Mathematical Geology, Vol. 23, No. 7. 1991

Influence of Precambrian Basement on the Chemical Composition of Mesozoic Granitoid Rocks in Northeastern Asia I M. A. R o m a n o v a 2

A hypothesis for effects of stable tectonic elements on chemical composition of Mesozoic granitoids in northeastern Asia is tested. Chemical compositional change of granitoid rocks is examined in nine-dimensional space of rock-forming oxides. Stable geologic structures of the region are outlined by trends of Euclidean distances between rock recognized as a standard in a space of major rock-forming oxides and composition of individual samples. A data-smoothing polynomial of the fourth order corresponds closely to the geology of the region. Chemically stable masses of quartz diorite are thought to be delivered directly from magmatic sources along deep faults. A great variety of acidic granites, which occupy for each analysis separate cells in the nine-dimensional classification, are presumed to be palingenetic in origin. KEY WORDS: vector of chemical composition of a rock, quantile, simplex, Euclidean distance, comparative trend surface analysis, stable element, mobile zones.

~TRODUCTION

Chemical composition of a rock (here a granite, in particular) commonly is characterized by a set of major rock-forming oxides: SiO2, TiO2, AI2 03, Fe2 03, FeO, MgO, CaO, Na20 and K20. Thus, examination of a whole rock analysis means a simultaneous study of the entire set of oxides. This necessity of simultaneous study of all major rock-forming oxides resuited in a special kind of analysis that started in the 1970s at the Laboratory of Mathematical Geology. The first results published in 1978 (Vistelius et al., 1978) involved volcanogenic formations of mobile margin in the far eastern USSR. Because these analyses appeared to be effective and promising, they have continued to the present (Vistelius, 1985; Vistelius et al., 1982, 1982a, 1983). I Manuscript received 24 April 1989; accepted 2 January 1991. 2 Laboratory of Mathematical Geology of the Institute of Geology and Geochronology of the Precambrian, Academy of Science of the USSR, 12 Voinov St., Leningrad 191197, USSR. 959 0882-812i/91t|000~)959506.5011© 199! lmemationa|Associationfor Mathcmalical Geology

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This paper includes the main results of the above-mentioned studies. During this work, the following two conclusions were recognized: 1. When operating with a complete set of rock composition oxides, the mode and combinations of oxides in a rock must be recognized from the point of view that content in a given rock is practically identical with simple sampling (Wilks, 1967). 2. A mapping technique for representing whole rock composition must be formulated as isolines within a sampled area. Thus, an extensive part of Asia--delimited on the west by the Khubsugol meridian (Mongolia), on the south by the China-Korea boundary, on the east by the continental coastline and adjoining islands (Sakkalin, etc.), and on the north by the coastline and adjacent islands--was selected for study. Within this area, Mesozoic granitoids were selected for analysis. Workers at the Laboratory, in cooperation with local Geological Surveys, eventually collected 4600 wet chemical analyses of Mesozoic granitoids. Analyses were made in chemical laboratories of the respective Surveys. Net sampling was as uniform as the available mapping of granites permitted. Every sample point (Table 1) was characterized by geographical coordinates, stratigraphic control of a massif, and a consise petrographic description of the rock. These granitoid intrusions are designated with a symbol 3'5 on Russian, Vietnamese, and Chinese geologic maps. All chemical analyses were qualified as described (Vistelius, et al., 1980, p. 84-127). PRINCIPAL DETERMINATIONS AND P R O B L E M STATEMENT The chemical composition of a rock recorded by a set of major rock-forming oxides may be considered a random value that varies in its characteristic within some range. Every major rock-forming oxide considered here is called a vector component, and the number of accounted major rock-forming oxides is called the number of vector components, respectively. Vectors that fully characterize rock composition have a number of components with a sum amounting to a constant quantity ( - 100% ). In Cartesian coordinates and Euclidean space, all vector components and the point representing rock composition appear to be situated inevitably within a geometric figure of a multidimensional polyhedron, along which every axis of the coordinate system a component content might be varying from 0-100%. This figure is called a simplex in mathematics. Aitchison (1986) has studied probability distributions on simplexes describing rock composition and special aspects of these distributions. This has resulted in the elaboration of a completely new technique of analysis in petrology.

4

Totals

222

108 0 0 0 0 6 107 62 43 4

897

114 0 0 0 0.5 20 527.5 316 29 4

96

120 0 0 0 0 1.5 63 19.5 12 0

36

126 0 0 0 0 5 30 1 0 0 92

132 1 2.5 51.5 3 0.5 30.5 2 1 0

iii

1205

138 1 66 69.5 2 14 116 317 465.5 154 814

144 29 112 97.5 137 26.5 104 188 119 1

East of Greenwich

279

150 1 49 48 169 4 4 0 4 0 238

156 0 38 13 172 15 0 0 0 0 146

162 0 7.5 52.5 66 0 18 1 I 0 173

168 0 45 78 48 2 0 0 0 0 130

174 0 86 36 5 1 0 0 0 0

i

93

180 0 60 30 3 0 0 0 0 0

i

131

174 0 45 86 2 0 0 0 0 0

44

168 0 1 41 2 0 0 0 0 0

West of Greenwich

4600

Totals 32 510 605 609.5 95.5 1002 908.5 674.5 163

'~Decimals indicate sampled points on lines dividing geographic cells. Final number of specimens were obtained after rounding 0.75 to 1, 0.25 to 0. Cells are arbitrary 6 ° longitude by 4 ° latitude. Each sample represents one rock analysis.

