I.tn~N:\l. or,' ~I.:IIIMI.:N'IARV ['ETROLI)CY. ~'tJI_. -l(], NO. 1, 1'. 298-323 Fins. 1-18, MAters, 1970
STUDIES IN FLUVIATILE SEDIMENTATION: A COMPARISON OF FININGUPWARDS CYCLOTHEMS, WITH SPECIAL REFERENCE TO COARSE-MEMBER COMPOSITION AND INTERPRETATION 1
J. R. L. ALLEN 5edimentology Research Laboratory, Department of Geology, The University, Reading, England. ABSTRACT The finlng-upwards cyclothems repeated through thick stratigraphic sections in the Old Red Sandstone (Devonian) of Britain and the Appalachian region of North America comprise a maximum of six major facies. The cyclothems when complete consist each of a lower coarse member and an upper fine member, between which the facies are distributed. An analysis of facies transitions is made to arrive at an understanding of the compositiotl and variability of these cyclical deposits. The coarse members, which as regards the variety of facies and numbers of facies representatives are more variable than the fine members of the cyclothems, are shown to have been formed through processes of lateral deposition in streams with sinuous talwegs. A quantitative physical nlodel, partly based on general hydraulic principles and partly empirical, is advanced to show how the different facies sequences observed in the coarse members cau be understood in terms of the chief variables involved in river flow. Specifically, the model reproduces the vertical patterns of grain size and sedimentary structure observed in the coarse members. The model also shows how the coarse members may be interpreted in terms of stream power and channel sinuosity.
INTRODUCTION The concept of the fining-upwards cyclothem is first explicit in the work of E. E. L. Dixon (1921), whose description of the predominantly fluviatile Old Red Sandstone of South Wales, contains reference to the repetition on a large scale of thickness of a polyphase sedimentary unit composed of conglomerate, sandstone and siltstone beds, in that upward order. Fluviatile fining-upwards cyclothems have since been very widely recognized, particularly in Devonian, Carboniferous and Neogene rocks (table 1). The cyclothems have, however, been studied in greatest detail from the Old Red Sandstone facies (Devonian) of lands bordering the North Atlantic, notabty in Britain (Allen, 1962a, 1962b, 1963a, 1964a, 1965a), Spitsbergen (Friend, 1965; Moody-Stuart, 1966), and the Appalachians (Allen and Friend, 1968). The Old Red Sandstone rocks of the Atlantic Borderlands are of especial interest, as they appear to record vast coastaI plains of alluviation that fringed the rising hills and mountains of the Caledonide fold-belt during its final paroxysms in the Devonian. Although fining-upwards cyclothems have been widely recognized, our knowledge of them is still rather broad and unsupported by the detailed and comparative studies necessary for the elucidation of many outstanding problems. It seems that comparative studies would be of greatest value if, in the first instance, they were i Manuscrlot received May 9. 1969.
confined to cyclical formations of a similar general geological setting. We could then go on to compare cyclothems formed under different general conditions. Accordingly, this paper presents as a first step towards attaining these objectives a comparison of fining-upwards cyclothems in the Old Red Sandstone of Britain and the Appalachian region of North America. But the comparative differences between cyclothems in a single exposure, and between different stratigraphic sections as regards their component cyclothems, can become meaningful only to the extent to which we also understand the processes of fluviatile deposition. Several models of fluviatile sedimentation have been published and found helpful (Alien, 1963b, 1964a, 1965b; Beerbower, 1964; MoodyStuart, 1966; Potter, 1967; Potter and Blakeley, 1967; Visher, 1965a, 1965b). Unfortunately, none of these models is quantitative, and more than one embodies concepts which are physically suspect. We shall therefore advance in this paper a quantitative model of fluviatile sedimentation applicable to the detailed interpretation of fining-upwards cyclothems, notably the very variable coarse grained parts. This model, though remarkably successful, will not however be found either complete or without limitations. STRATIGRAPHIC SECTIONS STUDIED General The ten stratigraphic sections analysed herein comprise a total thickness of 1498 meters of
3"I'~JD1ES IA,; F L U UI.I T I L E StiDI~I ! E N T A TIO N
299
. . . ...................
STAG E
NORTH AMERICA
BRITAI N
Famennlan
Frosnion
I
2K
Givetian
~,~
Elfelion
m Eo,,o°
I
s,,0,°,o0
lY
ill
,"
.
77 ,
'k~, 150 ,~o
\~// ~x~tt
FIG. 1.--Location map and correlation chart for sections containing finlng-upwards cyclotlaems studied.
beds. The first seven sections ( I - V I I ) come from different parts of Britain, specifically South Wales and the Welsh Borderland, while the last three ( V I I I - X ) were measured in the Catskill Formation of New York State and Pennsylvania (fig. 1). The sections are all excellently exposed, chiefly on coastal cliffs or along highways, and covered intervals are either few and short or absent. In total they represent 1014 facies representatives, 1004 transitions from one facies state to another, and 231 complete fining-upwards cyclothems.
Section I This exposes 151.8 meters of the Sandstoneand-Marl Group (Dixon, 1921), probably of middle Gedinian to early Siegenian (I.. Devonian) age, at Freshwater West in Pembrokeshire, South Wales (British National Grid Reference SM 884993-884988). The section discussed from here is that summarised by Allen (1963a, textfig. l), with later minor revisions.
Section [[ This section, from the east side of Swanlake Bay (SN 04.5977), Pembrokeshire, is also from the Sandstone-and-Marl Group, but at a slightly higher stratigraphical level than Section 1 16 kilometers to the west. It comprises 83.5 meters ~ff beds and has ,lot previously been described.
Section i i [ The third section, lying nearly 250 kilometers to the east of Sections I and II, was measured on the north .-ide of Motorway 50 (SO 665261663260), near Ross-on-Wye, Herefcwdshire. It exposes 192.7 meters of beds low down in the St.
Maughans Group, of middle Gedinian to early Siegenian age, and has not previously been described.
Section I V This section, of 90.0 meters of beds in the uppermost part of the St. Maughans Group, also comes from Motorway 50 but at a different site (SO 658256) than Section III. Section IV has not previously been described.
Section V Section V, comprising 221.6 meters of beds, is the longest that will be analysed. It displays the Porth y M o t Beds, magnificently exposed on the northeast coast of Anglesey, North Wales (SH 490885-494878), and is with minor revisions that figured by Allen (1965a, PI. 8). The Porth y Mor Beds are of uncertain, but probably L. Devonian, age and compare closely with strata assigned in South Wales and the Welsh Borderland to the middle-late Gedinian and early Siegenian (Allen, 1965a).
Section VI This section, of 214.6 meters of beds, occurs on the north side of Motorway 50 (SO 658256650258) close to Ross-on-Wye, Herefordshire. The rocks exposed are assigned to the Brownstones which, in the Forest of Dean area, appear to range from the middle Siegenian into the Emslan (Allen, Halstead and Turner, 1968). The section is hitherto undescribed.
Section VII The seventh section, from a stream valley on the western sh)pes of Brown Clee Hill (SO
J. R. L. A L L E N
300
583848-587844), Shropshire, comprises 113.8 meters of beds assigned to the Clee Sandstone Formation (Allen, 1961), probably of middle Siegenian to Emsian age. The section discussed is that earlier described by Allen (1962b, fig. 19). Section VII is some 60 kilometers north of Section VI in which are rocks of a similar age.
Section V I I I This section, a part of Dyson's (1963) measured section in the Buddy's Run Member of the Catskill Formation, comprises 152.6 meters of beds and is from U. S. Rt. 22 alongside the Juniata River, north of the Newport (Pennsylvania) bridge road-junction (locality 21 of Allen and Friend, 1968). The Buddy's Run Member is of uncertain, but probably Famennian (U. Devonian), age (Arndt, Wood and Trexler, 1962).
Section I X This section is also from Pennsylvania but lles 120 kilometers to the east-northeast of Section VIII, on U. S. Rt. 209 near Jim Thorpe (Mauch Chunk) in the Lehigh Gap (locality 20 of Allen and Friend, 1968). The section comprises 210.3 meters of beds and forms a part of Glaeser's (1963) longer section from the Lehigh Gap. The age of the beds is considered to be Upper Devonian.
Section X The final section, in the Catskill Formation of New York State, is from a roadside exposure in the Gilboa Formation on N. Y. 23A near Haines Falls in the Kaaterskill Quadrangle (locality 1 of Allen and Friend, 1968). The beds involved total 67.4 meters. The Gilboa Formation, assigned to the uppermost Givetian (M. Devonian), was recently described by Fletcher (1963). FACIES STATES
General Six main facies states are represented in the ten sections listed above, namely: 1. 2. 3. 4.
State A--Conglomeratic Facies State Bt--Cross-bedded Sandstone Facies State B r - F l a t - b e d d e d Sandstone Facies State B3--Cross-laminated Sandstone Facies 5. State C - - A l t e r n a t i n g Beds Facies 6. State D Siltstone Facies.
These states are quite distinct from one another, but within themselves show different degrees of variation as regards overall texture, total thickness, and thickness and number of constituent sedimentation units, In many of the ten stratl-
graphic sections, representatives of all six s t a t e s are found. In a few, however, one or more states a r e unrepresented.
Conglomeratic Facies (A ) This is widely represented by comparatively thin beds of intraformationa[ conglomerate which are generally thickest and most numerous in those sections with eoncretionary carbonates in facies C and D. The gravel giving the characteristic texture comprises fragments of siltstone, very fine sandstone, and rolled calcareousdolomitic concretions in varying proportions. The clasts are usually well rounded and generally of pebble grade, although in some sections, notably VII and X, intraformational cobbles and boulders are found. In sections V, VII, IX and X the intraformational clasts are mixed with substantial, and in some beds dominant, amounts of exotic gravel seldom coarser than pebble grade. Exotic gravels are not known in the remaining sections, although the intraformational conglomerates are commonly numerous. Quartz sand generally forms the matrix of the clasts, but in some beds there is a fill of mineral cement only. Horizontal bedding emphasized by stringers of sandstone is the predominant internal structure of the conglomerates. Large-scale crossbedding, in solitary or grouped sets, is subordinate. The soles of the conglomerate beds are invariably sharp and erosional, bearing structures including the moulds of shallow channels, rills, flutes, polygonal marks developed from joints in the underlying sediments, and, rarely, grooves. Particular descriptions of the conglomerate facies are given by Allen (1962a, 1962b, 1963a, 1965a), Allen and Friend (1968), and Friend (1965).
Cross-bedded Sandstone Facies ( B1) This facies is well represented by rather thick beds composed of one, a few, or very many sedimentation units. The facies comprises largescale cross-bedded sandstones, in solitary or grouped sets, made up of sedimentation units seldom thinner than 10 cm and rarely thicker than 80 cm. Some of the solitary sets are tabular while others occupy shallow troughs or scoops. The grouped sets are more numerous than the solitary ones and fall mainly into Allen's (1963) pi and omikron varieties of cross-stratification. The cross-stratification azimuths indicate unidirectional current regimes. The sandstones are chiefly fine and medium grained (fig. 2, table 2), and very few beds are very fine, coarse or very coarse textured. Small lenses and pavements of intraformational and
STUDIES
LV F L U V I A T I L E
301
SEDIMENTAT/ON
TAnLE 1.--Outline occurrence of fining-upwards cydothems. Continent or country
Age
Key authors
Europe and Scandinavia
Devonian
ALLEN, 1964a, 1965a, 1965c, 1965d; BURGESS, 1960; COE and SELWOOD, 1968; DINELEV, 1960, 1966; DINELEY and GOSSAGE, 1959; FRIEND, 1965; MOODY-STUART, 1966; NILSEN, 1967; READ and JOHNSON, 1967
U.S.A.
Devonian
ALLEN and FRIEND, 1968; McCAVE, 1968.
Australia
Devonian
CONOLLY, 1965.
Europe
Carboniferous
DE RAAF, READING and WALKER, 1965; ELLIOTT, 1968; JABLOKOV, BOTVINKINA and FEOFILOVA, 1963; KELLING, 1968.
North America
Carboniferous
BELT, 1968; BEUTNER, FLUECKINGER and GARD, 1967; FERM and CAVAROC, 1968; LAURY, 1968; MUTCH, 1968; POTTER, 1963, 1967; SIMON and HOPKINS, 1966; STANLEY, 1968.
Antarctica, Australia India
Permian
Europe, North America
Mesozoic
BARRETT, 1965; BOOKER, 1960; BOOKER, BURSILL and McELROY, 1953; BOOKER and McKENZIE, 1953; NIYOGI, '1966; RAO, 1964; RATTIGAN, 1967. i ALLEN, 1965c; BRUCK, DEDMAN and WILSON, 1967; ]KOSTER, 1956; REINEMUND, 1955.
Europe (Alps)
Tertiary
iBERSIER, 1938, 1958; CROUZEL, 1957; SKALA, 1968.
U.S.A.
Tertiary
'!PICARD and LEE, 1968.
occasionally exotic clasts are often found in the coarser grained cross-bedded sandstones. Allen (1962a, 1962b, 1963a. 1965a) and Allen and Friend (1968) describe particular cases of the facies.
