- Email: [email protected]
Fabric studies in the Llwyd Mawr Ignimbrite, Caernarvonshire, North Wales
Tectonophysics Elsevier Publishing
FABRIC
Company,
STUDIES
Amsterdam
IN THE LLWYD
CAERNARVONSHIRE, 5. ROBERTS
NORTH
in The Netherlands
MAWR IGNIMBRITE,
WALES
and A.W.B. SIDDANS
Geo1og.y Department, Geology Department, (Received
- Printed
March
Birkbeck College, London (Great Britain) Imperial College, London (Great Britain)
23, 1971)
ABSTRACT Roberts, B. and Siddans, A.W.B., North Wales. Tectonophysics,
1971. Fabric studies 12: 283-306.
in the Llwyd
Mawr Ignimbrite,
Caernarvonshire,
Recently developed techniques for the determination of strain are used to analyse the deformation of the LIwyd Mawr Ignimbrite. The deformation history consists of two discrete finite phases: the first associated with welding, compaction and development of eutaxitic structure; the second associated with fotding and development of cleavage. Variations in both deformations with height above the base of the ignimbrite sheet are found, which enable the volcanic and structural history of the ignimbrite sheet to be more fully understood.
INTRODUCTION
The Llwvd Mawr Innimbrite crops out over an area of about 22 km* in western Caernarvonshire, North Wales (Fig. 1). The degree of exposure is excellent in the northwest, north and east, but in the southwest much of the ignimbrite is overlain by, and concealed beneath, a thick drift cover. Continuous exposures through more than 300 m of bare rock can be examined in Cwm Dulyn, Cwm Silin and along part of the northern and eastern margins of the ign~brite sheet. The ignimbrite overlies slates of Llanvirnian age, but the upper contact is everywhere against drift. Mapping of the poorly exposed country to the southwest around Llanystumdwy suggests, but does not prove, that the ignimbrite is mid-Caradocian in age (Roberts, 1967, p. 376). It may correlate with either or both of the Pitt’s Head Ignimbrite flows exposed 5 km to the east on Moe1 Hebog. The rock is a pumice-lapilli, crystal-victric tuff. It is rhyolitic in composition and potassium-rich throughout. Four zones have been recognised on the basis of welding deformation of shards (Roberts, 1969, p. 345), viz. IV. zone of complete sintering (II. parataxitic zone eutaxitic zone II. I. non-welded basal zone. Since the highest rock exposed is still in the zone of complete sintering it follows that an unknown thickness of the flow has been removed by erosion. At least 700 m remain at the present day. Tecto~ophysics,
12 (1971)
283-306
284
B.ROBERTSAND
A.W.B.SIDDANS
Various lines of evidence have been described (Roberts, 1969, pp. 338-347) which indicate that the sheet is a single cooling unit. One such line of evidence was the result of a two-dimensional study of the deformation of the pumice lapilli. The study was carried out on material from Cwm Silin, where two levelled traverses were made, and on material from Craig-y-garn, where a single traverse was made. Using an analysis of variance technique it was shown at Cwm Silin that pumice lapilli underwent progressive increase in distortion with height above the base of the sheet; but that at a height of about 60 m above the base the upward increase in distortion was interrupted and thereafter resumed. It was inferred from this anomaly that a still hot initial flow, some 60 m thick, was rapidly overlain by a second flow, after which the two flows cooled together. At the time the two-dimensional study was made it was not thought possible to deal simultaneously with both the deformation due to welding and the deformation associated with subsequent folding and development of cleavage. Because of this the tectonic deformation was ignored. Work on New Zealand and North American ignitnbrites of Tertiary and Quaternary ages indicates that the. welding process is accompanied by compaction and a reduction in volume. Quantitative evidence is supplied by systematic variations in the results of density and porosity measurements made within individual flows.Thus Martin (1959, p. 397) in a review of field and petrographic characteristics of American and New Zealand ignimbrites states that for heterolithic ignimbrites the specific gravity ranges from 1.4 in the nonwelded basal and upper zones to 2.4 in the intensely welded lithoidal zones. Ross and Smith (1961, p. 46) quote the specific gravity of glassy, intensely welded, rhyolitic tuffs as ranging from 2.34 to 2.40. Smith (1960, p. 825) states that compactibility is related to bulk porosity and therefore to the ratio of pumice to solid material. An accumulation of shards has an initial porosity of about 50% and rhyolitic pumice about 70%; most rhyolitic lapilli tuffs should therefore be expected to have an initial porosity of 50-60%. The Llwyd Mawr Ignimbrite has suffered welding, devitrification and, subsequently, deformation associated with cleavage formation. The basal non-welded zone has also been silicified and patchily cemented with carbonates. As a result of these post-welding events. density and porosity measurements are of little significance to a compaction study. Nevertheless the rocks still show abundant evidence that compaction and a reduction in volume took place during welding. Thus shards can be seen under the microscope to have been moulded around feldspar crystals and that generally, in areas between such crystals, the shards have been compacted into a planar eutaxitic structure devoid of any small-scale buckling (Fig. 2). This suggests compaction was unaccompanied by any appreciable lateral elongation, but rather was accompanied by a decrease in volume. Again, in the basal nonwelded zone, the pumice lapilli are vesicular. In the eutaxitic, parataxitic and completely sintered zones the pumice lapilli are devoid of vesicles and the lapilli are now represented by a very much coarser grained crystalline aggregate than the matrix (Fig. 3). It has been suggested by Ross and Smith (1961) that resolution of the volatiles contained in the vesicles in the pumice lapilli occurred during welding thus lowering the viscosity and leading to the growth of larger crystals than in the surrounding matrix. Such re-solution of gas into collapsing pumice again implies a decrease in volume during welding. The ignimbrite sheet now occupies the core of a large periclinal syncline, the Llwyd Mawr Syncline, of Caledonian age (Roberts, 1967, pp. 369-390). Congruous periclinal folds
FABRIC
STUDIES
IN NORTH
WALES
Fig. 1. Position and extent of the Llwyd Mawr Ignimbrite. I = drift; 2 = Llwyd Mawr Ignimbrite; 3 = Llanvirnian Slates; 4 = tuff filling vent; 5 = intrusive
285
rocks.
of lesser magnitude can be distinguished within the major structure, and the axial traces of the congruous folds can be traced for distances of 1.5 - 2.5 km. The folding was not intense, fold hinges are rounded and the limbs are curved, enclosing interlimb angles of about 90”. On the other hand the rocks have taken a moderate to strong, vertical to subvertical cleavage of Caledonoid trend (southwest to northeast). In lower parts of the ignimbrite sheet the cleavage is a true slaty cleavage, which passes upwards into a fracture cleavage (Fig. 4 and 5). The periclinal nature of Caledonian folding in North Wales has been noted by Shackleton (1959, p. 221) and by Roberts (1967, pp. 384-386). With few exceptions, e.g., Ghosh and Ramberg (1968, pp. 89-105), and Ghosh (1970, pp. 559-569) structural geologists Tectonophysics,
12 (1971) 283-306
286
Fig. 2. Photomicrograph Differential compaction
B. ROBERTS
AND A.W.B. SIDDANS
of welded tuff, Llwyd Mawr. A prominent eutaxitic texture is developed. of the matrix around the large feldspar crystal is shown. Plane polarised light.
have to date concentrated on the two-dimensional, plane-strain problems of cylindrical fold studies. The traverse through the Llwyd Mawr lgnimbrite discussed in this paper is part of a more general study of some periclinal folds in North Wales being undertaken by the authors, other areas of interest being the Yr Arddu Syncline and the Mymbyr Pericline. In all these areas structural, vulcanological, stratigraphical and sedimentological problems are intimately related. PROBLEMS
As a result of methods developed in the last few years and which are fully discussed in the next section, it was thought desirable to attempt the complete three-dimensional fabric analysis for a traverse through the ignimbrite sheet. A number of questions needed answering: (1) Was it possible to use deformed pumice lapilli to measure finite tectonic strain states at successive levels within the ignimbrite sheet? (2) What was the amount of deformation at successive levels within the ignimbrite sheet due to welding and compaction?
FABRIC STUDIES IN NORTH WALES
Fig. 3. Photomicrograph of a coarse grained, flattened, pumice lapillus in a fine-gained glass shards and dust. Llwyd Mawr. Crossed polarisers.
287
matrix of former
(3) Was it possible to recognize the two flows which the results of the earlier two-dirnensional analysis suggested were present? (4) Was there a directional component developed at any level in the ignimbrite sheet during welding deformation? (5) What was the theoretical thickness of the components of the cooling unit immediately after emplacement and prior to deformation by welding and compaction? (6) What was the thickness of the ignimbrite sheet after welding and compaction but prior to tectonic deformation’? (7) Did the degree of welding control the subsequent tectonic deformation and deveiopment of cleavage? A levelled traverse (Fig. 6A and B) was therefore made through more than 2 15 m of the ignimbrite sheet, midway between the traverses made previously on the West Wall and Back Wall of Cwm Silin (Roberts, 1969, p. 340). Large oriented specimens were collected through the sheet at irregular intervals ranging up to 30.48 m. Exposure was continuous throughout the length of the traverse.
Tectonophysics,
12 (1971)
283-306
288
B. ROBERTS AND A.W.B. SIDDANS
Fig. 4. Polished surface of the non-welded basal tuff (specimen 1) cut normal to the slatey cleavage.
ANALYSIS TECHNIQUES
The effects of tectonic deformation upon ellipsoidal objects have been discussed in several recent publications (Ramsay, 1967, pp. 202-226; Gay, 1968a, b; Dunnet, 1969a, b; Elliott, 1970; Dunnet and Siddans, 1971). Throughout the following discussion it is assumed that there was no ductility contrast between particles and matrix, that the particles originally approximated to ellipsoidal shapes, and that on the scale of each specimen deformation was homogeneous. Criteria for assessing the validity of these assumptions are discussed below. As an example of the techniques used the complete analysis of specimen 5 is presented in the text below. Terms used in the text Two-dimensional analysis :axial ratio of ellipse in deformed state. Rf : axial ratio of ellipse in undeformed state. Ri : angle between ellipse long axis and maximum @ in deformed state. e : angle between ellipse long axis and maximum in undeformed state.
principal extension
direction
principal extension
direction
289
FABRIC STUDIES IN NORTH WALES
Fig. 5. Polished surface of strongly welded tuff (specimen 16) cut normal to the fracture cleavage.
RS A;, A;
: finite strain ratio. : reciprocal quadratic elongations extension directions.
along maximum
and minimum
principal
Three-dimensional analysis : section planes in which polished surfaces were cut, in deformed orientation. A:B:C’ : section planes in which polished surfaces were cut, restored to undeformed ARC orientation, : deviator+ strain ratios in sections A : B.1 C 1 Ra, Rb, Rc Raffi Rbfr; Rcff: final ellipse axial ratios in sections A : B : C 1 Aiy, Biy, Ciy: lines of intersection ofA ; B ; C’on cleavage. : pitches of A_?y, Biy, Ciy on cleavage. $4 $6, @k axes of tectonic strain ellipsoid, X-Y-Z. X Y, Z I axes of final deformation ellipsoid, Xff-Yff-zfJ: Xffj Yffj Zff Xj~i Ypf, Zpf : axes of welding deformation ellipsoid, Xpf-Ypf-ZpJ 6 : pitch of X on cleavage. elir , 861, ec1 : pitches of final ellipse long axes on A : B ; C 1 8’al ^ 2 :pitchofZonA’-&ir.
