JotntXaL OF SEI)I MF.N'I;AI,~Y P~.;ntol.oc,e, VOL. 44, NO. 4j P. 1174-1185 Fits. 1-7, Dt~cl.:~*RV.U 1974

Copyright © 1974, The Society of Economic Paleontologists and Mineralogists

P A L E O C U R R E N T ANALYSIS OF A L L U V I A L S E D I M E N T S :

A D I S C U S S I O N OF D I R E C T I O N A L V A R I A N C E A N D

V E C T O R M A G N I T U D E L 2

A N D R E W D. MIALL Institute of Sedimentary and Petroleum Geology,

3303-33rd St. N.W., Calgary, Alberta, Canada, T2L 2A7

ABSTRACT: A tabulation of recent work on current indicators in modern rivers shows that directional variance increases with decreasing structure scale, in fairly close agreement with the structure hierarchy concept of Allen (1966).

Fluvial currents are vectors, definable by direction and magnitude, but most paleocurrent studies ignore magnitude. It is proposed that azimuth readings be weighted according to the cube of current structure thickness, this being a volume measure corresponding to the distance in all three dimensions over which a local flow vector might reasonably be assumed to maintain the same direction. It is also a measure of the quantity of sediment moved by the flow vector.

Examples are presented in which the proposed weighting factor is applied to data from the fluvial Isachsen Formation (Cretaceous) and deltaic Eureka Sound Formation (Creta- ceous-Tertiary) of Banks Island, Arctic Canada. It is shown that the use of the weighting factor can differentiate flow patterns on the "basis of sedimentary structure size, leading to interpretations of channel size, sinuosity, and other parameters of sedimentological im- portance. The weighting factor also provides an important check on calculations of vector mean.

INTRODUCTION

Much work has been carried out in modern rivers in recent years in an attempt to determine the reliability of paleocurrent indicators. In the present paper, an attempt is made to assem- ble this new data, with the aim of relat ing the results to the sedimentary s tructure h ierarchy of Allen (1966) and to r iver sinuosity. The methods for quant i fying directional variance are examined, and a new method is proposed for weight ing individual or ientat ion measure- ments. Earl ier studies of paleocurrent methods, of broader scope, were provided by Pet t i john (1962), Allen (1966), and Selley (1968).

R E L A T I O N S H I P BETWEEN FLOW VECTORS

A N D CURRENT STRUCTURES

Many authors have contributed to the ex- tensive l i terature on this subject. Of especial value are papers by Allen (1966, 1967, 1968, 1973) and a S E P M publication edited by Mid- dleton (1965). The subject is a very complex

1Manuscript received November 28, 1973; revised April 2, 1974.

Published with the permission of the Director, Geological Survey of Canada.

one, but from the point of view of paleocurrent analysis, the facts remain essentially simple. Most flow pat terns have an internal symmetry about their xy plane, where x is the direction of pr imary flow and y is the normal to the water surface. The major i ty of sedimentary structures are symmetrical about the same xy plane, a l though Allen (1968, Fig. 5.28) il- lustrates a few that are not. Thus, so long as the geologist can see the entire structure, he can always determine the direction of net flow.

The practical problem of incomplete exposure is one that has long been realized, especially in connection with t rough crossbeds, in which the t rough infill, produced by the migrat ion of large scale ripple forms (Allen, 1968, p. 108-112) commonly assumes a curved plan. Dott (1973) provides a detailed discussion of this problem. There is no final answer to the problem, other than to take care in measurement , and to reject questionable outcrop data. The problem of preservat ion potential is also an important one. A full consideration of its relevance to paleocur rent analyses is beyond the scope of this paper.

Divergence between flow direction and cross- bed dip certainly does occur. Smith (1972, Fig. 11 ) showed that flow over t ransverse bars may diverge as much as 90 ° from the direction of

P A L E O C U 1 R R E N T A N A L Y S I S OF A L L U V I A L S E D I M E N T S 1175

foreset dip measured immediately below. In his particular study location (Platte River, Ne- braska) his data show that only 42.6% of dip directions are within 10 ° of local current flow. However, the divergence is symmetrical, for his study also shows that the mean foreset dip azimuth corresponds very closely to mean chan- nel direction. The implications for students of ancient rocks are clear.

