GNEISSES Thickness distribution of layers and their lithologic transitioas
B. K A T Z
Katz, M.B. 1970: Banded gneiasea. Thickr~ess distribution of layers and their lithologic transitions. Lithos 3, 1-13. Measurements on sets of beds of sedimentary rocks have shown that the distribution of bed thickness tends to be log-normal. Similar studies on the banding and on the compositional layering in Precambrian highgrade metamorphic banded gneisses of Quebec, Canada, the highlands of Ceylon, and Norway reveal a s/milar statistical distribution. As was shown in sedimentary rocks, there appears to be a dependency among layers of certain lithologies. The apparent log-norma~ distribution of bed thickness found in sedimentary rocks and gneisses, md their lithologic relationships are discussed in terms of a criterion to determh~e the origin of metamorphic layering.
M. B. Katz, Dept. of Geology, University of Ceylon, Peradmiyv, Ceylon
Introduction Sedimentation units, such as beds and laminations vary in their thickness and persistence and in many cases the variations in thickness tend to have a log-normal distribution (Pettijohn 1957, p. 160). This statist;cal distribution impliee that beds of the lower range of thickness in a population of bed thicknesses are most frequent although there is a finite probability for the occurrence of much thicker beds ia the sequence. Also recent studies on lithologic transitions ir bedded sequences show statistical evidence of interdependency among the various lithologic units (Potter & Blakely 1968). The banding or layering so conspicuous in many gneisses of metamorphic terrains probably reflects original supracrustal layering, of which sedimentary bedding is the most important contributor (Dietrich 1960a). If this is true, the relict metamorphic layering should also retain thickness distributions and lithologic trans:~tions similar to what we find in the sedimentary rocka. Examples of thickness distributions retained in low grade metamorphic Precambrian varved schists of Finland (Simonen & Kouvo 1951) support this view. However statistical studies of layer thicknesses and lithologic transitions in banded gneis.ses of high-grade metamorphic rocks are very rare, if not totally lacking. Layering, banding and stratiform foliation in gneigses Penetrative planar structures in metamorphic rocks are of three kinds: (Turner & Weiss 1963, p. 91). 1 --
M~CHA~B. KATZ 1. Relict sedimentary bedding and other inherited surfaces of premetamorphic origin including volcanic and igneous layering. 2. Surface of metamorphic origin or foliations (cleavage, schistosity and metamorphic differentiation layering).
3. Joints. Usually it is not difficult to distinguish types 1)and 2) from 3); however to differentiate between types 1) and 2) may be a problem (Harker 1950, p. 204-7). 8ome criteria to distinguish relict sedimentary bedding and other surfaces of pre-metamorphic origin from banding and layering of metamorphic origin has been outlined by Dietrich (1960a) and Turner & Weiss (1963, p. 93-100). In the case of layering of volcanic or igneous origins criteria based on relict textures, structures, and mineralogy, together with the chemical compositions and field relationships would in most cases supply sufficient information to determine the origin. In layering of sedimentary origins, the presence of relict sedimentary structures such as cross-bedding, and heavy mineral concentrations may be important in determining the parentage, although the absence of these features cannot be considered as evidence against a sedimentary origin. The concordant interlayering of recognizable meta-sedimentary units, such as marbles, metaquartzites or meta-conglomerates would also be suggestive of a sedimentary origin. More important considerations are the chemical, mineralogical and petrographical compositions of adjacent layers. If these are considered in conjunction with any relict textures and structures they may provide some clues on the origin of these layers. Surfaces of metamorphic origin which resemble relict sedimentary bedding, especially layering formed by metamorphic differentiation, have characteristic features as follows (Turner & Weiss 1963, p. 99-100). 1. The scale of metamorphic layering is independent of the scale of bedding, which may be inferred from its chemical composition, mineralogy and large-scale structures. Fine differentiation laminations can be developed in rocks of diverse original bedding thicknesses. 2. The individual layers on close examination are actually very flat discontinuous lenses. 3. Chemically and mineralogically there is no correspondance between many types of metamorphic differentiated layers and ordinary sediments. Ahhough the above criteria may assist in the determination of the origin of layering in metamorphic rocks, in many cases these are by no means conclusive, especially when the rocks have been metamorphosed and completely recrystaUized at high temperatures and pressures. Often the original textures and structures are destroyed and in rocks whose original composi-