Tectonophysics,
12 (1971) 283-306
B. ROBERTS
EXTENSIVE
:
tdetres
S.E.
m
IO0
t
:
90
SCREE
AND A.W.B. SIDDANS
\
hletres 0
d
N
.w.
B
1
Fig. 6. Levelled traverse on the Back Wall of Cwm Silin. A. Map showing vertical section along line of traverse.
sampling
localities.
B. Composite
FABRIC STUDIES IN NORTH WALES
641^z
e Cl -2 8’ ^ Axy $1
h;,X;>h;
291
: pitchofZonB’B’bl. : pitch of2 on C’- BCr. : pitch ofsliy on A ‘- Brir. : reciprocal quadratic elongation along Z. : reciprocal quadratic elongations along Aiy, Bky, Cky.
~H,Jal, kplj* hq ’ XC?
: reciprocal quadratic elongations along long and short axes of final ellipses inA:B:CI hiY1, ?I&, , A&; reciprocal quadratic elongations along long axes of ellipses in any mutually perpendicular planes xy, yz, zx. QA, Q& Qc : lines of intersection of A, B, C on plane Q. : line of intersection of planes P and Q. Qf’ : reciprocal quadratic elongation along QP. A’QP : reciprocal quadratic elongation along line of intersection of plane P on x kty cleavage. Two-dimensional
analysis
By using fundamental equations derived by Ramsay (1967, eq. 5.22, 5.27) Dunnet (1969a) was able to express the relationships between Ri, 8, RA $, Rs, and he described a graphical method for determination of the strain ratio and initial shape fabric, in sections through deformed aggregates of initially randomly oriented ellipsoidal objects. The Rf/$ data are plotted on ordinates @and log RJ and the resulting scatter diagram is compared with theoretical Rf/@ curves. A computer programme for generation of standard sets of Rf/@ curves was presented by Dunnet and Siddans (1971). This type of analysis has been extended to sections through some non-random sedimentary fabrics (Dunnet and Siddans, 1971). It was shown that in order to investigate the type of three-dimensional fabric from sections through deformed or undeformed aggregates of ellipsoidal objects, it is essential to determine the distribution of Rip and/or Rf/@ data in both ratio and orientation, and to determine the symmetry of these distributions with respect to the bedding and/or cleavage traces in the section plane. The characteristic types of Rip diagram for sections through planar, semi-planar, and imbricate fabrics were described (Dunnet and Siddans, 1971, fig. 3,4). In the case of deformed planar and semiplanar fabrics graphical or numerical methods for determining both the initial shape fabric and strain ratio were described, and a computer programme (programme STRANE) for the numerical method was presented. In these methods use was made of the symmetry properties of the Rip and Rf/@ data relative to the bedding and cleavage traces. It was noted that in the undeformed state the Rip data were symmetric about the bedding trace, whereas in the deformed state the Rf/@ data were asymmetric to both the cleavage and bedding traces. In this analysis of sections through the lapilli tuff, there was no line element directly comparable to the bedding trace in the fabrics discussed above. However, it was clear from the nature of the Rf/# data that in specimens from the eutaxitic zones of the tuff, the pretectonic shape fabrics of pumice lapilli were not random. Earlier studies (Roberts, 1969, pp. 340-342) indicated that this fabric was of a semi-planar type. Thus in the use of proTectoono~hysics, 12 (1971) 283-306
292
B. ROBERTS AND A.W.B. SIDDANS
gramme STRANE, in this anaiysis, successive values of ISYM3 (Dunnet and Siddans, 197 1, pp. 324 were used alone in assessing diagram symmetry during the ‘“unstraining” routine. The procedure followed was to cut two sections, A ‘and B ‘, normal to each other and both normal to the cleavage, through large oriented specimens. The Rf/G data for about 50 ellipses were measured, together with the pitch of the cleavage trace (which defined the maximum principal extension direction, # = O”, in the section) on both sections. These data were analysed using progarmnle STRANE, with assesses the symmetry of the ~~~~ data, and if they are symmetric restores them to maximum symmetry (Ri/B data). The subsequent procedure was determined by the output of programme STRANE at this stage. If both sections A ‘and R ‘gave symmetric Rf/@ data, it was inferred that the pre-tectonic shape fabric was randomly oriented. A third section, C ‘, was then cut parallel to the cleavage, so that A ‘,B ‘and C’were mutually perpendicular. If both sections ,4 ‘and B ‘did not give symmetric Rf/$ data it was inferred that the pre-tectonic shape fabric was not randomly oriented. A third section, C ‘, was cut normal to the cleavage, to approximately bisect the angle between A ‘and B ‘. In both cases the ~~~~ data for the third section, and the pitch of the cleavage trace if necessary, were measured. If the specimen had a nonrandom initial shape fabric these data were analysed using programme STRANE. The best fitting standard Rf/@ curves were drawn on the Rf/@ and restored Ri/B diagrams, and the mean Rf/@ and mean RiftI points so enclosed were obtained. In the case of specimen 5, face A ‘gave a symmetric Rf/$ diagram (Fig. 7) faces B ‘and C’gave asymmetric Rf/ci, diagrams (Fig. 8A, B). The symmetric Riji3 diagrams for faces B and C are presented in Fig. 8C, D. For all specimens with sections giving asymmetric Rf/# diagrams it was found that the restored Rile diagrams were highly symmetric, and that standard Rf/# curves could be readily fitted. This implies that the semi-planar nature of the pre-tectonic shape fabric of the pumice lapilli was due to an earlier deformation, viz. that associated with welding and compaction of the ignimbrite and here called the welding deformation, of a random shape fabric (cf. Dunnet and Siddans, 1971, example 3). Thus the deformation history of the ignimbrite sheet consists of two discrete finite phases; the welding deformation, with associated development of eutaxitic structure; and the tectonic deformation, with associated development of cleavage. Since these deformations were not coaxial they result in a final deformation ellipsoid that is oblique to both the welding deformation and tectonic deformation ellipsoids. The two-dimensional data, mean Rf/$ point, mean Ri/O point, and Rs, from each of the three sections may be combined to give the axial ratios and orientations of each of the three deformation ellipsoids for each specimen. In the case of the specimens with randomly oriented pre-tectonic shape fabrics, there was no welding deformation, and the Rf/~ data record only the effects of the tectonic deformation and the original shape fabric. Three-dimensional analysis The tectonic deformation ellipsoid Using two-dimensional data from the three surfaces A : B ‘, C’ it is possible to determine the strain ratio in the plane of the cleavage. A graphical method, in which the Mohr circle is constructed, is described by Ramsay (1967, pp. 79-81). ~ternatively the analytical
293
FABRIC STUDIES IN NORTH WALES
20 15
10
Rf
2
,600
-300
00
300
60’
0
Fig. 7. Rf/@ data for specimen 5 section A,
method given below may be used, and has been programmed (programme SOSC, written in FORTRAN IV for the CDC6600, listings are available). The nature of the problem is illustrated stereographically in Fig. 9. Since slaty cleavage is parallel to the XY-plane of the finite tectonic strain ellipsoid, sections A ‘,B : C ‘intersect in a line that is parallel to the Z-axis of the strain ellipsoid. This direction is the common minimum principal extension direction in all three sections. Thus Xi, Ad, hi, expressed in terms of h ; are l/Ra2, ~/HI’, l/Rc* respectively. An equation relating the reciprocal quadratic elongation, h ‘, in a direction 0 ‘relative to the maximum principal extension direction, to hr’ and Xi is given by Ramsay (1967, eq. 3.31): X’=h~cos2~‘+h~sin2B’
(1)
Using eq. 1 and the relationship
sin* + cos* = 1, it follows that:
Xi = Xi f (Xi - h;)sin’@
- 0.J
@I
Xi = Xi + (Xi - X;)sin*(s
- t?d)
(2b)
Xi = A; + (hi -- X;)sin’(s
- 0:)
(2c)
Taking these equations (Xi - hi): (X,’ - hJsin*(&
in pairs, 2e2b,
2b-2c,
- 6d) + (1: - ?$)sin2(6
~ec~o~o~~y~~cs, 12 (1971) 283-306
and equating the resulting expressions
- 13;) t (hi - ha)sin2(6 - e;) = 0
for
(3)
294
B. ROBERTS AND A.W.B. SIDDANS
A
00
20 15
-
10
-
c
ml R1/0:3
I)
5/69’
7 RI
5
.
4
-
3
-
2 RS
t
I
I I
I
,,
C
300
0”
60° 6
900
1200
Fig. 8. A. Rf/@ data for specimen 5 section B. B. Rf/O data for specimen C. C. Restored Ri/tl data for section B after removal of a strain ratio Rs = 1.80. D. Restored Ri/8 data for specimen 5 section C after removal of a strain ratio Rs = 2.45.
Defining
known
constants:
terms in eq. 3, and collecting
C,=ha-hd,
C2=Xd-hd,
c,
=
c,
c02e;
+
terms are defined:
czcO?e;
and expanding
the sin’
like terms in 6:
Cqsin2S - CssinS cosS + C6cos2S = 0 where known constant
C,=hd-$,
+
c3c0s2e;
C5 =C,sin2e{+C2sin2e~+C3sin2e~
(4)
295
FABRIC STUDIES IN NORTH WALES
Fig. 9. Stereographic projection, lower hemisphere, equal area, of the three sections A : B : C ‘in the deformed state, and A, B, C after removal of the tectonic strain X/Y/Z = 2.49/1.57/1.00.
C, = C1sin26d
t Czsin26;
Fig. 10. Specimen 5 final fabric analysis; Xff/Yff/Zff = 2.76/2.34/1.00.
+Cssin’ed
Dividing through eq. 4 by cos’ 6 : Cqtan26 -Cstan
S tCg=O
(5)
Eq. 5 has a general solution of the form: c5 ‘f&2
6 = tan-’
- 4 C&)f
2C4 Eq. 2a-2b give an expression: x;
_
A;
=
hi - hi sin2(6-$,J
- sin*(&+J
(6)
(7)
Substituting the appropriate value of S into eq. 7, the resulting value of (&A;) may be substituted into eq. 2a to give the value of Xr’. Finally A; is obtained by substituting values of (hi-h,‘) and Xr’ into: x; = (A; -A;)+h;
(8)
The tectonic strain ratio, X/Y/Z, is thus (1 /A;)$ / (1 /A;)* / 1, the pitch of X on the cleavage is 6, and the minimum principal extension direction is parallel to Z, and the tectonic strain ellipsoid is completely specified.
