An Adequate Method of Grain-Size Determination in Sections

Roethlisberger, Hans

doi:10.1086/626296

Cited by 22 publications

(6 citation statements)

References 7 publications

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“…Several options are then at hand for implementing the above estimators, provided isolated profiles of a set are properly identified. The simplest and most efficient solution is probably to make the analyser perform point-sampling; it should not be overlooked that only points sample particles in proportion to volume, see Rothlisberger (1955) for a very early discussion of the virtues of point-sampling. An estimator of C, .…”

Section: Relationships To Other Estimatorsmentioning

confidence: 99%

Stereological estimation of the volume‐weighted mean volume of arbitrary particles observed on random sections*

Gundersen¹,

Jensen²

1985

Journal of Microscopy

455

337

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SUMMARY A stereological estimator of the weighted mean volume of particles of arbitrary shape is described. This unbiased estimator is based on simple point‐sampling of linear intercept lengths. The complete absence of shape assumptions effectively breaks the long‐standing ‘convexity‐barrier’: the only requirement here is that individual particles can be unambiguously identified by their profiles on random sections. Practical details of the simple estimation procedure and an example with very irregular particles are reported. Finally, an estimator of the variance of the weighted distribution of particle volume is discussed. This estimator is also valid for particles of arbitrary shape. For any mixture of ellipsoids (spheres, oblates, prolates and triaxial ellipsoids) the estimator is reduced to a simple function of measurements of diameters in the section plane.

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Section: Relationships To Other Estimatorsmentioning

confidence: 99%

Stereological estimation of the volume‐weighted mean volume of arbitrary particles observed on random sections*

Gundersen¹,

Jensen²

1985

Journal of Microscopy

455

337

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“…There exists, however, a stereological sampling procedure which is natural to use when the object is to estimate aspects of a volume-weighted distribution (Rothlisberger (1955)).…”

Section: Point-samplingmentioning

confidence: 99%

The stereological estimation of moments of particle volume

Jensen¹,

Gundersen²

1985

Journal of Applied Probability

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In stereology or applied geometric probability quantitative characterization of aggregates of particles from information on lower-dimensional sections plays a major role. Most stereological methods developed for particle aggregates are based on the assumption that the particles are of the same, known (simple) shape. Information on the volume-weighted distribution of particle size may, however, be obtained under fairly general assumptions about particle shape if particle volume is chosen as size parameter. In fact, there exists in this case an unbiased stereological estimator of the first moment under the sole assumption that the particles are convex. In the present paper, we consider a particle aggregate in ℝ and derive estimators of the q th moment of the volume-weighted distribution of particle volume, based on point-sampling of particles and measurements on q -flats through sampled particles. The estimators are valid for arbitrarily shaped particles but if the particles are non-convex it is necessary for the determination of the estimators to be able to identify the different separated parts on a q-flat through the particle aggregate which belong to the same particle. Explicit forms of the estimators are given for q = 1. For q = 2, an explicit form of one of the estimators is derived for an aggregate of triaxial ellipsoids in three-dimensional space.

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“…The size of about half of the particles on the lunar surface will be underestimated, and a range of sizes will be observed for grains that actually have the same mean diameter. Corrections required for this effect [Packham, 1955;Roethlisberger, 1955] are large if the actual range of particle size is small, and, conversely, the correction is small if the actual range of grain size is very large. The corrections will be ignored in the analysis presented here.…”

Section: If the Estimates Of Precision Are Correct It Can Be Seen Frmentioning

confidence: 99%

Physical Characteristics of the Lunar Regolith Determined From Surveyor Television Observations

Shoemaker¹,

Morris²

1970

Radio Science

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The new data on the physical characteristics of the lunar surface derived from the Surveyor pictures can be fitted to a simple ballistic model for the origin and development of the lunar regolith. At a given locality, the size-frequency distributions of craters on the lunar surface can be represented by two functions' Small craters follow a steady-state distribution of the form F --,I,c •, where F is the cumulative number of craters with a diameter >_c, c is the diameter of the craters, ,I, and • have the steady-state values ,I, --10 •0'0, and • ----2.00 at all five Surveyor landing sites. Larger craters are represented by the function F --xc x, where x < tz, and x varies from one landing site to another. The solution for c at the intersection of F --xc X with F --,I,c •', designated as c8, is the upper limiting crater diameter for the steady-state distribution. The value of c8 is a function of the age of the surface on which the regolith has formed. The thickness of the lunar regolith may be estimated from a variety of observational data. The estimated thickness of the regolith at a given Surveyor landing site is bracketed by the original depths of (1) the smallest blocky-rimmed craters that cut through the regolith and excavate coherent material beneath, and (2) the largest, sharp, raised-rim craters without blocks that have been excavated wholly within the slightly cohesive material that forms the regolith. Other direct estimates of the thickness of the regolith are the inferred original depth of the largest craters believed to have been formed by drainage of the regolith material into subregolith fissures and, at the Surveyor-7 site, the depth at which the surface sampler instrument encountered coherent material. The thickest regolith was found at the Surveyor-6 site, where it is estimated to be more than 10 meters thick, and the thinnest was found at the Surveyor-7 site, where it is estimated to be 2 to 15 cm thick. Particle counts from sample areas at each of the Surveyor landing sites show an approximately linear relationship between the log of the cumulative particle counts and the log of the particle size. A power function of the form N --KD x (where N is the cumulative number of particles with diameter equal to or larger than D, and D is the diameter of particles) can be fitted to the data at each site. The size-frequency distribution of resolvable fragments at the Surveyor 3, 5, and 6 landing sites was found to be the same, within errors of estimation, but at the Surveyor 1 and 7 sites coarse fragments are more numerous. Considering all five sites, we found a strong inverse correlation between the abundance of coarse blocks and the thickness of the regolith. The coarsest fragments are most abundant at the sites with the thinnest regolith. INTRODUCTION Five Surveyor spacecraft successfully landed on the moon between June 1966 and January 1968 and returned over 87,000 television pictures which have provided important new data on the physical characteristics of the lunar surface. Surveyors 1, 3, 5, and 6 ...

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An Adequate Method of Grain-Size Determination in Sections

Cited by 22 publications

References 7 publications

Stereological estimation of the volume‐weighted mean volume of arbitrary particles observed on random sections*

Stereological estimation of the volume‐weighted mean volume of arbitrary particles observed on random sections*

The stereological estimation of moments of particle volume

Physical Characteristics of the Lunar Regolith Determined From Surveyor Television Observations

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