tions are not diagnostic of sedimentary rocks (e.g. graywacke and arkoae), the mineralogical and chemical criteria may not be significant. It thus becomes increasingly difficult to assign these layered rocks to either a sedimentary or metamorphic origin. Many of the gneisses under study fall in this category of being of dubious origin in terms of relict structures, composition and other distinctive criteria. However, they all possess a characteristic, regular layered appearance and it is proposed that statistical studies based on their layer thickness distributions and lithologic transitions may serve as important criteria in determining their origin. M e t h o d s of s t u d y The gections measured were located on easily accessible well-exposed outcrops which show on cursory examination typical alternating leucocratic and melanocratic bands. On doser inspection the bands are observed to be concordant with a regular continuous planar aspect and consist of alternating, rather thin layers of at least two lithokgic types. Measurements of layer thiclmesses were taken along outcrop sections that were approximately perpendicular to the dip of the layers and thus represent true thickness dimensions. The thickness of each layer was determined at every major lithological break, although some measured bands actu~Jly consist of numerous thinne, bands which could not be measured accurately. These layers with recognizable thinner sub-units formed distinctive lithologica! "mits within the section. The measured layers varied in thickness from very thin laminations about .01 inches to layers over 16 inches thick. The analyzed thickness data were first grouped into class interval frequency distributions (Bryant 1960, p. 53-4) and subsequently plotted on implied logarithmic scale probability paper to test for log-normal distributions (Krumbein & Sloss 1963, p. 128). The contributions of the various lithologic units to the frequency distributions were also noted. Where more than two lithologic units occur in the section, the one-step dependency of these units is presented in terms of transition probabilities (Potter & Blakely 1968). The frequencies of contact pairs of lithologic types in each section are counted and presented in a data array. The transition matrix represents the one step lithologic transition probabilities for each possible lithologic pair. These probabilities are computed by dividing the frequency of each lithologic contact pair, as tabulated in the data array by the total number of contacts observed for each lithologic unit (the sum of each row in the data array). Independence tests can be made on either the data array or the transition matrix by a X 2 test using a contingency table (Bryant 1960, p. 104-10 ~nd Krumbein & Graybill 1965, p. 183-8). As t i e data array and the transition matrix have zeros down their main diagonal, for such a m × m table the degrees of freedom are (m-1)Z-m. For a full discussion on -he theor f and application of lithologic transition probabilities see Potter & Blakely (1968).
MXCH,~ . . KATZ L EGE NO PALAEOZOIC
----'] ORODVICIAN PRECA MBRIA N - ~ ' ] OUARIZOFELDSPATHIC GNEISS iDTITE AND HORNENDE GNEISS
NARBLE FORN A TION
SCALE 6 l~Niles i iii
Fig. 1. General geology of parts of Pontiac County, Quebec showing locations of sections A, B, C, D and E.
Layered gneisses of Quebec Geology of parts of Pontiac County. - The t'recambrian rocks of the Grenville group in Pontiac County consist of quartzofeldspathic gneisses, charnockitic biotite and hornblende gneisses, garnet gneisses and a meta-sedimentary formation with a characteristic marble member (Katz 1969). In this area, four exposures of layered gneisses were chosen for analysis (Fig. 1). The three exposures east of tile town of Waltham lie within the marble formation and the other locality occurs south of Greer lake in the biotite and hornblende gneiss terrain. Section ( A ) , at Waltham. - 62 layer thicknesses were measured from section
(A), which consists of an alternating ~eries of medium-grai,ed pink quartzofeldspathic gneiss (A1), fine-grained grey quartzofeldspathic gneiss (Az) and grey-blue biotite gneiss (An). The results are shown in Table 1 and Fig. 2. The frequency distribution of section (A) tends towards a log-normal distribution (Fig. 2), The separate lithological units also s~"~w a similar distribution with (A1) having a higher frequency of thicker beus. The transition data (Table 1) indicates that the frequency of the pink quartzofeldspathic gneiss (Ax) interlayered with biotite gneiss (As) is high and their respective transition probabilities are pla=.720 and pm--.739. The smallest transition probability is from biotite gneiss (An) to grey quartzofeldspathic gneiss (Az)
Table 1. Transition Matrices - Waltham, Quebec
Sect/on A At Az As Aa
- .280 .615 .739 .261 -
Sect/on B Bz
.720 ] .385 -
"°°° - _1
.NX) , 1 ~
Fig. 2. Cumulative curve of thickness of 62 layers of section A and 56 layers of section B from banded gneisses of Waltham, Quebec. Abscissa in inches, ordinate in percent.
