Using Quantitative Textural Analysis to Understand the

Using Quantitative Textural Analysis toUnderstand the Emplacement of Shallow-Level Rhyolitic LaccolithsÐa Case Studyfrom the Halle Volcanic Complex, Germany

A. MOCK1*, D. A. JERRAM2 AND C. BREITKREUZ1

1TECHNISCHE UNIVERSITAÈ T BERGAKADEMIE FREIBERG, BERNHARD-VON-COTTA-STRASSE 2, 09599 FREIBERG,

GERMANY

2DEPARTMENT OF GEOLOGICAL SCIENCES, UNIVERSITY OF DURHAM, SOUTH ROAD, DURHAM DH1 3LE, UK

RECEIVED FEBRUARY 1, 2002; ACCEPTED NOVEMBER 8, 2002

In qualitatively homogeneous magmatic bodies, quantitativetextural analysisÐsuch as crystal size distribution, modalabundance, and spatial distribution pattern analysesÐallowstheir internal heterogeneity to be measured and interpreted. Inthis study, these methods are applied to samples from a 300 mdrill core through one of the porphyritic rhyolitic laccoliths(Petersberg unit) of the �300Ma Halle Volcanic Complex,Germany.Qualitatively, thegeochemicallyhomogeneousPetersbergunit does not show much textural variation. Quantitatively,however, the crystal size distributions of the three most commonphenocryst phases (orthoclase, plagioclase and quartz) suggestcontinuous crystal growth during magma ascent and emplacement,but different growth histories of the phenocryst phases throughoutthe genesis of the laccolith. In situ cooling did not affect thephenocryst population. Size distributions of the phenocrysts varyon a centimetre to decimetre scale, but are similar on the scale ofthe laccolith. The modal abundance of the phenocryst phases isvery similar throughout the drill core. Quantification of thespatial distribution of phenocrysts, however, reveals a trend forclustering towards the interior or upper part of the laccolith, whichis attributed to flow and shear processes during emplacement anddiscontinuities in the interior relating to the intrusion of differentmagma pulses. Circular statistics of the orientation of long axes ofcrystals reveal a weak alignment of the orthoclase and plagioclasephenocrysts on the sample scale as a result of flow in the magma inspite of little acicularity. In general, laccoliths can be fedby several pulses of magma without major cooling betweenbatches.

KEY WORDS: crystal size distribution (CSD); Halle Volcanic

Complex (HVC); laccoliths; porphyritic rhyolites; spatial distribu-

tion patterns (SDP)

INTRODUCTION

Shallow-level intrusions represent high-level storagereservoirs during the final stages of transit of magmato the Earth's surface. Shallow-level silicic intrusionspotentially provide important information regardingthe magmatic plumbing systems feeding explosivevolcanoes (Eichelberger et al., 1986; Brophy & Dreher,2000). Studies of phenocryst populations in the pro-ducts of silicic eruptions commonly suggest a rathercomplex history of magmatic evolution (e.g. Kneselet al., 1999; Hawkesworth et al., 2000). On the otherhand, some systems seem to display a simple crystal-lization history (e.g. Higgins, 1996a, 1996b).In this study, we use a stratigraphically well-

constrained set of samples obtained by drilling of partof the Halle Volcanic Complex (HVC), Germany, toapply quantitative textural analysis to a rhyolitic,highly porphyritic, shallow-level laccolith intrusion.Another objective was to quantify possible in situgrowth effects on the phenocryst population.Samples were taken from a solid core drilled throughthe Petersberg unit of the HVC. Using the methods

JOURNAL OF PETROLOGY VOLUME 44 NUMBER 5 PAGES 833±849 2003

*Corresponding author. Telephone: �49-3731-392429. Fax:�49-3731-393599. E-mail: [email protected]

Journal of Petrology 44(5) # Oxford University Press 2003; all rightsreserved.

described below, we demonstrate changes in the sizeand packing arrangement of the phenocryst popula-tions throughout the unit. We then use these texturaldata to develop a model for the emplacement of thePetersberg laccolith that previously has been difficultto constrain because of a general lack of exposure. Thismodel has implications for processes occurring duringthe emplacement of shallow-level silicic laccoliths ingeneral.

Geological setting

The HVC is situated in the Saale Basin in EasternGermanyÐone of several late Palaeozoic transten-sional volcano-sedimentary basins in the area of thedecaying Variscan orogen (Eigenfeld & Schwab,

1974; Lorenz & Nicholls, 1984). The Saale Basindeveloped in the Saxothuringian zone and theMid-German Crystalline RiseÐstructural units ofthe Variscan Orogen [Fig. 1 and Romer et al.(2001)]. The overall tectonic setting in Central Europe20Myr after the culmination of the Variscan orogenywas one of dextral strike-slip (Arthaud &Matte, 1977).Roughly contemporaneous basins associated withPermo-Carboniferous rifting or transtension in Europewithin the orogen and its northern foreland can befound in the Oslo region, Norway (Sundvoll et al.,1990, and references therein), the Midland Valley,Scotland (Upton, 1994), the Saar±Nahe region,Western Germany (Stollhofen & Stanistreet, 1994;Stollhofen, 1998) and the Sudetic Mountains, Poland(Awdankiewicz, 1999). In all these basins, subvolcanicintrusive complexes are common.

Fig. 1. Location (a) and geological sketch map of Eastern Germany (b) and the HVC (c), the last showing the main units of rhyoliticporphyritic laccoliths. Names of the laccoliths given in the text correspond to the villages on the map. Location of drill hole of this study is alsoshown. Section line of Fig. 3 is indicated.