102 0 0 0 0 0 2 2 0 0

72 68 64 60 56 52 48 44 42

Latitude (degrees north)

Longitude (degrees)

Table 1. Distribution of Sampled Points (Analyzed Rock Specimens)"

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In our case, the fact that a strong correlation exists between separate oxides in granites is particularly important. Thus, two special groups of oxides are recognized. The first are SiO2 and K20 which, in most granites, display a positive correlation. Positive correlation exists also among TiO2, A1203, Fe203, FeO, MgO, and CaO. Na20 behavior remains uncertain. A negative correlation, however, dominates between the SiO2 and K20 group and the remaining oxides (excluding Na20). This fact is important for regional petrographic studies if every rock analysis is regarded as a point within a simplex specified by rock-forming oxides in positive quadrant. Under certain conditions, oxide behavior on the simplex may be qualified and may become a key to understanding regional relations. The petrological goal requires that this analysis of behavior of compositional points on the simplex must be done simultaneously with: (a) determining relations between points that correspond to rock composition sampled within the limits of the accepted dimensionality of sampiing space, and (b) determining interrelations between vectors of the composition of rocks in the sampled points and the vector for the rock which is accepted as standard. Thus, when using data of chemical analyses, geologists have at their disposal two methods of study which are suitable for daily usage: (1) plotting distributions of chemical analyses in the space of major rock-forming oxides; and (2) following major features of regional changes in chemical composition of a rocks within the area sampled. These methods are used below in solving problems of the influence of Precambrian basement on chemical composition of Mesozoic granitoids of the region. R O C K DISTRIBUTION IN T H E SPACE OF ROCK-FORMING

OXIDES With 4600 chemical analyses of Mesozoic granitoids from an extensive area, attempting to follow every single analysis relative to other analyses is useless. A reasonable approximation is adequate, and knowledge of its principlal aspects are satisfactory. The aim of analyses is recognizing stable combinations of different oxides with the identification of a relatively small number of rock types (classes). To solve this problem, a classification by composition for every rock group is needed. Then, a given sample may be assigned to a specific class of granitoids. All 4600 analyses of major oxides were tested. The oxide content was

Chemical Composition of Mesozoic Granitoid Rocks

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divided initially into 24 parts across equal intervals and then the distribution of preferred nine-dimensional space of all combinations of 24 classes of oxide concentrations was analyzed. In a space of nine oxides with 24 concentration classes, the possibility theoretically exists of hitting an exceedingly large number of cells which indicate different compositions. Examination of our set of analyses showed that only 8 pair cells contained 2 observations and only 1 cell held 3 (this case is not sufficiently clear, it is possible that different authors have sampled the same small outcrop). All other cells contained only a single analysis per cell or were empty. Thus, the number of cells should be reduced as far as possible. Common one-dimensional distributions of probability density of every separate oxide according to 24 classes reveal that different oxides in the granitoids under study display different types of densities. For example, Na20, K20, and A1203 have symmetrical distributions,whereas MgO exhibited many relatively small concentrations and had exceptionally large values. Thus, MgO has a skewed distribution, with the highest frequencies in the left end of the distribution (very small concentrations). Obviously, to study distributions of probability density according to classes with equal intervals or concentrations was undesirable. In that case, information on small concentrations is lost and certain groups of large concentrations are unstable. The method selected was to use new units of measurement for oxide concentrations. Quantiles were chosen as a unit of measurement that allowed every marginal distribution of separate components to be converted into uniform distributions. This permitted small concentration frequencies (in our case MgO and FeO) with necessary details. Simultaneously, large concentrations of each element with unstable densities were collected in a single class equal to the biggest quantile. Thus, the usual problem of instability of large concentration frequencies was avoided. Generally, all distribution was reduced to that in nine-dimensional space; across each axis, quantiles were laid off as units of division. Thus, each analysis may be expressed by a code number indicating the quantile attached to each oxide. If an analysis is between indicated values of n i and _ 75.15% and K20 > 5.0%, both of them have code seven (n = 7). So, the code (177 777 711) corresponds to oxide concentration of the most basic granitoid. Thus, this method of notation gives rise to petrographic problems; the geo-

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Table 2. Quantile Values for Each Oxide (Concentrations of Oxides Division When 7 Quantiles) III

Quantiles (n) 1 2 3 4 5 6 7

sio2 < 64.45 --<67.38 -<69.90 -<71.90 -<73.58 -< 75.15 > 75.15

TiO2

Al2Oa

Fe203

FeO

MgO

CaO

Na20

K20 (%)