(psa--.261). There is also a definite preference for the pink quartzofeldspathic gneiss (A1) to follow the grey quartzofeldspathic gneiss (As) in the sequence (p~1--.615; pz2--.280). Section ( B ) at W a l t h a m . - 56 layer thicknesses were measured from section (B) which is separated by about a thousand feet from section (A) and the results are presented in Table 1 and Fig. 2. This section is an alternating sequence of pink quartzofeldspathic gneiss (Bz), and dark amphibolite (B~), with minor interlayer~ of grey biotite gneiss (Bs) and laminated quartzofeldspathic gneiss (B4). The frequency distributions of both sections (A) and (B) are very similar and tend toward a log-normal distribution (Fig. 2). Both (Bx) and (Ba) show a similar distribution to the whole but the minor beds (Bs) and (B4) have a unimodal or bimodal nat~Jre with layer thicknesses greater than most frequently found in the other layers. This data for the minor beds are meagre and may not be significant. According to t.he transition matrix (Table 1), this section is essentially an interlayered sequence of quartzofeldspathic gneiss (BI) and a.~phibolite (B~) (p1~--~.880; ps1=.833). It is also noteworthy that the biotite gneiss (Bs) is in all cases found preceding the quartzofeldspathic gr:eiss (Bz). Certain units appear to be incompatible, such as the amphibolite (B~) and the biotite gneiss (Bs), and the biotite gneiss (Bs) and the laminated quart~Jeldspathic gneiss (B4)(p~--p~-----pu--
p~=O). This section, found east of sections(A) and (B) near Devonshire Park, is of a distinctly different appearance. Five hundred layer thicknesses were measured on this outcrop which consists of a laminated gneiss made up of thin alternating layers of grey qutrtzofeldspathic gneiss (Cz) and dark biotite gneiss (C2) with minor layers of coarser Section ( C ) near Devonshire Park. -
MICHAEL B. KATZ
pink quartzofeldspathic gneiss (Ca) and the results are presented in Table 2 and Fig. 3. The frequency distributions display a log-normal distribution (Fig. 3) and the lithologic units show a similar trend. The transition matrix (Table 2) indicates that this section is an interlayered series of quartzofeldspathic gneiss (Cz) and biotite gneiss (Cz) (plz----.951;pat--.917). The pink quartzofeldspathic gneiss (Ca) shows a high transition probability of preceding the biotite gneiss (Cz) (paz--.844). The lowest transition probability is from grey quartzofeldspathic gneiss (Cx) to pink quartzofeldspathic gneiss (Ca) (pla--.049) in spite of their similar composition. Table 2. Transition Matrix
Devonshire Park, Quebec
.IM9 ] .083 -
c, / n.
' o 2 5 .05
Fig. 3. Cumulative curve of thickness of 500 layers of section C from a laminated gneiss of Devonshire Park, Quebec. Abscissa in inches, ordinate in pe~'cent.
Sections ( D ) and ( E ) al' Greer Lake, Pontiac County. - Over 30 layer thicknesses were measured, from each of two sections separated by about 100 yards. The results are presented in Table 3 and Fig. 4. Section (D) is a thinly layered gneiss consisting of alternating grey biotite quartzofeldspathic gneiss (D1), pink quartzofeldspathic gneiss with large quartz rods (D2), dark amphibolite (Ds) and one layer of light grey quartzite (D,). Section (E) is of similar appearance and consists of alternating layers of pink quartzofeldspathic gneiss (E0, dark amphibolite (E~), grey biotite quartzofeldspathie gneiss (Es) with minor layers of pink quartzofeldspathie gneiss with large rods (E4) and light-grey quartzite (Es). The frequency distributions of sections (D) and (E) are similar and both show a log-normal distribution (Fig. 4). The separate lithologic units also tend towards a similar distribution. The transition matrix of section (D) Table 3. Transition Matrices - Greer Lake, Quebec Section D
D~ Da D4
.875 .750 .000
.000 .000 -
E,., Ea E4 E5
.583 .125 .750 .000
.625 .250 .000
E3 .250 .000 1.000
.167 .125 .000
.000 .125 .000 -
Fig. 4. Cumulative curve of thickness of 32 layers of section D and 38 layers of section E from banded biotite-quartzofeldspathic gneimes of Greer Lake, Quebec. Abscissa in inches, ordinate in percent.