JOURNAL OF PETROLOGY VOLUME 44 NUMBER 5 MAY 2003

834

In the HVC, volcanic activity commenced with theeruption of a trachybasaltic to trachydacitic suite oflavas and pyroclastics with minor intrusive activity,exposed during coal exploration drilling (Kampeet al., 1965; Siegert, 1967; Romer et al., 2001). A smallrhyolitic laccolith intruded during this period(Schwerz laccolith, 307� 3Ma, 1s error). This mainlyextrusive magmatic phase was followed by the empla-cement of the main porphyritic rhyolitic laccolith com-plex of about 200 km3 between 301 and 294 � 3Ma(1s errors; Landsberg, LoÈ bejuÈ n, Petersberg, Wettinunits). The ages of emplacement of the above-men-tioned laccoliths have been determined by Breitkreuz& Kennedy (1999), using the 206Pb/238U SHRIMPmethod on zircons. The presence of aphanitic SiO2-rich lavas overlying erosional debris from the intrusionssuggests that volcanism continued after the emplace-ment and partial exhumation of the laccoliths (RuÈ fferet al., 1998).Of the laccolith units, the L�obej�un, Landsberg and

Schwerz units have large feldspar phenocrysts (up to�30mm on the long axis); the Landsberg and Schwerzunits also contain a variant with smaller phenocrysts.The Wettin and Petersberg units both have smallerfeldspar phenocrysts (�10mm) with the Wettin unitcontaining small schlieren-like domains with largerphenocrysts. Within the Petersberg unit, the focus ofthis study, the apparent textural variation of thephenocrysts is very small.After much debate about the extrusive vs intrusive

mode of formation of the porphyritic rhyolite units,recent studies have reached the conclusion that allthe units, which are depicted in Fig. 1c, are intrusive(Kunert, 1995; Breitkreuz et al., 1998; Knoth et al.,1998; Mock et al., 1999, and references therein), theevidence for this being their large thicknesses (at leastseveral hundred metres), sedimentary rocks tilted dur-ing laccolith emplacement between the units, and thearchitecture of the internal flow structures [Fig. 2 andMock et al. (1999)]. Thin to absent contact meta-morphic aureoles and chilled margins advocate a veryshallow emplacement of these laccoliths. In some lac-colith units, e.g. the Petersberg unit, flow structures arerecognized in the field by layers of partly stretchedvesicles, bands of weakly aligned phenocrysts (mostlyfeldspars), or bands of higher phenocryst content.The drill samples used in this study were obtained

during coal exploration in the 1960s, which intersectedthe margin of the Petersberg laccolith. There are threestrongly altered zones apparent from the cores (at thesurface, at �100m, and at the lower contact of therhyolite at �300m, Fig. 3). The country rock belowthe lower contact consists of a succession of grey silt-and mudstones with several fine sandstone beds andcoal seams (Wettin beds, Fig. 3a) and a fluvio-limnic

succession of reddish grey conglomerates, siltstones,clays and sandstones with abundant volcaniclastics(Halle beds in Fig. 3a; Kampe & Remy, 1960; Knothet al., 1998). A short distance to the west, these sedi-ments crop out at the surface with a steep dip. Theyform a thin band of tilted sediments between thePetersberg and LoÈ bejuÈ n laccoliths (Fig. 3a, see alsoFig. 1b). The Petersberg laccolith forms the largest ofthe laccoliths in the HVC with an estimated volume of�60 km3. Flow structures (Fig. 2), and carapace facies(spherulitic groundmass texture) found at the summitof the Petersberg hill suggest that the level of erosion atthe drill site lies within the upper third of the laccolith.

METHODS

Data acquisition and analysis techniques

Samples of up to 30 cm in length were taken from the20 cm diameter drill core Petersberg 9, located in thecore depository of the Geological Survey of Sachsen-Anhalt in Halle (drill hole location indicated in Fig. 1).The relative stratigraphic position of the samples isindicated in Fig. 3b. Two or three plane faces rangingfrom 7000 to 20 000mm2 in area were cut verticallyand/or horizontally from each sample for imageanalysis (see Table 1).The rhyolite is chloritized and partly albitized and

haematized. Quartz crystals are unaltered and appearblack, greyish or clear depending on the remaining sizeof the crystal after cutting and its background in therock. Orthoclase crystals retain a pinkish red colourbut have abundant clear parts. Plagioclase crystalsappear greenish grey with abundant black inclusions.Twinning is abundant among the feldspars, zoning isnot. Automatic image classification of scans from theplane faces was not possible because of ambiguousvalues in the RGB colour scheme for the various phe-nocrysts. Staining of the samples was consideredimpractical because of large sample sizes and altera-tion. Therefore, orthoclase (OR), plagioclase (PL) andquartz (QZ) phenocrysts were outlined by hand on atransparency superimposed on each rock slab, assign-ing different, unambiguous colours to each phase. Thetransparencies were then scanned at a resolution of180 d.p.i. The digital images were double checkedwith the rock slabs to ensure correct identification ofeach phenocryst, that individual phenocrysts wereseparated from each other in the image, and that thecolours in the digital image were suitable for automaticimage analysis (Fig. 4a). The smallest grain size mea-surable with this technique is given by the width of thepen used to trace the phenocrysts on the transparency.It lies in the range of 0�1±0�5mm. Figure 4b shows threeexamples of the characteristic texture of the samples as

MOCK et al. SHALLOW-LEVEL INTRUSION EMPLACEMENT

835

monochrome images to emphasize the apparent simi-larity throughout the core.The digital images were analysed using image

analysis software KS300 (Rel. 2.0) by KONTRONELEKTRONIK Imaging System, to provide the area,the lengths of the long and short axes, their orientationexpressed as an angle from a horizontal line in thedigital image, and grain centre coordinates of the phe-nocrysts. Phenocrysts intersected by the edge of thesample slab were excluded from the analysis.

Quantitative petrography

Petrographic characteristics, such as the modal abun-dance of mineral phases and their grain size, have been

used extensively in rock classification. Recent develop-ments in the textural analysis of rocks provide addi-tional petrographic tools for the quantitativeinvestigation of magmatic rocks, which can be used inconjunction with geochemical studies to help under-stand their origin and evolution. In this study we focusparticularly on the size and spatial distribution of thecrystal population, and apply circular statistics toquantify trends in orientation data.

Crystal size distributionsAs minerals grow from a melt the actual size distribu-tion of crystals can provide valuable information aboutthe origin of the rock. Crystal size distribution (CSD)

Fig. 2. (a) Field measurements of flow banding in the Petersberg area (HVC). (b) and (c) steeply dipping flow structures in the Br�omme andHoffmann quarry. White lines indicate trend of structures. Height of quarry face in (c) is �10m.


