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Emplacement of pyroclastic dykes in Riedel shear fractures: An example from the Sierra de San Miguelito, central Mexico
Journal of Volcanology and Geothermal Research 250 (2013) 1–8
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Emplacement of pyroclastic dykes in Riedel shear fractures: An example from the Sierra de San Miguelito, central Mexico S.-S. Xu ⁎, A.F. Nieto-Samaniego, S.A. Alaniz-Álvarez Universidad Nacional Autónoma de México, Centro de Geociencias, Boulevard Juriquilla No. 3001, Querétaro, Qro., 76230, Mexico
a r t i c l e
i n f o
Article history: Received 5 March 2012 Accepted 15 October 2012 Available online 23 October 2012 Keywords: Domino faults Simple shear Riedel fractures Pyroclastic dykes Mexico
a b s t r a c t Although magmatic dykes are considered to be emplaced at depth, there are very few studies about the emplacement of pyroclastic dykes. There are two commonly accepted mechanisms for dike emplacements; namely, formation of a hydraulic (tension) fracture and filling of pre-existing fractures. In the Sierra de San Miguelito, central Mexico, there is a dike swarm with orientations that do not concur with any of the above two cases. Instead, the dikes have orientations resembling some type of secondary fractures within the fault-bounded blocks. Within a fault-bounded block, the reverse drag of the normal faults can be explained by simple shear. Based on the simple shear mechanism, we establish a series of equations to calculate the extension and the direction of the simple shear within a fault-bounded block. As an application of our methodology, the value of β, which is the angle measured from the vertical to the direction of the simple shear, is calculated from the domino faults in the Sierra de San Miguelito, Mesa Central, Mexico. The results demonstrate that the absolute values of β for the inclined shear are smaller than 34°. The inclined shear can be antithetic (β > 0), synthetic (β b 0) or vertical (β ≈ 0). The pyroclastic dykes in the study area have most of the strikes between 300° and 330° and are sub-parallel to the major faults. The preferred dips of the pyroclastic dykes vary from 80° to 90°. The distribution of the pyroclastic dykes in the study area indicates that the dikes were primarily emplaced along the R fractures due to simple shear. These results are different from the traditional understanding, which assumes that the dykes were mainly emplaced within the tension fractures. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Different mechanisms of emplacement of dykes have been proposed and are mainly dependent on the relationship between a tectonic stress field and fluid pressure. Tension fracture is the most common mechanism and consists of the formation of type I fractures by hydraulic stress (e.g., Anderson, 1951; Takada, 1994). Another such mechanism is the emplacement of magma in a pre-existing fracture and it depends on the difference between the normal stress on the fracture walls and the fluid pressure of the magma (e.g., Delaney et al., 1986). A less well known mechanism is the injection of magma during the movement of a fault. This mechanism can be inferred from the asymmetric structures within a dyke. These structures record the relative movement between the walls and the magma flow. Existing studies involve magmatic dykes emplaced at depths where the velocities of the flow of the magma are approximately 1 m/s (Correa-Gomes et al., 2001). In contrast, there are very few studies about the emplacement of pyroclastic dykes that are formed in an episodic manner in very shallow environments, with injection velocities faster than the magmatic dykes and most likely comparable to velocities encountered in pyroclastic column models that range from 100 to 300 m/s (e.g., Woods, 1998). ⁎ Corresponding author. E-mail address: [email protected] (S.-S. Xu). 0377-0273/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jvolgeores.2012.10.010
The Sierra de San Miguelito, in central Mexico, presents an ideal example to study the emplacement of pyroclastic dykes. The rhyolitic ignimbrites and the pyroclastic rocks of the Sierra de San Miguelito are crosscut by the San Luis–Tepehuanes fault system. No calderas have been identified in the Sierra de San Miguelito as potential sources for the deposits. A possible eruption of the ignimbrites through fissures has been proposed by some authors based on the presence of numerous pyroclastic dykes that are parallel to the main faults (LabartheHernández et al., 1982; Tristán-González, 1986; Labarthe-Hernández and Jiménez-López, 1994; Orozco-Esquivel et al., 2002; TorresHernández et al., 2006). A detailed study of the composition and internal structure of the pyroclastic dykes of Sierra de San Miguelito was performed by Torres-Hernández et al. (2006). The authors proposed that the dykes were either emplaced through the formation of new fractures or by the injection of magma into pre-existing fractures. They observed that the dykes were located in the hanging wall of the major faults, but they did not discuss the type of structure that would correspond to the orientation of the dykes in the fault system. There are three main aspects of this paper. First, we present new structural data of the pyroclastic dykes and the normal faults in the Sierra de San Miguelito, Mesa Central of México. From these data, the relationship between the normal faults and the dykes is inferred. Second, assuming that vertical shear was the mechanism that deformed the fault-bounded blocks (Xu et al., 2004), we obtained the
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from the fault planes. The tilting of these beds was interpreted by Xu et al. (2004) to be produced by a vertical shear. Furthermore, there are numerous small normal faults in the area that also show domino style (Fig. 2a, b). We measured some parameters of the normal faults of different sizes. The results indicate that most of the faults have strikes between 290° and 340° (Fig. 3a). Comparing the dips of all the faults (Fig. 3b) with the dips of only the major faults (Fig. 3c), it is evident that the dips of the numerous small normal faults are greater than those of the large normal faults. In contrast, the dominant pitch of the slickenlines on the faults is in the range 80°–90° (Fig. 3d). The faults with small pitches were most likely either formed during a different set of tectonic events for the Mesa Central as proposed by Nieto-Samaniego et al. (2005) or were a result of fault interaction during a single tectonic event (Xu et al., in press).