Other authors (Wright, 1959; Selley, 1968, p. 100) have suggested that a certain type of large scale crossbedding presumed to be most typical of point bar deposits in high sinuosity streams (Moody-Stuart, 1966), is built up in a direction perpendicular to the primary current direction, owing to the outward migration of the point liar on the concave side of a river meander, This particular type of crossbedding is typically large in scale and lithologically heterogenous. It was classified as epsilon cross- bedding by Allen (1963, p. 102). Selley (1968, Fig. 2A) suggested that a study of epsilon cross- bedding would show a unimodal current direc- tion with a vector mean 90 ° from the river trend. This would possibly be true only if a single point bar was studied, and only if the stream were of very high sinuosity. However, most point bar deposits are more complex than Selley's illustration would suggest. A study of randomly chosen erossbeds may show a bi- modal pattern with a vector mean close to that of the river trend.

One of the uncertainties in making highly sophisticated analyses of bed forms is the as- sumption that equilibrium exists between flow conditions and the resulting sedimentary struc- tures. Allen (1973) has summarized the sparse data that is available on this snbject, and it showed that a time lag of several days may exist between a change in flow character and the complete readjustment of the bed forms. For paleocurrent analysis this is probably not important. A preserved bed form is a valid indicator of current direction, taking into ac- count the type of divergence documented by Smith (1972), and whether or not the current changes in direction subsequently could not be determined from a single structure, although it may be detected by analysis of vertical vari- ability throughout a sedimentary succession. Such changes may have an effect on directional variance but it is arguable whether they would affect the vector mean.

T i I E S E D I M E N T A R Y S T R U C T U R E H I E R A R C H Y

A fundamental concept in the understanding of sedimentary structures and paleocurrent systems is that of hierarchy. It was first de-

fined by Allen (1966) whose thesis was that flow- fields and the sedimentary structures arising from them are of five orders of magni- tude. The largest, or highest ranking, consists of complete river systems, the next comprises the individual river, and so on. The concept is illustrated in Figure 1 and the ranks are described in Table 1. Rank numbers in the iI- lustration have been increased by two from Allen (1966) for Allen did not assign a number to the river system, and defined the river as rank zero (Table 1). Apart from these minor changes Figure 1 is derived directly from Allen's work.

The currents forming the smaller scale struc- tures are subsidiary to those forming the next Iargest in size ; they may be considered as eddies within the larger currents, at each scale of observation. Structures of ranks 5 and 6 are the ones most frequently available for study. Current directions derived from them will ap- proximate, statistically, those obtainable from the larger features, for the flow vector fields which give rise to the smaller structures are dynamically related to the field of the overall system. This has been demonstrated in nu- merous studies of modern rivers, e.g. Harms et al. (1963), Coleman (1969), Williams and Rust (1969), Bluck (1971), McDonald and Banerjee (1971), Rust (1972), Smith (1971, 1972); but the spread of readings is liable to be large, and this spread will itself vary, de- pending on the sinuosity of the river system under study.

An additional complication was discussed by Collinson (1971), who pointed out that under conditions of fluctuating diseharge, sedimentary structures will be formed under varying flow regimes. At stages of low flow, small scale structures such as ripple marks are formed by flow fields whose directional properties are likely to be strongly influenced by large bed- forms developed at higher energy levels. Con- siderable directional variance is thus possible.

This is a situation where the hierarchy con- cept is inappropriate, for the currents forming the ripples bear no genetic relationship to those forming the earlier, larger structures (in con- trast to the situation illustrated by Smith, 1972, Figure 4, where rank 5 planar cross-sets and rank 6 ripples form simultaneously from the same flow field).

D I R E C T I O N A L V A R I A N C E I N R E L A T I O N TO

S T R U C T U R E H I E R A R C H Y

The studies of modern rivers quoted earlier have had as one of their principal aims the investigation of directional properties. How-

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ever, few attempts have been made to relate these properties systematically to the sedimen- tary s tructure hierarchy. Allen (1967, p. 83- 86) considered the subject briefly, but very little hard data was available at the time his paper was written. This topic is considered in the following discussion; Allen's figures are quoted, together with recently published data on modern rivers, and some well-controlled studies of ancient rocks.