Tectonophysics,
12 (1971) 283-306
296
B. ROBERTS
AND A.W.B. SIDDANS
In the case of those specimens with a randomly oriented pre-tectonic shape fabric, i.e., those specimens with no welding deformation, the strain ratios for the three mutually perpendicular sections A : B : C ‘may be combined using the method given by Ramsay (1967, pp. 142-147, 199-200). Using this method there are two independent ways of computing XL in terms of h&i, which provides a check on the internal consistency of the two-dimensional data. This can be expressed as the percentage level of internal inconsistency by computing the value of:
1A,‘(‘) ~ A,‘@)1 x 1oo X’(l) z
(9)
+x’(z) z
Similarly two values of “4 in terms of h&r, and two values of A; in terms of h,‘, 1 can be computed, together with their internal inconsistency levels. Thus there are six independent ways of obtaining the strain ellipsoid, which provides a check on the accuracy of the determinations. This method has been programmed (programme PASE, written in FORTRAN IV for the CDC6600, listings are available), to perform all six determinations, select the pair that minimises the internal inconsistency level, and compute the result on the basis of the mean vaiue of the corresponding reciprocal quadratic elongation The final deformation ellipsoid Ramsay (1967, pp. 147-148) describes a general method for determining ellipsoid ratios and orientations from two-dimensional data on three oblique planes. A numerical solution is given below which has been programmed (programme FOSC, written in FORTRAN IV for the CDC6600, listings are available). The nature of the problem is illustrated stereographically in Fig. 10. In the determination of this ellipsoid the mean Rf/Q points from the three sections A ‘, B ‘, C’are combined. Since A ‘and B ‘are normal both to the cleavage and to each other the problem is in two parts; firstly to compute the two-dimensional component in a plane parallel to the cleavage, secondly to combine that component with the two-dimensional data from sections A ‘and B ‘. Since 2 is not in general parallel to Zff, it is necessary to derive expressions for the reciprocal quadratic elongations along Z, A~JJ, B$J, C’x?yinvolving only known angles and ratios, and a single unknown term. This may be done by setting up equations similar to those of Ramsay (1967, eq. 5.7 through 5.17). Using eq. 1 for each section, expressions for h; and Xa’>,, >c can be written, e.g., for section A ‘z h; = hiI cos2i3~, ^ z + hi2 sinZeal ha = h,‘, cos26~l ^ Axy+hi2 Since Bal - z = 90” f 0,i
sinZeal
-z
(10)
^ Axy
(11)
^ Axy :
sin20;l
- z =co?e;,
^
c0s2e;l
- z =sin20;r
.
AXY
AMY
Thus eq. 10 and 11 may be written:
x; = hi1 (cos2e
’
al
^z + Ra& sin’@;i
- ,)
= h&c;
(12)
'91
E~ABR~CSTU~IESINNORTH~~ALES ha = hi1 (sin’ea,
^ z +R~&.cos~@~~ , z)
= h.&C,
(13)
= h&C;
(14)
= x&c;
(!5)
Similarly for sections B ‘and C ‘I AL = Xi, (cos’O{ hi = hi,
(sin2Bd
1
^ z +Rb& sin2BrJi
I ^ 2 +RbZffcos%&
- %)
* z)
hl= hli (cos2@& _ z +Rc&sin28di
* ,)
= “d, c;
(16)
Ai = A& (sin*0&
I z)
= xpg
(17)
^ z + Rc&cos2t3dl
The terms in parentheses in eq. 12 - 17 are known constant terms, say Ci’ - CL respectively. Eq. 12, 14 and 16 are all expressions for A;, thus halCr’ = hb, C; = AL, C;, and hence: xi = ?Lpcq/c;
(18)
x; = x;* c;cg/c;
(1”))
Eq. 13, 18 and 19 express Xi, Xi, h: all in terms of known constant terms and a single unknown term ha 1. Using these values, together with ea, 0;, 0; in programme SOSC, the ellipse ratio and orientation in the plane of the cleavage is determined. Then the ellipse ratios and orientations for sections A 1B ‘and in the plane of the cleavage may be combined to give the final deformation ellipsoid axial ratio, Xff/Yff/Zff and orientation, by using programme PASE. Tt%ewelding deformation ellipsoid Determination of the welding deformation ellipsoid is complicated by the necessity to restore the section planes A : B : C’to their pre-tectonic orientations A, B, C (Fig. 9). The simple graphical method given by Ramsay (1967, pp. 130-l 32, using fig. 4.6) may be used: alternatively, as written into programme SOSC, the equation relating the orientation of line elements before and after deformation (Ramsay, 1967, eq. 3.34) may be used: tan 0 =Rs.tan
8’
(20)
where B and 8’ are the angles between the line element and the maximum principal extension direction before and after deformation. When the three sections are restored to their pretectonic orientations A and B are, in general, no longer normal to each other, though both are still normal to the cleavage. The nature of the problem is illustrated stereographically in Fig. 11. As in the case of the final deformation ellipsoid, by using programme FOSC the ellipse ratio in the plane of the cleavage is determined, together with its orientation. It is now necessary to specify another plane, F, normal to both the cleavage and A, and to determine the ellipse ratio and orientation in it. In order to do this a further plane, Q, is specified, and using eq. 1 on each of the restored sections A, B, C, the reciprocal quadratic elongations along QA, QB, QC are determined, and hence the ellipse ratio and orientation in Q is obtained. Again using eq. 1 the reciprocal quadratic elongation along QP is determined. If the reciprocal quadratic elongation alongPxy is obtained from the two-dimensional data in the Tecto~o~hysics, 12 (1971) 283-306
298
Fig. 11. Specimen 5 pre-tectonic fabric analysis;
xpfWpfjzpf = 7.82/2.89/1.00.
B. ROBERTS AND A.W.B. SIDDANS
Fig. 12. Stereographic projection, lower hemisphere, equal area, showing the geometric relations between the orientations of the tectonic, welding, and final deformation ellipsoids.
cleavage plane, using eq. 1, then in plane P hk, h&, and X&v are known, and the ellipse ratio and orientation in plane P may be obtained, as outlined above. An option has been written into progarmme FOSC to perform these computations once the planes P and Q, and the necessary angular relations, are specified. Using the ellipse ratios and orientations on planes A, P and in the cleavage, the axial ratio, Xpf/Ypf/Zpf, and orientation of the welding deformation ellipsoid are obtained using programme PASE. Assessment of validity of results
Criteria for assessing the validity of the results are available. This is very necessary in view of the fundamental assumptions made at the outset of this analysis, and the considerable scope for compounding inaccuracies during the successive computations. In the case of those specimens with no welding deformation, the only check required is that on the tectonic deformation ellipsoid. This is obtained from the output of programme PASE. Low internal inconsistency levels imply accurate results and justify the initial assumptions. A rapid visual estimate of the accuracy of the results may be obtained by plotting all six results on a deformation plot of a=X/Y against b=Y/Z (Flinn, 1962). In the case of specimens with a semi-planar pre-tectonic shape fabric, the three-dimensional strain analysis obtained from programme SOSC is a unique result. However, the welding deformation and final deformation ellipsoids were ultimately obtained using programme PASE. If the internal inconsistency levels for these ellipsoids are low, the implication is that the initial assumptions and results are valid. A totally independent check on the computations and assumptions is available. Knowing the tectonic strain ellipsoid, and either the final deformation or welding deformation ellip-
FABRIC STUDIES IN NORTH WALES
299
soid, it is a simple exercise in Cartesian tensors to compute the unknown ellipsoid. Dunnet (1969b, pp. 176-l 82, 3 14-3 19) discusses the deformation of elliptical or ellipsoidal shapes, and derives the relationship:
D=B.R.A.RT
(21)
where A is the initial diagonalised ellipsoid shape tensor; B is the diagonalised tensor of strain; R is the rotation matrix of direction cosines from the reference frame of the strain ellipsoid to the initial ellipsoid shape; R T is the transpose of R ;D is the final ellipsoidal shape tensor referred to the reference frame of the strain ellipsoid. A computer programme is presented by Dunnet (1969b, pp. 400-408) to perform the matrix algebra implied in eq. 2 1, and to determine the eigenvalues and eigenvectors of the final tensor D. These checks have been applied in every case, and it has been concluded that the initial assumptions are justified and that the results obtained are valid. The results for specimen 5 are summarised in Fig. 12. RESULTS
The results of the primary fabric analyses are presented in Table I. It is important to remember that the axial ratio of the pre-tectonic fabric is not in general the axial ratio of lapilli, but the axial ratio of the welding deformation ellipsoid. Of the various parameters available to describe the geometry of the welding deformation ellipsoid two have been chosen, and their variation with height above the base of the ignimbrite sheet plotted in Fig. 13 and 14. To describe the shape of the ellipsoid the k-parameter of Flinn (1962) is used:
kJv-
v/z -
1). 1)
k may vary from zero to infinity; its significance when there is no volume change may be summarised: k = 0. uniaxial oblate ellipsoids-pure flattening; k = 0 - 1, flattening type TABLE
I
Pre-tectonic fabric analyses
Tectonophysics,
12 (1971) 283-306
300
B. ROBERTS AND A.W.B. SIDDANS
175
105 . I
150 1
bo I(
I 125
0
75
I:
I
,
1.0
I.2
I
0.0 otAa,e
0.2
0.4
0.6
0.8 Z=Y y-z
J
# 1.1
1.6 prolate
m
z
K
Fig. 13. Graph of k-values of welding deformation ellipsoids it successive heights in the ignimbrite sheet. ellipsoids; k = 1, plane-strain ellipsoids; k = 1- infinity, constriction type ellipsoids; k = in finity, uniaxial prolate ellipsoids-pure constriction. Since the welding deformation ellipsoids have k-values in the range 0 - 1, some measure of the amount of flattening is required. The simplest parameter to visualize which expresses this is the percentage shortening of the Z-axis of the ellipsoid. The radius, r, of the sphere of equivalent volume to the ellipsoid is computed, then the percentage flattening is expressed: percentage
flattening
=q
X 100
In view of the uniformity amongst the data on porosity and density available for Tertiary and Quaternary rhyolitic pumice-lapilli tuffs, it may be possible to apply this data to the Llwyd Mawr Ignimbrite and to use estimates of the compaction from petrographic evidence as a control. The porosity data of Smith (1960) suggests a reduction in volume
301
FABRIC STUDIES fN NORTH WALES
z
Zone of complete
sintering
IV 200
120
I
----__________-_______.