836

studies originated in engineering (e.g. Randolph &Larson, 1988) and were introduced to igneous petrol-ogy by Marsh (1988) and Cashman & Marsh (1988).Marsh (1998) summarized the theory of CSD asapplied to the textures of igneous rocks. In the caseof a log±linear CSD in a steady-state open system,the population density (n) of the items in question(crystals, vesicles, etc.) is linked to their size (L), withgrowth rate (G) times residence time (t) and finalnucleation density (n0) being constants for oneparticular CSD, in the following equation:

n� n0 exp�ÿ L

Gt

�: �1�

Linear regression analysis of the CSD curveÐa plotof crystal size (L) vs logarithmic population density ofthat size [ln(n)]Ðprovides a measure of growth rate/residence time (slope) and nucleation density (inter-cept). Additionally, the shape of the CSD curve canreveal the operation of different processes duringthe crystallization of magma batches (Marsh, 1998;Zieg & Marsh, 2002). CSD analysis might also beused to characterize variations within apparentlyhomogeneous igneous bodies.In this study, the size distribution of the long axes of

phenocrysts of orthoclase, plagioclase and quartz

within each slab were corrected for two-dimensional±three-dimensional (2D±3D) effects using the methodand software of Higgins (2000): CSDCorrections 1.2.The 2D±3D effects are the intersection probability(a random section is more likely to intersect largergrains or crystals than smaller ones) and the cut sec-tion effect (one grain or crystal can produce different-sized sections in differently orientated cuts througha sample).Higgins (2000) developed this method of 2D±3D

correction following the work of Saltykov (1967) andSahagian & Proussevitch (1998) on stereological con-version of particle size distributions from 2D sections toactual 3D distributions. This method uses a quantifica-tion of the above-mentioned 2D±3D effects to calculatea 3D size distribution from the 2D intersectiondistribution. It is a non-parametric method thatdoes not require the shape of the distribution to beassumed beforehand, as opposed to Peterson's (1996)parametric solution.

Spatial distribution patternUnderstanding how crystals and grains in rock texturesare orientated spatially in relation to each other isfundamental in interpreting their history (Kretz,1969; Jerram et al., 1996; Jerram & Cheadle, 2000).A method to quantify the spatial distribution pattern(SDP) of grains in thin section was developedby Jerram et al. (1996). This applies the technique ofcluster analysis for automatic, objective and consistentclassification of particles. Based on R-values, it providesa measure of how clustered, random or ordered a dis-tribution of particles is; that is, the ratio of the meannearest neighbour distance (NND) of all particles in asample to the predicted mean NND for a randomdistribution of points, given by

R� rArE� 2

��rp P

rN

�2�

where rA is the mean NND in the sample, rE the meanNND in a random distribution of points,N the numberof individual points (grain centres), r the density ofthe observed distribution (N divided by the samplearea), and r the NND of one particular grain.This variation in the packing arrangement can bequantified in a matrix vs R-value diagram ( Jerramet al., 1996), and it can also be used to distinguishtouching from non-touching frameworks (Jerram et al.,2003). This plot compares 2D sections through 3Dtextures with 2D sections through 3D modelsof randomly packed spheres and it can thus be usedto quantify the variation in the spatial packingarrangement of those 2D sections from 2D sections ofrandom textures and from other 2D sections of 3D

Fig. 3. (a) Section through parts of the L�obej�un and Petersberglaccoliths [for approximate location see Fig. 1; inspired by figuresfromKampe et al. (1965)]. (b) Schematic log of drill core Petersberg 9and the position of samples in the drill core.


837

rock textures. Matrix vs R-value plots are discussed ina subsequent section.The positions of the centres of phenocrysts, deter-

mined by image analysis, were used to calculate anR-value [equation (2)] as a measure of the SDP ineach slab. We used a FORTRAN77 program for cal-culating a mean NND for all the crystal centres in oneslab. This was then divided by the mean NNDexpected for a random distribution of points of thesame population size and density (see above) to givethe R-value. An R-value for each slab as a whole wascalculated using all the grain centre data for all thedifferent phenocrysts. In a second step, R-values werecalculated for each crystal phase separately.

Circular statistics of orientationStatistical tests were performed on orientation datafollowing the procedures outlined by Davis (1986)and Capaccioni et al. (1997). The mean orientationangle is defined as

�y � arctan

Xni�1

sin yi

Xni�1

cos yi

0BBB@1CCCA �3�

where yi is the orientation angle of one crystal'slong axis. If the orientation of the sample is known,this is a good estimate of the flow structure'sorientation where flow structures are manifested bythe alignment of phenocrysts' long axes (see also thesection `Geological Setting' above). The mean resul-tant length of the mean orientation angle on a unitcircle ( �R) is a measure of the dispersion of the dataand hence a measure of the reliability of the flowstructure statistics. It is defined as

�R� 1

n

��Xni�1

cos yi

�2

��Xn

i�1sin yi

�2vuut �4�

where n is the number of measurements. It isindependent of sample size (see Capaccioni et al.,1997) and can be used as a test variable to look fora preferred orientation within a dataset. Accordingto Davis (1986), the 95% significance level forn4 50 observations lies at 0�244. If the value ofthe test variable falls below this threshold, thecrystals are orientated randomly. If it is larger thanthe threshold value, the crystals have a preferredorientation.

Table 1: Samples used for this study

Sample/slab Depth (m) Slab area (mm2) Orientation of slab No. of crystals Relative modal abundance (%) of

OR PL QZ OR PL QZ

90499 a 49�9 18918 Horizontal 1554 998 1085 39�71 30�02 30�2790499 b 49�9 13464 Vertical 1045 838 989 32�43 40�60 26�9690499 c 49�9 14043 Vertical 1198 897 812 37�42 35�49 27�0991671 a 167�1 18701 Vertical 1331 641 1340 40�61 40�67 18�7291671 b 167�1 16998 Vertical 810 550 853 41�31 37�57 21�1291843 a 184�3 13651 Vertical 634 545 563 42�27 36�22 21�5191843 b 184�3 13464 Horizontal 684 664 605 48�20 31�78 20�0291843 c 184�3 6947 Horizontal 391 340 495 44�38 33�73 21�8992235 a 223�5 11453 Horizontal 532 481 780 38�03 38�17 23�8092235 b 223�5 13911 Vertical 764 599 858 35�90 42�56 21�5492508 a 250�8 18764 Vertical 1057 1191 1064 47�02 36�03 16�9592508 b 250�8 13429 Horizontal 737 876 631 51�10 29�95 18�9592508 c 250�8 20171 Vertical 1264 856 806 39�77 34�27 25�9692860 a 286�0 11436 Vertical 713 626 563 43�35 35�23 21�4292860 b 286�0 10485 Vertical 651 621 714 37�88 44�53 17�5892860 c 286�0 12962 Horizontal 890 728 683 38�35 39�66 21�99

Letters after sample number indicate slabs of different orientation; depth in the drill hole Petersberg 9, area of slab, andnumber of phenocrysts are also stated. OR, orthoclase; PL, plagioclase; QZ, quartz.