A measure of directional spread is given by variance. Allen's (1967) figures for variance were not derived from statistical measurement but were estimates based on the assumptions t ha t : (1) the maximum observed spread of readings represents a var ia t ion of up to three s tandard deviations on either side of the sample mean, and (2) the sample population distribu- tion is normal. Since a total spread of six s tandard deviations represents 99.76% of the area of a normal curve, these assumptions are another way of saying that the observed spread represents 99.76% of the observable variation.

Some of the authors quoted below give not ar i thmet ic variance but vector magnitude, based on the circular frequency distribution calcula- tions of Curray (1956). tn these cases, a modificat ion to ar i thmetic variance for com- parat ive purposes has been carr ied out using Curray 's (1956, Fig. 3) conversion graph. The data is summarized in Table 1 and Figure 2 using the appropriate rank numbers f rom Figure 1.

It is important to hear in mind that var iance from alI sources within the s t ructure h ierarchy must be considered when assessing directional variation. Var ia t ion within each rank must be summed to that of the higher ranks as far as is locally appropriate. In Table 1 and Figure 2 all the data for ranks 3 to 6 has been related to rank 2, that of the single river. In some of the published studies of modern rivers, this has not been done, so that comparisons with other r ivers and other rock successions should be carr ied out with care. Thus Coleman (1969, Fig. 16) shows the directional var ia t ion in minor channels ( rank 4 of the present study) ex, i th in the major channel reaches of the Brahmapu t ra River. The maximum angular deviation ranges locally from 15 degrees to 112 degrees. To Coleman's figures must be added a variance of 290 to account for the 100 degree swing in the ma jo r course of the r iver within his sampling area. A similar summation must be carr ied out on Coleman's crossbedding data (Coleman, 1969, 43--45) which was measured on s traight reaches of the r iver or a ronnd bends using a symmetrical sampling plan. Similar manipula-

1178

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A. D. MIALL

. RANK 2.

[. R A N K 4 .

FIG. 1.--The sedimentary structure hierarchy, showing paleocurrent variability. Concept from Allen (1966), although rank numbers used are different from Allen's, as discussed in the text, and as listed in Table 1. Current rose diagrams illustrate directional variability present in the entire area shown for each rank. This must be added to the variability shown by the larger scale structures to arrive at the total vari- ability for the structures of each rank. The small squares show the areas chosen to illustrate the structures of the next smaller scale. Structures illustrating rank 6 are bifurcating ripple crests.

tions have been carried out on some of the other published figures. The result ing figures are given in Table 1.

The data in Table 1 indicate tha t there can be considerable variabil i ty in directional vari- ance, even within the s t ructures of a single rank of the hierarchy. This may be directly at- t r ibuted to di f ferent sinuosities of the r ivers under study. The amount of directional vari- ance is thus a rough guide to sinuosity. Other sinuosity indicators in the form of vertical s t ra t igraphie sequence and sedimentary struc- ture assemblage are discussed by Moody-Stuar t (1966), Allen (1970) and Fr iend and Moody- Stuar t (1972, p. 39).

Figure 2 shows that variance increases moving from high to low rank structures, the increase being especially marked between ranks 2 and 3 and between 4 and 5. However, the evidence available suggests tha t there is little difference between the reliability of rank 5 and rank 6 structures as paleocurrent indicators. This was one of the main conclusions of Bar re t t

(1970, p. 400--404) in a study of some Triassic fluviatile rocks, and is also apparent f rom the data provided by Picard and High (1973, Table X V I ) . Several rank 6 structures, including par t ing lineation, cuspate and sinuous ripples, are rated by them as much more reliable than avalanche-type cross-stratif ication, a rank 5 structure. It is not possible to include Pieard and High 's data in Table 1 as the figures pro- vided relate only to within-channel variation.

Rust (1972, Table II, I I I ) found tha t small scale s tructures ( rank 6) appeared to have a lesser directional var iance than did minor chan- nels ( rank 4) in his study of the Donjek River. Rust reports, however, (personal communica- tion, 1973) tha t owing to problems of accessi- bility his sampling of small scale s t ructures was not carr ied out over the entire sample area. He feels tha t on this account use of his var iance informat ion for comparison purposes may not be strictly valid.

