Sedimentary Geology, 52 (1987) 251-271 251 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

SIZE, S H A P E A N D O R I E N T A T I O N OF GRAINS IN S A N D S A N D S A N D S T O N E S - - I M A G E ANALYSIS APPLIED TO ROCK T H I N - S E C T I O N S

ANDREAS SCHAFER and THOMAS TEYSSEN

Geological Institute, Bonn University, Nussallee 8, D-5300 Bonn (F.R.G.) Koninklijke Shell Exploratie en Produktie Laboratorium, Volmerlaan 6, 2288 GD Rijswuk (The Nether-

lands)

(Received January 9, 1986; revised and accepted October 29, 1986)

ABSTRACT

SchMer, A. and Teyssen, T., 1987. Size, shape and orientation of grains in sands and sandstones--Image analysis applied to rock thin-sections. Sediment. Geol., 52: 251-271.

A computer based image-analysis system is used to determine the grain-size distribution, grain shape and grain orientation from rock thin-sections. A Monte Carlo simulation allows correction of the grain-size distribution for the corpuscle effect (grains cut marginally in the thin-section plane have smaller apparent diameters). Thin-section-derived grain-size distributions of modern and ancient samples have been compared with distributions obtained from sieving of the same samples. Different grain shape parameters have been compared with the Wadell formula. The grain orientation can be easily and reliably measured in thin-sections from different cuts of a sample. Grain orientation data can help to determine paleocurrent directions.

INTRODUCTION

Sands and sandstones are commonly described in terms of composition and grain-size distribution. The latter can be achieved either through sieving techniques of loose or disaggregated material or by microscopical studies of thin-sections. Many elaborate nomenclatural systems of grain-size distributions and compositions exist which serve almost every purpose (giving among other things grain-size averages, sorting, cementation, porosity).

Age and overburden transform sands to sandstones. These are subject to cemen- tation, diagenesis and weathering. The final result will be a mixture of stable and fragile components either as a grain framework or embedded in a matrix a n d / o r various cements. The sandstone composition may be obtained from microscopy of thin-sections. The determination of the grain-size distribution is more problematic since sieving after disaggregation of cemented sandstones may result in a cumulative curve strongly affected by broken friable grains, grain aggregates, or grains with

0037-0738/87/$03.50 © 1987 Elsevier Science Publishers B.V.

252

cement overgrowths. Furthermore, sieving techniques cannot be applied at all if only a little material is available, as in subsurface sampling.

Although this problem has long been known, no general solutions have been developed so far. O~y recently a further step could be made by application of a special computer aided technique: i.e, the image-analysis which may be applied to rock thin-sections while studying them under the microscope (Sch~ifer, 1982; Sch~ifer et al., 1982).

This paper describes a practical image-analysis procedure and discusses its application for sedimentological problems with special reference to the precision and reproducibility of the results. It will be demonstrated that image-analysis indeed is a valuable tool in geology.

TECHNICAL EQUIPMENT

The equipment used for image-analysis (in our case the "Videoplan" from Kontron-Electronic, Eching/Ml~nchen) may consist of the following devices: (1) A central micro-computer with two floppy disc drives each for the programs and for storage of the measured and calculated data: (2) a digitizer-tablet on which the information is entered into the computer by means of a special ballpoint stylus or a cursor, both equipped with a red LED-lamp; (3) a keyboard for starting the programs or for free programming (an additional menuefield to operate the measur- ing and calculation procedures is on the tablet and can be handled with the stylus or the cursor); (4) a monitor for immediate presentation of the measured data and/or the calculated results; (5) a matrix printer-plotter for print-out results; (6) a petrographical microscope together with a drawing mirror to project the thin-section on the digitizer-tablet (i.e.. to see the red LED-lamp of the stylus or the cursor being projected into the thin-section image); and (7) several measuring, calculation and statistics programs on floppy discs provided by the manufacturer together with a FORTRAN-COmpiler (or a BASle-interpreter) for setting up own programs.