838

RESULTS

Modal abundance, shape of phenocrysts,and CSD

The sum of the areas of the phenocrysts of one phaseexpressed as a percentage of the slab's area is avalid estimate of the modal abundance (volumetric

proportion) of that phase (Higgins, 2002, and refer-ences therein). The relative modal abundances of OR,PL and QZ were calculated for each of the 16 slabs(Table 1) from the results of image analysis as describedabove. They are very similar in all samples, with 41 �4�8% OR, 37 � 4�3% PL and 22 � 3�7% QZ (meanrelative modal abundances � one standard deviation).

Fig. 4. (a) Example of the texture of sample 92860c (scanned slab) and the digital image of the extracted phenocrysts, black (QZ), dark grey(OR) and white (PL), vector graphics made from the raster image used for image analysis. (b) Three examples of the spatial distribution ofphenocrysts OR, PL, and QZ as monochrome images as used for analysis of the SDP.


839

There is no apparent change with depth in the intrusionor intra-sample variation. The uppermost sample(90499), however, is richer in quartz by �4% (Fig. 5).Higgins (2000) suggested that the I/L ratio of the

crystal dimensions [longest (L), intermediate (I) andshortest (S)] can be estimated statistically by adding0�5 to the skewness of the width/length ratio distribu-tion. The skewness is then taken to be the mean minusthe mode divided by the standard deviation of thatdistribution. The S/I ratio is taken to be the mode ofthe width/length ratio distribution. Values obtained bythis method were either unrealistically large (e.g.1:3:50) or gave a value for L smaller than the valuefor I. The crystal dimensions for the input into thesoftware used for 2D±3D correction in this study wereestimated to be 1:2:3 for OR and PL, and 1:1�5:2 forQZ after careful examination of the samples using therecommendations of Higgins (1994). In Table 2, themean ratios of all the crystals' long and short axes arelisted. As observed qualitatively on the slabs, QZexhibits more equant shapes (crystals are rounded)than the other two phenocrysts and also always hashigher axial ratios (the difference between long andshort axes is small as expected for equant shapes),whereas OR and PL have lower axial ratios with ORforming the lower limit. The different dimensions ofQZ and the feldspars are justified by the different meanwidth/length ratios of these phenocrysts.Following the general convention, CSDs are plotted

as linear crystal size (L [mm]) vs logarithmic popula-tion density {ln(n) [mmÿ4]; Marsh, 1998; Higgins,2000}. The size according to Higgins (2000) is equalto the longest dimension of each crystal in 3D. TheCSDs for the phenocrysts are all straight and exhibit apower-law distribution over the range of grain sizesinvestigated in this study (Fig. 6). QZ has a smaller

maximum crystal size than the two feldspars, and itsCSDs are steeper. Linear regression coefficients (R2)are very close to unity for all CSDs (Table 2).For a linear CSD in a steady-state open system, the

slope is a measure of growth rate and/or growth time(characteristic length), and the intercept represents thefinal nucleation density of the crystals. These para-meters of the CSD are shown in Fig. 7. There is a linearrelationship between final nucleation density and char-acteristic length, meaning that the more nuclei form,the slower the crystals grow and vice versa. This rela-tion does not vary consistently with depth in the drillcore nor even within differently orientated slabs of asingle sample. However, there is a difference betweenthe two feldspars and QZ, as becomes also obviousfrom the CSD plots. QZ has a higher final nucleationdensity (larger intercepts) and a lower product ofgrowth rate and residence time (steeper slopes of theCSDs). Therefore, apart from being more equant, QZalso has a different growth history (Fig. 7). Higgins(2002) suggested the use of a diagram of volumetricphase proportion vs characteristic length to providemore information on magmatic processes (Fig. 8). Inthis diagram, the variation within each sample isalmost as large as the variation between samples.Nevertheless, the uppermost sample (90499) in Fig. 8aand the lowermost sample (92860) in Fig. 8b plot atopposite ends of the `cloud' of sample points. Thisindicates a very weak trend of open-system texturalcoarsening towards the bottom of the laccolith for thefeldspars (see discussion for details). Any systematicin situ growth variations such as textural coarseningwithin the laccolith cannot be seen in Figs 7 and 8.

Intra-slab variability

We carried out CSD analysis on sub-areas of the largestslab of the set of samples (92508 c, 20171mm2) tounravel small-scale variability of the CSDs (Fig. 9).An image of 10�5 cm � 7 cm was cut out of the originalimage by a frame at one end of the sample slab. Thenthe frame was moved by �2 cm and another imagewas cut out. In this fashion, 10 overlapping imageswere retrieved from sample 92508 c (Fig. 9a) andsubsequently analysed in the way described above.CSDs obtained from the different sub-images areshown in Fig. 9b±d. Apparently, they do not differ foreach of the phenocrysts. On a diagram of modal abun-dance vs characteristic length, however, plagioclaseshows a significant difference of the top and the bottompart of the slab, whereas the other two phenocrystsshow a limited spread that is not significant if the 1serror bars are considered (Fig. 9e).

Fig. 5. Triangular plot of relative modal abundances of thephenocrysts OR, PL and QZ of all the sample slabs of this study.


840

Spatial distribution of phenocrysts

The modal abundances of the phenocrysts as well asthe CSDs do not show systematic variation betweensamples within the intrusive body. The SDP, however,does show a systematic variation. According to theR-value method, crystals can be distributed either ran-domly, in an ordered manner, or clustered. Randomdistribution is represented by the random sphere dis-tribution line (RSDL) in Fig. 10 (Jerram et al., 1996).Populations of grains plotting above this line areordered, populations below this line are clustered.The crystals of the samples of this study are generally

randomly distributed (Fig. 10). In the uppermostsample (90499), the phenocrysts are slightly more clus-tered (R-value reduced by 0�1 compared with the sam-ples at the bottom of the drill core). In the lower partsof the intrusion, crystals are more randomly distributedand even plot beyond the RSDL to suggest a slightlyordered pattern. Therefore, there is a trend of cluster-ing of crystals towards the top of the intrusion. Thisbecomes even more apparent in a plot of R-value vsdepth in the drill core. Sample 91671 exhibits aremarkable deviation from this trend that we interpretasmarking a zone between twomagma pulses (Fig. 11).The significance of this will be elaborated in thediscussion section below.OR always has higher R-values than the other two

phases (Fig. 12). R-values of PL and QZ do nothave a consistent relationship within one sample or

throughout the drill core. Also, the two samples90499 and 92860 are distinctly different from theothers, forming opposite ends of the array on theR-value vs matrix plot, supporting the observed trendof Fig. 10.