I
105
175 ~
I
i
150
90
>
x
1 125
75
Parataxitic
zone
Iti
I
x
t
100
-I
-_--___
-w______---__-____-
75-L
x
-_-_-_
-
-
‘-
of pre-existing Eutaxitic
50
30
II
x
;
25 ~ !L_________________________---__, 0
I
-i
0
,I
, 20
40
60
flow
zone
80
Basal
non-welded
zone
I
100
Fig. 14. Graph of percentage flattening of welding deformation ellipsoids at successive heights in the ignimbrite sheet.
in zones III and IV the Llwyd Mawr Ignimbrite of the order of 40%. The specific gravity data of Ross and Smith (196 1) suggests a volume reduction for zones III and IV of 42%. Petrographic evidence (viz., the extent to which shards have been deformed around feldspar crystals) suggests volume decreases of 0% in zone I, 30% in zone II and 50% in zones III and IV. Thus it may be possible in Fig. 14. to superimpose upon the percentage flattening axis an additions scale representing volume decrease associated with welding, such that 0 - 83% percentage flattening corresponds with 0 - 50 or 60% volume decrease. On the graphs of k and percentage flattening against height above the base of the ignimbrite sheet (Fig. 13 and 14), the four textural zones recognised by Roberts (1969) are indicated. Zone I. Within the basal non-welded zone specimens 1 -- 3 show that there was no welding defo~ation at all. The final lapilli shapes and orientations record only their prewelding variations as modified by the tectonic finite strain. Tectonophysks, 12 (1971) 283-306
302
B. ROBERTS AND A.W.B. SIDDANS
Zone II. Within the eutaxitic zone there is a marked rapid upwards increase in the percentage flattening form 0 - 64lS.%, up to a height of some 65.23 m. At 76.06 m there is a marked reduction in this parameter to 48l/LL%,followed by a further upwards increase to 54% near the top of this zone at 87.48 m. At lower levels in the zone k-values approach 1, and decrease upwards to 0.42 at 65.23 m. At 67.06 m there is a marked increase in this parameter, which again approaches 1, followed by a further upward decrease to 0 near the top of the eutaxitic zone at 87.48 m. Zones ZZZ and IV. Within the parataxitic zone and the lower parts of the zone of complete sintering there is a general upwards increase in the percentage flattening from 64’/L%at 117.96 m to 83% at 218.24 m. Throughout these zones the k-value is always low, varying only from 0 - 0.2. The results of the tectonic strain analyses are presented in Table II, and the variation of the k-value of the tectonic strain ellipsoid with height above the base of the ignimbrite sheet is plotted in Fig. 1.5. There is a clear trend showing the k-value of this ellipsoid increasing upwards from 0.16 at the base of the non-welded basal zone to 11.35 up in the zone of complete sintering. There is, however, a reversal of this trend at the 67.06 m level, where this parameter is anomalously low. There is also a marked increase in the k-value of this ellipsoid from 1.54 to 8.35 between the 159.11 and 180.08 m levels. This occurs at the top of the parataxitic zone. DISCUSSION
Within the eutaxitic zone, at the 67.07 m level, there are marked reversals in the upward trends of both parameters of the welding deformation ellipsoid, the percentage flattening is anomalously low and the k-value anomalouly high. In the two-dimensional analysis of lapilli axial ratios (Roberts, 1969, fig. 74b) there was recorded an anomalously low distortion index at this level, which contrasted with the clear tendency to increase TABLE II Tectonic strain analyses
Axial
x:y:z
ratio
Cleavage strike,
dip
PIllWe X
K
Internal Inconsistency
Value
level
10 03 80
(Xl
303
FABRIC STUDIES IN NORTH WALES
7 I
225
zone IV
I
Zone
III
125
100
-------------------------------.
25
Fig. 15. Graph of k-values of tectonic strain ellipsoids at successive heights in the ignimbrite sheet.
upwards. Taken together these anomalies support the suggestion of Roberts (1969, p. 344) that this level marks the base of another flow emplaced on the still hot surface of the flow beneath, and that they then both cooled together. This conclusion is further supported by the low k-value of the tectonic strain ellipsoid at this-level; and by geochemical studies being undertaken by G. Hendry on these samples, who has found changes in Si, Al, Ca, Fe, Mn, Ti, P, S, Ba, Y, Ce, Th, and Pb at this level (personal communication, 1971). The high k-values of the welding deformation ellipsoids below the 67.07 m level indicate a directional component to the extension accompanying flattening. These are associated with relatively high dips of the pre-tectonic eutaxitic structure. The X-axes of these ellipsoids plunge at low angles to the east and southeast quadrant, and at higher angles to the south and southwest quadrant. Possibly these represent the sub-ignimbrite palaeoslope, the lower flow having accumulated on a southerly sloping surface in the region of Cwm Silin, whereas the upper flow accumulated on the more level hot surface of the lower flow. Tectonophysics,
12
(1971) 283-306
304
B. ROBERTS
AND A.W.B. SIDDANS
If it is assumed that the second ignimbrite sheet was emplaced in a single act, i.e., as a geologically instantaneous event, and that this was followed by compaction due to welding, then it is possible to compute the pre-welding thickness of the flow. A minimum value for this figure is of the order of 3,000 m which, if the assumption is valid, implies that the constraining walls were at least 3,000 m high. It seems unlikely that a Caradocian topographic depression exceeding 3,000 m in depth could have existed: certainly there is no corroborative evidence elsewhere in Caernarvonshire. It is just possible that caldera subsidence concurrent with eruption could have given the necessary depth. The probalility is, however, that the assumption is wrong. Instead it is suggested that the accumulation of the ignimbrite occured as the result of a series of successive eruptions, each pulse being separated from the next by an interval of hours or days, because there was no dectectable cooling during this time. (Peterson (1968, p. 222) has suggested a similar mechanism to account for a single cooling unit 610 m thick at Superior, Ariz.) Welding and compaction probably began rmmediately after the accumulation of the material produced by the first pulse, and continued with each successive pulse, so that it seems likely therefore that welding and compaction is geologically a very rapid process. It is clear that the anomalies at 67.06 m above the base indicate that a significant period free from eruption elapsed after emplacement of the first unit, prior to the rapid pulses which led to the emplacement of the second unit. Both units then continued to cool together. Interpretation of the tectonic strain analyses for this traverse alone is difficult, since both major and minor structures in the area are non-cylindrical. Work currently in progress by one of the authors (A.W.B.S.), using thin-plate theory to investigate the nature of periclinal buckling instabilities, and a finite element analysis technique to investigate their subsequent development, suggests that on a traverse through a periclinal syncline, such as has been described above, the k-values of the tectonic strain ellipsoids should tend to increase towards the core of the structure, within the stiff buckling plate, in the general way that they are seen to do so. Quantitative comparisons between the naive numerical model and observed structures are not possible to date. Indeed, the pre-tectonic ignimbrite sheet must have been a highly anisotropic plate by virtue of its welding deformation, with its well-developed systems of cooling joints (Roberts, 1969, pp. 346-349), so that at the present time a realistic numerical model is impossible to approach. Intuitively one suspects that the pre-tectonic fabric of the plate controlled each tectonic strain increment. The anomalous sudden increase in the k-value of the tectonic strain ellipsoid at the top of the parataxitic zone is also accompanied by geochemical changes in Si, Al, Ca, K, Na, P, Sr, Zr, Ba, Y and Ce (G. Hendry, personal communication, 1971). The reason for the change in tectonic strain is not understood, but there is need for further traverses and collections to be made. Should such traverses reveal similar tectonic anomalies at this level, problems of strain compatability will arise. A bulk figure for the tectonic thickening of the ignimbrite sheet is x S/3; hence the present day remanent thickness of 700 m has been produced from some 420 m of welded tuff. The nature of the cleavage associated with the foldingvaries upwards through the sheet. At lower levels, up to 22.16 m, a slaty cleavage is developed (Fig. 2). Upwards this passes into a fracture cleavage resembling a system of closely spaced cracks in the rock (Fig. 3). The exact transition is difficult to define, but specimen 4; from the 22.16 m level, with a welding deformation k-value of 0.92, a welding percentage flattening of 5%, and a tectonic
FABRIC STUDIES IN NORTH WALES
305
strain k-value of 0.18 has a slaty cleavage, whereas specimen 5, from the 44.50 m level, with a welding deformation k-value of 0.90, a welding percentage flattening of 64M%, and a tectonic strain &value of 1.03, has a fracture cleavage. The inference is that both types of cleavage have exactly the same mechanical significance; the one passes into the other, but that the resulting structure is controlled by the pre-tectonic fabric of the rock. Further discussion of these phenomena awaits the outcome of detailed petrofabric studies using the pole-figure goniometer currently being undertaken by one of the authors (A.W.B.S.). ACKNOWLEDGEMENTS
B. Roberts gratefully acknowledges help from the Central Research Fund of the University of London in assisting with fieldwork expenses during research on Llwyd Mawr. A.W.B. Siddans made the deformation analyses during the tenure of a Natural Environment Research Council Research Studentship. He is grateful to Professor J.G. Ramsay, under whose supe~~sion his research is being undertaken, and to Dr. D. Dunnet for their interest and encouragement. The writers are grateful to Dr. G. Hendry for making the results of his geochemical studies available to them, and to Professor Ramsay, Dr. Dunnet and Dr. R.S. Fiske for critically reading the manuscript.
REFERENCES Dunnet, D., 1969a. A technique of finite strain analysis using eiliptieal particles. ~ecr~~~~~~$~cs, 7: 117-136. Dunnet, D., 196913.Deformation in the Palaeozoic Rocks of Inglesiente, S. W. Sardinia. Thesis, Univ. London, London, 412 pp. Dunnet, D. and Siddans, A.W.B., 1971. Non-random sedimentary fabrics and their modification by strain. Tectonophysics, 12: 307-325. Elliott, D., 1970. Determination of finite strain and initial shape from deformed elliptical objects. Geol. Sot. Am. Bull., 81: 2221-2236. Flimt, D., 1962. On folding during ~ree~mension~ progressive deformation. Q. J. Geot. Sot. London, 118: 385-428. Gay, N.C., 1968a. Pure shear and simpfe shear deformation of inhomogeneous viscous fluids, 1. Theory. Tectonophysics,
5: 21 l-234.
Gay, N.C., 1968b. Pure shear and simple shear deformation of inhomogeneous viscous fluids, 2. The determination of the toal finite strain in a rock from deformed objects such as deformed pebbles. Tectonophysics, 5: 315-339. Ghosh, S.K. and Ramberg, H., 1968. Buckling experiments on intersecting fold patterns. Tectonophysics, 5: 89-105. Ghosh, SK., 1970. A theoretical study of intersecting fold patterns. Tectonophys~cs, 9: 559-569. Martin, R.C., 1959. Some field and petrographic features of American and New Zealand i~imbrites, N.Z.J. Geol. Ceophys., 2: 394-411. Peterson, D.W., 1968. Zoned ash-flow sheet in the region around Superior, Arizona. In: Southern Arizona Guidebook III. Ariz. Geol. Sot., PP. 215-222. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y., 568 pp. Roberts, B., 1967. Succession and structure in the Llwyd Mawr Syncline, Caernarvonshire, North Wales. Geol. J., 5: 369-390. Roberts, B., 1969. The Llwyd Mawr ignimbrite and its associated volcanic rocks. In: &Wood (Editor), The Pre-Cambrian and Lower Palaeozoic Rocks of Wales. Univ. Wales Press, Cardiff, pp. 337-356. Tectonophysics,
12 (1971)
283-306
306
B. ROBERTS AND A.W.B. SIDDANS
Ross, C.S. and Smith, R.L., 1961. Ash-flow tuffs: their origin, geologic relations and identification. U.S. Geol. Surv., prof: Pap., 366: 81 pp. Shackleton, R.M., 1959. The stratigraphy of the Moe1 Hebog District between Snowdon and Tremadoc. Liverp. Manch. Geol. J., 2: 216-252.
Smith, R.L., 1960. Ash Flows. Bull. Geol. Sot. Am., 71: 795-842.