Our technical set-up requires encircling of the grains on the digitizer-tablet while the pen is projected onto the microscopic picture by the drawing mirror. This has proved to be a relatively slow but by far the most practical method for grain-size analysis during which the geologist can introduce his interpretative skill. Grain-size and petrographical analyses are done by recording the two-dimensional shape of each grain and attributing it to pre-set compositional classes.

On the other hand, video-cameras transferring the thin-section image directly from the microscope to the computer work much faster. On the monitor a grain type discrimination can be done, followed by the appropriate calculations.

A fully automated procedure, however, m our opinion has not proved successful due to various reasons. First, different minerals cannot satisfactorily be identified and discriminated from their grey shade colour under crossed polarizers. If one. however, is only interested in the porosity (Ehrlieh et al., 1984) or in total grain

253

counts independent of the composition (Mazullo and Kennedy, 1985), a fully automated recording procedure can be successfully applied (also confirmed by H.C. Steen-Hansen, pers. commun., 1985).

Second, grain-shape resolution is often problematical. This is, for example, the case with rock fragments with polycrystalline quartz dispersed in a quartzose matrix, or with monoquartz overgrown by quartz cement. Therefore, from our experiments we believe that detailed petrographic investigations should rather be done with the digitizer-tablet. The higher workload is by far counterbalanced by the high reliability of the results.

RESULTS

The grains of a sand or sandstone differ according to their provenance. They can be different quartz types, feldspars, various rock-fragments together with micas, heavy minerals, opaque grains and intra- as well as extrabasinal carbonates in various proportions (see Zuffa, 1985, for detailed discussion). The fabric of a rock is dependent upon size, shape and orientation of the grains. Our petrographical study concentrates on the fabric.

Grain size

The size of grains in sands and sandstones is commonly determined by sieving. For simplicity, the content of all the sieves is weighed rather than the grain numbers counted in the sieves.

The resulting weights are recalculated as weight percentages, summed as cumula- tive percentages and plotted versus grain size on linear, lognormal, or probability paper. The population of sieved grains of various sizes is thus presented as weight proportions.

Thin-sections from sandstones on the other hand show grains cut along a random thin-section plane. Under the microscope they can be counted and measured with respect to their longest apparent diameter, and the grain shape can be digitized. However, one has to bear in mind that section diameters of randomly oriented grains are recorded rather than their maximal equatorial diameters as in sieving methods.

Therefore, grain-size distributions of sediments which are derived from thin-sec- tions are generally biased. The reason for this bias is the so-called corpuscle effect (see Burger and Skala, 1973 and 1976, for discussion of the various methods to determine the grain size from thin-sections and to account for the corpuscle effect). The bias of the thin-section-derived grain-size distribution is caused by the fact that the individual grains of the sandstone are cut randomly. Thus in many cases the two-dimensional sections of the grains may not be proportional to the maximum cross-section and the largest diameter of the grains in three dimensions. The

254

diameter measured i n the thin,section may either be correct (in the correct grain-size class) or too small. Diameters on the o the r hand can never be too large. The thin-section-derived grain-size distribution curve is therefore always biased towards

its finer tail. A reconstruction of the true grain-size distribution from the biased distribution

would allow a comparison with sieved samples. Such a reconstruction has to account for the incorrect classification of some of the grain diameters. This is

possible by means of a Monte Carlo simulation because such a process is a stochastic simulation (i.e., a simulation by a random process) of the physical cut of a

piece of rock to prepare a thin-section. The Monte Carlo simulation forms part of a program set for grain-size analysis implemented by the authors at the Kontron "Videoplan" and is based on the method described by Burger and Skala (1973,

1976). The main steps of such a procedure are summarized below (see Fig, 1).