equations for the extension and simple shear direction of the hanging wall of the major fault. Third, using these equations, the type of fracture orientations that would concur with the pyroclastic dyke orientations was determined. 2. Geology of the Sierra de San Miguelito, México The Sierra de San Miguelito is located in the physiographic province of Mesa Central, in central México (Fig. 1a) (Nieto-Samaniego et al., 2007; Tristán–González et al., 2009). The Mesa Central (MC) represents an intense acid volcanism episode comprising a large volume of lava and domes that were emplaced over an area of ca. 10,000 km 2. The pyroclastic deposits are located in the upper part of the stratigraphic column. The study area mainly consists of lava and pyroclastic rocks and comprises seven Oligocene units (Fig. 1b) (Labarthe-Hernández and Jiménez-López, 1994). From the bottom to top, the units are as follows: Portezuelo Rhyodacite, San Miguelito Rhyolite, Cantera Ignimbrite, Zapote Rhyolite, Lower Panalillo Ignimbrite, La Placa Basalt and Upper Panalillo Ignimbrite. Additionally, there are two units that unconformably overlay the Oligocene volcanic rocks, namely, the Halcones conglomerate and the alluvial deposits of Quaternary age. The Lower Cantera Ignimbrite and the Lower Panalillo Ignimbrite have better stratification than the other units (Fig. 1c). Therefore, the two ignimbrites were used as markers to measure the bedding length, bed dip and fault displacement. In the Sierra de San Miguelito, a system of normal faults (Fig. 1a) developed coevally with the Oligocene volcanic field. The normal faults show domino style that produces the tilting of blocks in a direction opposite to that of the dip direction of the faults (Figs. 1 and 2). The dips of the beds vary from a few degrees to 30°. The variation in the dips occurs both along the fault strikes and in cross-sections, which depends on the fault dips, displacements and distance away
3. Pyroclastic dykes in the study area Many pyroclastic dykes emplaced along the NW–SE faults have sub-vertical dips (Torres-Hernández et al., 2006). The dykes consist of pumice and rhyolite fragments, and broken crystals of quartz, sanidine and biotite. Some dykes show banded structure (Fig. 4a, b). The bands have different fragments, color and size. Some bands consist of symmetric structures, with the axis located near the center and parallel to the contact of the dyke with the wall rocks (Fig. 4b). This feature indicates that the dykes with the bands were formed by multiple intrusions. A comprehensive description of these dykes can be found in TorresHernández et al. (2006). On the walls of some of the dykes, slickenlines with a high angle of pitch (Fig. 4c) were observed. We measured the size of the pyroclastic dykes. In general, the dyke length varies from a few meters to hundreds of meters and their thickness varies from 1 cm to 80 cm. The thickness of the pyroclastic dykes ranges largely
(a)
(b) 05
2
1
3(km)
A
10
Upper Panalillo ignimbrite (26.8 Ma) La Placa Basalt (26.9 Ma)
F15
Lower Panalillo ignimbrite
F14
El Zapote rhyolite (27 Ma)
F18 F19
C
Mexico
Cantera ignimbrite (29 Ma) F13
B
San miguelito rhyolite (30 Ma)
F17
Study area
Oligocene
1
10
22
0
F16
AF12 F11
22
05
Portezuelo rhyodacite (30.6 Ma) Mesozoic rocks
F10 F9
F20
Upper Cantera (Ignimbrite)
F8
(c)
F7 F6 F4
F5
10 1
05
1 10
F3
10
F2
5 1 10
0 22
Lower Cantera (Ignimbrite)
F1
A
N
10 Fig. 1. (a) Normal faults in the San Miguelito, Mesa Central, Mexico, display a domino style. The insert shows the location of the study area. AA′ line is the measured cross-section. Dotted lines are the outcrops of the pyroclastic dykes. Gray circles are points of detailed observation of the pyroclastic dykes. (b) Simplified column of the stratigraphic sequence. (c) Photograph of the Cantera Ignimbrite showing good stratification.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8
3
SW
(a)
(b)
SW
(c) Fig. 2. (a) Normal fault with a dip-direction opposite to that of the bedding. (b) Normal faults show domino style. (c) Large normal faults with the domino style and with a dip-direction opposite to that of the bedding.