0.12 0.20 0.27 0.36 0,47 0.63 0.63

12.86 13.59 14.24 14.83 15.52 16.39 16.39

0.32 0,55 0.77 1.00 1.34 1.88 1.88

0.95 1.36 1.77 2.22 2.80 3.69 3.69

0.21 0.38 0.58 0.89 1.37 2.1 t 2. I 1

0.58 0.92 1.39 2.03 2.86 3.99 3.99

2,90 3.23 3.47 3.73 4.02 4.41 4.41

2.85 3.38 3.93 4.30 4.62 5.00 5.00

logical meaning of rock analyses grouping in one or another cell for all oxides simultaneously must be clear. Because little experience exists in treating these results, the selection of a set of analyses comprising the most complete geologic data was established empirically. Frequency distributions in the space of main rock-forming oxides were drawn (Fig. 1); the horizontal axis gives the number of analyses in a single cell (Ni), for division variants (n = 3, 5, 7, and 9), whereas the vertical axis is the number of cells with f~ analyses per cell. When the simplex axis are divided into three quantiles (n = 3, Fig. 1) many classes of analyses grouping are registered and their interpretation seems to be laborious. When the simplex is divided into five quantiles (n = 5, Fig. 1) the right "tail" of the distribution appears to decrease, although many isolated groups still exist. However, when the simplex axis is divided into 7 and 9 quantiles (n = 7 and n = 9, Fig. 1), the number of cells is reasonably limited and rock groups appear to give comprehendable petrographic information. The most important fact is that in all cases of division into oxides concentrations, the major portion of cells have just one analysis. Meanwhile, according to classical petrology, granitoids form natural groups by their chemical composition (e.g., Daly, 1933). In this case, the distributions obtained would have restrained the prevalent chemical compositions typical for the classes of rocks, with the cells containing all vectors belonging to this class of the rock. If vectors of granitoid chemical composition were independent, the most common combination occurring naturally among a tremendous quantity of component combinations in compositional space would occur only once. Furthermore, rocks of proper granite composition (alaskites, adamellites, etc.) should be expected to dominante. The existence of granitoid types requires a special investigation of distributions observed, and the recognition that particular causes lead to grouping

Chemical Composition of Mesozoic Granitoid Rocks

400

J00

fO0

20o

3OO

965

1o0

5o

200

~0 I00 20

10

20

30

JO

40

48

57 60 86 104 146

Ari

Fig. 1. Distribution histograms of chemical compositions for rocks per cell of nine-dimensional space divided by quantile values for Mesozoic granitoids in northeastern Asia. Ni indicates number of observations per cell in classes of quantile used, n is investigating values expressed in quantile measure for different number of quantiles (n is 3, 5, 7, and 9);~ is number of observations per cell for im class. Note: "Caving" of the first ordinate is determined by scale (exceedingly large number of observations in the first ordinate which cannot be expressed in the accepted scale). vectors in one o r another division. This is a problem for special investigation, and is well beyond this paper. Here, study is restricted to the preliminary interpretation o f observed frequences in terms o f granitoid composition, geologic environment o f intrusion, and regional features o f the sampled area.

RESULTS OF ANALYSIS Preliminary analysis reveals that granitoid samples with only one observation per cell, as emphasized, belong to different types o f granites ranging from adamellite to alaskite. These rocks seem to be close in composition to a different type o f granitic entectic for a nine-component system. Examination o f frequency distributions (Fig. 1) indicates clearly that most observations are in a single cell; frequencies thereafter descend rapidly to an interval with unstable frequencies in the middle part o f the distribution. The

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right side of each distribution is characterized by small frequencies, but their arrangement is stable and similar for all distributions. Each is typical for classes with a large number of observations per cell. From the point of view of classical statistics, such distributions could be neglected because they cannot be interpreted in mathematical test terms. However, after analyzing compositions of rocks which fill in these cells (right-hand tail), they geologically are the most basic granitoids studied; these are quartz diorites, tonalites, and diorites. Geographic position of these rocks and the sizes of these bodies are different than rocks in the first cells. Usually, they are small separate bodies. The chemical composition of rocks of the standard cell (code 177 777 711) summarized (Table 3) were taken from the summary of all analyses (sample numbers correspond to number of a general summary compiled with a thorough numeration). Geographically, they are scattered over a very big area (Table 1, Figs. 2 and 3). A brief geological description of the area and each sample, along with its petrographic characteristics, is given here for each sample comprising the standard rock.

Sp. 621--Quartz diorite in Taap Massif (Yakutiya). The intrusion is within an area of the Selennyach River watershed, which divides the Yana and Indigirka Rivers. The Kolyma median mass is to the east, terminating abruptly with a scarp. Westward is the Momo-Zyryan intermountain depression. It contains Paleozoic carbonate strata and Mesozoic terrigeneous sediments (Verkhoyansk complex). Here, an abyssal transform fault (Moma-Rift zone) and the Selennyakh abyssal fault are recognized. Crustal heterogeneity is traced to the upper mantle and is recorded in crustal thickness differences; within the zone, it amounts to 24-26 km, whereas southeastward the crustal thickness reaches 4044 km (Imayev et al., 1988). The quartz diorite exhibits a texture close to porphyritic. The intrusion was Early Cretaceous. Sp. 3278-Quartz diorite in the Yaaykan massif (Chukotka). The intrusion is on the western shore of Kolyuchin inlet, 3 km from Yaayakan Mountain, and is surrounded by the Eskimo median mass; the Kolyuchin abyssal fault occurs in this area. The rock texture is evidently close to porphyritic with zonal plagioclases and sometimes large ( - 1,7 % ) concentration of apatite. The intrusion was Late Cretaceous. Sp. 3291--Diorite in Pravy-Seymchan Massif. The intrusion is in the anticlinal core in the Upper Seymchan River basin. Its body is elongated latitudinally; the northern contact dips gently, whereas the southern contact subsides at an angle of 60-80 °. The rock is composed of plagioclase, potassium feldspar, biotite, hornblende, pyroxene, and accessory minerals. Wallrocks are repre-