Flat-bedded Sandslone Facies (B~) Representatives of this facies, in moderately thick beds, are widespread and numerous. T h e rocks are characterised by horizontal to lowangle laminations with a thickness rarely greater
Very fine sGnd
Fine
Medium
eo~d
eond
Very ¢ o o r n and coorse sond
IOO
t h a n 0.2 cm and a lateral persistence only occasionally less t h a n 50 cm and seldom more t h a n 5 meters. Very commonly, the surfaces of the laminae bear parting lineations, although this feature is not recorded from every example of the facies. T h e absence of p a r t i n g lineations from some representatives is, however, p r o b a b l y more a p p a r e n t t h a n real, as it seems t h a t this delicate structure can be blurred or even obliterated when sandstones host to it are strongly deformed a n d lightly metamorphosed. A case illustrating this point is section IX, in the strongly folded s t r a t a of the Lehigh Gap, Pennsylvania, where parting lineations are rare in TABLE 2.--Frequency of occurrence of sandstone
size classes in different facies states. Number percentage*
Facies state
B1 B2 B3 C FIG. 2.--Distribution of sedimentary structures between graln-size classes. Based on 778 obserwttions.
Very Medium and sand coarse sand
coarse
8.8 0.7 0.0 0.0
23.1 11.1 0.4 1.1
Fine sand 57.5 59.3 13.9 11.1
Very
Total
lille salld
28.9 85.7 87,8
160 298 230 90
* Certain facies representatives are made up of more than one sandstone size-class.
J. R. L. , ' t L L E N
302
spite of the abundance and good exposure of flat-bedded sandstones. Representatives of the facies are usually divided up internally into several sedimentation units by erosion surfaces seldom more than 60 cm apart vertically. These erosion surfaces are of various forms--plane, irregular, or shallow and trough-like--and are commonly cross-cutting. There are often clasts scattered on them. Very commonly, the inclination of the sandstone laminae and the azimuth of the parting lineations changes slightly across the erosion surfaces. The sandstones are chiefly fine grained and to a subordinate extent very fine grained (fig. 2, table 2). Flat-bedded sandstones coarser than these grades are rare. Allen (1964a, 1964b) and Allen and Friend (1968) describe particular representatives of the flat-bedded sandstone facies.
Cross-laminated Sandstone Facies (B~) This widely known and abundantly preserved facies is absent only from section VII. It occurs as rather thin beds which are chiefly very fine grained, seldom fine grained, and practically never medium grained or coarser (fig. 2, table 2). Representatives of the facies show crosslamination (small-scale cross-stratification) of a type depending on grain size. The coarser grained sandstones mainly have Allen's (1963c) nu type of cross-lamination, although examples of his kappa and lambda varieties are occasionally found. The sets of cross-laminae climb at shallow angles relative to the generalised bedding and are mainly related erosively to each other. The finer grained sandstones, on the other hand, normally reveal types of cross-lamination in which the sets climb steeply relative to the generalised bedding and are related non-depositlonally or gradationally. Allen's (1963c) kappacross-stratlfication is the most often recorded of these types. Bedding surfaces within representatives of the facies commonly display linguoid small-scale ripples and, less often, ripples with sinuous or nearly straight crests. A sharp ripplemarked top is often found on the beds. Internal erosion surfaces, suncracks, and flakes or pellets of siltstone have on occasions been recorded. The cross-laminated sandstone facies is described in detail from particular sections by Allen (1063a, 1965a) and Allen and Friend (1968).
Alternating Beds Facies ( C) This facies is the least frequent of the six and appears in moderately thick beds in all but two of the ten sections studied. It is marked by a vertical alternation of argillaceous with arenace-
ous units on a scale between a few centimeters and two or three decimeters. The coarse units can often be seen to pinch out laterally in a few tens of meters. Usually, the different units in each facies representative are of a similar thickness, with the argillaceous ones perhaps thicker by a little on the average. Ordinarily, between 5 and I0 beds are found in each representative; 25 beds was the largest number counted. The argillaceous units are chiefly massive, medium to coarse grained siltstones breaking with a blocky, rough to conchoidal fracture. In sections V I I I and X, both from the Catskill Formation, numerous beds show a distinctive vertical prismatic jointing. Traces of horizontal lamination and cross-lamination are rare in the siltstones and mainly restricted to the coarsest units, which border on very fine sandstone. Much more widespread is evidence foc bloturbation, ranging from scattered trace fossils of several kinds, to intersecting mottles that point to the total destratification of the sediment. The arenaceous units are chiefly very fine grained and only occasionally fine or medium grained (fig. 2, table 2). Usually, each unit is graded up from coarsest at the bottom to finest at the top, although some units show no grading in the field, and an occasional one is found to coarsen upwards. However, the change of grain size of whatever sort rarely exceeds half a Wentworth class. The base of the unit is almost invariably sharp, denoting a break in deposition. and very commonly irregular. The moulds of tool marks, flute marks, shallow flat-bottomed to V-shaped channels, pot-holes, and irregular flutings have all been recorded from beneath units whose bases are irregular. Siltstone clasts have often been found lying on or near such bases. Suncrack polygons, between 10 and 70 cm across, are often seen and frequently prove to have experienced some erosion. The soles of many sandstones are, however, smooth and sharp and free from features of relief, even the most delicate tool marks. The commonest internal structure of the sandstones is cross-lamination, with flat-bedding and parting llneation next in abundance. Cross-bedding, chiefly in solitary sets, is infrequent and restricted to the thicker and coarser grained units. The tops of the sandstones units are commonly sharp and ripple marked, but in equally numerous cases there is a gradual blending of the sandstone up into the overlying siltstone. The ripple marks are chiefly sinuous to linguoid types of current ripple. Occasionally, wave-current ripples are found, even though the internal structures below denote a unidirectional current. "['race fossils of several types are common in the sandstone beds. Concretions of calcareous or dolomitie composi-
~- • r ) 57 ( / I I :- S ]:V F L U I T . I T i L E
SI!I)I~I:L'VT:ITIOV
303
TABLE 3.--Frequency dislribulion e~'facies representatives between.facies states and stratigraphic sections. Number
Stratigraphic section
) e r c e n t;llge
Total
I
11 I11 IV V VI VII VIII IX X
A
Bi
B:
B;~
C
11
5.1 8.3 8.3 111.7 19.1 9.4 26.6 5.1 5.0 0.0
9.5 10.4 8.3 14.3 1.1 15.0 20.2 18.6 26.7 27.6
15.8 22.9 12.8 23,2 15.2 28.1 42.2 13.6 20.0 17.2
26.6 26.1 30.3 17.9 29.7 15.0 0.0 15.3 13.3 24.1
11.4 9.4 11.9 7.1 6.2 8.8 0.0 13.6 6.7 0.0
31.6 22.9 28.4 26.8 28.7 23.7 11.0 33.8 28.3 32.0
tion are sometimes a b u n d a n t in both the sandstones and siltstones. Allen (1965a) and Allen a n d Friend (19681 have described in detail the facies as represented in two of the ten sections.
158 96 109 56 178 160 109 59 60 29
Allen (1965a) gave a detailed description of the facies as developed in section V. FACIES RELATIONSHIPS
AS R E V E A L E D
BY A N A L Y S I S O F P O O L E D D A T A
Facies States Siltstone Facies (D) This facies has substantially more and thicker representatives t h a n any other and is, moreover, found in every section studied. The representatives comprise thick, medium to coarse grained siltstones breaking generally with a blocky, rough to conchoidal fracture, b u t in places having a crude vertical prismatic jointing. Traces of lamination are scarce, although here and there a stringer or biscuit of sandstone can be found. Evidence of h i o t u r b a t i o n is widespread and often a b u n d a n t , the silt having been throughly" mixed through a vertical interval commonly of two or three meters. Small knobbly concretions of calcareous to dolomitic composition occur in very m a n y representatives of the facies, though not in every one of the ten sections. The concretions occur either evenly scattered in the rock or concentrated in thick bands. In certain sections, notably V, they are closely packed into thick, massive beds of limestone or dolomite rock within the siltstones. Often in these massive c a r b o n a t e beds the proportion of c a r b o n a t e minerals gradually increases upwards until the sharp top is reached.
A good general impression of the c h a r a c t e r of the fining-upwards cyclothems present in the Old Red Sandstone can be o b t a i n e d from the pooled d a t a on the ten sections described. Table 3 gives the frequency distribution of facies representatives between facies states for these data. In descending order of abundance, the facies states are D, B2, Bz, Bt, A a n d C, b u t no one state is overwhelmingly a b u n d a n t . Table 4 lists for the pooled d a t a the thickness distribution and grand a r i t h m e t i c mean thickness of the six facies states, and figure 3 shows the distributions graphically. In ascending order of thickness, the states are A, B3, C, B2, B~, a n d D. ,Aside from states A and D, however, the facies states are similar in average thickness a n d thickness range. S t a t e A appears in comparatively thin beds of a considerable range of thickness. State D is also very variable in thickness, and is substantially thicker on the average t h a n any other state.
Facies Transitions As a method of analysing facies transitions in a stratigraphic section, Duff and Walton (1962)
TABLE 4.--Percentage frequency distribution of facies representatives betweenfacies states. Thickness in eentimetres, Facies state A Bi B~ B~ C D
I
25 50 50_100 10040o- [ 800 I I [ 2°° t '°° I 8°° I '°°° I
6 25 ~ 12 5 > 6 , 2 5 - - , - - 12:5 - ____fb~
10..~'~! 10.3%1 38.8%: 0.0' 0.0
0.0
1), (} 0.0
; I
0.0 0.0
1.4
O. (1 0.8
]
i
5,6 5,6
6. i 3,8 I .9
:
18.3 25,4 18.5 30.6 16,9 I 37.5 20,5 37.2 9,3!20.6
21.4 21 ,8 ] 32,9 [ 30.8 277
[ ]
19.8 18.5 4.7 5.1 23.7
[ [
7.1 4.6 0.5 1.3 10.9
I ]
2.4 0.4 0.0 1.3 3.9
I I
>1600
Grand l arithmetic [mean
Total
0.0 0.0 0,0 0.0 1,2
173 139 96 113
115 125 217 211 81 255
[ I
253
J. R. L. A L L E N
304 20 10 8
6
FACIES
/
° A
4
/ "
6~
"//~,~"
,,,*
/-//-
~o
o -= 2
=" i o.e
°
Z7
d/
l - 0.6
.22/ ° O.2 /~//j/ Q4
O.I 0,08
o/
,£/~...I
•/
/
/
/
/
006 004 I I I I o .P 0,5 2
] 5
I I0
I I 20
I I I 50
J
~ 60
I I I 9 0 95 9 8
I I 99.5 9 9 9
Percent thinner than slated value
Fro. 3 . - - T h i c k n e s s distributions off representatives
of the six facies states (see also table 4) and Duff (1967) set up a frequency table of the different types of cyclothem recognizable. From such a table, the modal cyclothem could be easily identified, together with types of cyclothem representing s u b o r d i n a t e modes. The technique is, however, cumbersome even when three or four facies states only are involved. In the present stud3", there are six facies states to account for, and the method of Duff and Walton is impracticable. Instead, the d a t a pooled from the ten sections were analyzed by the construction of an upward facies transition matrix, as described by C a r t el al. (1966), K r u m b e i n (1967) and Potter and Blakeley (1968). This technique allows a n y vertical p a t t e r n i n g of facies states to be elucidated w i t h o u t prior decisions as to w h a t
m a y constitute the cyclothem or with w h a t facies state the cyclothems are considered to begin. Table 5 is the grand upward facies transition matrix for the raw d a t a summarized in table 3. Each box shows the upward transition probability, p, which, in any row, sums to unity. The tree diagram of figure 4 show alternative upward p a t h s by which state D can be reached after s t a r t i n g out in this state. The p a t h s illustrated are limited to transitions for which p>_0.lS0. As can be seen from the tree diagram and the p a t h s listed with it, there are numerous alternative paths whereby state D can be regained. These p a t h s are characterised by similar values of the mean transition probability per transition. T h e largest m e a n probabilities, though only marginally greater t h a n several other values, are associated with the sequences D ~ B a ~ D , D~A~B2--,Ba~D, and D ~ B t ~ B 2 ~ B a - ~ D . It will be noticed from figure 4 t h a t there is a fairly strong probability of long series of upward transitions in which facies Bt and B2 alternate prior to eventual transition into state B~. However, table 6, listing the numbers of times t h a t different alternations of states B1 and B2 have been recorded, indicates t h a t long alternations are uncommon. It may be noted t h a t the upward transition B a ~ C ~ D is an essentially one-way path, for the transition probabilities of facies C to states other t h a n D are very small. These results suggest t h a t if cyclothems are indeed present in the sections analyzed, then they are highly variable in character, particularly as regards the coarser grained facies elements.