Circular statistics of orientation data

The results of the statistical analysis of orientation dataare presented in Table 3. Most of the vector lengths (r)exceed the threshold value of 0�244 (italics in Table 3,second column). Therefore, there is a preferred orien-tation of the long axes of the phenocrysts in the rhyo-lites as a conjugate set of mean angles at �45� and at�135�. These values do not depend on the orientationof the slab (horizontal cuts are in italics in Table 3,third column), nor are they a reflection of changingtrends in the flow structures with depth.

DISCUSSION

In the following discussion we would like to addresssome possible physical properties influencing the spa-tial and size arrangement of phenocrysts in a magmaduring various stages of its development. We will usedata of this study to constrain the importance of thosefor the case of the Petersberg laccolith.

Table 2: Regression coefficients of CSDs and mean ratios of long and short intersection axes

Sample/slab OR n0 OR CL OR R2 OR S/L PL n0 PL CL PL R2 PL S/L QZ n0 QZ CL QZ R2 QZ S/L

90499 a 0�119 1�067 0�991 0�648 0�050 1�191 0�954 0�650 0�230 0�692 0�985 0�67890499 b 0�078 1�034 0�952 0�610 0�088 1�063 0�954 0�667 0�218 0�699 0�999 0�67090499 c 0�124 0�969 0�990 0�612 0�126 0�923 0�986 0�675 0�124 0�684 0�963 0�65491671 a 0�092 1�121 0�994 0�616 0�069 1�048 0�970 0�634 0�299 0�634 0�986 0�66291671 b 0�032 1�361 0�963 0�641 0�069 1�053 0�991 0�641 0�195 0�652 0�958 0�68391843 a 0�032 1�288 0�966 0�632 0�068 1�040 0�983 0�659 0�357 0�543 0�986 0�71891843 b 0�054 1�180 0�978 0�631 0�215 0�798 0�998 0�642 0�294 0�564 0�988 0�69791843 c 0�062 1�195 0�989 0�598 0�109 0�968 0�988 0�652 0�642 0�500 0�987 0�66392235 a 0�045 1�118 0�986 0�668 0�143 0�832 0�992 0�660 0�212 0�604 0�963 0�68392235 b 0�098 0�974 0�998 0�618 0�075 1�050 0�982 0�662 0�434 0�537 0�987 0�69692508 a 0�043 1�285 0�984 0�653 0�090 1�105 0�981 0�660 0�238 0�580 0�994 0�69592508 b 0�028 1�447 0�964 0�646 0�069 1�208 0�976 0�662 0�322 0�576 0�984 0�68192508 c 0�044 1�285 0�988 0�616 0�075 1�043 0�992 0�674 0�111 0�719 0�976 0�68392860 a 0�063 1�180 0�994 0�636 0�064 1�104 0�982 0�676 0�137 0�673 0�988 0�70192860 b 0�073 1�047 0�978 0�647 0�059 1�166 0�972 0�663 0�309 0�568 0�968 0�65392860 c 0�071 1�113 0�997 0�650 0�121 0�989 0�998 0�661 0�179 0�673 0�995 0�736

n0, final nucleation density [exp(intercept)]; CL, characteristic length (±1/slope); R2, regression coefficient of the linearregression of the CSD; S/L, mean ratio of the short over long intersection axis.


841

Fig. 6. CSD plots of all slabs: (a) orthoclase, (b) plagioclase, (c) quartz; 16 CSDs each. The different scale on the length axis in (c) and smallvariation within a sample should be noted.


842

Influence of magma flow on the spatialdistribution of crystals

In addition to crystal nucleation and growth, flow andshear in a rising magma batch will influence the spatialdistribution of phenocrysts. Let us consider a dyke:provided that flow is laminar, which is very likely forviscosities of 1012 Pa s and more typical for rhyoliticmelts, crystals are distributed according to the velocityprofile that develops across the dyke (Fig. 13a). Largecrystals are transported towards the interior of the dykeanalogous to grains affected by laminar flow in a pipe

(see Leeder, 1982). Thus, the CSDs there becomeflatter and the maximum crystal sizes larger. Also, theR-value increases whereas the matrix proportiondecreases following the compaction trend in Figs 10and 11. Conversely, increased clustering (reducedR-values) can be expected at the walls or edges of anintrusion, between successive batches of magma, andclose to flow foliation planes (Fig. 2). It remains to beestablished whether flow parameters such as flow velo-city, viscosity of the magma, size of the phenocrysts,and bed shear stress are in the right range for these

Fig. 7. Intercept vs characteristic length of the CSDs of this study.The different distribution for QZ and the two feldspars and the non-systematic variation with depth (indicated by number of slab) shouldbe noted. Closure limits are calculated according to Higgins (2002).Horizontally cut slabs are shaded.

Fig. 8. Volumetric phase proportion vs characteristic length (growthrate � growth time) according to Higgins (2002). Horizontally cutslabs are shaded. Arrows indicate a trend for textural coarsening.


843

sorting mechanisms to be strongly effective. In zones offocused shear (Fig. 13d), random distributions of crys-tals become spatially modified by shear flow. Thisbrings the crystals closer together in one direction andthus lowers the R-value (see Jerram et al., 1996). Thedecreasing R-values can be seen on the R-value vsdepth plot for the Petersberg samples (Fig. 11).Additionally, flow of viscous magma should cause

more effective redistribution of crystals with highaspect ratios than of equant crystals. Although thereare no significant changes in the CSD characteristicswith depth in the drill core through the Petersberglaccolith, trends in the characteristic length vs modal

abundance plots and the SDP of phenocrysts are morenoticeable for the feldspars (higher aspect ratios) thanfor QZ (Figs 8 and 12).

Flow sorting during emplacement

When the magma reaches the level of intrusion, thedirection of flow of the magma is turned 90� to form asill. Two end-member scenarios may take place: (1) theredirection of flow homogenizes the inherited spatialdistribution of crystals in the magma or (2) the condi-tions prevailing in the dyke are turned by 90� and thespatial pattern of phenocrysts is preserved from the

Fig. 9. Intra-sample variability. (a) Classified image of slab 92508 c with the orientation of the slab in the drill core and 10 overlappingsmaller images cut out and analysed according to the above-mentioned procedure. (b)±(d) CSDs of OR, PL and QZ of the 10 sub-images ofslab 92508 c. (e) Diagram of characteristic length vs modal abundance of the 10 sub-images of slab 92508 c. Error bars are one standarddeviation of the dataset of each phenocryst phase.


