's contribution to a spatial orientation perceptual system may vary. This variability may be a contributing factor to the development of pilot/astronaut disorientation and may also be implicated in the occurrence of motion sickness.

Parker, D. E.↗
NASA NTRS1982

Statistics of Delta v magnitude for a trajectory correction maneuver containing deterministic and random components

A number of interplanetary missions now being planned involve placing deterministic maneuvers along the flight path to alter the trajectory. Lee and Boain (1973) examined the statistics of trajectory correction maneuver (TCM) magnitude with no deterministic ('bias') component. The Delta v vector magnitude statistics were generated for several values of random Delta v standard deviations using expansions in terms of infinite hypergeometric series. The present investigation uses a different technique (Monte Carlo simulation) to generate Delta v magnitude statistics for a wider selection of random Delta v standard deviations and also extends the analysis to the case of nonzero deterministic Delta v's. These Delta v magnitude statistics are plotted parametrically. The plots are useful in assisting the analyst in quickly answering questions about the statistics of Delta v magnitude for single TCM's consisting of both a deterministic and a random component. The plots provide quick insight into the nature of the Delta v magnitude distribution for the TCM.

Bollman, W. E.↗
NASA NTRS2019

Measurement of Cyanobacterial Bloom Magnitude Using Satellite Remote Sensing

Cyanobacterial harmful algal blooms (cyano HABs) are a serious environmental, water quality and public health issue worldwide because of their ability to form dense biomass and produce toxins. Models and algorithms have been developed to detect and quantify cyanoHABs biomass using remotely sensed data but not for quantifying bloom magnitude,information that would guide water quality management decisions. We propose a method to quantify seasonal and annual cyanoHAB magnitude in lakes and reservoirs. The magnitude is the spatio temporal mean of weekly or biweekly maximum cyanobacteria biomass for the season or year. CyanoHAB biomass is quantified using a standard reflectance spectral shape based algorithm that uses data from Medium Resolution Imaging Spectrometer (MERIS). We demonstrate the method to quantify annual and seasonal cyanoHAB magnitude in Florida and Ohio (USA) respectively during 2003-2011 and rank the lakes based on median magnitude over the study period. The new method can be applied to Sentinel-3 Ocean Land Color Imager (OLCI) data for assessment of cyanoHABs and the change over time, even with issues such as variable data acquisition frequency or sensor calibration uncertainties between satellites. CyanoHAB magnitude can support monitoring and management decision making for recreational and drinking water sources.

Sachidananda Mishra↗
NASA NTRS2016

A Statistical Analysis of the Accuracy of the Digitized Magnitudes of Photometric Plates on the Timescale of Decades with an Application to the Century-Long Light Curve of KIC 8462852

We present a statistical analysis of the accuracy of the digitized magnitudes of photometric plates on the timescale of decades. In our examination of archival Johnson B photometry from the Harvard DASCH archive, we find a median rt mean square scatter of light curves of the order of 0.15 magnitude over the range B approximately equal to 9-17 for all calibrations. Slight underlying systematics (trends or flux discontinuities) are on a level of less than or equal to 0.2 magnitudes per century (1889–1990) for the majority of constant stars. These historic data can be unambiguously used for processes that happen on scales of magnitudes, and need to be carefully examined in cases approaching the noise floor. The characterization of these limits in photometric stability may guide future studies in their use of plate archives. We explain these limitations for the example case of KIC 8462852, which has been claimed to dim by 0.16 magnitudes per century, and show that this trend cannot be considered as significant.

digitized magnitudes of photometric plates↗
NASA NTRS1992

Application of magnitude estimation scaling to the assessment of subjective loudness response to simulated sonic booms

A laboratory study was conducted for the following reasons: (1) to investigate the application of magnitude estimation scaling for evaluating the subjective loudness of sonic booms; and (2) to compare the relative merits of magnitude estimation and numerical category scaling for sonic boom loudness evaluation. The study was conducted in the NASA LeRC's sonic boom simulator and used a total of 80 test subjects (48 for magnitude estimation and 32 for numerical category scaling). Results demonstrated that magnitude estimation was a practical and effective method for quantifying subjective loudness of sonic booms. When using magnitude estimation, the subjects made valid and consistent ratio judgments of sonic boom loudness irrespective of the frequency of presentation of the standard stimulus. Presentation of the standard as every fourth stimulus was preferred by the subjects and is recommended as the standard presentation frequency to be used in future tests.

S McDaniel↗
NASA NTRS1998

Improved instrumental magnitude prediction expected from version 2 of the NASA SKY2000 master star catalog

The SKY2000 Master Star Catalog (MC), Version 2 and its predecessors have been designed to provide the basic astronomical input data needed for satellite acquisition and attitude determination on NASA spacecraft. Stellar positions and proper motions are the primary MC data required for operations support followed closely by the stellar brightness observed in various standard astronomical passbands. The instrumental red-magnitude prediction subsystem (REDMAG) in the MMSCAT software package computes the expected instrumental color index (CI) [sensor color correction] from an observed astronomical stellar magnitude in the MC and the characteristics of the stellar spectrum, astronomical passband, and sensor sensitivity curve. The computation is more error prone the greater the mismatch of the sensor sensitivity curve characteristics and those of the observed astronomical passbands. This paper presents the preliminary performance analysis of a typical red-sensitive CCDST during acquisition of sensor data from the two Ball CT-601 ST's onboard the Rossi X-Ray Timing Explorer (RXTE). A comparison is made of relative star positions measured in the ST FOV coordinate system with the expected results computed from the recently released Tycho Catalogue. The comparison is repeated for a group of observed stars with nearby, bright neighbors in order to determine the tracker behavior in the presence of an interfering, near neighbor (NN). The results of this analysis will be used to help define a new photoelectric photometric instrumental sensor magnitude system (S) that is based on several thousand bright star magnitudes observed with the PXTE ST's. This new system will be implemented in Version 2 of the SKY2000 MC to provide improved predicted magnitudes in the mission run catalogs.