FABRIC
Company,
STUDIES
Amsterdam
IN THE LLWYD
CAERNARVONSHIRE, 5. ROBERTS
NORTH
in The Netherlands
MAWR IGNIMBRITE,
WALES
and A.W.B. SIDDANS
Geo1og.y Department, Geology Department, (Received
- Printed
March
Birkbeck College, London (Great Britain) Imperial College, London (Great Britain)
23, 1971)
ABSTRACT Roberts, B. and Siddans, A.W.B., North Wales. Tectonophysics,
1971. Fabric studies 12: 283-306.
in the Llwyd
Mawr Ignimbrite,
Caernarvonshire,
Recently developed techniques for the determination of strain are used to analyse the deformation of the LIwyd Mawr Ignimbrite. The deformation history consists of two discrete finite phases: the first associated with welding, compaction and development of eutaxitic structure; the second associated with fotding and development of cleavage. Variations in both deformations with height above the base of the ignimbrite sheet are found, which enable the volcanic and structural history of the ignimbrite sheet to be more fully understood.
INTRODUCTION
The Llwvd Mawr Innimbrite crops out over an area of about 22 km* in western Caernarvonshire, North Wales (Fig. 1). The degree of exposure is excellent in the northwest, north and east, but in the southwest much of the ignimbrite is overlain by, and concealed beneath, a thick drift cover. Continuous exposures through more than 300 m of bare rock can be examined in Cwm Dulyn, Cwm Silin and along part of the northern and eastern margins of the ign~brite sheet. The ignimbrite overlies slates of Llanvirnian age, but the upper contact is everywhere against drift. Mapping of the poorly exposed country to the southwest around Llanystumdwy suggests, but does not prove, that the ignimbrite is mid-Caradocian in age (Roberts, 1967, p. 376). It may correlate with either or both of the Pitt’s Head Ignimbrite flows exposed 5 km to the east on Moe1 Hebog. The rock is a pumice-lapilli, crystal-victric tuff. It is rhyolitic in composition and potassium-rich throughout. Four zones have been recognised on the basis of welding deformation of shards (Roberts, 1969, p. 345), viz. IV. zone of complete sintering (II. parataxitic zone eutaxitic zone II. I. non-welded basal zone. Since the highest rock exposed is still in the zone of complete sintering it follows that an unknown thickness of the flow has been removed by erosion. At least 700 m remain at the present day. Tecto~ophysics,
12 (1971)
283-306
284
B.ROBERTSAND
A.W.B.SIDDANS
Various lines of evidence have been described (Roberts, 1969, pp. 338-347) which indicate that the sheet is a single cooling unit. One such line of evidence was the result of a two-dimensional study of the deformation of the pumice lapilli. The study was carried out on material from Cwm Silin, where two levelled traverses were made, and on material from Craig-y-garn, where a single traverse was made. Using an analysis of variance technique it was shown at Cwm Silin that pumice lapilli underwent progressive increase in distortion with height above the base of the sheet; but that at a height of about 60 m above the base the upward increase in distortion was interrupted and thereafter resumed. It was inferred from this anomaly that a still hot initial flow, some 60 m thick, was rapidly overlain by a second flow, after which the two flows cooled together. At the time the two-dimensional study was made it was not thought possible to deal simultaneously with both the deformation due to welding and the deformation associated with subsequent folding and development of cleavage. Because of this the tectonic deformation was ignored. Work on New Zealand and North American ignitnbrites of Tertiary and Quaternary ages indicates that the. welding process is accompanied by compaction and a reduction in volume. Quantitative evidence is supplied by systematic variations in the results of density and porosity measurements made within individual flows.Thus Martin (1959, p. 397) in a review of field and petrographic characteristics of American and New Zealand ignimbrites states that for heterolithic ignimbrites the specific gravity ranges from 1.4 in the nonwelded basal and upper zones to 2.4 in the intensely welded lithoidal zones. Ross and Smith (1961, p. 46) quote the specific gravity of glassy, intensely welded, rhyolitic tuffs as ranging from 2.34 to 2.40. Smith (1960, p. 825) states that compactibility is related to bulk porosity and therefore to the ratio of pumice to solid material. An accumulation of shards has an initial porosity of about 50% and rhyolitic pumice about 70%; most rhyolitic lapilli tuffs should therefore be expected to have an initial porosity of 50-60%. The Llwyd Mawr Ignimbrite has suffered welding, devitrification and, subsequently, deformation associated with cleavage formation. The basal non-welded zone has also been silicified and patchily cemented with carbonates. As a result of these post-welding events. density and porosity measurements are of little significance to a compaction study. Nevertheless the rocks still show abundant evidence that compaction and a reduction in volume took place during welding. Thus shards can be seen under the microscope to have been moulded around feldspar crystals and that generally, in areas between such crystals, the shards have been compacted into a planar eutaxitic structure devoid of any small-scale buckling (Fig. 2). This suggests compaction was unaccompanied by any appreciable lateral elongation, but rather was accompanied by a decrease in volume. Again, in the basal nonwelded zone, the pumice lapilli are vesicular. In the eutaxitic, parataxitic and completely sintered zones the pumice lapilli are devoid of vesicles and the lapilli are now represented by a very much coarser grained crystalline aggregate than the matrix (Fig. 3). It has been suggested by Ross and Smith (1961) that resolution of the volatiles contained in the vesicles in the pumice lapilli occurred during welding thus lowering the viscosity and leading to the growth of larger crystals than in the surrounding matrix. Such re-solution of gas into collapsing pumice again implies a decrease in volume during welding. The ignimbrite sheet now occupies the core of a large periclinal syncline, the Llwyd Mawr Syncline, of Caledonian age (Roberts, 1967, pp. 369-390). Congruous periclinal folds
FABRIC
STUDIES
IN NORTH
WALES
Fig. 1. Position and extent of the Llwyd Mawr Ignimbrite. I = drift; 2 = Llwyd Mawr Ignimbrite; 3 = Llanvirnian Slates; 4 = tuff filling vent; 5 = intrusive
285
rocks.
of lesser magnitude can be distinguished within the major structure, and the axial traces of the congruous folds can be traced for distances of 1.5 - 2.5 km. The folding was not intense, fold hinges are rounded and the limbs are curved, enclosing interlimb angles of about 90”. On the other hand the rocks have taken a moderate to strong, vertical to subvertical cleavage of Caledonoid trend (southwest to northeast). In lower parts of the ignimbrite sheet the cleavage is a true slaty cleavage, which passes upwards into a fracture cleavage (Fig. 4 and 5). The periclinal nature of Caledonian folding in North Wales has been noted by Shackleton (1959, p. 221) and by Roberts (1967, pp. 384-386). With few exceptions, e.g., Ghosh and Ramberg (1968, pp. 89-105), and Ghosh (1970, pp. 559-569) structural geologists Tectonophysics,
12 (1971) 283-306
286
Fig. 2. Photomicrograph Differential compaction
B. ROBERTS
AND A.W.B. SIDDANS
of welded tuff, Llwyd Mawr. A prominent eutaxitic texture is developed. of the matrix around the large feldspar crystal is shown. Plane polarised light.
have to date concentrated on the two-dimensional, plane-strain problems of cylindrical fold studies. The traverse through the Llwyd Mawr lgnimbrite discussed in this paper is part of a more general study of some periclinal folds in North Wales being undertaken by the authors, other areas of interest being the Yr Arddu Syncline and the Mymbyr Pericline. In all these areas structural, vulcanological, stratigraphical and sedimentological problems are intimately related. PROBLEMS
As a result of methods developed in the last few years and which are fully discussed in the next section, it was thought desirable to attempt the complete three-dimensional fabric analysis for a traverse through the ignimbrite sheet. A number of questions needed answering: (1) Was it possible to use deformed pumice lapilli to measure finite tectonic strain states at successive levels within the ignimbrite sheet? (2) What was the amount of deformation at successive levels within the ignimbrite sheet due to welding and compaction?
FABRIC STUDIES IN NORTH WALES
Fig. 3. Photomicrograph of a coarse grained, flattened, pumice lapillus in a fine-gained glass shards and dust. Llwyd Mawr. Crossed polarisers.
287
matrix of former
(3) Was it possible to recognize the two flows which the results of the earlier two-dirnensional analysis suggested were present? (4) Was there a directional component developed at any level in the ignimbrite sheet during welding deformation? (5) What was the theoretical thickness of the components of the cooling unit immediately after emplacement and prior to deformation by welding and compaction? (6) What was the thickness of the ignimbrite sheet after welding and compaction but prior to tectonic deformation’? (7) Did the degree of welding control the subsequent tectonic deformation and deveiopment of cleavage? A levelled traverse (Fig. 6A and B) was therefore made through more than 2 15 m of the ignimbrite sheet, midway between the traverses made previously on the West Wall and Back Wall of Cwm Silin (Roberts, 1969, p. 340). Large oriented specimens were collected through the sheet at irregular intervals ranging up to 30.48 m. Exposure was continuous throughout the length of the traverse.
Tectonophysics,
12 (1971)
283-306
288
B. ROBERTS AND A.W.B. SIDDANS
Fig. 4. Polished surface of the non-welded basal tuff (specimen 1) cut normal to the slatey cleavage.
ANALYSIS TECHNIQUES
The effects of tectonic deformation upon ellipsoidal objects have been discussed in several recent publications (Ramsay, 1967, pp. 202-226; Gay, 1968a, b; Dunnet, 1969a, b; Elliott, 1970; Dunnet and Siddans, 1971). Throughout the following discussion it is assumed that there was no ductility contrast between particles and matrix, that the particles originally approximated to ellipsoidal shapes, and that on the scale of each specimen deformation was homogeneous. Criteria for assessing the validity of these assumptions are discussed below. As an example of the techniques used the complete analysis of specimen 5 is presented in the text below. Terms used in the text Two-dimensional analysis :axial ratio of ellipse in deformed state. Rf : axial ratio of ellipse in undeformed state. Ri : angle between ellipse long axis and maximum @ in deformed state. e : angle between ellipse long axis and maximum in undeformed state.
principal extension
direction
principal extension
direction
289
FABRIC STUDIES IN NORTH WALES
Fig. 5. Polished surface of strongly welded tuff (specimen 16) cut normal to the fracture cleavage.
RS A;, A;
: finite strain ratio. : reciprocal quadratic elongations extension directions.
along maximum
and minimum
principal
Three-dimensional analysis : section planes in which polished surfaces were cut, in deformed orientation. A:B:C’ : section planes in which polished surfaces were cut, restored to undeformed ARC orientation, : deviator+ strain ratios in sections A : B.1 C 1 Ra, Rb, Rc Raffi Rbfr; Rcff: final ellipse axial ratios in sections A : B : C 1 Aiy, Biy, Ciy: lines of intersection ofA ; B ; C’on cleavage. : pitches of A_?y, Biy, Ciy on cleavage. $4 $6, @k axes of tectonic strain ellipsoid, X-Y-Z. X Y, Z I axes of final deformation ellipsoid, Xff-Yff-zfJ: Xffj Yffj Zff Xj~i Ypf, Zpf : axes of welding deformation ellipsoid, Xpf-Ypf-ZpJ 6 : pitch of X on cleavage. elir , 861, ec1 : pitches of final ellipse long axes on A : B ; C 1 8’al ^ 2 :pitchofZonA’-&ir.