Even within the confines of a single rank there is some evidence that certain s t ructures

t ) A L E O C U R R E N T AA:ALYSI5" OF A L L U U I A L S E D I M E N T S 1179

I0000

800C

6000

4000

2000

i 2 3 4 5 6 sedimentary structure rank

FIC. 2.--The range of directional variance shown by sedimentary structures of different rank. Data from Table 1.

are more reliable as paleocurrent indicators than others. Thus, Agterberg, et al. (1967) and High and Picard (1974) found that trough crossbeds gave lower directional variance than did planar crossheds (both of rank 5). Their interpreta- tion of this result was that their planar cross- beds represented the slip-off faces of hars oriented obliquely to the curren} direction, whereas trough axes coincided more closely with stream direction. An alternative explana- tion is that the two types of structure were formed under different flow conditions. How- ever, Meekel (1967) found that variance shown by trough crossbeds was very close to that shown by planar crossbeds.

The concept of sedimentary structure hier- archy would lead one to suspect that rank 6 structures should show greater directional vari- ability than any others. Either the hierarchy concept is insufficient to explain the variability of directional information, or the data at pres- ent available is insufficient to provide a valid test of the idea. The latter may well be the case, but at the same time it should be pointed out that there are many complications sur- rounding the formation and orientation of sedi- mentary structures, and in many cases there is still dispute over their exact mode of origin (Picard and High, 1973). Such factors as flow regime, fluctuation of discharge (Collinson, 1971), bedform tag (Allen, 1973), variable sinuosity, and so on, all contribute to directional

characteristics, and it may never be possible to account for all these effects in unified sedi- mentary models. It is certainly beyond the scope of the present paper (useful discussions are provided by Banks and Collinson, 1974; Smith, 1974).

The field sampling scale will have an effect on the variance shown by paleocurrent readings (Olson and Potter, 1954; Potter and Olson, 1954), and it is important to relate this variance to the correct level of sedimentary structure hierarchy. For example, Kelling (1969, p. 866) suggested that between-outcrop variance may be "determined by deviation in the alignment of laterally (or vertically) adjacent sand bodies within the major stream courses, and, by the same token, variance at the between-sectors level is presumably a function of the differing orientation of adjacent streams or portions of streams."

T H E P R O B L E M OF V E C T O R W E I G H T

A fluvial current is a vector, definable by direction and magnitude, but presently accepted practices in processing directional data deal only with direction. The usual method is to assign equal weight (unity) to each azimuth reading when calculating mean direction, yet if struc- tures of more than one rank are used equal weight is thereby assigned to lower rank (smaller) structures, which are the least reliable from the point of view of regional paleoslope determinations.

What is the relative importance of azimuth readings taken on the various types of struc- ture ? The discussion to this point has provided a qualitative answer to the problem, but few workers have attempted to deal with the subject on a quantitative basis. It must be appreciated that the volume of a large scale planar cross- bed set (50 cm thick, or more) may be several hundred thousand times greater than that of a small scale ripple (1 cm thick, on average). This volume contrast is a direct measure of the relative quantity of dispersed sediment moved by the current which gave rise to the structures and hence is an indication of the relative magnitude of the current system itself. It is therefore rec- ommended that structures of such markedly different size (different rank) never be ana- lyzed together for paleocurrent purposes. To do so is to lose information by confusing the effects of current flow fields of different mag- nitudes. Each structure type and each rank has its own type of directional variance which it may be important to analyze.

Several authors have dealt with the problem of vector weight. Thus Allen (1967, p.

118() A. I). M I A L L

78) proposed that azimuth measurements be "weighted by some property of the rock struc- ture that serves as an estimation of quanti ty of sedinlent," and suggested using cross-set thick- ness. ]r iondo (197.3) suggested giving "each measurement a value equal to the volume o:f sedimentary unit it represents." In the case of several measurenlents being made on the same unit, it was suggested by l r iondo that the volume be distributed proportionally between each nleasurement.