Cyclotherns T h e upward p a t h s of transition shown in figure 4 are a l t e r n a t i v e facies sequences which can be regarded as modal fining-upwards cyclothems in the fight of a closer e x a m i n a t i o n of the field evidence. However, the p a t h s seen in figure
TABLE 5.--Grand upward transition probability matrix. D
rronsiti ~ . ~ C ~
p=o.oe3
:~--~=3.22
p=0.646
p .0.243
~=u9
~=,.36
~ • 0.6,6
,, • 0 , ~
,
K =380 p =0,583 K =571
p • 00,~ K =0.31
~ - i " ~
8a
p =0.129 /~ = 063.9 .
Ip =0.2~ K = l Z. 6
B~
p =o.o52 K = o.nl
p =0.o,6 . • o.zsJ
P = 0.001
P = 0.062 i P " 0.062 K = 0,46,~ K = 0.124
p = 0,O60 K = 0.050
p "0287 K = 80,3
p "0.168 K = 779
p "0.294 K = 0.676
B
=
~
~.~ ~
K =0T92 ~ . ~ ~b ~ . ~~ p .o.,o9 ; K = o.z66
;
"0192 = 1.65
~ ~ . ~ '~.~.z~
p=o.o
Total
p = 0.026 K = 0.020
115
K =2.16
p • 0.088 K = 0.128
125
p =0,069 K = 8.04
p = 0361 K = 0.608
217
p =o.,88 K = ~8.
p = 0.635 K = 1.48
211
p = 0.815 K = 0.998
8t
.00~6
~j.7~.~
255
5"7"UI)IES I N t : L U U I A T t L E
£1ilqMF.NTAT"I()N
305
TAnLE 6.--Frequency of sequences involvingfacies states B~ and B~. Number of transitions
Facies sequence B, B.2 or B.2B, B~ B2 B~ or B~. Bt Bz
Number of instances 133 19 5 3 2 2
or BaB~B,B~ B, B~B~ B~ B, or B~B: B2 B~ B~ 13~B2BjBe
BL BaB~ BaB~ B2 or B~B~ B=B~ B~B~ B~ B2 B~ B2 B~ B~ B~ or B~ B~ Bo B~ B~ B~ B~ B~ B~ B~ B2 B~ B= B~ B~ or B~ B~ B~ B, B~ B, B= B~
0 1
B~ Ba B~ B~ B, B= Bt B~ B~ or B= B~ B~ Bt B= B~ B~ B~ B=
4 depend on transition probabilities which ignore the differing absolute a b u n d a n c e s of the various facies states. If we could say what the likelihood was t h a t a given state tended to occur in sequence immediately before some other state, then it composite cyclothem in the sense of Duff and Walton (1962) might be constructed. We are here searching for a criterion of prior deposition. In other words, is there in the s e d i m e n t a r y system leading to the beds in question some factor, or group of factors, which tends to make one facies state a p p e a r earlier in time, or lower in space, t h a n some other state? A suitable criterion for prior deposition is a r =
--
,
(1)
in which K is the prior deposition criterion, ni~ is the n u m b e r of upward transitions from state i to state j, Ni is the n u m b e r of representatives of state i, nji is the n u m b e r of upward transitions from state j to state i and ~%. is the n u m b e r of representatives of state j. W h e n K = 1 state i is as likely' to precede state j as state j is likely to 0.294
OB~ D OBz B3 O DAB2030 DABz BiBZEIsD DABz BiB2 B3 O
COMMON SEQUENCES Meon p
Meon p
0465 04e3 Q458 0.435 0.440
DBz BiB3D DB2 Bt B3 CD DO, B2 B3 D DBiB2 B3CD DBi B30
0319 0.410 ~450 0.433 0.331
DBi B3CD
0.339
FIG. 4.--Tree diagram showing upward facies transition probabilities (p >0.150) for pooled data (see also table 5).
precede state i. If K > 1, however, state i has the greater likelihood of appearing first in a vertical sequence of states. But should K < I , then state j has the greater likelihood of being deposited earliest. Table 5 lists the values of .K calculated for the pooled data. C o n t r a r y to intuitive expectation, the values of K could not be interpreted in terms of a single composite sequence, b u t r a t h e r in terms of a l t e r n a t i v e and almost equally probable composite sequences, as shown in the tree diagram of figure 5. T h e path of transition with the largest mean value of K per transition is D ~ A~B1---,Ba--oC+D, a path which does not appear in figure 4 based on the transition probability values alone. T h e position of state B= in figure 5 is of interest and, it will later appear, of major significance. I t is seen as an equally likely precursor of facies BI, Ba or C, but has little intrinsic likelihood of following a n y one of these three. M a n y of the paths of facies transition shown in figures 4 and 5 are encountered in the field as a large scale s e d i m e n t a r y unit to which the general namefining-upwards cyclothem has been applied. These cyclothems, as thus far known from the field (Allen, 1965c; Allen and Friend, 1968), are characterised by four principal features: 1) a basal erosional surface of wide lateral extent, 2) a lower coarse-grade group of sandstones with commonly a basal i n t r a f o r m a t i o n a l conglomerate, 3) an upper fine-grade group of siltstones, commonly with thin sandstones in the lower part, a n d 4) a thickness of the order of a few or
/
~
~
I 48
.... "A .... ~aI .... . ~ 2 5 4 ~ 0 998~>~
FIG. 5.--Tree diagram showing upward facies transition sequences based on the prior desposition criterion (K> 1 except for transition C---~D).
J. lq. L. A L L E N
306
TABt.E 7.--Thicknesses of cyclolhems in different stratigraphic sections. Stratigraphic
Cyclothem thickness (metres)
section
I
VI
3 12 22 8
4 2 11 6
7 It
Number observed
45
23
26
29
Arithmetic mean thickness (metres)
3.37
3.63
8.25
3.92
8.38
9.00
several meters and a composition of numerous sedimentation units. The lower coarse-grade beds are referred to collectively as the coarse member, and the upper fine-grade strata are called thefine member. In the field it is the coarse members that show greatest variation between cyclothems in one section and between cyclothems from different sections. It follows from this general introduction to the fining-upwards cyclothem that there is good agreement between the results of the transition probability analysis and the field observations. It will be recalled that the transition probability analysis was independent of any decisions as to the stratigraphical composition of, or bounds on, the cyclothems that might be supposed to exist. On the basis of the fi)ur characteristics cited above, the ten sections have been divided into a total of 231 COml)lete fining-upwards cyclothems. Table 7 shows that the cych>thems vary greatly in thickness. The distribution of cyciothem thickness for the pooled data is approximately logI00 --~
,
,
,
_wii__?_ x
?
I
observed
Number
Percentage number ob,~er r e d
13 26 82 69 3t 1O
5.6 ll.3 35.5 29.9 13.4 4.3
Total =231
9.93
13.14
Total =tOt).()
i 16.09
normal (fig. 6), and the grand arithmetic mean thickness is 6.46 meters. Inspection of table 8 will show that the number of facies representatives per cyelothem is also strongly variable, between 2 and 13, but in terms of the pooled data appears to follow a Poisson distribution (fig. 7, table 8). Cyelothems composed of either two, three or four facies representatives account for very nearly two-thirds of the total number. FACIES BY
RELATIONSHIPS
ANALYSES
OF
AS REVEALED
INDIVIDUAL
SECTIONS
Facie, States Table 3 displays some important similarities and differences between the ten sections studied. The three sections ( V I I I - X ) from the Catskill Formation resemble each other in having similar amounts of facies Bi, B~, B3 and D. They differ, however, in the varied representation of facies C, which is absent from section X but present to the notable extent of 13.6 percent in section VIII. In a lesser degree, the three sections from the Catskill Formation differ in the degree of representation of facies A. Turning to the British sections
SO 60 40
24 22 20
!
~ 2o
IB
".'.::(:: ! :t';T:i
16
~ io ~ s
14
. :..:.- ....
g. io 4
8 6
I
4
:" " : !b :'" :'"':
•
......
2
.)17::.
i(!i
0
[
I OI
I I 0.5
I 2
I 5
I I0
Percent
J 20
I
I
I I 50
thinner than
I
I 80 stated
I I 90 95
I 98
value
F16.6.--Thlckne~s of fialng-upward~ cyclothems (see also table 7).
I
I 99.5 9g.9
2
3
4
5
Number
6
7
of f o c l e $
8
9
I0
11
12
13
repre|entatlvee
F I G . 7.--Distribution of numbers of facies representatives in fining-upwards eyclothems (see also table 8).
STUDIES
IN FLUI'I:ITiLE
SEDIMENT+iTION
307
TABLE 8.--Number of facies represeniatiees per cydothem by stratigraphic section. I
Number of facies ] representatives I in cyclothem I
Stratigraphic section
7
2 3 4 6 7 8 9
II
III
IV _ _ V
4 4
4 5 3 3 4 3
2 9 11 7 12 2 3 3 2 2
2 5 47 8 1 3 13
1
1 2
.
2 2 2
VI
1
1(1
Number
VII
VIII
IX
X
observed 51 48 52 28 11 23 4 6 3 2 2
1
6 1
1 1
, 2
2
1
i
11 12 13
11 1
Totals
45
J
23
23
10
40 - - ~ - - - - ~ - -
(I-VII), which as a group are s o m e w h a t different from those of the Catskill, the chief differences are between section VII, which s t a n d s alone in lacking representatives of either s t a t e B3 or C, and sections I-VI which form a relatively homogeneous group. These differences and similarities are reinforced by table 9 in which is listed the a r i t h m e t i c mean thickness of the representatives of each facies state in every section. T h e sections from the Catskill F o r m a t i o n ( V I I I - X ) again s t a n d apart, by virtue of states two to four times thicker on the average t h a n in the British sections. This is particularly n o t e w o r t h y in the case of state B~, which is not only much thicker in the Catskill sections t h a n in a n y British section, b u t also a b o u t twice as a b u n d a n t (table 3). On the other hand, facies A is poorly represented in the Catskill Formation compared to the British rocks, for the reason t h a t in the A p p a l a c h i a n region the Devonian c o n t i n e n t a l deposits contain few or no concretionary c a r b o n a t e beds.
Facies Transitions T h e d a t a of table 3 gave the upward transition probability matrices shown in table 10 and the three diagrams (state D ~ D ) , for values of p_>0.15, of figure 8. For each section the se-
15
16
Percentage number observed 22.1 20.8 22.4 12.1 4.8 10.0
1
1.7 2.6 1.3 0.9 0.9 0.4
231
100.0
quence of transitions associated with the largest mean transition p r o b a b i l i t y is shown in bold letters. T h e p a t h s o b t a i n e d for the individual sections as seen in figure 8 are in m a n y respects simpler t h a n for the pooled d a t a (fig. 4). In sections I and II the more c o m m o n paths comprise only two transitions, the sequence being D ~ B a ~ D . One state more occurs in the tree diagram for section VI I, the d o m i n a n t p a t h being D ~ A ~ B 2 ~ D . Four sections, II and IV-VI, have the dominant path D+A+B2+B~+D, with facies B1 occupying a reversible Ioop from facies B2; the same loop is in the tree diagram for section VII. In three of these sections, and also in sections I and III, facies C occurs in a one-way loop which forms an i m p o r t a n t a l t e r n a t i v e p a t h to the transition of facies B~ direct to D. The three Catskill F o r m a t i o n sections differ from the British sections in t h a t facies Bt appears in every case in the d o m i n a n t sequence of transitions, and not as the outer element in a reversible loop from facies B~. Moreover, facies C occurs either not at all, or in the d o m i n a n t sequence. Facies B3 is relatively u n i m p o r t a n t in the Catskill F o r m a t i o n sections, as compared to the British sequences, and in two of t h e m c o n t r i b u t e s to the short but u n c o m m o n p a t h D -,B3--~D.