(Table 3) indicates that the pink quartzofeldspathic gneiss (D,) and amphibolite (Ds) show a higher transition probability of following the biotite q u ~ f e l d s p a t h i c gneiss (DI) than preceding it (p91--.875; p19--.500 and psi--.750; pxa---.426). In section (E) the highest transition probability is quartzofeldspathic gneiss with large quartz rods (F4) followed by quaxtzofeldapath/c gneiss (E]) (p4~=.750), although most of the section is an alternating series of quaxtzofeldspathic gneiss (El) and amphibolite (E2) (pig---pal =.583). Also the transition probability of biotite quartzofeldspathic gneiss followed (Ea) by amphibolite (F4) is greater than the opposite relationship (pn=.625; p~--.ZSO).
Layered g , eisses of Ceylon Geology of the Kandy and Kadugannasva areas, Highland Series.- The Highland Series of Ceylon is composed of two major groups of rocks: the Khondalite Group consisting of a variety of meta-sediments such as sillimahire-garnet gneiss, quartzite, marble and graphitic schist, and the charnockires (Cooray 1967, p. 89-108). In the Kandy area at the Getembe quarry the rocks are mainly garnetiferous charnockites, although a m~rble formation outcrops nearby. At Kadugannawa the rocks ~re finely banded amphibolites which make up a distinct unit in the Highland Series known as the 'Kadugannawa Gneiss' (Cooray 1967, p. 100-1). The exact details of the geology of both these areas have not been published. In this area two outcrops, one from each of the two localities mentioned above were chosen for analysis (see Fig. 5). Section (F) at Getembe Quarry, Kandy. - 160 layer thicknesses were ~easured from this locality. The results are presented in Table 4 and Fig. 6. This section ,;onsists of an alternating sequence of light pink garnetiferous quartzofeldspathic gneiss (F,~), greyish blue garnc~ charnockitic gneiss (F~) with minor layers of dark pyroxene amphibolite (Fs), and grey quartzite(F4). It is apparent that the layer thicknesses have a log-normal distribution (Fig. 6) and the individual lithologic units also have a similar tendency except that the amphibolite (F3) favours much thicker units. The transition data (Table
MICHAEL B. KATZ
~,EGENO ~.~ P R EC A ,VIB RIAN ~ HIGHLAND SERIES . WITH MARBLE BANDS V/JAYAN SERIES
4pMitts . ~
I"ilt. 5. General geology of Ceylon showing location8 of sections F and G. Table 4. Transition Section F Fl Fa F: F - 1.000 F2 [ .949 Fs .250 .500 F4 .000 .500
Matrix - Kandy, Ceylon Fs .000 .038 .500
F4 .000 .013 .250 -
4) shows that this section is an interlayered sequence of quartzofeldspathic gneiss (F0 and charnockitic gneiss (F2) (p12= 1.00; p21=.949). There is also a marked preference for the quartzite (F4) to precede either the charnockitie gneiss (F2) or the amphibolite (Fa) (p42=p4s=.500). Section G at Kadugannawa Pass, Kadugannawa.- 200 layer thicknesses were measured from outcrop for this locality and the results are presented in Fig. 7. This section consists simply of a regular laminated sequence of dark biotite-hornblende gneiss (G1) alternating with grey quartzofeldspathic gneiss (G2). The frequency distributions of the whole sequence and the individual units tend towards a log-normal nature with the quartzofeldspathic gneiss (G2) having a higher frequency of thicker layers.
Fig. 6. Cumulative curve of thickness of 160 layers of section F from a charnockitic banded gneiss of Kandy, Ceylon. Abscissa in inches, ordinate in percent.
i -5 (~
Fig. 7. Cumulative curve of thickness of 200 layers of section G from a laminated gneiss from Kadusannawa, Ceylon. Abscissa in inches, ordinate in percent.