58.60 55.68 50.03 52.48 51.14 50.40 55.40 54.95 50.90 55.44

621 3278 3298 3291 3294 3296 4a.44 4449 4457 4569

0.83 1.09 0.80 1.58 1.20 1.15 0.99 0.94 1.00 1.13

TiO2

17.28 17.00 19.40 20.47 20.56 18.03 17.92 19.64 17.76 17.53

AI203

2.55 2.60 5.31 3.65 3.90 4.21 2.03 4.33 2.6I 4.42

Fe20~ 4.96 6.40 4.09 6.61 6.94 5.22 5.88 3.72 8.99 4.02

FeO

iiii

3.72 2.84 4.92 2.52 2.79 5.84 4.10 4.25 5.07 4.50

MgO 0.13 0. I0 0.01 O. 17 0.06 0.16 0.15 O. 14 O. 10 O. 14

MnO 6.80 7.14 11.29 7.25 9.36 8.45 7.00 7.95 8.46 6.78

CaO

iiii

2.68 2.70 2.83 2.55 2.41 2.68 2.62 1.81 2.66 2.90

Na20 1.97 2.54 0.75 1.53 1.07 2.24 2.10 1.98 1.64 1.78

K20 0.65 1,00 0.48 0.98 0.54 1.49 1.56 0.68 0.80 1.26

l.i.

i

iii

0.11 0.34 -O. 13 0.30 0.47 0.26 0.27 0.26 0.22

P20~

100.28 99.43 99.9l 99.95 100.27 100.34 100.01 100.66 100.25 100.12

Sum

°Analyses cited are from old original materials; authors are (in the order of cited analyses) A. N. Vishnevsky, 1967; S. P. Stojalov, 1961; M. G. Ravich, 1938; t. V. Mamich, 1949; E. K. Ustiev et al., 1942; N. N. Remizov et al., 1967; L. F. Nazarenko et al., 1976; A. I. Burde, 1964; A. A. Sasko et al., 19xx; I. M. Mersalov et al., 1969. Loss at 110°C is omitted; --, the oxide is not determined.

SiO2

ID no.

ii lu

Table 3. Chemical Composition of Rocks Recognized as Standard (Cell 177 777 711)

gh

ig

~

°

g.

!

B

O

¢3

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0 i

JOOkm i

\ Fig. 2. Geographical location of sample points included in the cell accepted as standard: (1) for division into seven quantilies, code (177 777 71 I); (2) sampled points for division into seven and nine quantiles, code (199 999 911); (3) main faults in the region (from geological map of Eurasia, scale 1 : 5,000,000, published in Russian, edited by Peyve, et al., 1979).

sented by Early and Late Cretaceous effusives, the intrusion was Late Cretaceous. Sp. 3294--Pyroxene-homblendediorite in V e r k h n y - S e y m c h a n Massif. T h e i n t r u s i o n is w i t h i n the watershed s u r r o u n d e d by the O k h o t s k m e d i a n mass; a zone o f abyssal faulting crosses this area. T h e rock is c o m p o s e d o f plagioclase,

Chemical Composition of Mesozoic Granitoid Rocks

969

,# 0

300km

%

!

¢

~z

~-----Is Fig. 3. Relations between geological structure of the region and position of isolines approximating Euclidian distances [d from Eq. (2)], sampled points from the standard rock for division into seven quantiles: (1) Nippon geosyncline; (2) stable elements of structure [the Siberian Platform with median masses (K)--Kolyma, (Om)-Omolon, (Ok)--Okbotsk, (B)--Bureya]; (3) isolines of Euclidian distance of sampled points from standard rock; (4) western border of Mesozoic intrusions; (5} position of samples composing the cell accepted as standard, numbers indicate identification number of the analysis used in original compilation.

m i c r o c l i n e , quartz, biotite, diopside, h o r n b l e n d e , a n d apatite. T h e intrusion was Late Cretaceous. Sp. 3296--Diorite in E t a n ' d z h a Massif. E x p o s u r e s o f diorite-granodioritep o r p h y r y o c c u r at the site o f transection o f the M a y m a k a n - O k h o t s k M a s s i f and