The input grain-size distribution derived from image-analysis of the thin-section is stored in the array N ( 1 ) with I grain-size classes. The process of reordering starts

with class I containing the largest diameters. The boundaries are az+~ and a t . Then a grain which belongs to this class is arbitrarily chosen using a random-number-gen-

erator. Calling the random-number-generator again allows simulation of a random cut of this particular grain and the calculation of a section diameter.

r~-S~mulation, Reconstruction of the ~nbiased sample i

INPUT ARRAY I OUTPUT ARRAY

Array N(1) A r ray M(]}

1 1 Random number generator

a l ~ - . ~ Simulation of a grain diameter of crass I

~ _ _ ~ - - ~ ~ ' . ~ - - ~ - ~ ' J ~ / _ Immm[ , Sim~[ation of a section diameter of that

al 7, or al_j* -

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I ~ 1 ~ t / J ~ " • i l l . i t Continue [ . _ _ / 4 ~ f l Imlnmlm ~ ~ " ~ ~ + If N( I ) :O,cont inue with class I - I

2 2 The procedure stops if al~ input sect ion

- - - - e 2 diameters have been reordered

1 al=O 1

Crass Crass Crass number boundary number

Fig. I. The working principle of the KOGROMO correction program (Monte Carlo simulation sensu Burger and Skala, 1973, I976) as implemented to the Videoplan (further description see text). A frequency distribution of biased grain cuts measured in a rock thin-section will be corrected to true grain diameters.

255

Consider now two possible cases: the simulated section-diameter belongs to class I (if the grain is cut in or near its center) or it belongs to class I -J with smaller

diameters (if the grain is cut marginally). In the first case the element N(I) of the input distribution will be decreased by

one I N ( I ) ~ N ( I ) - 1] and the element M(I ) of the output distribution will be incremented by one [ M ( I ) --* M(I ) + 1].

In the second case the element N(I -J ) will be decreased IN(I -J ) ~ N( I -J ) - 1] and M(I) increased [ M ( I ) ~ M(I) + 1]. The reordering can transfer the grains to the same class of the output distribution or to a class with larger diameters. That procedure continues until class N(I) is empty: all grains of input class N(1) have then been transferred to output class M(I), but M(I) additionally contains some grains which previously belonged to classes with smaller diameters of the input distribution.

The simulation process then continues with input class N ( I - 1) until that class is empty. Then the process continues with input class N ( I - 2 ) and so on. The simulation process stops, if all grains of the input distribution N ( I ) are transferred to the output distribution M(I).

The output distribution M ( I ) now contains all diameters which previously were in N(I). As a result the median slightly shifted towards the coarse side of the diagram and the standard deviation of the grain distribution achieved smaller values.

The process simulates the physical cut of the rock. This is done in such a way, that both the correct and the incorrect grain-size class of each individual grain is known, thus enabling the reconstruction of the true grain-size distribution.

The whole procedure is carried out independently ten times which leads to ten output grain-size distributions. From these ten distributions an average is computed being the final result of the simulation.

As it is now possible to correct apparent section-diameters of the grains in a randomly cut rock towards true equatorial diameters, the effect of that correction

will be demonstrated on several samples:

Modern samples (Fig. 2a) Sample 1: Rhein-Mondorf (marginal river bank of the lower Rhine river). Sample 2: Ahr-Br~cke (point-bar of the lower Ahr river). Sample 3: Bausand (artificial sand mixture for concrete production). Sample 4: Buschdorf (sand pit, middle terrace of Pleistocene Rhine river). Sample 5: Wangerooge (lower shoreface of a southern North Sea barrier island). Sample 6: Bou Saada (eolian Sahara dune in southern Algeria).

Ancient samples (Fig. 2b) Sample 7: Birgel 3A (Lower Triassic, Buntsandstein of the Eifel mountains in W.

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259

Sample 8: km 2 (Upper Triassic, Middle Keuper, Schilfsandstein from Heilbronn, arkosic arenite)

Sample 9: SNB 112 (Lower Permian, Lower Rotliegendes, Kusel Beds of the Saar-Nahe Basin, W. Germany; lithic arenite)

Sample 10: MEIS 16 (Lower Permian, Lower Rotliegendes, Lebach Beds of the Saar-Nahe Basin, W. Germany; well Meisenheim 1; lithic arenite)