dykes to have a close spatial relationship with the secondary faults. The following section addresses the origin of the secondary faults that were generated by simple shear in the hanging walls of the major normal faults.
between 1 cm and 10 cm (Fig. 4d). The dyke lengths are smaller than the major faults in the study area, have strikes that range largely between 300° and 330° (Fig. 4e), and are sub-parallel to the major faults (Fig. 3a). In contrast, the preferred dips of the pyroclastic dykes vary from 80° to 90° (Fig. 4f), which are greater than the dips of the large normal faults (Fig. 3c) but similar to the dips of the numerous minor faults (Fig. 3b). From the characteristics described above and because the dykes were emplaced within the fault-bounded blocks, we interpret the
4. Simple shear produced by the large normal faults Normal faults develop progressively and the dips diminish as the extension progresses (e.g., Sibson, 1985). As a consequence of fault
N
(b)
330°
30° 50°
lt
p di
70°
290°
u Fa
310°
Total number
90° 80° 70° = 120 50 60° 40 50° 40° 30 30° 20 20°
Number
(a)
10 90°
270°
(d)
80
7
75
Fault dip (°)
70
Fault 1
65
10 12
3
5 11
60 55
40 SW
13 14
9 8
50 45
Fault 15
Number
(c)
0
2
4
6 NE
40 35 30 25 20 15 10 5 0
10° 0
10
20 30 40 50
0°
Number
Total number = 99
10° 20° 30° 40° 50° 60° 70° 80° 90°
Angle of pitch
Fig. 3. (a) Rose diagram of the strikes of all the faults. (b) Rose diagram of the dips of all the faults. (c) Dips of the large faults measured along the A–A′ section shown in Fig. 1. (d) Histogram of the pitch angles measured on the small and large faults.
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(a)
(b)
(c)
40
dyke
(d)
35
Total number = 95
Number
30
Slicklines
25 20 15 10 5 0
10
20
30
40
50
60
70
80
Thickness (cm) N 330°
310°
30°
90° 80° (f) 70° 50 60° 40 50° 40° 30 30° 20 20°
Total number = 90
Number
(e)
50°
70° 290°
10 270°
0
90°
Dyke dip 0
10
10°
20 30 40 50
0°
Number Fig. 4. (a) Example of a dyke with two bands and different sized fragments. (b) A dyke showing flow structures and bands. (c) Slickenlines on the dyke wall with a high angle of pitch. (d) Histogram of the dyke thicknesses. (e) Rose diagram of the dyke strikes. (f) Rose diagram of the dyke dips.
faults, the tilt angles of the beds and faults are equal to each other and there is no internal deformation in the fault-bounded blocks (e.g., Axen, 1988; Twiss and Moores, 1992, p. 94). The second mechanism is the vertical shear mechanism proposed in Westaway and Kusznir (1993), where it was argued that the internal deformation within a fault-bounded block is due to vertical shear. The third mechanism is the inclined shear model (White et al., 1986), wherein the internal deformation within the blocks is due to an arbitrary oblique shear, which is not necessarily parallel to the fault plane. We grouped the latter two under the “simple shear model”. Kerr and White (1996)
rotation, the beds in the fault-bounded blocks also tend to rotate. There are two viable mechanisms of bed rotation: 1) The normal rotation, or the normal drag, in which beds on the hanging wall dip in the same direction as the fault. 2) The reverse rotation, or reverse drag, in which beds on the hanging wall dip in a direction opposite to that of the fault (Rykkelid and Fossen, 2002). The reverse drags are formed because of the decrease in the displacement with distance along the fault plane. There are three main mechanisms for bed tilting in reverse drags. The first mechanism is based on the rigid body rotation model and assumes that the rigid blocks are bounded by normal
(a)
(b)
h
D´
C
Dt
D L0 90°+
B´
Lb A
90°- -
Fig. 5. Sketch showing the inclined shear (a) in the initial stage and (b) the geometrical configuration of the inclined shear after faulting.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8 Table 1 Values of β for the faults that crosscut the section A–A′ shown in Fig. 1a. The values were obtained by using Eq. (9) in the text. θ = average tilt of beds in the block; δ = fault dip. Fault number