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the Bilyakchin fault zone. Chains of intrusive bodies are along the contact of Precambrian block of the Okhotsk Massif with Permian terrigenous-sedimentary complex. The rock displays a near porphyritic texture and consists of plagioclase (55 % ), potassium feldspar (2-3 % ), dark-colored minerals (up to 40%), zircon, sphene, allanite, and apatite. The intrusion was Late Jurassic. Sp. 3298--Diorite of the Vukhney Massif, in the Eluchi spring Basin, an area north and west of the Omolon median mass. The South-Anyuy abyssal fault is in this area. Northward, Upper Triassic strata are exposed, whereas Upper Jurassic strata comprise a southern, subsided block. The South-Anyuy depression is regarded as a rift structure that separates the Omolon median mass from the Chukotka miogeosyncline. The rock is composed plagioclase (up to 73 % ), diopside and bronzite (up to 11% ), hornblende, biotite, quartz, apatite, sphene, magnetite, and allanite. Accessory minerals are about 2%. The intrusion was Early Cretaceous. Sp. 4444--Diorite of the Ternisty Stock (Sikhote-Alin'). The intrusion is in a zone jointly of the main synclinorium of Sikhote-Alin' and the Nearshore zone. The stock covers 1.5 km 2. It is a steeply dipping body on the southwest limb of an anticline. Rocks are plagioclase (60%), potassium feldspar (2%), quartz (3-5%), biotite (25-30%), pyroxene (10-15%), and magnetite (1-2%), and are assigned to monzodiorites (Ivanov et al., personal communication, 1980). The intrusion was Late Cretaceous. Sp. 4449--Quartz diorite in a stock near Moshchny Spring within the Sikhote-Alin' structure closer to Nearshore zone boundary. The rocks are composed of plagioclase (up to 60% ), potassium feldspar, quartz, biotite, hornblende, pyroxenes, apatite, magnetite, and sphene. The intrusion was Late Cretaceous. Sp. 4457--Quartz diorite in the Verhneplotnik Stock near the Kungulaz Massif, also within the limits of the Sikhote-Alin' structure. The rock is composed of plagioclase (55-66%), potassium feldspar (5%), quartz (3-10%), hornblende, biotite apatite, and allanite. The intrusion was Late Cretaceous. Sp. 4569--Diorite in a stock within the Penzhin-Anadyr' fault zone among strata surrounding the Omolon median mass on the east. The rift zone of the northwestern part of the Pacific Ocean mobile belt consists of a chain of depressions (axial part) and uplifts from the Uda Inlet to the Penzhin-Anadyr' folded zone. The rift system is asymmetrical, with the Okhotsk-Chukotka volcanic belt on the continental margin. The quartz-diorite stocks cut volcanic-sedimentary and terrigenous-tuffaceous strata that range in age from Early Cretaceous to Late Cretaceous. Thus, a stability of rock assemblages exist as even more narrow intervals (n = 5 ---' 7 ---, 9) in the major oxide concentrations are used (Fig. 2). Samples

Chemical Composition of Mesozoic Granitoid Rocks

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of the cell designated as a standard appear to be in zones of abyssal faults that separate stable structures from folded mobile areas. These samples belong to small intrusions; commonly, these are stocks or central structures with steeply dipping contacts. The rocks are close in composition to diorites or quartz diorites, Their structure is porphyritic with zonal plagioclases. The rocks are rich in A1203 and FeO (Table 3). Dominance of plagioclase over potassium feldspar is typical; hornblende is common and its concentration is greater than biotite. Pyroxene concentration reaches 17%, sometimes garnet, apatite, sphene, allanite, and magnetite (up to 2 % in Terney Massif) are present. The intrusions, in most cases, are Late Cretaceous. Thus, studies of frequency distributions using analyses of all 4600 samples of Mesozoic granitoids from northeastern Eurasia reveal that these rocks may be divided reasonably into three major types. • One part embraces acidic variety granites. They are characterized by one sample per compositional cell, which means they display extreme variety (left portion of distribution). • Another part embraces rocks that approximate quartz diorites. They include up to several analyses in one compositional cell and probably form a separate group of rocks (right portion of distribution, Fig. 1). This conclusion is certainly preliminary. • A third part embraces granitoids of different types of intermediate composition. They lie between the extremes of the compositional distribution. The rocks might be summarized as two main compositional distributions. The first represents varieties of granitic rocks which are scattered widely over the whole territory. This class of rocks is characterized by a single sample in each compositional cell. The second group includes quartz diorites, tonalites, and other basic granitoids. These rocks are more localized near dip faults. Separating compositional observations into 5, 7, and 9 quantiles does not change these main groupings; thus, this pattern is rather robust. These facts suggest two different processes of granitoid generation. One process generates acid-granitic rocks characterized by great compositional diversity and widespread geographic disposition. The second process generates basic granitoids having more or less the same composition and which are localized near deep crustal faults. These rocks are homogeneous in mineral composition and textures. They occupy the same definite position in the regional tectonic structure of the region (Fig. 2). The next phase of the studies concerns the problem of the relations of rock composition and regional geologic structures of the area sampled.

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R E G I O N A L S T R U C T U R E AND V A R I A T I O N S O F C H E M I C A L COMPOSITION OF GRANITOID INTRUSIONS Studies here are aimed principally at analyzing structural effects of large stable blocks with Precambrian basement (platforms, median masses) and zones of geosynclinal mobility on the chemical composition of granitoids. Which rock compositions on the simplex fall in areas adjoining stable zones and areas that adjoin to mobile zones will be clarified. All chemical compositions of the rocks were plotted as sets of points on the nine-dimensionals compositional simplex. All points occur in a positive quadrant of a rectangular system of coordinates. As noted, points corresponding to vectors of rock composition stretch from a portion of greater concentration of SiO2 and K 2 0 components with lesser concentrations of TiO2, AI203, Fe203, FeO, MgO, and CaO to that part of the simplex which relatively is poor in SiO 2 and K 2 0 but rich in the remaining oxides. Quantiles are accepted as space coordinates, so that every chemical analysis of a rock is drawn as a vector in nine-dimensional space of oxide concentrations, with an identical unit value on each axis that is determined by quantile value. Vectoral changes in granitoid composition within the sampled area (i.e., the mode of vector variations in rock composition relative to each other) required an introduction of "length of a vector" in oxide space; when using it, the distance between them may be estimated. Here, Euclidean distance is as usually accepted,

d

~ti= l

(1)

with x ~°) designating a given oxide concentration in a standard and x t;) is the concentration of that same oxide in a sample, the distance to which is to be measured. In full form, expression (1) can be represented in this case as d = x/(SiO~i~ - SiO~20~)2 + . . .