Tectonophysics,
12 (1971) 283-306
B. ROBERTS
EXTENSIVE
:
tdetres
S.E.
m
IO0
t
:
90
SCREE
AND A.W.B. SIDDANS
\
hletres 0
d
N
.w.
B
1
Fig. 6. Levelled traverse on the Back Wall of Cwm Silin. A. Map showing vertical section along line of traverse.
sampling
localities.
B. Composite
FABRIC STUDIES IN NORTH WALES
641^z
e Cl -2 8’ ^ Axy $1
h;,X;>h;
291
: pitchofZonB’B’bl. : pitch of2 on C’- BCr. : pitch ofsliy on A ‘- Brir. : reciprocal quadratic elongation along Z. : reciprocal quadratic elongations along Aiy, Bky, Cky.
~H,Jal, kplj* hq ’ XC?
: reciprocal quadratic elongations along long and short axes of final ellipses inA:B:CI hiY1, ?I&, , A&; reciprocal quadratic elongations along long axes of ellipses in any mutually perpendicular planes xy, yz, zx. QA, Q& Qc : lines of intersection of A, B, C on plane Q. : line of intersection of planes P and Q. Qf’ : reciprocal quadratic elongation along QP. A’QP : reciprocal quadratic elongation along line of intersection of plane P on x kty cleavage. Two-dimensional
analysis
By using fundamental equations derived by Ramsay (1967, eq. 5.22, 5.27) Dunnet (1969a) was able to express the relationships between Ri, 8, RA $, Rs, and he described a graphical method for determination of the strain ratio and initial shape fabric, in sections through deformed aggregates of initially randomly oriented ellipsoidal objects. The Rf/$ data are plotted on ordinates @and log RJ and the resulting scatter diagram is compared with theoretical Rf/@ curves. A computer programme for generation of standard sets of Rf/@ curves was presented by Dunnet and Siddans (1971). This type of analysis has been extended to sections through some non-random sedimentary fabrics (Dunnet and Siddans, 1971). It was shown that in order to investigate the type of three-dimensional fabric from sections through deformed or undeformed aggregates of ellipsoidal objects, it is essential to determine the distribution of Rip and/or Rf/@ data in both ratio and orientation, and to determine the symmetry of these distributions with respect to the bedding and/or cleavage traces in the section plane. The characteristic types of Rip diagram for sections through planar, semi-planar, and imbricate fabrics were described (Dunnet and Siddans, 1971, fig. 3,4). In the case of deformed planar and semiplanar fabrics graphical or numerical methods for determining both the initial shape fabric and strain ratio were described, and a computer programme (programme STRANE) for the numerical method was presented. In these methods use was made of the symmetry properties of the Rip and Rf/@ data relative to the bedding and cleavage traces. It was noted that in the undeformed state the Rip data were symmetric about the bedding trace, whereas in the deformed state the Rf/@ data were asymmetric to both the cleavage and bedding traces. In this analysis of sections through the lapilli tuff, there was no line element directly comparable to the bedding trace in the fabrics discussed above. However, it was clear from the nature of the Rf/# data that in specimens from the eutaxitic zones of the tuff, the pretectonic shape fabrics of pumice lapilli were not random. Earlier studies (Roberts, 1969, pp. 340-342) indicated that this fabric was of a semi-planar type. Thus in the use of proTectoono~hysics, 12 (1971) 283-306
292
B. ROBERTS AND A.W.B. SIDDANS
gramme STRANE, in this anaiysis, successive values of ISYM3 (Dunnet and Siddans, 197 1, pp. 324 were used alone in assessing diagram symmetry during the ‘“unstraining” routine. The procedure followed was to cut two sections, A ‘and B ‘, normal to each other and both normal to the cleavage, through large oriented specimens. The Rf/G data for about 50 ellipses were measured, together with the pitch of the cleavage trace (which defined the maximum principal extension direction, # = O”, in the section) on both sections. These data were analysed using progarmnle STRANE, with assesses the symmetry of the ~~~~ data, and if they are symmetric restores them to maximum symmetry (Ri/B data). The subsequent procedure was determined by the output of programme STRANE at this stage. If both sections A ‘and R ‘gave symmetric Rf/@ data, it was inferred that the pre-tectonic shape fabric was randomly oriented. A third section, C ‘, was then cut parallel to the cleavage, so that A ‘,B ‘and C’were mutually perpendicular. If both sections ,4 ‘and B ‘did not give symmetric Rf/$ data it was inferred that the pre-tectonic shape fabric was not randomly oriented. A third section, C ‘, was cut normal to the cleavage, to approximately bisect the angle between A ‘and B ‘. In both cases the ~~~~ data for the third section, and the pitch of the cleavage trace if necessary, were measured. If the specimen had a nonrandom initial shape fabric these data were analysed using programme STRANE. The best fitting standard Rf/@ curves were drawn on the Rf/@ and restored Ri/B diagrams, and the mean Rf/@ and mean RiftI points so enclosed were obtained. In the case of specimen 5, face A ‘gave a symmetric Rf/$ diagram (Fig. 7) faces B ‘and C’gave asymmetric Rf/ci, diagrams (Fig. 8A, B). The symmetric Riji3 diagrams for faces B and C are presented in Fig. 8C, D. For all specimens with sections giving asymmetric Rf/# diagrams it was found that the restored Rile diagrams were highly symmetric, and that standard Rf/# curves could be readily fitted. This implies that the semi-planar nature of the pre-tectonic shape fabric of the pumice lapilli was due to an earlier deformation, viz. that associated with welding and compaction of the ignimbrite and here called the welding deformation, of a random shape fabric (cf. Dunnet and Siddans, 1971, example 3). Thus the deformation history of the ignimbrite sheet consists of two discrete finite phases; the welding deformation, with associated development of eutaxitic structure; and the tectonic deformation, with associated development of cleavage. Since these deformations were not coaxial they result in a final deformation ellipsoid that is oblique to both the welding deformation and tectonic deformation ellipsoids. The two-dimensional data, mean Rf/$ point, mean Ri/O point, and Rs, from each of the three sections may be combined to give the axial ratios and orientations of each of the three deformation ellipsoids for each specimen. In the case of the specimens with randomly oriented pre-tectonic shape fabrics, there was no welding deformation, and the Rf/~ data record only the effects of the tectonic deformation and the original shape fabric. Three-dimensional analysis The tectonic deformation ellipsoid Using two-dimensional data from the three surfaces A : B ‘, C’ it is possible to determine the strain ratio in the plane of the cleavage. A graphical method, in which the Mohr circle is constructed, is described by Ramsay (1967, pp. 79-81). ~ternatively the analytical
293
FABRIC STUDIES IN NORTH WALES
20 15
10
Rf
2
,600
-300
00
300
60’
0
Fig. 7. Rf/@ data for specimen 5 section A,
method given below may be used, and has been programmed (programme SOSC, written in FORTRAN IV for the CDC6600, listings are available). The nature of the problem is illustrated stereographically in Fig. 9. Since slaty cleavage is parallel to the XY-plane of the finite tectonic strain ellipsoid, sections A ‘,B : C ‘intersect in a line that is parallel to the Z-axis of the strain ellipsoid. This direction is the common minimum principal extension direction in all three sections. Thus Xi, Ad, hi, expressed in terms of h ; are l/Ra2, ~/HI’, l/Rc* respectively. An equation relating the reciprocal quadratic elongation, h ‘, in a direction 0 ‘relative to the maximum principal extension direction, to hr’ and Xi is given by Ramsay (1967, eq. 3.31): X’=h~cos2~‘+h~sin2B’
(1)
Using eq. 1 and the relationship
sin* + cos* = 1, it follows that:
Xi = Xi f (Xi - h;)sin’@
- 0.J
@I
Xi = Xi + (Xi - X;)sin*(s
- t?d)
(2b)
Xi = A; + (hi -- X;)sin’(s
- 0:)
(2c)
Taking these equations (Xi - hi): (X,’ - hJsin*(&
in pairs, 2e2b,
2b-2c,
- 6d) + (1: - ?$)sin2(6
~ec~o~o~~y~~cs, 12 (1971) 283-306
and equating the resulting expressions
- 13;) t (hi - ha)sin2(6 - e;) = 0
for
(3)
294
B. ROBERTS AND A.W.B. SIDDANS
A
00
20 15
-
10
-
c
ml R1/0:3
I)
5/69’
7 RI
5
.
4
-
3
-
2 RS
t
I
I I
I
,,
C
300
0”
60° 6
900
1200
Fig. 8. A. Rf/@ data for specimen 5 section B. B. Rf/O data for specimen C. C. Restored Ri/tl data for section B after removal of a strain ratio Rs = 1.80. D. Restored Ri/8 data for specimen 5 section C after removal of a strain ratio Rs = 2.45.
Defining
known
constants:
terms in eq. 3, and collecting
C,=ha-hd,
C2=Xd-hd,
c,
=
c,
c02e;
+
terms are defined:
czcO?e;
and expanding
the sin’
like terms in 6:
Cqsin2S - CssinS cosS + C6cos2S = 0 where known constant
C,=hd-$,
+
c3c0s2e;
C5 =C,sin2e{+C2sin2e~+C3sin2e~
(4)
295
FABRIC STUDIES IN NORTH WALES
Fig. 9. Stereographic projection, lower hemisphere, equal area, of the three sections A : B : C ‘in the deformed state, and A, B, C after removal of the tectonic strain X/Y/Z = 2.49/1.57/1.00.
C, = C1sin26d
t Czsin26;
Fig. 10. Specimen 5 final fabric analysis; Xff/Yff/Zff = 2.76/2.34/1.00.
+Cssin’ed
Dividing through eq. 4 by cos’ 6 : Cqtan26 -Cstan
S tCg=O
(5)
Eq. 5 has a general solution of the form: c5 ‘f&2
6 = tan-’
- 4 C&)f
2C4 Eq. 2a-2b give an expression: x;
_
A;
=
hi - hi sin2(6-$,J
- sin*(&+J
(6)
(7)
Substituting the appropriate value of S into eq. 7, the resulting value of (&A;) may be substituted into eq. 2a to give the value of Xr’. Finally A; is obtained by substituting values of (hi-h,‘) and Xr’ into: x; = (A; -A;)+h;
(8)
The tectonic strain ratio, X/Y/Z, is thus (1 /A;)$ / (1 /A;)* / 1, the pitch of X on the cleavage is 6, and the minimum principal extension direction is parallel to Z, and the tectonic strain ellipsoid is completely specified.