TABLE 9.--A rithmetic mean thickness of facies represenlatives by stratigraphic section. Mean thickness in metres by stratigraphic section
Facies state
A B~ B~
C 1)
0.20 0.81 O. 56 O. 88 0.81 I. 50
ll
lll
IV
0.26 0.94 11.73 o, 69 (1,58 1.60
0.46 1.39 1.32 0.97 I.I0 3.71
0.19 1.32 1.27 o. 48 1.16 3.98
i\ - -
I 0.99 0.73 1.07
1.01 2.36
VI 0.93 1.58 I 2.04 I (}.76 0.72 1.14
VII
VIII
IX
X
0.27 0.57 1.80 0.0 0.0 ~ 0.97
0.05 2.80 1.58
0.38 4.41 2.07
0,0 2,27 0.87
1.14
1.61
1.8¢)
3.19 3.92
1.44 5.94
1 0.0 iI 3.51
,tl,~
J. R. L. A L L E N TABLE 10.--Upward transition probability matrices for stratigrapkic sections. I A:eilB2!Bs C O : A ~.LO.,5 ~0.I3 0.~0.0 ! 0 0
1I A i B :82 8310
D
•
A ~.-'~ 0.O10750250.0'o.0 S I ~1~70.0~0.~00;40 610~0
~i °.°Fo.'~o= ~ , ~ ~ s~ o.o iO.o4Fo.~~
-~ o,o~;~oo.~5o.= i
O Z 011 0.0 /~0.81 0.0410.04
B3 0 . l r 0.0!0.02~.-'~-..~0.I~0.70
% oo oo I021;/.025!054
C . 9o~o-o~0,o o.oz~o-~
C 0.0 O,0,0.140.O-- F/10.86
c
o.olo.o~o.oio.oD-]~oo
o o.,,To.,4b, To.=o.o~F; ~I
AjSl
IS
Is
A 8,'82J=,i ere
, B,iS,P=,ic re
A ~0. I~O~O.00140 O0 83 O0 003 BI 0.0~)-'~+1.00~0.0 0.00.0 ~ o.4,o ~ i % - % ~ ¥ 0 ozz
:oo, ...-'~_ . L "q ~~Oz~.lg,04 - ~,t:" +018 '
"" ~ B2 0 II ;, 0 "~ J
e~ o.o: 00:06 ~
o.o
C 0.0 0.0 0 . 0 ' 0 . 0 ~
0.0
o i0.4~ 0.0 J0.14[036~.011~ ~
! C i 0
o.,, o.o
o ~=~ ro,~o ,;
5 L[0.0 /IT OJO . . . . iel . I1~~ 0~( ~020"060 ~ ]
zA
o co
o o oio0¢oo o oTCCo.,=
Bl D.13~" ...0.74!0.15. 0.010.0
D
o.0
~ffo.48
C 0.0! 0.0'0.12 OJ2 ~.-"~076
B~ o;o Io ~E--~o.5,;O.oo'o ,~
83; C
i=>10
o.oj ~
X Ale, B z r % l c !m A ~ 0~0 5 0 ~ 6 1-0~3 8 '_0.0~ - -Io= 81 0.6-'7.--)~.0.0 =0.0 10.50i0.50
A ,S I ,82
, ~o..!oso!o.,, o.oloo
8, I=
2BI D.oTro.o ~o~f~O:~9 o.o 0.14 B
o o.33[o.~¢o.,~o.~ io.~T,/~ [
,
~.~o.~oooio.~4
A
D 0.91'0.09i0.0 0,~010."O"
C D ~A ~-" . ] , ,I~_~O.0 i = = 083 O0 0.0 !0.0
/
A|B
B2 83 C I O
i
I
!
[ A ~J.~o.olo.olo.o o.o,o.o
.0~50.060 19
s= o.13~--~-~.--~i oo o.o h~o.37
1o;26o.o~Io.~
S} 0.0, O0'O,Illx~O~O.O 089
~:2510.75
c ,--Oo!o.~srO.o O.l~~ o . ~ r F " ~ ~ 7:'----
--
D o.l~loz6!o.i iOZSlo
c
/.~
co
~
( o o~o.6-FEo[o.o F.--T
ooio25
-o o o ~ o = ! o , ~ o ~ E
o.,91o.o~
Cyclothems Tables 7 and 8 give for the ten sections the distributions of cyclothem thickness and numbers of facies representatives per cyclothem. T h e sections display a n approximately five-fold range of variation in terms of the a r i t h m e t i c mean thickness of the cyclothems present. The three sections from the Catskill F o r m a t i o n contain, on the average, the thickest cyclothems and no
o.o~o.o-oY.~o2oolo~a o.2c
cyclothem t h i n n e r t h a n 2.5 meters, in contrast to the British sections with a b u n d a n t comparatively thin cyclothems. T h e British sections are, however, more variable t h a n the Catskill ones as regards the n u m b e r s of states in the cyclothems. I t will be seen on comparing table 8 with figure 8, t h a t there is generally excellent agreement between the modal n u m b e r of facies representatives per cyclothem in each section
,13Z D~A~Bz~B3~D
D~A~Ba--~-B3~D
\. I/
/c\
I
°\?°\ S2 ,
It
"--"BB
°?i\
° " Bi
\I
/0\
D ~ / B 3
'
B2
11Sl D~A~
Bz~B3~D
\/
"D
S3.
I
3Zig D ~~-- B i ~ B 2 ~
~D
° /
• A,
C
D C --5D
~
"-\
9 2 \ \\
I \I~D
I
"Bi
D
" Bi
F[G. 8.--Tree diagrams showing upward facies transition probabilities (p >_0.15) for the stratigraphic sections examined (see also table 10).
" B3~D
STUDIES
I:V F L U V I A T I L E
and the n u m b e r of transitions in the d o m i n a n t p a t h of the tree diagram. However, the distribution of facies representatives per cyclothem in each section is strongly asymmetrical, the modal n u m b e r of facies representatives per cyclothem being low at two, three or four. The m a x i m u m n u m b e r of facies representatives recorded from a cyclothem is 13 (section V).
Composition of Coarse Members
,
r
i
f
,
309
representatives are found, then a t least one of the states present must be repeated. It is e v i d e n t from the graphs t h a t there is a fair correlation between the coarse m e m b e r thickness and the n u m b e r of c o m p o n e n t facie~ representatives. Hence the facies representatives take a thickness to some extent characteristic of the section. T h e characteristic thickness would, of course, be given by the slope of the line plotted on each graph. A careful e x a m i n a t i o n of the composition of the cyclothems showed t h a t the correlation was c o n t r i b u t e d to by the repetitive or actually multi-storey character of m a n y of the coarse members, even some of those containing four or fewer facies representatives. Some c o m m o n sequences of transitions illustrating this repetitive or multi-storey character are: B 2 ~ B t ~ B 2 (table 6), B ~ - ~ B ~ B ~ B ~ , A - ~ B ~ B ~ A - ~ B ~ , A~B~A~B,, A~B~Ba-*A~B~B~. Sixtytwo of the 231 cyclothems had a coarse m e m b e r in which at least one facies state was repeated.
The eyclothems are most variable, b o t h within a section and between sections, as regards the composition of the coarse members. T h e fine members, being simpler, show a far less striking variation. Figure 9 gives for each section a plot of the thickness of the cyclothem coarse-member against the total n u m b e r of facies representatives contained in the member. A possible m a x i m u m of four facies states (A, B1, B~, B~) can occur in each coarse member. If more t h a n four facies 6
SEDIMENT,4TIOX
12
6
,
,
i
J
i
i
, /
~4
=4 I1¢
0
' I
~
~2,
'
'
'
'
2
3
4
5
0 6
0
2
I
3
4
5
6
7
I
i
,
i
.,
i
,
8
,
7
~Z
,
•
,
,
3
4
5
6
7
8
Representatives 2 2
6
2
Representatives
Represe~tottves
i
,
,
,
,
,
,
,
2
•
|
*
0
i
i
J
.
.
.
.
.
.
.
.
2O
J
18
6
~4
5
.
4 3
2 i
I
i"
~8 6
0
't'
~
I
2
I 3
4
6
7
4
8 0
'
'
0
Representatives
'
2
'
.
4
.
.
.
.
6
'
8
'
I0
12
Representatives
2:
J
i
i
4
i
i
6
r
8
=
i
I0
12
Representatives
~2
II
,
,
,
,
,
II
i• 9
Q
O
~7
~6
18
18
16
; 16
1,4
114
12
ii2
~s
I0
! I0
8
'8
2
t
I
• i
0 0
i
J
4 2 0
~. ~ ,; 0
I Representatives
I
~
Representatives
4
.
.
.
.
.
*
.
~5
Q
4 a 0
, 2
.
~6
3 2 I
6
3
.
9
~e ~7 O
~E ~4
.
X
s ii
0
2
4
Representatives
13'
i
i
2
J
i
,
4
i
6
i
i
8
Representatives
FIt;. 9.--Thickness in meters of coarse member of cyclothem as a function of number of facies representatives for each of the ten stratlgraphic sections examided.
J. R. L. A L L E N
310
Bz
50
B2
BZ
gO
B2
BS
SO
B2
FIG. 10.--Facies composition by percentage thickness of coarse members of fining-upwards cyclothems in the ten stratigraphlc sections examined. Representatives of facies A are excluded. There is, however, considerable scatter in the d a t a shown in figure 9, implying t h a t the n u m b e r of facies representatives making up the coarse members is to a n i m p o r t a n t extent i n d e p e n d e n t of the thickness of the members. This result will achieve significance in the light of the depositional model for the coarse m e m b e r s developed later in the paper. Figure I0 is a set of triangular diagrams showing the percentage thickness composition of individual coarse m e m b e r s from the ten sections, the s a n d s t o n e facies Bh Bz and B:j only being considered. Facies A is ordinarily a minor component and therefore is excluded. T h e cyclothems of sections I-IV are very variable, as shown by the wide scatter of points, but there is evidence t h a t facies B3 is favored compositionally. Sections V-VII comprise cyclothems of a more uniform character, p l o t t i n g either along the B2Bs or B~B~ axes. The cyclothems of the Catskill F o r m a t i o n are as variable as the British ones in sections I-IV but cluster near the B~ r a t h e r t h a n the B3 apex. In s u m m a r y , figure 11 gives the average thickness composition of the cyclothems in each section. T h e British sections plot in the lower part of the graph, parallel to the B~Bs axis, whereas those from the Catskill F o r m a t i o n plot
near to the B1 apex. Beside each point in figure 11 appears the a r i t h m e t i c mean cyclothem thickness a n d the ratio of the sum of the thickness of all A and B facies states to the total thickness of the section. Bi LEGEND
/
B3
\
so
(o~sl- Thi~kr~s_.___.A÷B~,-~ _~
B2
FIG ll.--~acies composition of coarse members of fining-upwards cyclotbems averaged over each stratigraphic section. Representatives of facies A are excluded.