+ (Na20ti~ - Na2OtO)) 2 + (K20 ~;~ - KzOtO~)2

(2) This Euclidean distance can be referred to as norm, for abbreviation (however, " n o r m " usually means a distance from zero). Many authors have proposed it [D. Shaw (1968) in particular].

Chemical Composition of Mesozoic Granitoid Rocks

973

The task is complicated by the fact that a single scale must be employed for all oxide concentrations. This is especially important in petrology because SiO2 concentration, if it is measured in percent, appears dominant or the most important factor for the norm value. Use of a single scale for all oxides is most important in reaching a satisfactory solution; here, the problem is resolved using quantile scales. A standard (x t°~) must be chosen to which the distance of all remaining points must be measured. Certainly, any x t°~ could be chosen, as isolines of equal quantiles would not necessarily form a pattern describing the peculiarities of interest in the area, since they can be arranged symmetrically relative to a given point (the norm has no sign). As noted, the goal consists in analyzing changes in chemical composition of Mesozoic granitoids relative to stable continental elements and marginal mobile belts. Analysis of distributions in compositional simplexes with subdivision into seven and nine quantiles shows that additional distributions are arranged just within the mobile continental margin, and a tendency to occur in zones of deep faults. Examination of distributions (Fig. 1) demonstrates that cells with 10, I 1, and 12 analyses are most typical of the mobile continental margin. And granitoids that are mostly distinct in relation to their basicity appeared to be rocks of the quartz diorite type, having a quantile code of cell (177 777 711). Rocks of this cell were recognized as "standard" (x t°~). The sampled granitoids exhibit various compositions and belong to intrusions of different shapes and sizes. Besides, they are not distributed uniformly in the area. Thus, smoothing of isolines for distances of granitoids from the accepted standard is desirable. Trend-analysis seems the best method of approximating these values. This idea of using a trend analysis with polynomials raised to power of e and related to the major geologic aspects of an area with a simultaneous smoothing of minor details was proposed more that 25 years ago (Vistelius and Yanovskaya, 1963). This method was tested systematically and modified to some extent while mapping Kara-Kum Recent sands (Romanova, 1971). It was referred to then as comparative trend-surface analysis (see Appendix). However, a series of models were compared to determine that model which corresponds most closely to the geologic structure of the area. In other words, if this event is recorded in nature, the trend lines of Euclidean distance should reflect the Siberian continental margin. Furthermore, the isoline pattern must be considered only within the sampled area, because no general mathematical model known describes the process that determines rock distribution according to their composition. Neither are any grounds recognized for allowance of gradual changes in granitoid composition within the sampled area. The d-trend isolines, in particular, do not contradict a supposition that the area is composed of separate blocks that became unified under the effect of continential plate movements and that

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those blocks achieved a position in which their isoline pattern answers the geologic concepts. If it is valid, the rigid blocks had a position that led to a certain distribution or rock chemical compositions within the limits of the area. In our analyses, a comparative trend analysis fourth-order polynomial is used that can, if it is recorded in nature, demonstrate by plotted isolines the effect of median masses of a platform against a general geosynclinal background, and an abyssal, probably, relatively more basic magmatism within mobile zones. Isoline patterns (Fig. 3) are estimated by mapping the difference between x t°~ and x ti~ for all 4600 analyses, d-Isolines reflect relationships between elements of stable structures and mobile areas. Isolines with larger values surround the eastern boundary of the Siberian Platform, and their configuration is influenced by median mass blocks. Similarly, slightly different d values in mobile zones reveal the northwestern termination of the Nipponian geosyncline. The stability of the isoline pattern was investigated by plotting isolines for the same sampled area using a scale of nine quantiles (Fig. 4). In this case, the same data were analyzed as for seven quantiles with x c°~ (Fig. 3). The isoline pattern (Fig. 3) is similar (Fig. 4), showing that the method has some robustness. If isoline patterns are refined Chukotka, according to d-values in both schemes, then this indicates proximity of the plateform margin or of the Chukotka (Eskimo) median mass. Note that d-values increase northeastward toward Alaska. However, this area lies on the extreme margin of the area sampled, and such an increase might be merely a function of the polynomial used. However, early in the work, the behavior of the oxide K20 content in Mesozoic granitoids, and also polynomials of the third order, led to the conclusion that this growth of trend isolines was due to stable block structure (Vistelius et al., 1969). Here, supplementary work to test this supposition was done. Using a random numbers generator, the area sampled was divided into northern and southern parts, and the trend of K20 content was estimated for each part separately; the patterns obtained showed that K~O values in both parts behave similarly to d-values for all observations. So, using chemical analyses from Mesozoic granitoids, the existence of the Hyperborean platform in extreme northeastern Asia or the Eskimo median mass, as it is now called, apparently is confirmed. All data available, including trend schemes drawn using other coefficients (Vistelius et al., 1974, 1977), define independently, and one-to-one, the Kolyma median mass, although debates on its existence still continue. In conclusion, the method applied here, with approximation, allows for the definition of only the largest elements of a structure. Relatively small blocks (e.g., Argun' or Khankay) cannot be identified separately on the trend schemes, although rocks in those structures must influence the d-isoline patterns.

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9! 32 ~J []5

Lr~

Fig, 4, Isolines of Euclidian distance from the standard rock division into nine quantiles. All designations are similar to Fig. 3, except that black dots indicate geographic position of samples composing the standard cell for division into nine quantiles. The position of the isoline surrounding K, OM, and OK median massifs can be explained easily by the pattern of sampling.