Tectonophysics,
12 (1971) 283-306
296
B. ROBERTS
AND A.W.B. SIDDANS
In the case of those specimens with a randomly oriented pre-tectonic shape fabric, i.e., those specimens with no welding deformation, the strain ratios for the three mutually perpendicular sections A : B : C ‘may be combined using the method given by Ramsay (1967, pp. 142-147, 199-200). Using this method there are two independent ways of computing XL in terms of h&i, which provides a check on the internal consistency of the two-dimensional data. This can be expressed as the percentage level of internal inconsistency by computing the value of:
1A,‘(‘) ~ A,‘@)1 x 1oo X’(l) z
(9)
+x’(z) z
Similarly two values of “4 in terms of h&r, and two values of A; in terms of h,‘, 1 can be computed, together with their internal inconsistency levels. Thus there are six independent ways of obtaining the strain ellipsoid, which provides a check on the accuracy of the determinations. This method has been programmed (programme PASE, written in FORTRAN IV for the CDC6600, listings are available), to perform all six determinations, select the pair that minimises the internal inconsistency level, and compute the result on the basis of the mean vaiue of the corresponding reciprocal quadratic elongation The final deformation ellipsoid Ramsay (1967, pp. 147-148) describes a general method for determining ellipsoid ratios and orientations from two-dimensional data on three oblique planes. A numerical solution is given below which has been programmed (programme FOSC, written in FORTRAN IV for the CDC6600, listings are available). The nature of the problem is illustrated stereographically in Fig. 10. In the determination of this ellipsoid the mean Rf/Q points from the three sections A ‘, B ‘, C’are combined. Since A ‘and B ‘are normal both to the cleavage and to each other the problem is in two parts; firstly to compute the two-dimensional component in a plane parallel to the cleavage, secondly to combine that component with the two-dimensional data from sections A ‘and B ‘. Since 2 is not in general parallel to Zff, it is necessary to derive expressions for the reciprocal quadratic elongations along Z, A~JJ, B$J, C’x?yinvolving only known angles and ratios, and a single unknown term. This may be done by setting up equations similar to those of Ramsay (1967, eq. 5.7 through 5.17). Using eq. 1 for each section, expressions for h; and Xa’>,, >c can be written, e.g., for section A ‘z h; = hiI cos2i3~, ^ z + hi2 sinZeal ha = h,‘, cos26~l ^ Axy+hi2 Since Bal - z = 90” f 0,i
sinZeal
-z
(10)
^ Axy
(11)
^ Axy :
sin20;l
- z =co?e;,
^
c0s2e;l
- z =sin20;r
.
AXY
AMY
Thus eq. 10 and 11 may be written:
x; = hi1 (cos2e
’
al
^z + Ra& sin’@;i
- ,)
= h&c;
(12)
'91
E~ABR~CSTU~IESINNORTH~~ALES ha = hi1 (sin’ea,
^ z +R~&.cos~@~~ , z)
= h.&C,
(13)
= h&C;
(14)
= x&c;
(!5)
Similarly for sections B ‘and C ‘I AL = Xi, (cos’O{ hi = hi,
(sin2Bd
1
^ z +Rb& sin2BrJi
I ^ 2 +RbZffcos%&
- %)
* z)
hl= hli (cos2@& _ z +Rc&sin28di
* ,)
= “d, c;
(16)
Ai = A& (sin*0&
I z)
= xpg
(17)
^ z + Rc&cos2t3dl
The terms in parentheses in eq. 12 - 17 are known constant terms, say Ci’ - CL respectively. Eq. 12, 14 and 16 are all expressions for A;, thus halCr’ = hb, C; = AL, C;, and hence: xi = ?Lpcq/c;
(18)
x; = x;* c;cg/c;
(1”))
Eq. 13, 18 and 19 express Xi, Xi, h: all in terms of known constant terms and a single unknown term ha 1. Using these values, together with ea, 0;, 0; in programme SOSC, the ellipse ratio and orientation in the plane of the cleavage is determined. Then the ellipse ratios and orientations for sections A 1B ‘and in the plane of the cleavage may be combined to give the final deformation ellipsoid axial ratio, Xff/Yff/Zff and orientation, by using programme PASE. Tt%ewelding deformation ellipsoid Determination of the welding deformation ellipsoid is complicated by the necessity to restore the section planes A : B : C’to their pre-tectonic orientations A, B, C (Fig. 9). The simple graphical method given by Ramsay (1967, pp. 130-l 32, using fig. 4.6) may be used: alternatively, as written into programme SOSC, the equation relating the orientation of line elements before and after deformation (Ramsay, 1967, eq. 3.34) may be used: tan 0 =Rs.tan
8’
(20)
where B and 8’ are the angles between the line element and the maximum principal extension direction before and after deformation. When the three sections are restored to their pretectonic orientations A and B are, in general, no longer normal to each other, though both are still normal to the cleavage. The nature of the problem is illustrated stereographically in Fig. 11. As in the case of the final deformation ellipsoid, by using programme FOSC the ellipse ratio in the plane of the cleavage is determined, together with its orientation. It is now necessary to specify another plane, F, normal to both the cleavage and A, and to determine the ellipse ratio and orientation in it. In order to do this a further plane, Q, is specified, and using eq. 1 on each of the restored sections A, B, C, the reciprocal quadratic elongations along QA, QB, QC are determined, and hence the ellipse ratio and orientation in Q is obtained. Again using eq. 1 the reciprocal quadratic elongation along QP is determined. If the reciprocal quadratic elongation alongPxy is obtained from the two-dimensional data in the Tecto~o~hysics, 12 (1971) 283-306
298
Fig. 11. Specimen 5 pre-tectonic fabric analysis;
xpfWpfjzpf = 7.82/2.89/1.00.
B. ROBERTS AND A.W.B. SIDDANS
Fig. 12. Stereographic projection, lower hemisphere, equal area, showing the geometric relations between the orientations of the tectonic, welding, and final deformation ellipsoids.
cleavage plane, using eq. 1, then in plane P hk, h&, and X&v are known, and the ellipse ratio and orientation in plane P may be obtained, as outlined above. An option has been written into progarmme FOSC to perform these computations once the planes P and Q, and the necessary angular relations, are specified. Using the ellipse ratios and orientations on planes A, P and in the cleavage, the axial ratio, Xpf/Ypf/Zpf, and orientation of the welding deformation ellipsoid are obtained using programme PASE. Assessment of validity of results
Criteria for assessing the validity of the results are available. This is very necessary in view of the fundamental assumptions made at the outset of this analysis, and the considerable scope for compounding inaccuracies during the successive computations. In the case of those specimens with no welding deformation, the only check required is that on the tectonic deformation ellipsoid. This is obtained from the output of programme PASE. Low internal inconsistency levels imply accurate results and justify the initial assumptions. A rapid visual estimate of the accuracy of the results may be obtained by plotting all six results on a deformation plot of a=X/Y against b=Y/Z (Flinn, 1962). In the case of specimens with a semi-planar pre-tectonic shape fabric, the three-dimensional strain analysis obtained from programme SOSC is a unique result. However, the welding deformation and final deformation ellipsoids were ultimately obtained using programme PASE. If the internal inconsistency levels for these ellipsoids are low, the implication is that the initial assumptions and results are valid. A totally independent check on the computations and assumptions is available. Knowing the tectonic strain ellipsoid, and either the final deformation or welding deformation ellip-
FABRIC STUDIES IN NORTH WALES
299
soid, it is a simple exercise in Cartesian tensors to compute the unknown ellipsoid. Dunnet (1969b, pp. 176-l 82, 3 14-3 19) discusses the deformation of elliptical or ellipsoidal shapes, and derives the relationship:
D=B.R.A.RT
(21)
where A is the initial diagonalised ellipsoid shape tensor; B is the diagonalised tensor of strain; R is the rotation matrix of direction cosines from the reference frame of the strain ellipsoid to the initial ellipsoid shape; R T is the transpose of R ;D is the final ellipsoidal shape tensor referred to the reference frame of the strain ellipsoid. A computer programme is presented by Dunnet (1969b, pp. 400-408) to perform the matrix algebra implied in eq. 2 1, and to determine the eigenvalues and eigenvectors of the final tensor D. These checks have been applied in every case, and it has been concluded that the initial assumptions are justified and that the results obtained are valid. The results for specimen 5 are summarised in Fig. 12. RESULTS
The results of the primary fabric analyses are presented in Table I. It is important to remember that the axial ratio of the pre-tectonic fabric is not in general the axial ratio of lapilli, but the axial ratio of the welding deformation ellipsoid. Of the various parameters available to describe the geometry of the welding deformation ellipsoid two have been chosen, and their variation with height above the base of the ignimbrite sheet plotted in Fig. 13 and 14. To describe the shape of the ellipsoid the k-parameter of Flinn (1962) is used:
kJv-
v/z -
1). 1)
k may vary from zero to infinity; its significance when there is no volume change may be summarised: k = 0. uniaxial oblate ellipsoids-pure flattening; k = 0 - 1, flattening type TABLE
I
Pre-tectonic fabric analyses
Tectonophysics,
12 (1971) 283-306
300
B. ROBERTS AND A.W.B. SIDDANS
175
105 . I
150 1
bo I(
I 125
0
75
I:
I
,
1.0
I.2
I
0.0 otAa,e
0.2
0.4
0.6
0.8 Z=Y y-z
J
# 1.1
1.6 prolate
m
z
K
Fig. 13. Graph of k-values of welding deformation ellipsoids it successive heights in the ignimbrite sheet. ellipsoids; k = 1, plane-strain ellipsoids; k = 1- infinity, constriction type ellipsoids; k = in finity, uniaxial prolate ellipsoids-pure constriction. Since the welding deformation ellipsoids have k-values in the range 0 - 1, some measure of the amount of flattening is required. The simplest parameter to visualize which expresses this is the percentage shortening of the Z-axis of the ellipsoid. The radius, r, of the sphere of equivalent volume to the ellipsoid is computed, then the percentage flattening is expressed: percentage
flattening
=q
X 100
In view of the uniformity amongst the data on porosity and density available for Tertiary and Quaternary rhyolitic pumice-lapilli tuffs, it may be possible to apply this data to the Llwyd Mawr Ignimbrite and to use estimates of the compaction from petrographic evidence as a control. The porosity data of Smith (1960) suggests a reduction in volume
301
FABRIC STUDIES fN NORTH WALES
z
Zone of complete
sintering
IV 200
120
I
----__________-_______.