Sample 11: TV 319 (presumably Lower Cretaceous of the Amir Formation, Nubian Sandstone of Nahal Amran, Negev, Israel; quartzose arenite; kindly pro- vided by Weissbrod, Geol. Surv. of Israel)

Sample 12: GO 3 I (Holocene kurkhar from the Mediterranean coastal plain at Givat Olga, north of Tel Aviv, Israel; biogenic calcareous arenite of eolian/marine origin; kindly provided by Weissbrod, Geol. Surv. of Israel)

Some of these samples have already been used in Sch~ifer (1982) and Sch~ifer et al. (1982). Samples 1-6 show modern sediments whereby only samples 2, 4 and 5 still had their natural bedding when they were taken with a boxcorer and prepared for thin-sections; samples 1 and 3 were transported and redeposited in a test flume and sampled from there; sample 6 was mechanically densified in a beaker. Samples 7-12 are rock samples. All twelve samples were cut vertical to their bedding.

A classification by sieving was done on all modern as well as on the ancient samples 7, 11 and 12. After disaggregation they were sieved with water in automated sieving machines: the samples 1-7 according to the German DIN-scale in half class-steps (based on mm); the samples 11 and 12 according to the Wentworth-scale in quartered class-steps (based on phi).

The sieving curves are placed at the fine-end side of the section-diameter curves. The sieving curves of the modern samples show fine-end tails. The fines of the ancient samples may be derived from the matrix, but more likely from broken friable grains (such as feldspars) and even fragmented cement. The coarse-end tails of the sieving curves of both modern and ancient samples stem from coarse particles which can be sieved in a bulk sample of about 100 g. They are, however, statistically not properly represented in only one thin-section plane.

Although it should be expected from the above explanations that section-distri- butions and sieving-distributions have always the same relation to each other (sieving curves depicting coarser, section-diameter curves depicting finer popula- tions), the above examples do not show this. The most likely explanation is that sieving curves cannot be used in all cases to test the validity of section-diameter curves. The actual sieving procedure, the time used and the shape of the sieves and of the machine will strongly influence the precision of the result (Batel, 1960). The image-analysis results seem to be more reproducible, although the precision of the analyses is clearly hampered by their relatively small sample sizes.

The matrix problem may be compensated to a certain degree, if the components in the fine ground mass are resolved with higher microscope magnification (which only may cause technical problems while counting the main constituents). But like

260

the composition, the m a t ~ is c o n t r ~ by post-depositional processe s such as diagenesis and weathering, so an excess of fines within the interstices of the sand fraction should be neglected in image-analysis.

Thus, the biasing factors of section,diameter curves are known and mostly controllable. They are not hampered by variable effects as sieving-curves are.

Grain shape

A standard,set of measurements of basic grain parameters in our image-analysis procedure contains area, perimeter, maximal diameter (dmax), diameter A (long) and B (short) of the ellipse (den A and dell B), and the diameter of the circle having the same area as the grain ( d ~ e ) . It is necessary to trace the apparent grain shape on the digitizer-tablet with the stylus from one of the two ex~eme points (where the radius of the curvature is smallest) onward. The most important parameter is dma ~. It defines the m ~ apparent grain size, which has always been a measure for comp~son with sieved samples and a base for correlation equations (SchMer, 1982).

The shape analysis of Wadell (1932, 1935) has been accepted as a basic approach

3 I

/.

Fig. 3. Five "geometric prototypes" redrawn from WadeU (t935) to adopt his well-known method Of shape analysis to modern use aided by image-~ulysis.

261

tO the measu remen t of the shape of sed iment grains (Fig. 3 and Tab le 1). He

descr ibed this shape b y means of the ra t io:

p rac t ica l spher ic i ty = dc/Dc

where dc is the d iamete r of a circle equal in a rea of the gra in and Dc the d iamete r

of the smal les t circle c i rcumscr ib ing the grain. W a d e l l or ig inal ly conf ined this

measure to pebble-s ize clasts of 7 cm length rest ing on one of their larger faces. He

p r o p o s e d this " s t a n d a r d size" to keep a compa ra b l e level of exactness dur ing the

measurement . In our image-analys is procedure , sand grains are cons ide rab ly mag-

n i f ied to a large and near ly cons tan t size of a half to several cent imeters .