844

dyke, i.e. large crystals continue to be concentrated inthe interior of the sill (Fig. 13b). In the former case, thesize-dependent redistribution of crystals by flow willstart anew in the direction of sill intrusion; in the lattercase, the inherited spatial distribution of crystals will beenhanced.If the sill transforms to a laccolith by inflation, i.e.

several batches of magma intrude each other (Corry,1988), a pattern of crystal distributions equivalent toseveral sill-like spatial arrangements should be found ina drill core through the laccolith (Fig. 13c). In the caseof homogenization of the spatial arrangement ofcrystals, the trends in the CSD and the SDP might beobscure.In the Petersberg samples, the phenocrysts display a

preferred orientation. They show a � conjugate set ofmean angles (Table 3). This is evidence for the impor-tance of flow sorting of phenocrysts in the intrudingmagma. If there was no preferred orientation ofphenocrysts, it would be a strong indication for vigor-ous homogenization of the phenocryst texture and thusdetailed textural investigations of this nature would befutile. Contrarily, the occurrence of preferred orienta-tions provides a base for the considerations at thebeginning of this section.The data of this study show that the SDP in the

Petersberg laccolith is changing from a random to a

more clustered distribution with no significant changein the CSD. The difference in the SDP can be ascribedeither to the physical movement of the magma asdescribed above or to a change in the spacing ofnucleation. In the latter case, one would expect anoticeable difference in the CSDs between samples.As that is not the case, a physical movement of a pre-existing crystal population is preferred. Additionally,the rather insignificant trend in the CSD characteris-tics (Fig. 8) advocates a degree of homogenization ofthe spatial pattern of phenocrysts upon intrusiondespite a lack of turbulent conditions, so that the SDPevidence for the two-pulse model becomes even moresignificant.Unfortunately, a general lack of exposure in and

around the Petersberg laccolith inhibits recovery offurther evidence for multiple pulses of intrusion.Many better exposed subvolcanic laccoliths do showevidence for such intrusive mechanisms; for example,the Donnersberg in the Saar±Nahe basin, Germany(Haneke, 1987) and the Henry Mountains, Utah,USA (Corry, 1988; Friedman & Huffman, 1998).Therefore, the SDP pattern observed in the Petersberglaccolith can be explained by such an interpretation.Furthermore, the simple, linear CSDs suggest thatthese pulses took place during the same crystallizationperiod.

Comparison with CSDs from othersystems

While a magma is cooling and crystallizing, a numberof circumstances will affect the CSD. Changesin growth and nucleation rate away from constantconditions will alter the slope and intercept of the

Fig. 10. R-value vs matrix per cent plot of all the samples. Only datafrom vertically cut slabs are plotted. Errors from Jerram et al. (1996,fig. 6) depend on the number of crystals. All crystals of each sampleare considered together. The random sphere distribution line(RSDL) separates clustered from ordered spatial arrangements ofcrystals. Distributions of crystals plotting in the shaded area have atouching framework of crystals. The inset demonstrates the influenceof different means of redistribution of crystals on their spatialarrangement.

Fig. 11. R-value vs depth in the drill core (only data from verticallycut slabs are plotted). Sample 90499 is clearly separated from theother samples. Deviation of sample 91671 should be noted; thissuggests at least two different pulses of magma intrusion.


845

CSD of a population of crystals. At later stages ofcrystallization larger crystals will grow at the expenseof smaller ones, with the effect that smaller crystals aredestroyed and the CSD kinks downwards at the smallsize end. This is known as Ostwald ripening, texturalcoarsening, or annealing (Higgins, 1998; Marsh,

1998). Also, at the margins of an intrusion, where cool-ing is more effective, nucleation should become moreimportant than growth and the CSD becomes steeperwith a smaller maximum and characteristic crystal sizethan in the interior of the intrusion. Mixing of popula-tions of phenocrysts with different CSDs might benoticeable by changes of slope in the resultant compo-site CSD.Two examples of the above-mentioned processes are

given. Plagioclase phenocrysts in dacites from Kamenivolcano, Greece, yielded strongly curved CSDs thatwere interpreted to stem from the mixing of two mag-mas with differing populations of crystals (Higgins,1996b). CSDs of K-feldspar megacrysts in theCathedral Peak granodiorite, California, show evi-dence of textural coarsening (Higgins, 1999). Thesetwo examples represent extreme end-members of pos-sible time±temperature±crystallinity paths of magmas,the former leading to eruption as lava, the latter beingbuffered by earlier and later intrusions of differentmaterial. The simple CSDs of the phenocrysts of thePetersberg laccolith display an intermediate position:there is no indication of magma mixing in the CSDsnor in the chemistry (Romer et al., 2001), i.e. thelaccolith formed by several intrusive batches derivedshortly after one another from the same magma; andthere is only a very weak indication of annealing(Fig. 8), i.e. the magma forming the Petersberg lacco-lith had only one population of phenocrysts thatnucleated and grew continuously until a substantialincrease of undercooling led to nucleation and growthof the groundmass phases after emplacement. Thephenocryst populations were thus not affected bypost-emplacement processes.In the light of these considerations, the emplacement

model for the Petersberg laccolith is far from being

Fig. 12. R-value vs matrix per cent plot of single phases. Uppermost (90499) and lowermost (92860) samples are clearly separated from therest. Vertically cut slabs are plotted.

Table 3: Statistical parameters of

orientation data; whole slab analysis

(all phenocrysts)

Sample/slab vector length phi mean (deg) st. dev. (deg)

90499 a 0�486 47�4 1�390499 b 0�430 52�2 1�790499 c 0�333 43�2 2�291671 a 0�282 133�7 2�591671 b 0�301 45�8 2�891843 a 0�206 50�3 4�791843 b 0�263 134�9 3�491843 c 0�286 133�6 4�092235 a 0�356 132�2 2�692235 b 0�405 42�4 2�092508 a 0�341 134�9 2�092508 b 0�594 45�9 1�392508 c 0�406 46�1 1�892860 a 0�362 42�6 2�592860 b 0�379 136�4 2�392860 c 0�298 133�2 2�8

Vector length is the length of the mean angle vector on a unitcircle (in italics where above the threshold value); phi mean isthe mean angle calculated after Capaccioni et al. (1997) forungrouped orientation data (italics for horizontally cut slabs);st. dev. is one standard deviation for the mean angle.