5"TUI~IES IN t ; L U U L I T I L E S l i D 1 M E N T : I T I O N The seven British sections display a distinct trend (figure ll). With an increase of the thickhess ratio, there goes an increase in the proportion of facies B~ relative to facies B3, and of facies Bi relative to facies By This trend is also of stratigraphical significance for, in proceeding from left to right across figure 11, we ascend the l.ower Old Red Sandstone succession. The average cyclothem thickness for British sections is between 3.37 and 9.00 meters, with no significant stratigraphical variation. The cyclothems of the Catskill Formation are substantially thicker than the British ones but, excepting sections VI and VII, have similar thickness ratios. Their coarse members are, however, much richer in facies B,, and correspondingly poorer in states B2 and Ba. GENERAL
ENVIRONblENTAL
311
! FACIES
surface
B
~
D
~
Time line
INTERPRETATION
Of the ten sections described above, six have already been the subject of a general environmental interpretation (Allen, 1962b, 1963a, 1965a; Allen and Friend, 1968). The remaining four sections, described herein for the first time, can each be explained using this same general interpretation, namely, that the beds are fluviatile. However, a sketch of the evidence and arguments is needed before we pass on to interpretation at a more detailed level. Briefly and simply, the beds are assigned to a fluviatile origin by comparison with modern alluvial sediments, recently reviewed by Allen (1965b). The sandstones and conglomerates (facies A, Bt, B2, and B3) are deposits which, in textures, sedimentary structures, detailed stratigraphical succession and organic content, compare very closely with the channel sediments of modern streams as, for example, described by Fisk (1944), Harms and Fahuestock (1965), Harms, MacKenzie and McCubbin (1963), Sarkar and Basumallick (1968), and Sundborg (1956). The finer grained beds, that is, the siltstones and the thin siltstones and sandstones in alternation (facies C and D), closely resemble modern floodplain sediments in possessing proofs of repeated submergence and emergence of the sedimentary surface and evidence of sediment deposition mainly from suspension. Especially close comparisons can be made with deposits described by Jahns (1947), Happ, Rittenhouse and Dobson (1940), McKee (1939), McKee, Crosby and Berryhill (1967), and Shantzer (1951). Since each fining-upwards cyclothem has a lower coarse member (facies A, Bt, B2, B3) preceding a fine member (facies C, D), it follows that each cyclothem records the establishment of some kind of channel system and then its abandonment by the stream and burial beneath
FrG. 12.--Multiple composite finlng-upwards cyclothem. (In the legend, the B's are Bl, B~, and Ba respectively.) a floodplain. The sections described are made up of repeated cyclothems, often numbering several tens, from which we must conclude that channel establishment and abandonment was repeated many times at a given site. The repetition of cyclothems was attributed by Allen (1962a, 1965a), Allen and Tarlo (1963), and Allen and Friend (1968) to factors intrinsic to the fluvial regime (autocyclic factors of Beerbower, 1964), and not primarily to external factors such as base-level change and tectonism. However, external factors cannot entirely be ignored in the context of the Old Red Sandstone, as this formation accumulated on the edges of a sea-bordered continent during a period of great tectonic activity. These are, then, the main features of the general interpretation of the sections being discussed. In the present paper, however, we are concerned with interpretation at a higher level of detail, notably of the coarse members of the cyclothems. LATERAL
VERSUS
VERTICAL
DEPOSITION
OF
THE COARSE MEMBERS
Having seen that the fining-upwards cyclothems described above are alluvial in origin, the question now arises as to the explanation of the vertical changes in grain size and sedimentary structures recorded from the coarse members of the~,e cyclothems. Figure 12 is an a t t e m p t to summarize these changes by means of a somewhat idealized composite cyclothem based on the above data. The changes in the coarse member have been explained in various ways. Allen (1963b) and Allen and Friend (1968) related them to the
312
.I. I~'. L. A L L E N
spatial variation of hydraulic parameters within river channels, specifically meandering channels which underwent lateral migration because of erosion of the outer bank and deposition on the inner one. Moody-Stuart (1966), Potter and Blakeley (i967), and Belt (1968), studying other sequences containing fining-upwards cyclothems of fluviatile origin, made similar suggestions. However, Moody-Stuart (1966) claimed for certain numerous fining-upwards cyclothems of the Wood Bay Formation (Devonian) of Spitsbergen that deposition took place from low-sinuosity streams whilst these vertically aggraded and finally abandoned their channels. These cyclothems show the same upward changes of grain size and structure that appear in cyclothems attributed to lateral deposition. In the case of these further cyclothems described by MoodyStuart, then, the textural and structural variations are thought to imply changes in hydraulic conditions in time and not in space. This is in sharp distinction from the hypothesis of other workers, that the vertical lithological changes represent variations of hydraulic conditions priinarily in space and not in time. Thus, MoodyStuart's idea is that the coarse members arise by processes of vertical sedimentation, whereas the notion of Allen and others is that the coarse members depend on lateral &position. It is important that Moody-Stuart has drawn attention to a possible mode of behavior of low-sinuosity streams in depositing fining-upwards cyclothems but it is another question whether streams of this sort really behave in the manner envisaged. Two considerations seem to have influenced Moody-Stuart (1966) in reaching his position. Firstly, he claims, with examples, that there are many low-sinuosity streams whose channel shoals and banks do not depend on lateral deposition. Secondly, he could not find in much of the Wood Bay Series any direct field evidence for the lateral deposition of the coarse members of many cyclothems, notably those formed closest to the presumed stream heads. We may take the second point first. The best direct evidence for lateral deposition is Allen's (1963c) epsilon-cross-stratifieation. A unit of this type embraces a large part if not the whole of a cyclothem coarse-member and consists of generally two or more lithologies combined in gently sloping layers, commonly of sigmoidal vertical profile, whose strike is very nearly parallel with the palaeocurrent direction. Epsiloncross-stratification was found abundantly in the well-exposed Old Red Sandstone of Anglesey (Allen, 196Sa) and Wood Bay Series of Spitsbergen (Moody-Stuart, 1966). A single unit, 7 meters thick, was described from a large roadcut in the Catskill Formation of New York State
by Alien and Friend (1968), and another, at least 12 meters thick, was reported by Beutner, Flueckinger and Gard (1967) from an open working for coal in the Kittaning Formation (Pennsylvanian) of Pennsylvania. These are the only known fossil instances of epsilon-cross-stratification. They were recognized as such for one or (usually) both of the following reasons: 1) the comparatively steep transverse slope of the component sigmoidal beds, and 2) the lithological heterogeneity of the deposit (siltstones, sandstones and intraformational conglomerates in thin beds to some extent intermingled). The twenty-two epsilon-crossstratified units of Allen (1965a) and MoodyStuart (1966) gave dips on the sigmoidaI bedding surfaces between 4 ° and 15° . Transverse slopes on the unit of Allen and Friend (1968) range up to a maximum of 22 °. Slopes between 10° and 20 ° iypify the example of Beutner et al. (1967). Sediment bars with transverse slopes as steep as the above values are uncharacteristic of stream bars existing today. Table 11 lists average values of the transverse slope, ~, of sediment bars accumulated by lateral deposition in the channels of modern streams. Only for Watts Branch and Baldwin Creek--both very small streams compared with those inferred from the Devonian and Carboniferous exposures--does the mean transverse slope exceed the lower limit of 4 ° reported above. The largest single value of transverse slope is 12.1 ° (Baldwin Creek) which is only half the largest value recorded for epsiloncross-stratification. Moreover, it is with little doubt unfair to compare a stream such as Baldwin Creek, having a channel depth of about one meter, with the cross-stratified units several meters thick in the Old Red Sandstone and the Kittaning. It appears from table 11 that as streams grow in size so the transverse slope of their sediment bars decreases. This is consistent with the finding of Leopold and Maddock (1953) that channel width increases faster than depth with ascending stream discharge. Evidently the epsilon-cross-stratified units thus far seen and used for the identification of ancient lateral deposits are atypical as regards transverse slope. The typical ones, therefore, must still go unrecognized, primarily because of difficulties of detection arising from the low ( ~ 2 °) transverse gradients of the constituent beds. These difficulties are compounded with those arising from the fact that, in the field, a lateral deposit can be easily detected only when the component beds strike at a high angle to outcrop trend. The other contention of Moody-Stuart (1966), that there is an important class of streams, specifically of low-sinuosity, whose sediment
STUI)IF.S
IN FLUUIHTILE
SEDIMENTATION
313
"I'AF3LE11.IChannel cross-sectional geometry in bends of modern rivers. River and authority
h* (meters)
wl* (meters)
B* (degrees)
Mean/3 (degrees)
Baldwin Creek, U.S.A. l.eopold Wolmatl, 1960
0.68, 0.82, 0.75
6.4, 3.8, 3.7
6.1, 12.1, 11.4
9.9
Watts Branch, U.S.A. Leopold and Wolman, 1960 \Volnum and Leopold, 1957
I .3, 0.75, 0.90
9.4, 7.6, 7.0
7.9, 5.6, 7.3
6.9
Snov, U.S.S.R. Rozovskii, 1963
1.1, 0.95
27, 30
2.4, 1.8
2.1
Red Deer, Canada Oureshi, 1962
2.1, 2.2, 1.3, 1.9
61, 52, 56, 24
1.9, 2.4 1.3, 4.5
2.5
Klar~ilven, Sweden Sundborg, 1956
2.5, 5.0, 3.0, 3.2
80, 120 170, 91
1.8, 2.4 1.0, 2.0
1.8
l)esna, U.S.S.R. Rozovskii, 1963
8.0,6.25, 6.75
! 125, 145 125
3.7,2.5, 3.1
3.1
Niger-Benue, W. Africa Nedeco, 1959
3.65, 6.40, 9.15, 5.18, 3.65, 7.30, 5.45
78(I, 535,375 595,540, 270 540
0.3, 0.7, 1.5. 0.5, 0.4, 1.6, 0.6
0.8
Mississippi, U.S.A. Fisk, 1947
14.6,14.0,10.7, I 8.5, 14.5, 10.7, 8.8, 13.5, 25.5, 32.0
560,430,550, 850, 670, 640, 970, 640, 510, 640
1.5,1.9,1.1, 0.6, 1.2, 1.0, 0.5, 1.2, 2.9, 2.9
1.5
* h = maximum channel depth; w~ =chalmel width from inner hank to talweg; B = transverse slope of sediment bar. shoals travel down-channel without lateral deposition being involved, is not supported by the evidence. Portions of two stream systems, the Niger-Benue in West Africa (Nedeco, 1959) and the Yellow River of China (Chien, 1961), are cited as examples by Moody-Stuart. In each case the high-stage channel is relatively straight. However, in each case the channel embraces sediment bars, spaced out along alternate banks, between which a sinuous talweg winds. The bars are of sand in the Niger-Benue, hut coarse silt and sand in the Yellow River, and they shift down-channel, maintaining their regular spacing, at a rate proportional to stream power. Since the talweg is sinuous, the downstream movement of the bars inevitably involves lateral deposition, though this process is seldom made manifest in the same striking manner as in a high-sinuosity stream such as the Mississippi (Fisk, 1944, 1947). Sedimentation in the two sorts of stream is, with little doubt, of the same kind, differing onh, in degree. Several other rivers clearly illustrate lateral deposition in channels of low sinuosity. These are the Mur and Vistula, discussed by Leliavsky (1966), and the Volga described by Shantzer (1951). The growth and migration of the channel bars by lateral deposition in the Volga is strikingly shown by gently curved levee-like
features analogous to the meander scrolls of high-sinuosity streams (Melton, 1936). Other low-sinuosity streams illustrating lateral deposition are described by Schaffernack (1950) and Leopold and Wolman (1957). There are even experimental examples (Leopold and Wolman, 1957; Stebbings, 1963). Indeed, I have been unable to find any examples of a stream whose behavior was unequivocally that envisaged by Moody-Stuart (1966). The possession of a sinuous talweg, if not a sinuous high-stage channel, seems to be an essential feature of all streams, and lateral deposition is the dominant process of bar movement wherever such sinuosities of channel or talweg occur. In conclusion, lateral deposition seems to be an ubiquitous process in natural streams carrying a bed-material load, though deposition on this style is developed to a degree controlled by stream sinuosity. As regards the cyclothem coarse-members, we may conclude that although only the atypical lateral deposits amongst them have thus far been recognized, it is very probable that nearly all represent lateral deposition to an important degree. Vertical deposition of the coarse members as envisaged by MoodyStuart (1966) can therefore be ruled out, even where repeated lateral deposition at a place has resulted in a multi-storey coarse member. The
.I. I¢. I.. A L L E N
314
PLANE OEO (Upper phoa)
~o4 o
6 4
g I0~
~
.,
~/J////////Y//~
/i;
e 6
3
~
4
P
L
A
N
E
BED (L.phase)
8 6
4
NO
O.'oI
0.02 . . 003 .
BED MATERIAl,.
. 0.04 . . 0.05. . 0.06
MOTION
007
008
0.09
O.~o O,II
D (©m)
Fx6. 13.--Bed form and internal structure in relation to stream power (co) and caliber of load. Based on Allen (1963b), with numerical data of Guy, Simons and Richardson (1966, tables 1-11), and Williams (1967). chief textural and structural changes shown by the coarse members must therefore depend on changes in hydraulic conditions in space r a t h e r t h a n in time. A conclusion on this point is obviously an inlportant prerequisite for any q u a n t i t a t i v e model aimed at explaining the remarkable variation observed in the coarse members of the cyclothems. A QUANTITATIVE
MODEL OF LATERAL
DEPOSITION
OF T H E C O A R S E M E M B E R S
Since in figure 12 equal-time surfaces slope across the coarse m e m b e r a n d lie parallel to the depositional b a n k of the stream, we are obliged to account for the simultaneous existence of four sedimentary facies. From bottom to top of the channel, these are: 1) intraformational conglomerate (state A), 2) fine grained cross-bedded sandstone (state BE), and 3) very fine grained cross-laminated sandstone (state Ba). The fourth facies, state B._,, can occur at different levels, according to the anah'sls in terms of K values (fig. 5). Using the experimental d a t a of Guy, Simons and Richardson (1966) and Williams (1967), the lateral and vertical changes can at once be explained in terms of a gradual decrease of stream power from the deeps to the shallows of the channel (fig. 13). B u t this is a crude interpretation which does not explain immediately why grain size as well as s e d i m e n t a r y s t r u c t u r e changes over the profile. Moreover, it emerges t h a t a l t h o u g h the appearance of ripples and dunes depends on stream power, the occurrence of upper-phase plane beds is otherwise deter-
mined. Figure 14 shows t h a t there is a substantial overlap as regards stream power between upper-phase plane beds on the one hand and ripples and dunes on the other. However, the overlap between ripples, dunes and lower-phase plane beds, is no larger t h a n can be explained by experimental error. I n t e r p r e t a t i o n s in t e r m s of stream power alone seem not to bring to light all the factors relevant to the system. As regards stream bed-material loads, we can estimate the changes of grain size a n d bed form in a transverse profile of a channel bend by considering the force balance on a particle travelling in substantially continuous contact with the bed and parallel to the channel banks. For we know (l.eopold and Wolman, 1960; K o n d r a t ' e v , 1962; Rozovskii, 1963) t h a t there is a spiral secondary circulation in stream bends, such t h a t the bed shear stress vector has one c o m p o n e n t directed perpendicularly in towards the inner b a n k and a n o t h e r parallel to the mean flow direction. Hence, in a transverse profile of the channel, each near-bed sediment particle is acted on by an upslope fluid force and a downslope body force arising from its own weight. Thus a particle will follow a c o n s t a n t p a t h only when these forces are equal and opposite. Consider the segment of a channel bend shown in figure 15, in which: x = d i s t a n e e parallel to channel centerline; y = l o c a l channel d e p t h ( t a k e n as positive); z = p e r p e n d i c u l a r distance across channel measured from inner b a n k : w l = p e r p e n d i c u l a r distance between inner b a n k a n d talweg; w~ = full channel width; h=maximum channel depth, a t talweg (taken as positive); r = radius of c u r v a t u r e of channel measured to channel centerline; S = longitudinal water surface slope measured parallel to channel centerline; /3 = local transverse slope in degrees of channel bed; a = a n g l e oil channel bed between local bed shear stress vector and channel centerline; p = fluid density; g = acceleration due to gravity; r~ = bed shear stress vector; r, = c o m p o n e n t of bed shear stress vector parallel to channel eenterline; D = d i a m e t e r of sediment particle in equilibrium on channel bed; = density of sediment particle. We represent the direction of the bed shear stress vector by the skin-frictlon lines shown in figure 15. We may conveniently represent the transverse
STUDIES 0.4
IN
i
i
I
F L U f.'I..l T I L E i i
i
0.4
O = 0.019 cm
0.2
SE1)IMI~NT":iTION I
315 i
I i
i
I !