_\llen's suggestion is not a complete answer to the problem for thickness, being a one-di- mensional measure, is not appropriate to define fully sediment quantity, l r iondo's suggestion is also inappropriate, for two reasons. Firstly, the volume of a sedinaentary structure, es- pecially a large scale featnre such as a t rans- verse bar or its component cross-sets, is almost impossible to determine from the two-dimen- sional outcrops characterist ic of ancient rocks. Secondly, an azimuth measured at a given point within a sedimentary s t ructure will not neces- sarily be typical of the entire structure. For example, the orientat ion of an avalanche face at the margin of a bar may fluctuate laterally (\Villiams, 1971, P1. IV C, D) , giving rise to variable azinmth directions, as i l lustrated by Smith (1972, Fig. 7).

t ) lson and Pot ter (1954, p. 43-45) proposed a weighting process having an entirely di f ferent purpose. They were 1lot concerned with the relative weight of the individual current vector and the resultant sedimentary structnre, but with the validity of statistical information calculated from samples at d i f ferent levels of their sam- piing hierarchy. They calculated reliability es- t imators for use as weighting factors when com- bining data from more than oIae sample location. \Vhen data is sparse it may be important to use these est imators for combining scattered out- crop data, :is only in this maturer may reliable local mean azinmth figures be calculated. Eut the present author regards this approach as insufficient, for it does not take into account the problem discussed by Allen (1%7) and lr iondo (1973), namely the relative weight of the individual vector. As noted above, the pres- ent author does not agree with the suggestions offered by these two authors. A new method is proposed below.

An azimuth reading is taken over a small ex- posed portion of an individual sedimentary structure. It is generally valid for the full thickness of the structure, and it is argued that it is also valk[ in plan view parallel and per- pendicular to the current direction for a dis- tahoe equal to the s tructure thickness. The

lat ter is an indication of flow field size, and may also be regarded as the distance in all three dimensions over which the flow field may be reasonably assumed to mainta in constant direc- tion. In addition this figure, when considered in three dimensions, is a measurement of the volume of sediment displaced by the current, within the region of assumed constant current direction. The relative weight of the flow vector may thus be assessed using this volume measurement, and it is therefore proposed that the cube of s tructure thickness be used to weight the individual azimuth readings in vector mean calculations.

The method can be readily applied to any structures where the relationship of s t ructure to current is clear and unaml)iguous. Thus, it could not be applied to tool markings, but may be used for all types of crossbedding as well as for ripple structures of large and small scale. Some inaccuracy in the proposed method may accrue from the loss of thickness result ing from erosion prior to final burial of a sedimentary structure. However, this is not thought to be a serious problem.

T I l E U S E OF A \ V E I G I t T I N G F A C T O R :

g O M E E X A M P L E S

Method

The most commonly used method of pro- cessing or ientat ion data is that based on the circular normal distribution as is described by Curray (1956) and Krumbein and Graybill (1965, p. 128-131).

Mean azimuth 0 is given by the following formula,

tan 0 = 2~n sirt 0

Xn cos O'

where 0 represents the azimuth observations, from 0 ° to 360 ° . The quanti ty n is defined by Curray (1956, p. 119) as the "observat ion vector magnitude or, in the case of grouped data of unit vectors, it is the number of observations in each group." Ii1 this paper ungrouped data are used, and 11 is used as a weighting factor to control for vector magnitude, in this case the cube of cross-set thickness.

Curray 's equations are used to calculate L, the magnitude of the resul tant vector and p, the Rayleigh significance test.

5"oarce of data

The examples used herein are derived from the author 's study of the Isachsen Format ion (Neocomian to Apt ian) and the Eureka Sound

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Fro. 3.--Location of field stations.

Formation (Maastrichtian to Eocene) of Banks Island, Arctic Canada. Locations are shown in Figure 3. The lsachsen Formation is fluvial in origin; the most abundant sedimentary struc- ture is planar crossbedding of rank 5. The F.ureka Sound Formation is a deltaic deposit containing numerous rank 5 and 6 sedimentary structures.