~ •~ •"~
$0 40 30
/ "0$ .! LAYER
r 6 3"2
Layered gneisses of Norway Geology of the Randesund area. - The geology of the Randesund area has
been described by Dietrich (1960b). Briefly the banded gneisses are part of the Bamble rock series of the southern Norway Precambrian complex. The gneisses are highly folded and locally closely jointed and compme part of a large fault block, the movement of which was such that the granitic g~eisses of the Telemark area which are exposed northwest of the fault zone are possibly ~imilar to the rocks that underlie the banded gneisses (Dic~rich, 1960b, p. 16). Section ( H ) near bridge across Fidjekilen Fjord, Rw:,desund. - 76 layer
dime, sions were taken from information published by Dietrich (1960b, p. 17-19) and analyzed. This section consists of a banded gneiss composed of alternating layers of dark grey biotite-actinolite gneiss and schist (Hi) impure quartzite (H2), pink alaskitic and granitic gneisses (H3) with :~xinor layers of greenish epidote-chlorite schist (H4) and dark amphibolite (Hs). The frequency distribution of layer thicknesses appears to be log-normal and the individual lithologic units also seem to follow this trend although the granitic gneiss (Ha) hss a distinctly different distribution (Table 5 and Fig. 8). Table 5. Transition matrix - Rande:'und, Norway Section
HI Hi Hi [" - .722 H9 I .591 H8 .333 .444 144 .250 .500 H5 .000 .600
Hs .167 .182 .250
H4 .111 .045 .112 -
H5 .000 -[ .182 .112 .00~
MICHAEL B. KATZ
According to the transition matrix, the transition probabilities are highest between the biotite-actinolite gneiss (H 0 and the impure quartzites (He) (p12----.722; p21--.591), Apparently the biotite-actinolite gneiss (H 0 and the amphibolite (Hs) are never associated (p51--pls--0.000). 99 ~" =: Lu LU ~. LU ~. Z
95 90 70 60 50 ~0 30 20
Fig. 8. Cumulative curve of thickness of 76 layers of section H from a banded gneiss from Fidjekilen Fjord, Randesund, Norway (data from Dietrich 1960b, p. 17-9). Abscissa in inches, ordinated in percent.
/ .Z ,
Discussion of results It is apparent that the distribution of layer thicknesses in all measured sections and most of their individual lithologic units are highly skewed towards the minimum class interval measurements. Thus the highest frequency of measured layers are the thinnest units in any particular section. This distribution tends towards a log-normal density with a high variance (02) or it can be considered to be approximated by a gamma density with pa~ameters about r = 1, ~ = 1. Both di,tributions are consistent with populations of sedimentary bedding thicknesses (Krumbein & Graybill 1965, p. 99-100; 110-1). When the data are plotted on logarithmic probability paper they are found to lie approximately on a straight line which confirms thdr log-normal nature. The analyses of the one-step lithologic transitions in any particular section show that many lithologic pairs have about an equally high transition probability, especially when they are intimately interlayered. Other pairs show unequal transition probabilities and have a definite preference for either tbllowing a certain unit or preceding it. Certain lithologic pairs appear to be incompatible with each other and have a zero transition probability, in all cases X 2 tests made on the data arrays as contingency tables rejectec~ the hypothesis of independence. This suggests that the trarLsition probabdities actually indicate a high degree of in'~erdependency among various lithologic pairs. The log-normal distribution of layer thicknesse.,~ and their lithologic dependency probably reflect original stratigraphic control. If this is true each layer represents an original sedimentary bed which has been altered and metamorphosed bu~ renmins essentially unchanged in terms of its dimensions and geometry. If the metamorphism is isochemical each layer should reflect the original sedimentary composition and attempts to explain
the meaning of the individual transition prob~ilities in terms of original stratigraphy may be possible. However if t h e e have been changes in the composition during metamorphism ~ e n~.ture of the original composition will be obliterated and criteria on the origin of these layers, based on chemical and mineralogical data may prove to be L.~conclusive and explanations on their transitional probabilities an impossible task.
Origin of layering in metamorphic rocks Attempts have been made to determine whether the layers in the schists and gneisses are of pre~metarnorphi, (sedimentary or volcanic) or metamorphic origins. In general, studies on these banded, layered and laminated motamorphic rocks, based largely on chemical and mineralogical data, favour formation by some sort of metamorphic differentiation processes often influenced by deformation and tectonic movements (Turner 1941, Ljunggren 1957, Kretz 1960). The exact mechanisms of these processes have yet to be derived and the inherent physico-cheraical problems implied for these processes have not been satisfactorily solved (Dietrich 1960a, p. 112-5 and Turner & Verhoogen 1960, p. 581-6). Certainly the possibilities of reactions, solutions and differential movements are apt to occur during metamorphism, but these would only be relatively local in extent and could not reasonably explain the large-scale regular layering observed in many metamorphic terrains (Dietrich 1960a, p. 117). At best these agencies of metamorphic differentiation would only modify the pre-existing, relict layering without
greatly affecting the overall size, shape and extent of the layers.