W h e n deciphering trend patterns (Figs. 3 and 4), the peculiarities o f the function used must be considered, otherwise the trend analysis has no meaning. Using trends o f increased orders (e.g., sixth order), which are supposed to refine patterns, pictures are obtained that are almost impossible to interpret if no conceptual model exists that allows for independent testing.

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R E S U L T S O B T A I N E D AND TASKS POSED FOR T H E F U T U R E A special geological interpretation is not needed when using a conceptual mathematical model because the model should embrace all existing geologic ideas. During problem solving, "response models" were used which permitted certain important geologic features of the area structure, in descriptive terms, to be accepted or rejected. In this particular case, it helped to test a hypothesis concerning the influence of stable elements of the regional structure on chemical composition of Mesozoic granitoids as a whole; that is, the simultaneous influence on all nine major rock-forming oxides that comprise the rock. Analyses showed that more acidic varieties of granitoids in major intrusion exhibit an extremely varied composition according to varieties of granitoids; here, a quartz diorite is of limited distribution, and these rocks are grouped into closed sets according to the oxide content of which they are composed. At the same time, rocks distinctly different from quartz diorite (acidic and ultraacidic granites) show a tendency to occur in stable elements of tectonic structures. Basic granitoids (quartz diorites and varieties similar to them) exhibit a tendency to be grouped in zones of abyssal faults, and show a preference toward the mobile continental margin (Fig. 2). An extremely great compositional variety of granites, and their rather uniform distribution over the whole area as well as their growing abundance near Precambrian stable elements of the area, is suggestive of palingenetic origin. Palingenesis is typified by the fact that the rock is formed in the process of melting, up to eutectic composition, at an initial phase of crystallization. Insignificant contamination might result in a great variety of the rocks. Furthermore, considering the multicomponent composition of sedimentary and volcanic strata and their disequilibrium in the process of melting, these rocks could be expected to produce eutectics of absolutely different composition. But naturally, sediments lying in the zone of ultrametamorphism would be subjected to palingenesis, and these evidently were the Precambrian formations. Thus, paradoxically at first sight, the grouping of rocks in cells of simplexes that contain just one analysis per cell is a natural result of granitic origin during palingenesis. The process of differentiation of basic magma proceeds according to a certain system, and the final results of the magmatic process are more uniform rocks. The granitoid group of quartz diorite type, stable in their chemical composition and occurring in zones of abyssal faults, represents, as noted above, a differentiation of mantle material, and probably is related to all Mesozoic granitoids in both location and age. The formation of rocks through different types of genesis within this ex-

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tensive area, which is so tectonically heterogeneous, does not contradict the scheme proposed here. If a special metaUogeny existed in Precambrian formations, the Mesozoic granitoid metallogeny is but a transformed reflection of Precambrian metallogeny. But a different idea on petrogenesis and metallogeny of the area sampled is prompted from distributions of points on simplexes of chemical composition of Mesozoic granitoids. Preliminarly results were presented about 15 years ago (Vistelius et al., 1974) concerning tin-bearing granitoid formation relative to melting of older material during the Mesozoic Era. But this problem requires further study. Further work is also required to test the following: • Response models which allow use of a comparative trend analysis could help in refining and critically evaluating the functional behavior at margins of the area sampled when additional sampling and extension of control on Chukotka and Mongolia become available. • Sampling of granitoids is to be supplemented by zircon age determinations from Mesozoic granitoids, if only for a limited number of samples. This will be useful in testing the conclusion of a Precambrian source for the Mesozoic magma. If zircons display a discordant older age for a sufficient number of samples, the problem of Precambrian basement being a decisive factor and its effect on Mesozoic granitoid composition may be regarded as accomplished and indisputable; to a great extent, if concerns determination of localities of ore deposits in these rocks. • Comparative trend analysis is rather crude and requires the development of special tests for mutual comparison of patterns obtained for different objects. To elaborate this method faithfully, it is difficult because many aspects of intrusion formation and origin of their magma are still unclear and require additional study. APPENDIX Comparative Trend Analysis

An example from experience will illustrate the idea of comparative trend analysis in the simplest way (Romanova, 1971). Assume a plateau is covered with sands and that it terminates by a cliff. The cliff can be approximated on a map by a straight line. A lowland lying in front of the cliff is also covered by sands. Strong winds blow in a direction perpendicular to the cliff from plateau to lowland. The problem to be solved by comparative trend analysis is which of the following alternative hypotheses is most nearly correct of the following alternative hypotheses:

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Ho--Heavy fraction sands from the plateau are precipitated under the cliff by wind transport, in which case the quantity of heavy fractions is greatest under the cliff and diminishes away from the cliff. H~--The position of the cliff has no influence on the concentration of heavy fraction sands of the lowland, in which case the distribution will tend to be uniform. The simplest way to solve which alternative is better is to smooth by some polynomial which contains a linear component observations on the content of heavy fraction minerals in lowlands of sand. If the trend surface computed by these observations gives a linear function, such that isolines of this trend surface tend to be straight lines subparallel to the cliff, and isolines of the greatest content of heavy fraction is near the cliff (with other lines showing lesser heavy fractions), the better alternative is/4o. In other cases, the position of isolines relative to the cliff will reject H 0, indicating that H~ should be accepted. Variance, quality of smoothing, and behavior of finite differences are not important in this case. Only the coincidence of direction of isolines with alignment of the cliff and arrangment of heavy fractions are important in this case. This is comparative trend-analysis. Of course, some measure of, or test of, coincidence of direction of cliff and trend isolines is desirable. However, this has not yet been resolved. Nonetheless, many cases are obvious without additional computations being necessary. Here obviously (Figs. 3 and 4), coincidence of direction of isolines of Euclidean distance and terminations of Siberian Platform, median masses, and mobile zones exist.