O =0.027,0.028
0.21
f
i
f o.I
0.08 0.06
o c
• .
o.I
°oo °
• •e
•
0.06
.
o
GO4
o
0.08
-
o
•o < . . ¢ ' ¢ : .
o
0.04 U
0.02
0.02
Q
0.01 10 2
t
I
I
I I
l
I
I
I I
2
4
6
8 103
2
4
6
8 10 4
Stream
I 2
0.01 4
power (ergs/cmZ/sec)
I
I
I
, Dunes
I
I
I
~
• i
I
o
(ergs/cm z/secl
[] Plane I
I
I
bed (u. phase) I
I
I
I
I
D = 0 . 0 9 3 cm
0.1 • •
| •
•
O0~
0.02 I
I 4
I I
[
I
6 810 ~
2
4
I
Stream
power
(ergs/cm
,all 6 8 104
. *"
O.OE 0.0,
2
~. • t . , . . •
O.OE
o •o o •
i0 z
I I 6 8104
LEGEND
0.0,
D.OI
power
I 4
Q2
o
ida o
0.06
I 2
f
o o
I I I 6 8 103
Plane bed [I.phase) 0,4 I ;
D=0.045 r m
0.2 f o.I 0.08
I
I 4
Stream
GENERAL
• Ripples 0.4
I 2
I0 a
I 2
" t , ~ .~"
O.OI 4
2 /see)
i0 z
I 2
I 4
I 6
"
I I 8103
Stream
power
I 2
I 4
(erg$/cm
I [ I 6 8104
I 2
4
2/sec)
FIG.. 14.--D~cy-Weisbach friction coefficient f as a function of stream power and caliber of load. Based on data of Guy, Simons and Richardson (1966, tables 1-11). profile of the c h a n n e l bend by the p o w e r relationship It =
,
(z _
12)
31 = klz",
(3)
(6)
w h e n c e eq. (4) finally b e c o m e s tanc~ = ! l - - s i n r
which can be r e w r i t t e n as
in which kt, describing t h e is h/w]". T h e e x p o n e n t n, with unity, describes the c u r v a t u r e of the profile. a s s u m e d to vary as
h
tan tr(m~) = I! - - ,
,
(z < wO.
C7)
FlOW
flatness of t h e profile, e x p e c t e d to c o m p a r e degree a n d kind of T h e angle a will be
tana=tana<~)sin(r~,.~),
(z
(4)
wherein a(~,x~ is the m a x i m u m value a t t a i n e d by a. But we are only c o n c e r n e d with z
(z _< u,,),
(5) W2 - - 1
in which k2=w~/w2. E x p e r i e n c e t e a c h e s t h a t ks is close to 0.8. Following results discussed by Rozovskii (1963), we have
FIG. 15.--Definition diagram for flow and bed forces acting on a sedimentaD' particle at the bottom of a curved stream channel.
316
J. R. L. A L L E N
T h e magnitude of the bed shear stress vector parallel to flow is given by r~ = 0gSy cos 3,
(8)
r~ = pgS'y,
/9)
which reduces to since ~ is a small angle and cos/5 therefore compares with unity (see table 11). We shall take it t h a t S is a c o n s t a n t across each channel profile. Hence r~ becomes dependent only on the local flow depth. We now consider the force balance on a sedim e n t a r y particle (fig. 15). T h e body force acting on the particle in the plane of the transverse profile is 4 (-~)'(a G = - - ~- 0)~ sin 3, 3
(10)
tangentially down the slope. T h e fluid force exerted tangentially upslope on the particle is, however, F = ~r
if)'
r, sin ~.
(11)
For particle equilibrium F = G , whence, noting that fl is a small angle so t h a t sin 3 = t a n /3= dy/dz, w e deduce from eqs. (2), (10) and (11) that ,, sin D=
16.5Sh o k~n(o- - o)r
"
sediment bar contained in the bend. As can be seen in figure 16, the shape of the grain sized e p t h curve is sensitive to changes in the exponent n governing the kind and degree of curvature of the profile. T h e prediction of bed form, and hence internal sedimentary structure, c a n n o t be so satisfactorily founded on general principles, though some progress is possible knowing how bed shear stress, caliber of bed material a n d stream power vary in the profile, and how bed roughness \,aries with bed form. T h e essential first step is to decide how to deal with the question of bed roughness which, as Simons and Richardson (1966) have shown, is far from simple. T h e Darcy-Weisbach coefficient, which can be used to express resistance to flow in open channels, depends on bed-material caliber, bed form, sediment t r a n s p o r t rate, and Reynolds number. However, where high accuracy of prediction is not justified, as at present, we can take it t h a t each type of bed form gives a unique value of the friction coeOficient. The d a t a of figure 14 yield the following representative values: fl = 0.02 (plane beds, antidunes) (13) f2 = 0.08 (ripples and dunes).
(~-k~z)
\-~/
, (cm),
0.1
(12)
z (~ ~)
valid for z _ < w , . By equilibrium we mean t h a t the particle continues on a path parallel to the inner b a n k of the channel, whence it follows t h a t if for some reason F were to become unequal to G, the particle would proceed to migrate to some new p a t h a t a new transverse distance z measured outward from the inner bank, where equilibrium would once more be restored. I t follows from eq. (9) t h a t if F were to become less than G the particle would travel out to a p a t h lying deeper in the channel and further from the inner bank t h a n before. If F were changed so t h a t it exceeded G in value, the particle would shift its path to one lying in a shallower d e p t h and closer toward the inner bank. Eq. (12) is a major result of the analysis. I t states, assuming t h a t all sizes of debris are available, t h a t the general caliber of the bed-material load in a channel bend increases with ascending slope and flow depth, but decreases with increasing radius of curvature. F u r t h e r m o r e , eq. (12) shows t h a t in each cross-section the caliber of the bed-material load generally speaking decreases inwards from the tahveg, i.e., there is an overall decrease of grain size upwards in the
0.2
0.3
C~4 h 0.5
0.6
0.7
0.8
0.9
LO
0
0.2
0.4
0.6
0.8
1.0
12
1.4
O/O(ref)
FIG. 16.--Calculated variation of grain size with relative channel depth for different shapes of channel cross-section. The grain sizes are made dimensionless by reference to the grain size D(,er~ at y / h = 1.0.
ST UDIES
[N
I;L UIIA
According to Kennedy (1963), a n t i d u n e s exist only when the Froude n u m b e r exceeds Fr =0.84, the critical value being in any case insensitive to even large changes of flow conditions. A n t i d u n e s will therefore be the bed form in the channel profile if
TiLE I0 j 8 6
,
'
LE'GEND
.
.
.
.
Y//".-.." ......
2
whereas sonle other bed form, either plane beds, ripples or dunes, will appear if
4
l"r < 0.84.
2
Writing the bed shear stress parallel to flow in the form f~ Ir2 r~ = ~-p 2~' (16)
,
317
O I0 0 8
(15)
i
4
(14)
l"r > 0.84,
7",4 T I O N
SEDiMEN
6
i0-1 8 6 4
aas
d,
0'a
os
J4
o'*
o.e' o'.7
oi*
o9
,o
T
in which V is the mean flow velocity a t any station, we obtain Fr .
.
.
.
(17)
CgY
It follows from our assumption of c o n s t a n t S t h a t if the inequality (14) is satisfied at one station on the profile, then a n t i d u n e s exist at all stations. A hed form other than a n t i d u n e s appears if the inequality (14) is not satisfied. Bagnold (1966) and I/ill (1966) showed theoretically, with experimental justification, t h a t an upper-phase plane bed will occur if 0
Tx
-
> 0~t},
i n which 0 is a dimensionless stress and 0~o,.) is
the critical value of t h a t stress for the existence of a plane bed. S u b s t i t u t i n g for D from eq, (12), we can write eq. (18) for any station on the transverse profile of the channel bend as klnr
Z (n-l)
> O
seems to depend chiefly on the stream power which, using earlier equations, can be wirtten = Vr~ =
(z -< w~),
(19)
16.5h sin x--w~z in which, from Bagnold (1966), 01e~m = 0.27, (D > 0.20 cm) 1 0,~,itl = (0.56 -- 1.43D), (0.025 < D < 0.20cm) i" (20) 0(~it) = 0.52, (D < 0.025 cm) Figure 17 is a plot of eq. (19) from which it wiU be seen t h a t an upper-phase plane bed is the only possible bed form in channel bends of sufficiently large radius of curvature. In channels of sufficiently small curvature, however, ripples and dunes will be the p r e d o m i n a n t bed form, upper-phase plane beds being limited to the channel sides. Ripples, dunes or lower-phase plane beds appear if the inequality (18) is not satisfied. Which of these bed forms actually is developed
)p
(21)
(ogSy) sly,
in which w is the power. T h e bed form is dunes if o~ > o0¢,ri~),
(22)
where W(ora) is the critical power for the appearance of dunes, b u t ripples or a lower-phase plane bed, depending on grain size (figure 13), when
(18)
g l ) ( a - o) -
0 . . . . . . .
FIG. 17.--Dimensionless shear stress as a function ef relative channel depth with the ratio of channel radius to width (to talweg) as the third variable.
oo < ~(cri~).
(23)
F r o m figure 14 we o b t a i n the following critical values o~(orl,)= 750 ergs cm-~ sec-t, w
(D--<0.023 cm) 1 (0.023 < D_<0.036 cm) [ (24) (0.036< D--<0.069 cm) ~" [ (D>0.069 cm) J
The above model is incomplete a n d certainly oversimplified. For example, it t r e a t s a n u m b e r of variables as i n d e p e n d e n t which are perhaps b e t t e r regarded as dependent. I t does, however, provide for the first time an indication of the way grain size and s e d i m e n t a r y s t r u c t u r e could v a r y within lateral deposits formed by streams h a v i n g sinuous talwegs. I t remains to consider the implications of the model for the coarse members of the fining-upwards cyclothems discussed above. COARSE-MEMBER
FACIES TRANSITIONS
THE LIGHT OF THE
[N
MODEL
M a n y profiles of grain size and s e d i m e n t a r y s t r u c t u r e were generated using the above model, realistic values of water surface slope, channel width, and channel d e p t h being chosen with the aid of Leopold, W o l m a n and Miller (1964). A
318
J. k . L. . I L L E N 0
_L o.~ h
\
0.2 0,3 O4 05 06 0.7 0.8 0,9 1.0
.
0 "~" y o.t LT.~. ~
o
it
O4 °~oO go°
~
(crn)
O.6f 0.7 0.8 0.9 I.O
~'
....
0 . Z o.i h 0.2 03 0.4 0.5 0,6 0.7 0.8 0.9 1.0
(cm~
Y o
~o.I
"
I.O °~O8o
~r
GENERAL
~_~.
o.2 k ~
'~"
0.,¢1 - ~ °.~ K , _ ~ , \
0"6t~
~
t'\
I
o~.~ ooOo°~
Ripl)les ~ . ~
Co
°
0.2 0.5
~
V (crn/sec)
o~,_Oog
"t .
I
I-
5
Y 0.1
B
o.z I - L ~
o°
D V (cm) (crn/sec)
D (cml
V (cm/sec)
o
ea ,¢ V (cm/sec}
LEGEND Dunes
~
Plane beds
o
I
li
o8OoO8
oo
I
0.a I - ~
~,a
\
0.9 1.0
- ~ o 8_o°
o ~
-oJ
O V (cm) (cm/sec}
D V (cm) (cm/sec)
FIG. 18.--Profiles of sedimentary" structure, grain size and flow velocity calculated for coarse members of finingupwards cyclothems according to theoretical model proposed (.see table 12 for values of parameters). representative selection of profiles is given in figure 18, based on the p a r a m e t e r s recorded in table 12. Each profile shows the vertical variation of bed form a n d internal structure, grain size, and mean flow velocity. T h e velocity discontinuities arise from the a b r u p t changes of Froude n u m b e r consequent on assigning unique values of the friction coefficient to the different bed forms. The six profiles comprise an e n d - m e m b e r state, a n o t h e r very nearly e n d - m e m b e r state, and four mixed states. The coarse m e m b e r represented by profile A comprises sands all deposited in an upper-phase plane bed regime and, therefore, marked by flat-bedding. These features are hardly surprising as the water surface slope a n d channel c u r v a t u r e are both relatively large. M a n y coarse members similar to profile A are to be found in section VII (figs. 8, 10). At the other extreme is profile F, showing a lateral deposit composed of relatively fine grained sands with some silt deposited for the
most p a r t in the current ripple regime (fig. 18). The lowermost and uppermost parts of the sand body were, however, deposited in the upperphase plane bed regime. T h e facies sequence of profile F is associated in the ten sections described with comparatively large values of the transition probability, as can be seen in figures 4 and 8. For convenience, the relevant partial sequence of states is shown in figure 18. The partial sequence of states represented by profile TABLE 12.--Main parameters for calculated grain size and structure profiles. Profile*
(metres)
h (metres)
100 100 100 100 100
5,0 5,0 2.5 2.5 2.0
W2
r
(metres) i
A
B C D E F
200 200 500 2O0 500
0.0008 0.0003 0.0001 0.00025 0.0001 0.0001
* For all profiles n = 1, (or- p ) = 1.65 gm/cnff, k~= 0.8.