Conclusions The variations of layer thicknesses me;~ured from banded gneisses of Quebec, Ceylon and Norway reveal a log-normal distribution. There is a high degree of interdependency among lithologic pairs in the sections. These statistical features found in the layered gneisses are also present in stratified sedimentary rocks. This analogy suggests that the metamorphic layering in the sections under investigation were derived from original sedimentary bedding. The thickness distribution of layered igneous or volcanic sequences is not known, however criteria based on relict textures, struc~res, mineralogy and field relationships should provide enough information to assess banded gneisses of these origins. The only alternative is formation by metamorphic differentiation. Studies on proved metamorphic differentiated layers have not been made so their statistical parameters are not known. As the processes of metamorphic differentiation are not we~l understood it would indeed be a fortuitous event if the various intricate processes involving solution, crystallization and deformation acting together or in complex combinations could form a regular layered sequence with certain characteristic statistical distributions and lithologic dependencies so similar to those found in sedimentary bedding. It is proposed that studies of layered gneisses should t~:e
MICHAI~. B. KATZ
into account the statistical distributions of layer thicknesses and lithologic dependencies a~, additional criteria to determine the origin of the.~e layered and banded metamorphic rocks.
ACKNOWLEDGEMENTS.The field work in Canada in the season of 1967 was sponsored by the Quebec Dept. of Natural Resources; Dr. Robert Bergeron, director. Studies on the rocks of Ceylon were undertaken while the author was a Canadian-Colombo Plan lecturer at the University of Ceylon, Peradeniya during the period 1967-9. The author is grateful for the interest ~of Dr. R.V. Dietrich of the Virginia Polytechnic Institute, who along with Dr. P. Potter of Indiana University read the manuscript and offered many useful suggestions. May 1969
REFERENCES Bryant, E.C. 1960: ,°tatistical Analysis. McGraw-Hill. Cooray, P.G. 1967: An Introduction to the Geology of Ceylon. National Museums of CeyLon. Dietrich, R.V. 1960a: Banded gneisses. Jour. Petrology 1, 99-120. Dietrich, R.V. 1960b: Banded gneisses of the Randesund area, southeastern Nor~;ay. Norsk Geol. Tidssh. 40, 13-63. Harker, A. 1950: Metamorphism, Methuen & Co. Katz, M. B. 1969: Geology of parts of Pontiac County, Quebec. Quebec Dept. Nat. Res., Prel. Rapt. (in press). Kretz, R. 1960: Preliminary exanlinetion of quartz-plagioclase layers and veins in amphibolite facies gneisses, southwt stern Quebec. Proc. Geol. Assoc. Canada 12, 23-43. Krumbein, W.C. & Sloss, L.L,. 1963: Stratigraphy and Sedimentation, W.H. Freeman & Co. Krumbein, W.C. & Graybill, F.A. 1965: An Introduction to Statistical Models in Geology. McGraw-Hill. Ljungj~ren, P. 1957: Banded gneisses from Gothenburg and their transformations. Geol. Foren. Stockholm 69, 113-32. Pettijohn, F.J. 1957: Sedimentary Rocks. Harper & Bros. Potzer, P.E. & Biakely, R.F. 19~8: Random processes and lithologic transitions. ~our. Geology 76. 154-70. Simonen, A. & Kouvo, O. 1951: Archaen varved schists north of Tampere in Finland. Bull. Comm. G~ol. Finlande 24, 93-114. Turner, F.J. 1941: The development of pseudo-stratification by metamorphic differentiation in the schists of Otago, New Zealand. Am. ~. Sci. 239, 1-16. Turner, F.J. & Verhoogen, J. 1960: Igneous and Metamorphic Petrology. McGraw-Hill. Turner, F.J. & Weiss, L.E. 1963 : Structural Analysis of Metam,~rphic Tectonites. McGrawHill. Accepted for publication June 1969
Printed Jan aary 1970