Wade l l ' s fo rmula was rewri t ten by Mi~ller (1964, 1967):

measured spher ic i ty = (4/7r × Ap )a/2/Dp

where Ap is the a rea of the gra in p ro jec t ion and Dp the above -men t ioned Dc, being

the d iamete r of the smallest circle c i rcumscr ib ing the gra in projec t ion .

Both formulas are ident ica l (dc = dcircle, Dc = dmax; Ap = area, Dp = dmax).

Circles will give 1, e longated shapes will tend to 0.5.

The form-fac tors ca lcu la ted au tomat i ca l ly by the compu te r are all spher ic i ty

measures (Table 2):

fo rm-fac to r el l ipse = dell B / d e l l A

fo rm-fac to r pe r imete r = 4~r X a r e a / p e r i m e t e r 2

fo rm-fac to r area = a r e a / ( c r / 4 ) × dm~ x × drain

G r a i n - s h a p e figures f rom SchneiderhShn (1954; see Miil ler , 1964, 1967) were

used to demons t r a t e the value of those ca lcula t ions (Fig. 4). A l though their overal l

TABLE 1

Dimensions of Wadell's "geometric prototypes" together with the calculation formulas given by Wadell (1935) and Mi~ller (1964)

Length Width Area Perim. Max. diam. Practical Measured d = 2.48 sphericity sphericity

1 4.83 7.79 2.48 1.00 1.000 2 2.00 2.00 4.00 8.00 2.83 0.79 0.799 3 4.00 2.00 8.00 12.00 4.47 0.71 0.713 4 5.00 3.20 16.00 16.40 5.94 0.75 0.759 5 8.00 2.00 16.00 20.00 8.25 0.54 0.546

"Five geometric prototypes in their most stable position of rest" (Wadell, 1935, p. 265)

practical sphericity = dc/Dc

dc = diameter of a circle equal in area to the area obtained when the grain rests on one of its larger faces; Dc = diameter of the smallest circle circumscribing the grain reproduction (from Wadell, 1935).

measured sphericity = (4/~r X Ap)l/2/Dp

Ap = area of the grain projection; Dp = the above Dc (from Miiller, 1964).

262

TABLE 2

A test to handle Wadell 's five "geometric p r o t o t ~ , ! by image,-analysis and its calculation routines,

whereby the automatically calculated form-factor PE is quite close to Wadelt 's shape measure (spheric-

ity)

Area Perim. dma x dell A dell B dcircle form ELL form PE form AR Wadell

1 4.79 8:06 2.46 2.50 2.44 2.47 0.98 0.93 1.00 1.000

2 3.99 8.08 2.83 2.33 2.29 2.25 0.99 0.77 0.95 0.795

3 8.03 12.07 4.48 4.66 2.30 3:20 0.49 0.69 0.95 0.714

4 16.02 16.51 5.95 5.78 3.69 4:52 0.64 0.74 0.96 0.759

5 16.12 20.18 8.26 9.26 2.32 4.53 0.25 0.50 0.96 0.548

Wadell 's five geometric prototypes measured and calculated on the Videoplan (a mean of five measure-

ments each is given)

dell A = major axis; dell B = minor axis of an ellipse; d~trde = diameter of an equivalent circle for a measured area; form ELL = A / B

form PE = 4~r x area/(perimeter) 2

form AR = a rea / ( r r / 4 )X A x B

Wadell = dcircle/dmax or (4/~r ×area)l/2/dma x

shape is quite well characterized by Wadell's sphericity measures, the form-factor perimeter contains more information about the smaller-scale features b y giving details in the more angular shapes.

Grain orientation

A random grain-cut can cause different section-diameters, where the grain has an irregular shape. Grains with elongated, ellipsoidal, or platy shapes can make up an oriented grain fabric. One particular section through such a fabric may therefore show large grain sizes while other sections preferentially show smaller ones. This indeed confines the determination of "exact" grain sizes by image-analysis (but hampers the sieving procedure as well!). Therefore the question on the orientation of grains in bedforms of sands and sandstones needs to be considered. In the following at least a preliminary answer should be found towards the criticism on image-analysis, that exact grain sizes cannot be found, especially not in randomly oriented sections.