N7"tr/UEN I:V FLUI'I.-ITILE SEPI,1I/:.NT,.tTION t; is very common in sections I-VI from Britain, the lowest transition, from plane beds to current ripples, being associated with probabilities between 0.24 and 0.81. Coarse members resembling profile F are, however, rather rare in cyclothems from the Catskill Formation. Profile B of figure 18 compares with profile A in that a coarse member is dominated by a single type of structure. However, profiles similar to B are infrequent in the fining-upwards cyclothems discussed. Profiles C-E of figure 18, each including the ripple, dune and upper-phase plane bed regimes, are abundantly represented by coarse members from the Catskill Formation and are common in the British sections (figs. 4, 8, 10). We see from table 12 and figure 17 that the channels typified by profiles C-E are all strongly curved. Therefore upper-phase plane beds occur only at their margins or, if the radius of curvature is small enough, are restricted to the inner bank. Profiles C-E also illustrate the effects of halving depth although keeping all other parameters constant. The general stream power relevant to profile E is substantially reduced compared with profile C, with the result that current ripples occur where, in the deeper flow, dunes existed. The extent to which plane beds are developed is not affected by the depth change. It seems particularly important that the model, as exemplified by the profiles of figure 18, should predict that upper-phase plane beds can occur in a lower stratigraphical position than either current ripples or dunes. It will be recalled that the use of the prior deposition criterion revealed that facies B~ could readily precede in the coarse members ~f the cvclothems either facies B~. Ba, er C, but not readily succeed them (table 5, fig. 5). The model also shows that, as was inferred from the data of figure 9. there is no fixed number of facies states or facies representatives in the coarse member. In profile A, for example, there appears role representative of one facies state; profile I), on the other hand, combines three facies states and four facies representatives. The coarse member represented by profile B is twice as thick but comprises only two facies representatives. It is also worth noting that the model predicts the same relationship Imtween grain size and sedimentary structnre that was fcnmd in the cvcl~thems (fig. 2, table 2). By inspecting figure 18 we see that plane beds are represented by a very wide range of grain sizes, dunes by narrower range of comparatively coarse sizes, and current ripples by a narrower range of comparatively fine sizes. These representative cases show that the principal variables of channel depth, width, curvature and slope need only be changed by small
319
amounts to yield substantially different profiles of grain size and sedimentary structure. The greater part of the variation of coarse member character described earlier in this paper can therefore be explained in terms of the model represented by eq. (12) and the principal inequalities above. The remaining variation, for example, the infrequent but long repetitions of facies B1 and B~, and the repetition of a short facies sequence involving three or more states, can all be explained in terms of the recurrence of lateral deposition at a place. The sensitivity of coarse-member character to the principal variables associated with openchannel flow might suggest that a powerful interpretative and discriminatory tool was now available. Unfortunately, because of the number of variables involved, we cannot with the present model make unequivocal interpretations of individual coarse members from cyclical successions. Caliber of load, for example, is fixed according to eq. (12) by slope, channel width and channel curvature, whilst bed form depends on grain size, channel width and curvature, and stream power. Given the truth of the fluviatile interpretation, however, it follows that in proceeding from the Ba to the B1 apex in figure 1l, we are moving from low-powered to highpowered streams. By constrast, in going from the Ba B~ axis to the B2 apex, we move from high-sinuosity to low-sinuosity streams. This also means, as Hamblin (1958) has demonstrated, that we are examining cyclothems deposited progressively closer to the stream source, since channel sinuosity decreases proximally. In the British sections, the trend from the B.~ B~ axis to the B,. apex is associated with beds of decreasing age (figs. 1, 11), the sequence of measured sections being (I, II, I I I ) - * I V - ~ V I --+VII. This is consistent with Allen's (1962a) conclusion, based on independent evidence, that throughout l.ower Devonian time there was a progressive increase in tectonic activity in the \Velsh area, with the result that the surface of alluvial deposition was gradually steepened and lmshed southward. The model is imperfect and it should be clearly understood wherein its imperfections lie. We have treated the channel geometry and water surface slope as wholly independent variables, and the caliber of load and flow velocity as wholly dependent. In the prototype, however, only the aqueous and sediment discharges can be regarded as wholly independent quantities. In justification of the simple-minded view adopted, we may say that the model is broadly consistent with reality in most important respects and, furthermore, yields some significant insights into the meaning of fluviatile sediments. It does
J. R. L. A L L E N
320
not embody the whole truth of the comple× fluvial environment. CONCLUSIONS
1. Fining-upwards eyclothems are numerous and well developed in Devonian rocks (Old Red Sandstone facies) deposited on the borders with the sea of the Caledonide fold-belt in Europe, Spitsbergen and North America. The cyclothems are also well known from other formations of continental origin. 2. Six major facies states are recognizable in fining-upwards cyclothems from the Old Red Sandstone of Britain and the Appalachian region of North America. These are: 1) Conglomeratic Facies, 2) Cross-bedded Sandstone Facies, 3) Flat-bedded Sandstone Facies, 4) Cross-laminated Sandstone Facies, 5) Alternating Beds Facies, and 6) Siitstone Facies. 3. Analysis shows t h a t the facies states and the cyclothems of which they are a part assume characteristic thicknesses which depend on stratigraphical and geographical position. The cyclothems consist of a lower coarse memher followed by an upper fine member. The analysis of transition probabilities and the use of a prior deposition criterion confirms t h a t the coarse members are extremely variable, within as well as between sections which differ in geographical and stratigraphica[ position. The fine inemhers are simpler in composition and much less variable. 4. A consideration of modern alluvial sediments show that the cyclothems can be attributed to stream action. The coarse members are interpreted as channel deposits, but the fine members appear tu have formed on floodplains.
The cyclicity means that channel and floodplain have followed each other many times at a place subject to subsidence. 5. A further consideration of modern streams shows t h a t the coarse members can be a t t r i b u t e d to processes of lateral deposition in streams with sinuous talwegs, whether or not the high-stage channels are also sinuous. Vertical d e p o s i t i o n - aside from its role in producing multi-storey coarse m e m b e r s - - c a n he ruled out. 6. A consideration of forces acting on sediment particles travelling down sinous streams leads to a quantitative physical model showing how grain size and sedimentary structure vary vertically in a coarse member accumulated through processes of lateral deposition. The model yields profiles of grain size and structure which closely match the coarse members of cyclothems in the Old Red Sandstone. The profiles which can be generated are, like the coarse members, very variable. 7. From the model flow insights into the reasons for the high variability of the coarse members of fining-upwards cyclothems. The model also leads to some general conclusions regarding the interpretation of fining-upwards cyclothems. We can now say that the stream was low-powered where a coarse m e m b e r is dominated by the Cross-laminated Sandstone Facies, but high-powered where beds representing the Cross-bedded Sandstone Facies are the rule. However, as the proportion of rocks attributable to the Flat-bedded Sandstone Facies decreases, the parent stream increased in sinuosity. At the present day, this change is associated with an increasing distance from the stream ~ource.
REFERENCES ALLEN, J. R. L., 1961, The highest Lower Old Red Sandstone of Brown Clee Hill, Shropshire: l?roc. Geol. Assoc. London, v. 72, p. 205-219. --, 1962a, [ntraformational conglomerates and scoured surfaces in the Lower Old Red Sandstone of the Anglo-Welsh Cuvette: Liverpool and Manchester Geol. Journ., v. 3, p. 1-20. .... , 1962b, Petrology', origin and deposition of the highest Lower Old Red Sandstone of Shropshire, Engl;md. Jour. Sedimentary Petrology, v. 32, p. 657-697. ---, 1963a, Depositional features of Dittonian rocks: Pembrokeshire compared with the Welsh Borderland: Geol. Mag., v. 100, p. 385-400. ---, 1963b, Henry Clifton Sorby and the sedimentary structures of sands and sandstones in relation to flow conditions: Geol. Mijnbouw, v. 42, p. 223-228. ----, 1063e, The classification of cross-stratlfied units, with notes on their origin. Sedlmentology, v. 2, p. 93114. . . . . . , 1964a, Studies in fluviatile sedimentation: six cydothems from the Lower Old Red Sandstone, AngloWelsh Basin: Sedimentology v. 3, p. 163 198. - - -, 1964b, Primary" currem lineation in the Lower Old Red Sandstone (Devonian), Anglo-\Velsh Basin: Sedhnentology, v. 3, p. 89 108. ---, 1965a, Sedimentation and palaeogeography of the Old Red Saadstone of Anglesey, North 'Wales: Yorkshire Geol. Soc. Proc., v. 35, p. 139-185. --, 1965b, A review of the origin and characteristics of recent alluvial sediments: Sedimentology, v. 5, p. 89 191. ---, 1965c, Fining-upwards cycles in alluvial successions: Geological Jour. v. 4, p. 229-246. --, 1%5d, Upper Old Red Sandstone (Farlovian) paleogeography in South Wales and the Welsh Borderland: Jour. Sedimentary Petrology, v. 35, p. 167 195.
STUDIES IN FLUVIATiLE SEDIMENTATION
321