846

complete. It is evident, however, that detailed texturalinvestigations of this kind are a powerful tool to revealmechanisms important in igneous petrology andmechanics.

CONCLUSIONS

In this study, textural analysis techniques havebeen applied to quantify the evolution of a veryhomogeneous rhyolitic laccolith from the HVC.Specifically, we focused on the growth history of differ-ent phenocrysts as reflected in their CSD. Further-more, we employed SDP analysis and statistics ofphenocryst orientation to determine different packing

arrangements of crystals and the influence of flow sort-ing. We reach the following conclusions:

1. The CSDs suggest that crystals grew continuously inthe magma during ascent and emplacement of thePetersberg unit. Systematic variation of crystalgrowth related to in situ coolinghasnotbeendetected.

2. In spite of little acicularity, feldspar phenocrystsare orientated with a preferred orientation of theirlong axes by flow shearing in the intruding magmabody.

3. Redistributionof crystals as a result of flow is reflectedin the spatial distribution pattern, as R-valueschange with sample position in the laccolith.

Fig. 13. Simplified sketch of the possible distribution of crystal sizes in a rising and intruding magma batch in (a) a dyke, (b) a sill, and (c) alaccolith. The three stages can be connected to each other. (d) Enlargement of parts of the intrusion to show the influence of magma flow andgradients in flow velocity and undercooling on the spatial arrangement of phenocrysts. Further explanation is given in the text.


847

4. The SDP also strongly suggests that the emplace-ment of the laccolith involved successive pulses ofmagma intruding each other.

5. Size distributions are affected by the flow on acentimetre to decimetre scale, but are not differentin subsequent magma pulses.

6. Laccoliths can potentially be fed by pulses ofmagma with little or no major cooling betweenbatches as indicated by the uniformity of the CSDsthroughout the drill core.

7. Internal heterogeneities of apparently homogeneousmagmatic bodies can be measured and interpretedby detailed, quantitative textural analysis.

ACKNOWLEDGEMENTS

We thank Michael Higgins for providing theCSDCorrections software and Michael Magnus for intro-ducing KS300 to A.M. Bruce Charlier is thanked forcomments on an earlier version of this manuscript.Thanks are due to B.-C. Ehling and the LandesamtfuÈ r Geologie und Bergwesen Sachsen-Anhalt in Halle/Saale for the opportunity to take samples from the coalexploration drill core Petersberg 9. Reviews by PhilipCandela, Michael Higgins and Michael Zieg are muchappreciated. Most parts of this work were donewith the help of grant Br 997/18-1 from the DeutscheForschungsgemeinschaft.

REFERENCESArthaud, F. & Matte, P. (1977). Late Paleozoic strike-slip faulting

in southern Europe and Northern Africa: results of right-lateralshear zone between the Appalachians and the Urals. GeologicalSociety of America Bulletin 88, 1305±1320.

Awdankiewicz, M. (1999). Volcanism in a late Variscan intra-montane trough: Carboniferous and Permian volcanic centres ofthe Intra-Sudetic Basin, SW Poland. Geologica Sudetica 32, 13±47.

Breitkreuz, C. & Kennedy, A. (1999). Magmatic flare-up at theCarboniferous/Permian boundary in the NE German Basinrevealed by SHRIMP zircon ages. Tectonophysics 302, 307±326.

Breitkreuz, C., Exner, M. & Schwab, M. (1998). QuantitativeErfassung des Platznahme- und Kristallisationsgef�uges rhyo-lithischer Lakkolithe am Beispiel des oberkarbonen WettinerPorphyrs bei Halle/S. Terra Nostra 98(2), 34±36.

Brophy, J. G. & Dreher, S. T. (2000). The origin of compositiongaps at South Sister Volcano, central Oregon; implications forfractional crystallization processes beneath active calc-alkalinevolcanoes. Journal of Volcanology and Geothermal Research 102,287±307.

Capaccioni, B., Valentini, L., Rocchi, M. B. L., Nappi, G. &Sarocchi, D. (1997). Image analysis and circular statistics forshape±fabric analysis: applications to lithified ignimbrites. Bulletinof Volcanology 58, 501±514.

Cashman, K. V. & Marsh, B. D. (1988). Crystal Size Distribution(CSD) in rocks and the kinetics and dynamics of crystallizationII: Makaopuhi lava lake. Contributions to Mineralogy and Petrology99, 292±305.

Corry, C. E. (1988). Laccoliths; Mechanics of Emplacement and Growth.Geological Society of America, Special Paper 220, 1±110.

Davis, J. (1986). Statistics and Data Analysis in Geology. New York:John Wiley.

Eichelberger, J. C., Carrigan, C. R., Westrich, H. R. & Price, R. H.(1986). Non-explosive silicic volcanism. Nature 323, 598±602.

Eigenfeld, F. & Schwab, M. (1974). Zur geotektonischen Stellungdes permosilesischen subsequenten Vulkanismus in Mitteleuropa.Zeitschrift f�ur Geologische Wissenschaften 2, 115±137.

Friedman, J. D. & Huffman, J. A. C. (1998). Laccolith Complexes ofSoutheastern Utah; Time of Emplacement and Tectonic Setting; WorkshopProceedings. Reston, VA: US Geological Survey.

Haneke, J. (1987). Der Donnersberg. Bad DuÈ rkheim: PollichiaÐPfalzmuseum fuÈ r Naturkunde.

Hawkesworth,C. J., Blake, S., Evans,P.,Hughes,R.,MacDonald,R.,Thomas, L. E., Turner, S. P. & Zellmer, G. (2000). Time scales ofcrystal fractionation in magma chambers; integrating physical,isotopic and geochemical perspectives. Journal of Petrology 41, 991±1006.

Higgins, M. D. (1994). Numerical modeling of crystal shapes in thinsections; estimation of crystal habit and true size. AmericanMineralogist 79, 113±119.

Higgins, M. D. (1996a). Crystal size distributions and otherquantitative textural measurements in lavas and tuff fromEgmont Volcano (Mt. Taranaki), New Zealand. Bulletin ofVolcanology 58, 194±204.