Three samples each were cut out of two modem and two ancient ripple bedforms in three different planes: the first one in the ac-plane (parallel to the bedform migration), the second one in the bc-plane (perpendicular to the bedform migration), and the third one in the ab-plane (bedding plane).

This was done with two modern samples from a 2.5 m-long test-flume containing the fine sands demonstrated with sample 1 (Rhein-Mondorf; but from a different sample site). They were cored from the moist flume bed 63 and 175 cm off the flume

263

form ell Q91 0.65 0.64 0.60 0.86

form pe 0.55 0.59 0,61 0.65 0.69

form or 0.96 0.95 0.94 0.97 0.98

WADELL 0.88 0.74 0.80 0.73 0.90

U 0u,o form eli 0.56 0.57 0.84 0.73 0.81 form pe 0.51 0.55 0.60 0.57 0.64

form er 0.92 0.90 0.92 0.93 0.96

WADELL 0.71 0.71 0.78 0.76 0.88

SUbn-ded ~.~ ~ ~ ~. form etl 0.63 0.81 0.83 0.91 0.63 form pe 0.60 0.72 0.77 0.65 0.71 form er 0.91 0.99 0.98 0.88 0.95

WADELL 0.72 0,84 0.85 0.83 0.75

rounded ~_~ ~ ~.~ ~__~ ~.~ form ell 0.86 0.62 0.78 0.82 0.98 form pe 0.75 0.74 0.75 0.74 0.71

form or 0.96 0.98 0.98 0.93 0.91

WADELL 0.85 0.77 0.81 0.55 0.92

form ell 0.52 0.62 0.65 0.84 0.93 form pe 0.75 0.81 0.80 0.87 0.88 form ar 0.99 1.00 1.00 1.00 1.00

WADELL 0,74 0.79 0.81 0.94 0,96

Fig. 4. Grain-shape figures from Schneiderh6hn (1954) measured by image-analysis on the graphical tablet (the dots on each grain-shape trace are the starting points to get the grain diameters dm~ x properly). A computerized calculation of the three form-factors (see Table 2) is given together with Wadell 's shape parameter "sphericity".

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266

The long axes of the ellipsoidal grains show a more or less pronounced maximum parallel to the slip faces of the ripple bedforms (ac-plane). The view rectangular to the flow direction (bc-plane) shows that the apparent long axes of the grains are oriented horizontally. And the view on the bedding-plane (ab-plane) shows that there exists as well quite a good orientation of the apparent grain axes parallel to the flow-direction (which is towards "east" on the rose diagrams).

As the grains in all four samples are ellipsoids and therefore irregular in shape, they show different grain sizes in the three cuts (Table 3). The longest axes (the maximal grain sizes) are seen if viewed into the bedding-plane (ab-plane). In addition, the form-factor perimeter as well as Wadell's shape show that the apparent grain shapes are roundest if determined in this bedding-plane.

DISCUSSION

Image-analysis has become a helpful tool for the textural investigation of sediments (Neumann-Mahlkau. 1967; Gahm. 1975; SchMer, 1982: and recently Ehrlich et al., 1984; Kennedy and Ehrlich. 1985: Mazullo and Kennedy, 1985).

Modem sedimentary environments have tong been accepted as models for the interpretation of ancient rock suites. But a standardization of grain analysis has never been achieved. Therefore, we would like to recommend that all analyses on grain sizes and shapes for comparative purposes should be done following the same procedure, preferentially on thin-sections of rocks and on loose samples embedded in resin respectively.

This recommendation seems to be justified, also considering Wilson and Pitt- mann (1977, fig. 20, p. 25). They show an eolian sandstone, the grain-size cumula- tive curve of which was prepared before and after removal of diagenetic silt and clay. This example demonstrates best that the "fines" in between the grain frame- work often falsify the distribution of grains originated from the original depositional process.