Sande, C. B.↗
NASA NTRS2001

Magnitude and sign correlations in heartbeat fluctuations

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.

NASA Discipline Cardiopulmonary↗
NASA NTRS1972

The methods of paired comparisons and magnitude estimation in judging the noisiness of aircraft

The point of subjective equality in regard to perceived noisiness for each of 14 pairs of aircraft noises was obtained using both magnitude estimation technique and the method of paired comparisons. Both methods gave approximately the same estimates of the points of subjective equality for the noise pairs, and both showed similar correspondence to predictive physical measures. Nevertheless, the two methods appear to have greater face validity to the listeners. However, the magnitude estimation technique appears to be more efficient; for a given level of reliability it requires approximately 50% of the testing time required by the paired comparison method. The functions relating physical intensity to the estimated magnitude of subjective noisiness had slopes ranging from about .61 to .29 for the aircraft noises employed in this study, indicating a required change of about 5 to 10 db for a doubling in subjective magnitude. Some physical units of noise measurement were found to be very predictive (standard errors of estimate as low as 1.9 db) of the subjective judgements of noisiness.

Clarke, F. R.↗
NASA NTRS1981

The visual surface brightness relation and the absolute magnitudes of RR Lyrae stars. II - RR Lyrae and X Arietis

The theoretical surface brightness relation for RR Lyrae stars has been combined with new VR photometry to determine distances, radii, and absolute magnitudes for X Arietis and RR Lyrae. For X Arietis, a pulsational variation in the radius from 5.06 solar radii to 5.96 solar radii, a distance of 495 + or - 50 pc, and an intensity mean absolute magnitude of +0.59 + or - 0.25 is obtained. The corresponding quantities for RR Lyrae are 4.81-5.67 solar radii, 263 + or - 39 pc, and an intensity mean absolute magnitude of +0.61 + or - 0.35. The larger errors quoted for RR Lyrae are due to uncertainties arising from the Blazhko effect. Results are discussed in the context of the dependence of RR Lyrae absolute magnitudes on metal abundance.

Manduca, A.↗
NASA NTRS1982

Distance and absolute magnitudes of the brightest stars in the dwarf galaxy Sextans A

In an attempt to improve present bright star calibration, data were gathered for the brightest red and blue stars and the Cepheids in the Im V dwarf galaxy, Sextans A. On the basis of a magnitude sequence measured to V and B values of about 22 and 23, respectively, the mean magnitudes of the three brightest blue stars are V=17.98 and B=17.88. The three brightest red supergiants have V=18.09 and B=20.14. The periods and magnitudes measured for five Cepheids yield an apparent blue distance modulus of 25.67 + or - 0.2, via the P-L relation, and the mean absolute magnitudes of V=-7.56 and B=-5.53 for the red supergiants provide additional calibration of the brightest red stars as distance indicators. If Sextans A were placed at the distance of the Virgo cluster, it would appear to have a surface brightness of 23.5 mag/sq arcec. This, together with the large angular diameter, would make such a galaxy easily discoverable in the Virgo cluster by means of ground-based surveys.

Sandage, A.↗
NASA NTRS1984

A reevaluation of the 20-micron magnitude system

The 20-micron infrared magnitude system is reexamined by observing primary infrared standards and seven A V stars. The purpose is to determine whether Alpha Lyr has colors consistent with the average of A0 stars and to determine the relative magnitude of the primary standards to that of Alpha Lyr. The data presented are consistent with the interpretation that the spectrum of Alpha Lyr is a blackbody and that it is a viable flux standard at 10 and 20 microns. The absolute flux density scale, the physical quantity of interest, is found to be consistent with an extrapolation of the Alpha Lyr spectrum from the near infrared on the basis of the comparison of stars to Mars and asteroids. Adoption of a 0.0 magnitude for Alpha Lyr requires that the magnitudes given by Morrison and Simon (1973) and by Simon et al. (1972) be revised downward by 0.14 mag.

Tokunaga, A. T.↗
NASA NTRS1998

Examination of two methods for statistical analysis of data with magnitude and direction emphasizing vestibular research applications

When the dependent (or response) variable response variable in an experiment has direction and magnitude, one approach that has been used for statistical analysis involves splitting magnitude and direction and applying univariate statistical techniques to the components. However, such treatment of quantities with direction and magnitude is not justifiable mathematically and can lead to incorrect conclusions about relationships among variables and, as a result, to flawed interpretations. This note discusses a problem with that practice and recommends mathematically correct procedures to be used with dependent variables that have direction and magnitude for 1) computation of mean values, 2) statistical contrasts of and confidence intervals for means, and 3) correlation methods.

Vestibule↗