, ANDFRIEND, P. F., 1968, Deposition of the Catskill facies, Appalachian region: with notes on some other Old Red Sandstone basins: in Klein G. de V., ed., Late Palaeozoic and Mesozoic Continental Sedimentation, northeastern North America, Geol. Soc. America Spec. Paper 106, p. 21-74. , HALSTEAD, L. B. AND TURNER, SUSAN, 1968, Dittonian ostracoderm fauna from the Brownstones of Wilderness Quarry, Mitcheldean, Gloucestershire: Proc. Geol. Soc. London, no. 1649, p. 141-153. , AND TARLO, L. B., 1963, The Downtonian and Dittonian facies of the Welsh Borderland: Geol. Mag., v. 100, p. 129-155. ARNDT, H. H., WOOD, G. H., AND TREXLER, J. P., 1962, Subdivision of the Catskill Formation in the western part of the Anthracite Region of Pennsylvania: U. S. Geol. Survey, Prof. Paper 450-C, p. 32-36. BAGNOLD, R. A., 1966, An approach to the sediment transport problem from general physics: U. S. Geol. Survey, Prof. Paper 422-I, 37 p. BARRETT, P. J., 1965, Geology of the area between Axel Heiberg and Shackleton glaciers, Queen Maud Range, Antarctic: New Zealand Jour. Geology Geophysics, v. 8, p. 344-370. BEERBOWER, J. R., 1964, Cyclothems and cyclic depositional mechanisms in alluvial plain sedimentation: Bull Kansas Geol. Survey, no. 169, p. 31-42. BELT, E. S., 1968, Carboniferous continental sedimentation, Atlantic Provinces, Canada: in Klein G. de V., ed., Late Palaeozoic and M esozoic Continental Sedimentation, northeastern North America, Geol. Soc. America Spec. Paper 106, p. 127-176. BERSIER, ARNOLD, 1938, Recherches sur la groiogie et la stratigraphie du Jorat: Bull. lab. de gdolog[e l'Ualversitd de Lausanne, no. 63, 128 p. , 1958, SEquences detritiques et divagations fluviales: Eclogae geologicae Helveticae, v. 51, p. 854--893. BEUTNER, E. C., FLUECKINGER,L. A., AND GARD, T. M., 1967, Bedding geometry in a Pennsylvanian channel sandstone: Geol. Soc. America Bull., v. 78, p. 911-916. BOORER, F. W., 1960, Studies in Permian sedimentatlml in the Sydney Basin: New South Wales Department of Mines, Tech. Report No. 5 (1957), p. 10-62. , BURSILL,C. AND MCELROV, C. T., 1953, Sedimentation in the Tomago Coal Measures in the SingletonMuswells Rock coalfield: an introductory study: Jour. Proc. Roy. Soc. New South Wales, v. 87, p. 137-151. , AND McKENzlE, P. J., 1953, The Ravensworth State Coal Mine Reserve: New South Wales Department of Mines, Tech. Report No. 1 (1953), p. 13-19. BRL'CK, P. M., DEDMAN, R. E. AND WILSOr~, R. C. L., 1967, The New Red Sandstone of Raasay and Scalpay, Inner Hebrides: Scottish Jour. Geol., v. 3, p. 160-180. BURGESS, I. C., 1960, Fossil soils of the Upper Old Red Sandstone of south Ayrshire: Geol. Soc. Glasgow Trans., v. 24, p. 138-153. CARR, D. D., HOROWITZ,ALAN, HRABAR,S. V., RIDGE, K. F., ROONEY, R., STRAW, W. T., WEBB, W., AND POTTER, P. E., 1966, Stratigraphic sections, bedding sequences and random processes: Science, v. 154, p. 1162-1164. CHIEN, NING, 1961, The braided stream of the Lower Yellow River: Sci. Sinica (Peking), v. 10, p. 734-754. COL, KENNETH, AND SELLWOOD,E. B., 1968, The Upper Palaeozoic stratigraphy of West Cork and parts of South Kerry: Royal Irish Academy Proc., v. 66 (B), p. 113-131. CONOLLY, J. R., 1965, Petrology and origin of the Hervey Group, Upper Devonian, Central New South Wales: Jour. Geol. Soc. Australia, v. 12, p. 123-166. CROUZEL, FERNAND, 1957, Le Miocene continental du Bassin d'Aquitaine: Serv. Carte G~ologique de France Bull., No. 248, 264 p. DE RAAF,J. F. M., READING,H. G., ANDWALKER, R. G., 1965, Cyclic sedimentation in the Upper carboniferous of North Devon, England: Sedimentology, v. 4, p. 1-52. DINELEY, D. L., 1960, The Old Red Sandstone of easterrt Ekmanfjorden, Vestspitsbergen: Geol. Mag., v. 97 p. 18-32. - 1966, The Dartmouth Beds of Bigby Bay, south Devon: Geol. Soc. Lond., Quart Joar., v. 122, p. 187217. AND GOSSAGE, D. W., 1959, The Old Red Sandstone of the Cleobury Mortimer area, Shropshire: Proc. Geol. Assoc. London, v. 70, p. 221-238. DIXON E. E. L., 1921, Geology of the South Wales Coalfield, Part 13. The country around Pembroke and Tenby. Geol. Survey Great Britain Mere., 220 p. DEFy P. McL. D., 1967, Cyclic sedimentation in the Permian Coal Measures of New South Wales: Jour. Geol. Soc. Australia, v. 14, p. 293-308. AND WALTON, E. K., 1962, Statistical basis for cyclothems: a quantitative study of the sedimentary succession in the East Pennine Coal Field: Sedlmentology, v. 1, p. 235-255. DYsoN J. L., 1963, Geology and mlneral resources of the New Bloomfield Quadrangle. Geol. Surv. Pennsylvania Atlas 137A, B, 63 p. ELLIOTT, R. E., 1968, Facies, sedimentation succession and cyclothems in Productive Coal Measures in the East Midlands, Great Britain: Mercian Geologist, v. 2, p. 351-372. FERM, J. C. AND CAVAROC,V. V., 1968, A nonmarine sedimentary model for the Allegheny rocks of West Virginia: in Klein, G. deV. ed., Late Palaeozoic and Mesozoic Continental Sedimentation, northeastern North America, Geol. Soc. America Spec. Paper 106, p. 1-19. FISK, 1t. N., 1944, Geological investigation of the alluviM valley of the Lower Mississippi River. Mississippi River Commission, Vicksburg, Miss., 78 p. , 1947, Fine grained alluvial deposits and their effects on Mississippi River activity. Mississippi River Commission, Vicksburg, Miss., 82 p. FLETCHER, F. W., 1963, Regional stratigraphy of Middle and Upper Devonian non-marlne rocks in southeastern New York: i n Shepps V. C., ed. Symposium on Middle and Upper Devonian Stratigraphy of Pennsylvania and adjacent States, Geol. Survey Pennsylvania Bull. G39, p. 25-41. FRrEND, P. F., 1965, Fluvlatile sedhnentary" structures in the Wood Bay Series (Devonian) of Spitsbergen: Sedlmentology, v. 5, p. 39-68. GLAI';SER, D. J., 1963, Catskill reference section and its correlation to other measured surface sections ill north-
-
-
-
322
Y. R. L. A L L E N
eastern Pennsylvania: in Shepps V. C., ed. Symposium on Middle and Upper Devonian Stratigraphy of Pennsylvania and adjacent States, Geol. Survey Pennsylvania Bull. G39, p. 51-62. Guy, H. P., SIMONS, D. B., AND RICHARDSOn',E. V., 1966, Summary of alluvial channel data from flume experiments, 195(6-61. U. 5. Geol. Survey, Prof. Paper 462-1, 96 p. HAMBLIN, \V. K., 1958, Cambrian sandstones of Northern Michigan: Geol. Survey Michigan Publ. 51,194 p. HAPP, S. C., RITTENHOUSE, GORDAN, AND DOBSON, G. C., 1940, Some aspects of accelerated stream and valley sedimentation: U. S. Dept. Agriculture Teeh. Bull. 695, 134 p. HARMS, J. C. AND FAHNESTOCK, R. K., 1965, Stratification, bed forms, and flow phenomena (with an example from the Rio Grande) : in Middleton G. V., ed. Sedimentary Structures and their Hydrodynamic Interpretation, S.E.P.M. Spec. Publ. No. 12, p. 84--115. HARMS, J. C., MAcKENzIE, D. B. AND McCImBIN, D. G., 1963, Stratification in modern sands of the Red River, Louisiana: Jour. Geol., v. 71, p. 566-580. HILL, H. M., 1966, Bed forms due to a fluid stream: Am. Soc. Civil Engineers Proc., v. 92, no. HY2, p. 127-143. JABLOKOV, r . S., BOTVINKINA, L. N., ANn FEOFILOVA, A. P., 1963, Sedimentation in the Carboniferous and the significance of alluvial deposits. C. R. 4th Congr~.s pour l'Avancement des l~,tudes de la Stratigraphie Carbonif~re, Heerlen, v. 2, p. 293-299. JAHNS, R. H., 1947, Geologic features of the Connecticut Valley, Massachusetts, as related to recent floods: U. S. Geol. Survey Water-Supply Paper 996, 158 p. KELLINC~, GILBERT, 1968, Patterns of sedimentation in Rhondda Beds of South Wales: Am. Assoc. Petroleum Geologists Bull., v. 52, p. 2309-2382. KENNEDY, J. F., 1963, The mechanisms of dnnes and antidunes on erodible-bed channels: Jour. Fluid Mechanics, v. 16, p. 521-544. KONDRAT'EV, N. E., 1962, River flow and river channel formation. Israel Program for Scientific Translations, Jerusalem, 172 p. K6slt~tt, E., 1955, Aufbau and Sedimentatlonsrythmen der t'~ger~Sdformation in der Bohrung Klappe in nordweslicheu Schonen: Geol. FSren. F6rhandl. Stockholm, v. 78, p. 463-497. KRUMBElX, W. C., 1967. Fortran IV computer programs for Markov chain experiments in geology: Computer Contributions Geol. Survey Kansas, no. 13, 38 p. LAURY, R. C., 1968, Sedimentulogy of the Pleasantview Sandstone, southern Iowa and western Illinois: Jour. Sedimentary Petrology, v. 38, p. 568-599. LELIAVSKV, SERGE, 1966, An introduction to fluvial hydraulics. Dover, New York, 257 p. LEOPOLD, L. B. AND ~,IADDOCK,J. T., 1953, The hydraulic geometry of stream channels aud some physiographic implications: U. S. Geol. Survey, Prof. Paper 252, 57 p. , AND \VOLMAN, 3[. G., 1957, River channel patterns; braided, meandering and straight. U. S. Geol. Survey, Prof. Paper 282-B, p. 39-85. , AXD , 196(/, River meanders: Geol. Soc. America Bull., v. 71, p. 769-794. , AND ~;IILLER, J. P., 1964, Fluvial processes in geomorphology, Freeman, San Francisco, 522 p. MCCA~"E, I. N., 1959, Correlation of lnarine and non-marine strata with example from Devonian of New York State: Am. Assoc. Petroleum Geologists Bull., v. 53, p. 155-162. McKEE, E. D., 1939. Some types of bedding in the Colorado River delta: Jour. Geology, v. 47, p. 64-81. , CROSBY, E. J., AND BERRVHILL, H. L., 1967, Flood deposits, Bijou Creek, Colorado, June 1965: Jonr. Sedimentary Petrology, v. 37, p. 829-85i. MV;L'rOx, F. A., 1936, An empirical classification of floodplain streams: Geograph. Review, v. 26, p. 593-610. MOODY-S'IUART, MARK, 1966, High-and low-sinuosity stream deposits, with examples from the Devonian of Spitsbergen: Jonr. Sedimentary Petrology, v. 36, p. 1102-1117. MUXCH, T. A., 1968, Penusvlvanlan nomnarine sediments of the Narragansett Basin, Massachusetts and Rhode Island : in Klein G. de~., ed. Late Palaeozoic and Mesozoic Continental Sedimentation, northeastern North America, Geol. Soc. America Spec. Paper 106, p. 177-209. NE I)ECO (Netherlands Engineering Consultants), 1959, River studies and recomtnendations on improvement of Niger and Benue. North-Holland, Amsterdam, 1000 p. NiLst~x, T. H., 1967, Old Red sedimentation in the Solund district, VYestern Norway, in Oswald, D. H. ed. International Symposium on the Devonian System. Alberta Society of Petroleum Geologists, Calgary, Alberta, p. 1101-1115. NiYOGi, DIPAXKAR, 1966, Lower Gondwana sedimentation in Saharjuri Coalfield, Bihar, India: Jonr. Sedirnentary Petrology, v. 36, p. 960--972. PICARD, M. D. AND I.EI.;, R. Ill., 1968, Sedimentary cycles in the Green River Formation (Eocene), Uinta Basin, Utah: Jour. Sedimentary' Petrology, v. 38, p. 378-383. POTTER, P. E., 1963, Late Palaeozoic sandstone of the Illinois Basin: Geol. Surv. Illinois Rept. Investigations no. 217, 92 p. - - , 1967, Sand bodies and sedimentary environments: a review: Am. Assoc. Petroleum Geologists Bull., v. 51, p. 337-365. - - , AND BLAKELEY, R. F., 1967, Generation of a synthetic vertical profile of a fluviat sand body: Jour. Petroleum Technology, v. 7, p. 243-251. , and - - , 1968, Random processes and lithologic transitions: Jour. Geology', v. 76, p. 154-170. QURESHI, 3,1. A., 1962, Report on regime relations in a gravel reach of the Red Deer River, Alberta: Government of Province of Alberta, Dept. of Water Resources, Edmonton, Alberta (Canada), 192 p. RAp, P. V., 1964, Geology and mineral resources of India: Rept. 22nd Internat. Geological Congress, Delhi, 44 p. RATTIGAN, J. H., 1967, Depositional, soft sediment and post-consolidation structures in Palaeozoic aqueoglacial sequence: Jour. Geol. Soc. Australia, v. 14, p. 5-18. REAL), W. A., AND JOHNSON, S. R. H., 1967, The sedimentology of sandstone formations within the Upper Old Red Sandstone and lowest Calciferous Sandstone Measures west of Stirling, Scotland: Scottish Jour. Geology, v. 3, p. 242-267. REINEMr>:D, J. A., 1955, Geology of the Deep River Coal Field, North Carolina: U. S. Geol. Survey, Prof. Paper 246, 259 p.
STUDIES IN FL U ~IA TILE SEDIi]IENTA TION
323
ROZOVSKII, I. L., 1963, Flow in bends of open channels: Israel Program for Scientific Translations, Jerusalem, 233 p. SARKAR, S. K., ANn BASUMALLICK,SUDHIR, 1968, Morphology, structure and evolution of a channel island in the Barakar River, Barakar, West Bengal: Jour. Sedimentary Petrology, v. 38, p. 746--754. SCHAFFERNAK, F., 1950, Grundriss der Ftussmorphologie und des Flussbaues. Springer-Verlag, Wien, 115 p. SHANTZER, E. V., 1951, Alluvium of plains rivers in a temperate zone and its significance for understanding the laws governing the structure and formation of alluvial suites (in Russian): Tray. Inst. Sci. Geol. Akad. Nauk, v. 135, p. 1-271. Si~oxT, J. A., AN'DftOFKIXS, M. E., 1966, Sedimentary structures and morphology of Late Palaeozoic sand bodies in southern Illinois: Geol. Survey Illinois Guidebook Series No. 7, 67 p. SIMONS, D. B., AND RICHARDSON, E. -V., 1966, Resistance to flow in alluvial channels: U. S. Geol. Survey, Prof. Paper 422-J, 61 p. SKALA, ~,~'OLFDIETRICft, 1968, Lithologisehe Untersuchungen an den Sanden der Kirchberger-KarnbergerZwischenserie (Pannon C, Steirisches Beckon), Mitt. Geol. Gesellschacht in Wien, v. 60, p. 69-95. STANLEY, D. J., 1968, Graded bedding-sole markings-graywacke assemblage and related sedimentary structures in some Carboniferous ttood deposits, Eastern Massachusetts: in Klein, G. deV. ed. Late Palaeozoic and Mesozoic Continental Sedimentation, northeastern North America, Geol. Soe. America Spee. Paper 106, p. 211-239. STEB~INGS, Jonx, 1963, The shapes of self-formed model alluvial channels: Institution Civil Engineers Proc., v. 25, p.o485-510. SUNDUO~G, AKE, 1956, The River KlarMven: a study of fluvial processes: Geog. Ann., Stockholm, v. 38, p. 127316. VISHER, G. S., 1965a, Use of vertical profile in environmental reconstruction: Am. Assoc. Petroleum Geologists Bull., v. 49, p. 41-61. - - , 1965b, Fluvial processes as interpreted from ancient aim recent fluvial deposits: in Middleton, G. V. ed. Primary Sedimentary Structures and their Hydrodynamic Interpretation, S.E.P.M. Spee. Publ. No. 12, p. 116-]32. WILLIAMS, G. P., 1967, Flume experiments on the tra,~sport of a coarse sand: U. S. Geol. Survey, Prof. Paper 562-B, 31 p.