In addition, the above cited figure resembles accurately those which are given by Sch~fer (1982), Sch~ifer et al. (1982), and those presented here (Figs. 2 and 3). The fine-grained tail of the curves from ancient samples needs to be interpreted with caution as this mostly is derived from the break-down of friable grams and disaggregated cement. Curves of "clean" (i.e. normally distributed) samples should be straight on probability plot paper. "Clean" samples are received only then. if they are confined to small-scale sedimentary units which are laid down by only one particular depositional process. A bulk sample, which is necessary for sieve-analysis in many cases, may comprise a mixture of more than one sedimentary unit. A careful size-analysis from thin-sections may furthermore show the bimodal distribu- tion of sand-sized grains more clearly and may allow a better interpretation of sands, which for example were deposited under combined current and wave action.

267

The comparison of sieve-analysis and image-analysis also suffers from the problem produced by the sample size. This was the case in earlier studies such as those by Friedman (1958, 1962); Kellerhals et al. (1975); Adams (1977); Harrell and Eriksson (1979); Sch~fer (1982); Sch~ifer et al. (1982), which all tried to prove the validity of grain-size curves from section-diameter frequencies in comparison with weight frequencies.

From the above examples it might be deduced that " t rue" grain-size distributions cannot be estimated from the thin-section curves. On the other hand, the validity of the sieve curves needs to be considered also. The sieving procedure firstly has always caused technical problems and is influenced by many parameters (sieving time, wet or dry sieving, choice of sieves, quality of sieves and others). Secondly, a bulk sample comprises many more grains than those belonging to one sedimentary unit as for example a single turbidite layer, a high energy parallel bed, a cross-bed unit, a small-scale ripple avalanche, an eolian single-grain sheet, or others.

Griffiths (1967) stated that a comparison of two different cumulative frequency distributions will bring together weights of sieved grains and numbers of section diameters. Burger and Skala (1973, 1976) also criticized such a comparison and stated an objection to regression equations. These indeed have long been a way to link one technique to the other (Friedman, 1958; Sch~ifer, 1982) that can easily be done, but may not be generally valid. Regression equations need to be verified in each case.

We think, however, that distribution curves based on grain-number data in the sieve classes rather than on grain weights, better represent the "natural" distribution and are more valuable for sedimentological interpretations. The image-analysis procedure described in this paper gives such a grain-number distribution and is therefore one reliable way for sandstone grain-size analysis. The number of neces- sary sections and grain counts depends upon the sorting of the sandstone and has to be determined in a pilot study. The greater the effort to obtain all information out of a thin-section (300-600 counts), the better is the resulting frequency distribution of one or more components. The possibility of determining grain-size distributions separately for different components without additional effort is especially valuable for provenance studies, as well as for particular sedimentological problems (Teyssen, 1984, fig. 7).

These section diameters can be counted with only little er ror- -wi th a computer or by ha nd - - a nd give a true picture of what is seen in the thin-section. They indeed should be estimated as the " t rue" distribution of grain sizes. The bias, which the section-diameters still suffer from, is the unknown shape of the individual grain in the framework of the rock. Section-diameters are mostly smaller and never larger than equatorial diameters which can only be considered as " t rue" grain sizes.

Therefore the necessary step is the Monte Carlo simulation as proposed by Burger and Skala (1973, 1976), where the section-diameters are corrected to equa- torial diameters. The grain-size curves are corrected for the bias caused by the

268

corpuscle effect as outlined above. This procedure is now incorporated into the image-analysis.

Weight-frequencies are not calculated here, although they originally were pre- pared. We followed the plea of Adhikari et al. (1980), who stated that size frequencies of grains are very much different from their weight frequencies. In addition, they can only be calculated correctly, if the shapes of the grains are known.