The details of regional geology are not rele- vant to the present stndy, in which it is intended to show only the effects of using a vector magnitude weighting factor on calculations of mean azimuth and vector strength. The in- terested reader may, however, refer to the work of Thorsteinsson and Tozer (1962), Cassan and

Evers (1973), Jutard and Plauchut (1973), and Miall (1974).

Results and discussion

Table 2 lists the data calculated for 174 azimuth and thickness measurements made in rank 5 structures at five field stations exposing

the Isachsen Formation. Vector mean, 0, vector magnitude L and p, the Rayleigh probability test, have been calculated for each of the five stations using both unweighted and weighted data. The last two columns tabulate the differ- ences that are brought about in mean and dis- persion using the weighting method proposed herein.

It will be noted that the effect on mean azimuth is comparatively minor, but that the effect on vector magnitude is variable. In two of the five cases vector magnitude is diminished when weighted data is used, in three it is in- creased. Current rose diagrams are provided for the two field stations for which the two calculation methods give rise to the strongest differences, locations 29 (Fig. 4) and 30 (Fig. 5). In both cases the unweighted data have a bimodal distribution, with a strong primary mode and a weaker secondary mode. Vector strength is comparatively high (81.5 to 83.3) and corresponds to a variance of approximately 1,300. This figure cannot be compared directly with the variance for other rank 5 measure- merits in Table 1, as the data relate to single outcrops each exposing 28 m of section. There is thus a fair probability that the larger scale sources of variance, such as inter-channel varia- tion, are not fully represented in the sample.

The process of weighting has markedly dif- ferent effects on the data from the two stations. That from loc. 29 (Fig. 4B) becomes polymodal, whereas the Ioc. 30 data (Fig. 5B) becomes much more strongly unimodal, and the second- ary mode virtually disappears. It is not the purpose of this paper to enter into detailed local

TABLE 2. Paleocurrent data for fluvial deposits (Isachsen Formation)

No. No. No. Total ~u Lit Pu ~,~- Lw Pw 0,,.-0a Lw-L~ Loc. alpha epsilon theta obs.

26 2 23 1 28 34 92.7 <10 -~° 63 93.4 <10 -~° A9 0.7 24 0 18 0 18 15 94.6 .Q10-' 18 96.3 <10 -~ A3 1.7 31 2 20 3 25 40 80.3 <10-" 32 77.5 <10 " C8 - 2.8 29 1 29 0 30 12 83.3 K10 -D 21 71.6 <10 ~ A9 -11.7 30 13 57 3 73 2 81.5 .(10 -~ 351 89.9 ~10 -~ Cll* 8.4

Subscripts: u, w: u = unweighted, w ~ weighted; 0 = vector mean azinmth; L =vector strength; p = probability of randomness; C = clockwise, A = anticlockwise. * = t-test shows difference b e t w e e n means is significant at 95% confidence level.

Greek letters refer to sedimentary structure types of Allen (1963).

1182 d . D . M I A L L

6 ' ' ' ' 5 ' 0 %

A . unweighted d a t a

n - 3 0

p = < l O - 9

FiG. 4. Current rose diagrams for rank 5 sedi- mentary structures fluvial deposits (Isachsen Fm.) at Ioc. 29. These diagrams and those in Figures 5 to 7 are drawn with segment radius proportional to square root of percent number of readings, so that percent is directly proportional to segment area. North is to the top, as in Figures 5 to 7.

interpretations but a few preliminary con- clusions will be drawn, in order to demonstrate how the process of taking cross-set thickness into account does bring certain facts into focus that might not otherwise be noticed.

I11 the case of loe. 30 (Fig. 5) the secondary mode in the 40 ° to 60 ° azimuth class is clearly of minor importance. Re-examination of the data shows that it is made up of lithologically heterogenous planar cross-sets (epsilon type of Allen, 1963) 6 to 15 cm in thickness. The primary mode is represented by larger struc- tures, including a few of epsilon type 100 to 150 cm in thickness. The larger structures prob- ably represent the main channel whereas the smaller cross-sets were developed by the oc- casional spasmodic influence of a smaller chan- nel in the area. The beds exposed at loc. ,30 are interpreted as the deposits of a braided river of low sinuosity (Miall, 1974), within which were located active and inactive channels of several different sizes.