I
105
175 ~
I
i
150
90
>
x
1 125
75
Parataxitic
zone
Iti
I
x
t
100
-I
-_--___
-w______---__-____-
75-L
x
-_-_-_
-
-
‘-
of pre-existing Eutaxitic
50
30
II
x
;
25 ~ !L_________________________---__, 0
I
-i
0
,I
, 20
40
60
flow
zone
80
Basal
non-welded
zone
I
100
Fig. 14. Graph of percentage flattening of welding deformation ellipsoids at successive heights in the ignimbrite sheet.
in zones III and IV the Llwyd Mawr Ignimbrite of the order of 40%. The specific gravity data of Ross and Smith (196 1) suggests a volume reduction for zones III and IV of 42%. Petrographic evidence (viz., the extent to which shards have been deformed around feldspar crystals) suggests volume decreases of 0% in zone I, 30% in zone II and 50% in zones III and IV. Thus it may be possible in Fig. 14. to superimpose upon the percentage flattening axis an additions scale representing volume decrease associated with welding, such that 0 - 83% percentage flattening corresponds with 0 - 50 or 60% volume decrease. On the graphs of k and percentage flattening against height above the base of the ignimbrite sheet (Fig. 13 and 14), the four textural zones recognised by Roberts (1969) are indicated. Zone I. Within the basal non-welded zone specimens 1 -- 3 show that there was no welding defo~ation at all. The final lapilli shapes and orientations record only their prewelding variations as modified by the tectonic finite strain. Tectonophysks, 12 (1971) 283-306
302
B. ROBERTS AND A.W.B. SIDDANS
Zone II. Within the eutaxitic zone there is a marked rapid upwards increase in the percentage flattening form 0 - 64lS.%, up to a height of some 65.23 m. At 76.06 m there is a marked reduction in this parameter to 48l/LL%,followed by a further upwards increase to 54% near the top of this zone at 87.48 m. At lower levels in the zone k-values approach 1, and decrease upwards to 0.42 at 65.23 m. At 67.06 m there is a marked increase in this parameter, which again approaches 1, followed by a further upward decrease to 0 near the top of the eutaxitic zone at 87.48 m. Zones ZZZ and IV. Within the parataxitic zone and the lower parts of the zone of complete sintering there is a general upwards increase in the percentage flattening from 64’/L%at 117.96 m to 83% at 218.24 m. Throughout these zones the k-value is always low, varying only from 0 - 0.2. The results of the tectonic strain analyses are presented in Table II, and the variation of the k-value of the tectonic strain ellipsoid with height above the base of the ignimbrite sheet is plotted in Fig. 1.5. There is a clear trend showing the k-value of this ellipsoid increasing upwards from 0.16 at the base of the non-welded basal zone to 11.35 up in the zone of complete sintering. There is, however, a reversal of this trend at the 67.06 m level, where this parameter is anomalously low. There is also a marked increase in the k-value of this ellipsoid from 1.54 to 8.35 between the 159.11 and 180.08 m levels. This occurs at the top of the parataxitic zone. DISCUSSION
Within the eutaxitic zone, at the 67.07 m level, there are marked reversals in the upward trends of both parameters of the welding deformation ellipsoid, the percentage flattening is anomalously low and the k-value anomalouly high. In the two-dimensional analysis of lapilli axial ratios (Roberts, 1969, fig. 74b) there was recorded an anomalously low distortion index at this level, which contrasted with the clear tendency to increase TABLE II Tectonic strain analyses
Axial
x:y:z
ratio
Cleavage strike,
dip
PIllWe X
K
Internal Inconsistency
Value
level
10 03 80
(Xl
303
FABRIC STUDIES IN NORTH WALES
7 I
225
zone IV
I
Zone
III
125
100
-------------------------------.
25
Fig. 15. Graph of k-values of tectonic strain ellipsoids at successive heights in the ignimbrite sheet.
upwards. Taken together these anomalies support the suggestion of Roberts (1969, p. 344) that this level marks the base of another flow emplaced on the still hot surface of the flow beneath, and that they then both cooled together. This conclusion is further supported by the low k-value of the tectonic strain ellipsoid at this-level; and by geochemical studies being undertaken by G. Hendry on these samples, who has found changes in Si, Al, Ca, Fe, Mn, Ti, P, S, Ba, Y, Ce, Th, and Pb at this level (personal communication, 1971). The high k-values of the welding deformation ellipsoids below the 67.07 m level indicate a directional component to the extension accompanying flattening. These are associated with relatively high dips of the pre-tectonic eutaxitic structure. The X-axes of these ellipsoids plunge at low angles to the east and southeast quadrant, and at higher angles to the south and southwest quadrant. Possibly these represent the sub-ignimbrite palaeoslope, the lower flow having accumulated on a southerly sloping surface in the region of Cwm Silin, whereas the upper flow accumulated on the more level hot surface of the lower flow. Tectonophysics,
12
(1971) 283-306
304
B. ROBERTS
AND A.W.B. SIDDANS
If it is assumed that the second ignimbrite sheet was emplaced in a single act, i.e., as a geologically instantaneous event, and that this was followed by compaction due to welding, then it is possible to compute the pre-welding thickness of the flow. A minimum value for this figure is of the order of 3,000 m which, if the assumption is valid, implies that the constraining walls were at least 3,000 m high. It seems unlikely that a Caradocian topographic depression exceeding 3,000 m in depth could have existed: certainly there is no corroborative evidence elsewhere in Caernarvonshire. It is just possible that caldera subsidence concurrent with eruption could have given the necessary depth. The probalility is, however, that the assumption is wrong. Instead it is suggested that the accumulation of the ignimbrite occured as the result of a series of successive eruptions, each pulse being separated from the next by an interval of hours or days, because there was no dectectable cooling during this time. (Peterson (1968, p. 222) has suggested a similar mechanism to account for a single cooling unit 610 m thick at Superior, Ariz.) Welding and compaction probably began rmmediately after the accumulation of the material produced by the first pulse, and continued with each successive pulse, so that it seems likely therefore that welding and compaction is geologically a very rapid process. It is clear that the anomalies at 67.06 m above the base indicate that a significant period free from eruption elapsed after emplacement of the first unit, prior to the rapid pulses which led to the emplacement of the second unit. Both units then continued to cool together. Interpretation of the tectonic strain analyses for this traverse alone is difficult, since both major and minor structures in the area are non-cylindrical. Work currently in progress by one of the authors (A.W.B.S.), using thin-plate theory to investigate the nature of periclinal buckling instabilities, and a finite element analysis technique to investigate their subsequent development, suggests that on a traverse through a periclinal syncline, such as has been described above, the k-values of the tectonic strain ellipsoids should tend to increase towards the core of the structure, within the stiff buckling plate, in the general way that they are seen to do so. Quantitative comparisons between the naive numerical model and observed structures are not possible to date. Indeed, the pre-tectonic ignimbrite sheet must have been a highly anisotropic plate by virtue of its welding deformation, with its well-developed systems of cooling joints (Roberts, 1969, pp. 346-349), so that at the present time a realistic numerical model is impossible to approach. Intuitively one suspects that the pre-tectonic fabric of the plate controlled each tectonic strain increment. The anomalous sudden increase in the k-value of the tectonic strain ellipsoid at the top of the parataxitic zone is also accompanied by geochemical changes in Si, Al, Ca, K, Na, P, Sr, Zr, Ba, Y and Ce (G. Hendry, personal communication, 1971). The reason for the change in tectonic strain is not understood, but there is need for further traverses and collections to be made. Should such traverses reveal similar tectonic anomalies at this level, problems of strain compatability will arise. A bulk figure for the tectonic thickening of the ignimbrite sheet is x S/3; hence the present day remanent thickness of 700 m has been produced from some 420 m of welded tuff. The nature of the cleavage associated with the foldingvaries upwards through the sheet. At lower levels, up to 22.16 m, a slaty cleavage is developed (Fig. 2). Upwards this passes into a fracture cleavage resembling a system of closely spaced cracks in the rock (Fig. 3). The exact transition is difficult to define, but specimen 4; from the 22.16 m level, with a welding deformation k-value of 0.92, a welding percentage flattening of 5%, and a tectonic
FABRIC STUDIES IN NORTH WALES
305
strain k-value of 0.18 has a slaty cleavage, whereas specimen 5, from the 44.50 m level, with a welding deformation k-value of 0.90, a welding percentage flattening of 64M%, and a tectonic strain &value of 1.03, has a fracture cleavage. The inference is that both types of cleavage have exactly the same mechanical significance; the one passes into the other, but that the resulting structure is controlled by the pre-tectonic fabric of the rock. Further discussion of these phenomena awaits the outcome of detailed petrofabric studies using the pole-figure goniometer currently being undertaken by one of the authors (A.W.B.S.). ACKNOWLEDGEMENTS
B. Roberts gratefully acknowledges help from the Central Research Fund of the University of London in assisting with fieldwork expenses during research on Llwyd Mawr. A.W.B. Siddans made the deformation analyses during the tenure of a Natural Environment Research Council Research Studentship. He is grateful to Professor J.G. Ramsay, under whose supe~~sion his research is being undertaken, and to Dr. D. Dunnet for their interest and encouragement. The writers are grateful to Dr. G. Hendry for making the results of his geochemical studies available to them, and to Professor Ramsay, Dr. Dunnet and Dr. R.S. Fiske for critically reading the manuscript.
REFERENCES Dunnet, D., 1969a. A technique of finite strain analysis using eiliptieal particles. ~ecr~~~~~~$~cs, 7: 117-136. Dunnet, D., 196913.Deformation in the Palaeozoic Rocks of Inglesiente, S. W. Sardinia. Thesis, Univ. London, London, 412 pp. Dunnet, D. and Siddans, A.W.B., 1971. Non-random sedimentary fabrics and their modification by strain. Tectonophysics, 12: 307-325. Elliott, D., 1970. Determination of finite strain and initial shape from deformed elliptical objects. Geol. Sot. Am. Bull., 81: 2221-2236. Flimt, D., 1962. On folding during ~ree~mension~ progressive deformation. Q. J. Geot. Sot. London, 118: 385-428. Gay, N.C., 1968a. Pure shear and simpfe shear deformation of inhomogeneous viscous fluids, 1. Theory. Tectonophysics,
5: 21 l-234.
Gay, N.C., 1968b. Pure shear and simple shear deformation of inhomogeneous viscous fluids, 2. The determination of the toal finite strain in a rock from deformed objects such as deformed pebbles. Tectonophysics, 5: 315-339. Ghosh, S.K. and Ramberg, H., 1968. Buckling experiments on intersecting fold patterns. Tectonophysics, 5: 89-105. Ghosh, SK., 1970. A theoretical study of intersecting fold patterns. Tectonophys~cs, 9: 559-569. Martin, R.C., 1959. Some field and petrographic features of American and New Zealand i~imbrites, N.Z.J. Geol. Ceophys., 2: 394-411. Peterson, D.W., 1968. Zoned ash-flow sheet in the region around Superior, Arizona. In: Southern Arizona Guidebook III. Ariz. Geol. Sot., PP. 215-222. Ramsay, J.G., 1967. Folding and Fracturing of Rocks. McGraw-Hill, New York, N.Y., 568 pp. Roberts, B., 1967. Succession and structure in the Llwyd Mawr Syncline, Caernarvonshire, North Wales. Geol. J., 5: 369-390. Roberts, B., 1969. The Llwyd Mawr ignimbrite and its associated volcanic rocks. In: &Wood (Editor), The Pre-Cambrian and Lower Palaeozoic Rocks of Wales. Univ. Wales Press, Cardiff, pp. 337-356. Tectonophysics,
12 (1971)
283-306
306
B. ROBERTS AND A.W.B. SIDDANS
Ross, C.S. and Smith, R.L., 1961. Ash-flow tuffs: their origin, geologic relations and identification. U.S. Geol. Surv., prof: Pap., 366: 81 pp. Shackleton, R.M., 1959. The stratigraphy of the Moe1 Hebog District between Snowdon and Tremadoc. Liverp. Manch. Geol. J., 2: 216-252.
Smith, R.L., 1960. Ash Flows. Bull. Geol. Sot. Am., 71: 795-842.