As "shape influences the dynamic behaviour of particles" (Swan, t974), it is extremely desirable to have an easy access to shape measurements. Such an attempt was made by Cui and Komar (1983) measuring the three axial diameters of ellipsoidal pebbles and sands. They discussed the relationship between the true nominal diameters (calculated from the measured weight or volume) and the nominal diameters (calculated from their three measured axial diameters) of the geometric ellipsoids. Kennedy and Ehrlich (1985) found a differentiation of sand and silt shapes due to different sediment sources along a pathway of sediment transport as elaborated by fide, o-camera scans of grain mounts and subsequent Fourier analyses.

With the aid of our image-analysis equipment, form-factors can be calculated automatically, whereby the form-factor perimeter is the most sensitive one. These form-factors are a measure of "sphericity" (which is a degree to which particles are equidimensional in shape). It is also possible to achieve Wadell's "spherici .ty".

However, up to now Wadell's "roundness" cannot be calculated with our programs. The grain shapes from Schneiderht~hn (1954: as presented by Miiller. 1964, 1967) may demonstrate Wadell's limits for visual taxation of particle round- ness. Unfortunately our image-analysis system does not differentiate well between rounded and angular grain projections. Nevertheless, the variation of these grain shapes gives a good impression of how sediment particles can vary and how the automated calculation of the computer would handle them.

Barrett (1980) recently gave a critical review on current methods of shape calculations in use today.

Several aspects of grain-orientation of small-scale bedforms are roughly sketched in this paper, but not discussed in detail. This has already been done on various examples and with various methods by earlier authors. Zimmerle and Bonham (1962) and Sippel (1971) both used a photometer method; Shelton and Mack (1970) on the other hand measured the dielectric anisotropy of grains; Gibbons (1972) gave a concise review of various techniques in use; and only recently a study by Yagishita and Jopling (1983) was published on a laterally accreted outwash-bar with planar cross-bedding measuring the apparent long axes of grains.

It has to be stressed that a gram orientation will produce differences in section- diameters and this -should be taken into account if a precise gram-si__~ distribution is desired. Our experience, however, shows that a section vertical to the beading plane generally gives satisfactory results--also in comparison with sieve curves.

269

The grain projections are relatively the largest in the bedding plane. They are then oriented parallel to the current as shown with the example of small-scale ripple bedding.

This contrasts to the findings of Yagishita and Jopling (1983) who did not find any consistent preferred-orientation of grains on top of planar cross-beds parallel to the current. On the other hand, they found an up-slope imbrication in their cross-bedding strata. This was also reported by Shelton and Mack (1970) who demonstrated this by giving rose-diagrams of grain orientations. The same was also confirmed by us with additional samples from other larger-scale bedforms (not demonstrated here).

We might tentatively conclude that small-scale ripples may create a fabric where the long axes of the grains trend down-current and down the slip-face (which was also well documented by Von Rad, 1970). Thus, not only the dip of the slip-faces of small-scale ripples but also the grains involved in the sedimentation process could depict the paleocurrent.

The question from which section "correct" grain sizes should be taken by image-analysis cannot be fully answered up to now and depends on the actual grain fabric of the sandstone. But the grains of all sections from each sample investigated are of the same grain-size range and differ only by around 10 ~m. Image-analysis of thin-sections thus provides the possibility to determine grain-size distributions of different rock sections and infer the grain orientation. This may help in further sedimentological interpretations and both the oriented and the non-oriented sam- ples will give "correct" grain sizes by image-analysis. The results might only then be biased where the shapes of the grains are very irregular.

We feel that further work on the grain-fabric of sandstones is needed, especially since observations and measurements can now be performed with the aid of computerized tools with high precision. Thus, the question is open whether image- analysis might be accepted as a new standard for grain analysis.

ACKNOWLEDGMENTS

We would like to thank Dr. Wilhelm Sprenger, Dortmund, for the impetus he gave us when he set up a first version of the Monte Carlo routine, from which our own attempts started. Thanks are also due to Barbara Hudec, Albert Lenze, Otto R~ber and Willi Merten, all from the Geological Department of the University of Bonn, who provided valuable help producing the data for this paper.

The Deutsche Forschungsgemeinschaft is gratefully acknowledged for granting the technical equipment.

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