ACKNOWLEDGMENTS This paper summarizes the work done at the Laboratory of Mathematical Geology of V. A. Steklov Mathematical Institute of the Academy of Science of the USSR (Leningrad) up to 1987 and at the Institute of Geology and Geochronology of the Precambrian of the Academy of Science of the USSR to the present. The original data, including chemical analyses of Mesozoic granitoids from the eastern USSR with geographical control of sampling points, stratigraphic control of intrusion, concise petrographic description of rocks (collected by groups of geologists of the respective Territorial Geologic Departments) was collected at our Laboratory. In Eastern Siberia, Transbaikal, and Mongolia, I. N. Fomin (Chita) headed data collection and analyses; in Yakutia, V. I. Shur was the leader (Yaskutsk); in the Magadan area, the group on petrographic studies was involved (Magadan); in the Khabarovsk area, A. I. Aralina was responsible (Khabarovsk); in Primor'je, I. Z. Bur'yanova and Z. E. Nadezh-

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k i n a w e r e c o - w o r k e r s ( V l a d i v o s t o k ) ; in K a m c h a t k a , I. S. G u z i e v w a s i n s t r u m e n t a l . In o u r L a b o r a t o r y , O. V , G r a u n o v c a r r i e d o u t c o m p u t a t i o n s . T h e a u t h o r e x t e n d s h e r t h a n k s to all p a r t i c i p a n t s o f this s t u d y a n d to the former Ministry of Geology of the RSFSR that supported the collection of data in c o o p e r a t i o n w i t h s t a f f w o r k e r s o f t h e r e s p e c t i v e G e o l o g i c S u r v e y s . T h e a u t h o r is i n d e b t e d to the r e v i e w e r s o f this m a n u s c r i p t , J. C . B u t e r , C. J. M a n n , a n d E. H . T . W h i t t e n , w h o h e l p e d t h e a u t h o r in r e v i s i n g the text.

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Aitchison, J., 1986, The Statistical Analysis of Compositional Data: Chapman a Hall, London, 416 p. Daly, R. A., 1933. Igneous Rocks and the Depths of Earth: McGraw-Hill, New York, 598 p. Romanova, M. A., 1971, Recent Sand Deposits of the Central Kara-Kum: Nauka, Leningrad, 256 p. Shaw, D. M., 1966, On the Division of Data in Analytical Geology into Two Groups Using Remote Information, in Voprosy Mathem. Geology: Nauka, Leningrad, p. 98-110. Vistelius, A. B., 1977, On the Chemical Composition of the Mesozoic and Paleogenic Granitoids in the North-Eastern Asia and on the Regional Tin-bearing Potential of this Area, in Voprosy Regional Geology: izd. Leningradskogo Universiteta, v. 2, p. 118-124. Vistelius, A. B., 1982, On the Principal Types of Mesozoic Granitoids in the Noah-Eastern Asia: DAN, v. 265, p. 1211-1216. Vistelius, A. B., 1982a, On the Principal Trend-Variations in Potassium Concentration of the North-Eastern Asia and the Areas Adjoining: DAN, v. 226, p. 1444-1448. Vistelius, A. B., 1985, The Chemical Composition of Mesozoic Granitoids in the Noah-Eastern Asia and the Situation of Intrusion in the Tectonic Structures of the Area, in Tektonika Sibiri: v. 15, Nauka, Novosibirsk, p. 32-41. Vistelius, A. B., Aralina, A. l., Bur'yanova, 1. Z., Gel'man, M. L., Ivanov, D. N., Kuroda, J., Naryzhny, V. I., and Romanova, M. A., 1969, Principal Regularities in Distribution of Potassium in the Post-Jurassic Granites in the North-Eastern Asia and Adjoining Part of the Pacific Ocean: DAN, v. 184, p. 441-444. Vistelius, A. B., Ivanov, D. N., and Romanova, M. A., 1983, The Main Tectonic Structures of the North-Eastern Asia and the Chemical Composition of the Mesozoic Granitoids: DAN, v. 271, p. 142-145. Vistelius, A. B.. lvanov, D. N., and Romanova, M. A., 1974, Regional Trend in the Mesozoic Granitoids Composition and Determination of Tin Areas in North-Eastern Asia: Nauka, Leningrad, 33 p. Vistelius, A. B., Ivanov, D. N., Romanova, M. A., and Talmud, G. A., 1978, On the Chemical Composition of the Mesozoic and Paleogenic Rocks and on Deep Structures in the Northern Eurasia: DAN, v. 242, p. 386-389. Vistelius, Ai B., and Yanovskaya. T. B,, 1963, Programming of Geological and Geochemical Problems When Using Universal Computers: Geologya Rudnykh Mestorozhdeniy, no. 3, p. 34-48. Wilks, S. S., 1967, Mathematical Statistics: Nauka, Moscow, 632 p., (Russian translation). -aAll cited sources are in Russian, except Aitchison, J. DAN is the standard abbreviation of the title of the Journal Doklady Akademii Nauk SSSR (Reports of the Academy of Sciences of the USSR).