The foreset directions at loc. 29, by contrast, are strongly polymodal (Fig. 4B). It is prob-

A. unweighted data

n : 73

L = 81"5 p : ~ I 0 -21

B. we ighted d a t a

n = ' T 3 t~ = 351 L = 8 9 , 9 p = < 1 0 - 2 5

o 50% I I I I I 1

FIG. 5.--Current rose diagrams for rank 5 sedi- mentary structures, fluvial deposits (Isachsen Fro.) at loe. 30.

able that at least two channels were active in the area bringing in sediment from two dif- ferent directions. The major group of readings between 0 ° and 60 ° in the unweighted data (Fig. 4A) is split by the weighting process into two modes, at 0 ° to 20 ° and 40 ° to 60 ° . The original 20 ° to 40 ° mode is seen, from examina- tion of the data, to be composed of the smaller scale planar cross-sets, similar to those which gave rise to the secondary mode at loc. 30. It is possible that the larger structures, with azimuths on either side of the 20 ° to 40 ° mode, represent cross-sets formed at lateral bar mar- gins. The other two modes, at 100°-120 ° and 3200-340 ° are interpreted as the result of de- position within subsidiary channels. The modes are derived from one and six readings, respec- tively.

The weighted data has a vector mean signifi- cantly different (using t-test statistics) from that of the unweighted data in only one of the five data sets Iisted in Table 2 (loc. 30). This particular result was examined further by di- viding the loc. 30 field data into two equal-

I ) H L E ( ) C U R R E N T , q X H L Y S I S " O F A L L U V I A L S E D I M E N T S

TABLE 3.--Paleocurrent data for deltaic deposits (Eureka Sound Formation)

1183

Sed. No. } . L. P~ ?~ L~ P~ 0,.--~ Lw-L ~ 323-0. 323-0~ Loc, s truct . R a n k obs.

19 0 5 19 ~ 6 19 0, K 5,6 20 a, ~ 5 20 O, Tr 5 20 K 6 20 ~, ~, O, K, ~r 5,6 21 0 5 21 K 6 21 0, K 5, 6

19, 20, 21 or, ~, 0, ~r 5 19, 20, 21 K 6 19, 20, 21 ~,e, 0, K,,r 5,6

10 327 87 ,9 <10 -~ 324 96 .8 <10-" C3 8.9 C4 C1 10 336 91 .4 <10-' 341 9 6 . 8 <10-' A5 5.4 C13 C18 20 331 89 .4 <10-" 324 9 6 . 8 <10 -* C7 7.4 C8 C1 3 338 95.6 0.06 345 99.9 0.04 A7 4.3 C15 C22 8 273 96 .4 <10 -* 269 9 8 . 0 <10 ~ C4 1.6 A50 A54 9 195 41.5 0.21 006 71 .7 <10 -2 C21" 30 .2 A128 C43

20 267 48 .8 <10 ~ 317 79 .4 <10 -~ AS0* 30.6 A56 A6 15 325 94.7 <10 -s 330 97 .6 <10 -° A5 2.9 C2 C7 5 319 98 .3 <I0 -~ 319 98 .1 <10 2 0 -0.2 A4 A4

20 323 95.5 <10 s 330 9 7 . 6 <10" A7 2.1 0 C7 36 315 85 .9 <10 n 323 86 .3 <10 -n A8 0.4 A8 0 24 317 4 8 . 4 <10 ~ 342 94 .1 <10 -~ A25 45.7 A6 C19 60 316 70.9 <10 -x3 323 86 .3 <10 -a9 A7 15.4 A7 0

Symbols as in Table ,, "~ greek letters in column 2 refer to sedimentary structure types of Allen (1963).

sized subsamples and calculating mean and variance for each using weighted and un- weighted data. The differences between the subsamples were smaller than the differences tabulated for loc. 30 in Table 2, and were not significant at the 95% confidence level.

The fact that one of the five fhtvial data sets gives a significantly different vector mean using the weighting method, indicates that even in a braided stream environment, where variance is relatively low, the weighting method may pro- vide an important check on the validity of vector mean calculations. The weighting method may be equally important in providing additional in- formation relating to the overall distribution of current directions, as the preceding paragraphs have attempted to show.