Higgins,M.D. (1996b).Magma dynamics beneathKameniVolcano,Thera, Greece, as revealed by crystal size and shapemeasurements.Journal of Volcanology and Geothermal Research 70, 37±48.

Higgins, M. D. (1998). Origin of anorthosite by textural coarsening:quantitative measurements of a natural sequence of texturaldevelopment. Journal of Petrology 39, 1307±1323.

Higgins, M. D. (1999). Origin of megacrysts in granitoids bytextural coarsening: a crystal size distribution (CSD) study ofmicrocline in the Cathedral Peak Granodiorite, Sierra Nevada,California. In: Castro, A., Fern�andez, C. & Vigneresse, J. L. (eds)Understanding Granites: Integrating New and Classical Techniques.Geological Society, London, Special Publications 168, 207±219.

Higgins, M. D. (2000). Measurement of crystal size distributions.American Mineralogist 85, 1105±1116.

Higgins, M. D. (2002). Closure in crystal size distribution (CSD),verification of CSD calculations and the significance of CSD fans.American Mineralogist 87, 160±164.

Jerram, D. A. & Cheadle, M. J. (2000). On the cluster analysis ofgrains and crystals in rocks. American Mineralogist 85, 47±67.

Jerram, D. A., Cheadle, M. J., Hunter, R. H. & Elliott, M. T.(1996). The spatial distribution of grains and crystals in rocks.Contributions to Mineralogy and Petrology 125, 60±74.

Jerram, D. A., Cheadle, M. C. & Philpotts, A. R. (2003).Quantifying the building blocks of igneous rocks: are clusteredcrystal frameworks the foundation? Journal of Petrology (in press).

Kampe, A. & Remy, W. (1960). Mitteilungen zur Stratigraphie imRaume des Petersberges bei Halle. Monatsberichte der DeutschenAkademie der Wissenschaften zu Berlin 2, 364±374.

Kampe, A., Luge, J. & Schwab, M. (1965). Die Lagerungsverh�alt-nisse in der n�ordlichen Umrandung des L�obej�uner Porphyrs beiHalle (Saale). Geologie 14, 26±46.

Knesel, K. M., Davidson, J. P. & Duffield, W. A. (1999). Evolutionof silicic magma through assimilation and subsequent recharge;


848

evidence from Sr isotopes in sanidine phenocrysts, Taylor CreekRhyolite, NM. Journal of Petrology 40, 773±786.

Knoth, W., Kriebel, U., Radzinski, K.-H. & Thomae, M. (1998).Die geologischen Verh�altnisse von Halle und Umgebung.Hallesches Jahrbuch f�ur Geowissenschaften B 7±34.

Kretz, R. (1969). On the spatial distribution of crystals in rocks.Lithos 2, 39±65.

Kunert, R. (1995). Die Lithostratigraphie der Rotliegend-Schichtenin der n�ordlichen Saalesenke bei Halle.Mitteilungen des GeologischenLandesamtes Sachsen-Anhalt 1, 69±84.

Leeder, M. R. (1982). SedimentologyÐProcess and Product. London:Chapman & Hall.

Lorenz, V. & Nicholls, I. A. (1984). Plate and intraplate processes ofHercynian Europe during the Late Paleozoic. Tectonophysics 107,25±56.

Marsh, B. D. (1988). Crystal size distribution (CSD) in rocks andthe kinetics and dynamics of crystallization; I, Theory. Contribu-tions to Mineralogy and Petrology 99, 277±291.

Marsh, B. D. (1998). On the interpretation of crystal sizedistributions in magmatic systems. Journal of Petrology 39,553±599.

Mock, A., Exner, M., Lange, D., Breitkreuz, C., Schwab, M. &Ehling, B.-C. (1999). R�aumliche Erfassung des Flieûgef�uges derkleinporphyrischen Lakkolithe im Halle-Vulkanit-Komplex.Mitteilungen des Geologischen Landesamtes Sachsen-Anhalt 5, 169±175.

Peterson, T. D. (1996). A refined technique for measuring crystalsize distribution in thin section. Contributions to Mineralogy andPetrology 124, 395±405.

Randolph, A. D. & Larson, M. A. (1988). Theory of ParticulateProcesses. New York: Academic Press.

Romer, R., F�orster, H.-J. & Breitkreuz, C. (2001). Intracontinentalextensional magmatism with a subduction fingerprint: the late

Carboniferous Halle Volcanic Complex (Germany). Contributionsto Mineralogy and Petrology 141, 201±221.

R�uffer, T., Brecht, G. & Breitkreuz, C. (1998). Seesedimente imBereich des Halleschen-Lakkolith-Komplexes: ein permischesGilbert-Delta. In: Sediment '98. Erlangen: Erlanger GeologischeAbhandlungen, p. 84.

Sahagian, D. L. & Proussevitch, A. A. (1998). 3D particle sizedistributions from 2D observations; stereology for natural applica-tions. Journal of Volcanology and Geothermal Research 84, 173±196.

Saltykov, S. A. (1967). The determination of the size distributionof particles in an opaque matrix from a measurement of thesize distributions of their sections. In: Elias, H. (ed.) Stereology.New York: Springer, pp. 163±173.

Siegert, C. (1967). Zur Petrochemie der Vulkanite des HalleschenPermokarbonkomplexes. Geologie 16, 1122±1135.

Stollhofen, H. (1998). Facies architecture variations and seismigenicstructures in the Carboniferous±Permian Saar±Nahe Basin (SWGermany): evidence for extension-related transfer fault activity.Sedimentary Geology 119, 47±83.

Stollhofen, H. & Stanistreet, I. G. (1994). Interaction betweenbimodal volcanism, fluvial sedimentation and basin developmentin the Permo-Carboniferous Saar±Nahe Basin (south-westGermany). Basin Research 6, 245±267.

Sundvoll, B., Neumann, E. R., Larsen, B. T. & Tuen, E. (1990).Age relations among Oslo Rift magmatic rocks; implications fortectonic and magmatic modelling. Tectonophysics 178, 67±87.

Upton, B. G. J. (1994). Regional setting of Carboniferous volcanismin the Midland Valley of Scotland. Transactions of the Royal Societyof Edinburgh: Earth Sciences 84, 209±212.

Zieg, M. J. & Marsh, B. D. (2002). Crystal size distribution andscaling laws in the quantification of igneous textures. Journal ofPetrology 43, 85±101.


849

Date post:	02-Mar-2022
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Using Quantitative Textural Analysis to Understand the

Documents