Very similar results are shown by data from deltaic deposits of the Eureka Sound Forma- tion (Table 3). For each of the three localities, rank 5 and 6 structures have been considered separately, and then combined, and a similar treatment has been carried out on the data from all three locations grouped together. The last two columns of Table 3 list the deviations from the grand vector mean of 32,3 ° shown by mean azimuths derived from various portions of the data. The grand vector mean of 323 ° was cal- culated from all combined and weighted rank 5 data, and is regarded as the best estimate of regional paleoslope orientation.

It will be observed that when using weighted data, the addition of rank 6 structure informa- tion to that of rank 5 creates no change in mean azimuth and vector strength. The weighting process reduces rank 6 data to insignificant proportions, and this emphasizes the point made earlier that structures of more than one rank of the sediment hierarchy should not he ana- lyzed together.

Variance of the combined unweighted out- crop data compares closely to that of the data derived from modern rivers which are quoted in Table 1 (and which are also unweighted). Thus rank 5 data have a variance of 1020 and rank 6 data 4900. These values were derived from the figures for vector strength, using the graph supplied by Curray (1956). A stream of moderately low sinuosity is indicated.

' ' ' ' ' 55"0% 0

A, unweighted dora

n : 3 6 : 3 t 5

L = 8 5 " 9 p = < I0-11

B, weighted data

n=36 1~ = 3 2 3 L = 8 6 . 3 p - < 1 0 -It

F i e . 6.--Current rose diagrams for rank 5 sedi- mentary structures, deltaic deposits (Eureka Sound Fro.) locs. 19, 20, 21.

6

1184 J. 1-. . l t R A K O f [ C H A N D A . H, C O O G A N

50%

A, unweighted data

n = 2 4 = 317

L = Z l 8 . 4 19 = < ] 0 -2

B. weighted data

n = 2 4 = 3 4 2

L = 9 4 . 1 p =<10 -9

Fie;. 7.--Current rose diagrams for rank 6 sedi- mentary structures, deltaic deposits (Eureka Sound Fm.) locs. 19, 20, 31.

Figures 6 and 7 were constructed from the rank 5 and 6 data, respectively, using combined data from all three localities and as was seen to be the case with the previous example the process of weight ing has a s t rong effect on the modality of the sample. The secondary mode in the rank 5 data between 260 ° and 280 ° is made up primari ly of large scale solitary and grouped t rough cross-sets ( the ta and pi cross- s trat if icat ion types of Allen, 1963) at loc. 20. The reasons for the preferred directions of these part icular s tructures are not clear and need fur ther study.

Rank 6 data are all derived from climbing ripples of kappa type, in the classification of Allen (1963). The southerly directed mode shown in Fig. 7 is reduced to an insignif icant feature by the process of weighting. The reason is simply the smaller size of the ripples causing this mode, suggesting that they were produced by a low energy back-water eddy.

Two of the data sets in Table 3 show signifi-

cant differences between vector means calcu- lated using weighted and unweighted data (using t-test statistic at 95% confidence level). In both cases the weighted data gives a mean much closer to the best estimate of 323 ° .

CONCLUDING REMARKS

A valuable exercise that the author would like to propose, would be to gather weighted paleocurrent data in a modern fluvial system, where " t rue" current directions are known. This would provide a useful test of some of the ideas presented herein. A considerable amount of test ing in ancient deposits is also considered to be necessary, for the examples given here are regarded not so much as a proof of the weighting method but as il lustrations of its potential.

This paper has been primari ly concerned with the smaller scale structures tha t are preserved in alluvial rocks. The weighting method pro- posed could be applied to crossbedding of all types, ripples, par t ing lineation, certain types of sole structure, etc., but not to pebble imbrica- tion, in which structure thickness, and thus current size, are hard to assess.

ACKNOWLEDGMENTS

The author thanks J. Win. Kerr and D. C. Push for critically reading earlier versions of this manuscript. G. K. Williams and H. P. Tre t t in also provided helpful comments. The data calculations were carr ied out nsing the author 's ow-n programs and were run on the CDC 3300 computer of Computer Data Pro- cessors Ltd., Calgary.

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