1
2
3
4
5
θ (°) δ (°) β (°)
20 58 −6.3
22 62 −4.1
24.5 15 63 45 −5.5 −15
6
25 28 64 45 −4.9 −29.2
7
8
9
30 75 2.2
24 55 −13.8
18 58 3.2
Fault number or location
10
11
12
13
14
15
A
B
θ (°) δ (°) β (°)
18 75 13.7
22 65 −1.1
12 67 19.8
18 64 3.2
12 65 17.9
14 66 13.2
10 71 29.8
10 78 34
and Kerr et al. (1993) have used the inclined simple shear model on the hanging-wall of a fault to infer the geometry and slip vectors of listric normal faults. To study the relationship between the pyroclastic dykes and the large normal faults, it is necessary to know the direction of the simple shear in each fault-bounded block in the area. Although a vertical shear has been proposed by Xu et al. (2004), in this paper we re-
5
analyze the data of the faults and bed-tilting by using an inclined simple shear model. In the following section, the equations for the calculation of the angle of shear direction for the fault-bounded blocks are derived. 4.1. Theoretical angle of simple shear direction The definition of linear extension is e ¼ ðLf –L0 Þ=L0 ;
ð1Þ
where Lf is the final length and L0 is the initial length of a line. The sketch for a simple shear model of a normal fault-bounded block is shown in Fig. 5b. DB′ is the initial length of the bedding (L0). The length of the deformed bedding (Lb = AB′) is obtained from the triangle ADB′ using the law of sines:
Lb ¼ AB′ ¼
L0 sinð90 þ βÞ L cosβ ¼ 0 ; sinð90−β−θÞ cosðβ þ θÞ
ð2Þ
where β is measured from the vertical to the direction of simple shear and θ is the dip of the bed. Applying the law of sines to the
(a) R´
T R
P
45°
90°-
(b)
(c) R
R T
15
°
T
45°
15°
R´ R´
45°
15°
75°
45
°
45°
75°
P 15°
P 75°
45°
75°
Fig. 6. (a) Sketch map of the Riedel fractures. R fracture is synthetic to the movement of the principal shear plane. R′ fracture is antithetic to the movement of the principal shear plane. T fracture is the tensional fracture. P fracture is antithetic to the movement of the principal shear plane. φ is the angle of internal friction. (b) Assuming φ = 30° and β = 0°, the dips of the R, P and T fractures are 75°, 75° and 45°, respectively. (c) For β = 30°, the dips of the R, P and T fractures are 75°, 45° and 75°, respectively.
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triangle AD′B′, the total displacement AD′ can be deduced as follows: Dt ¼ AD′ ¼ L0
sinθ cos ðβÞ sin δ cos ðβ þ θÞ
ð3Þ
The value of the final horizontal length Lf = D′D + DB′ = D′C + CD + L0. D′C = Dt cosδ, where δ is the fault dip and CD = AC tanβ = D′C tanδ tanβ. Therefore, Lf = Dt cosδ (1 + tanδ tanβ) + L0. Substituting for Dt, we get the following: Lf ¼ L0
sinθ cosðβÞð1 þ tanδ tanβÞ þ1 : tanδ cosðβ þ θÞ
ð8Þ
This inequality indicates that the value of β has a limit, which depends on the value of θ. Generally, the bed dip (θ) is acquired during field work. 4.2. Application to the Sierra de San Miguelito
Lf −L0 sinθ cosðβÞð1 þ tanδ tanβÞ : ¼ tanδ cosðβ þ θÞ L0
ð5Þ
Applying cos(β+θ)=cosβ cosθ−sinβ sinθ to Eq. (5) and rearranging it, we obtain e¼
b b arcð1=tanqÞ:
ð4Þ
Substituting in Eq. (1)
e¼
obtained: 1 − tanθ tanβ > 0, and rearranging this expression, β satisfies the following:
tanθð1 þ tanδ tanβÞ : tanδð1− tanθ tanβÞ
To calculate the direction of the simple shear (β), we use the data published by Xu et al. (2004). According to the strain ellipsoid calculated by Nieto-Samaniego et al. (1999), Xu et al. (2004) estimated the extension in the measured cross-section A–A′ (Fig. 1) to be e = 0.18. Using that value for e, we calculated β for each fault block across the section. From Eq. (6),
β ¼ arctan
e cotθ− cotδ : 1þe
ð9Þ
ð6Þ
For the vertical shear (β = 0), the horizontal extension is tanθ : ð7Þ tanδ To determine the direction of the simple shear, Eq. (6) requires e > 0 for reverse drag of the beds. Consequently, the following inequality is
ev ¼
(a)
The calculated directions of the simple shear (β) vary from −29.2° to 34° (Table 1), with an average value of 3.3°. Our results are consistent with the argument of White et al. (1986), who proposed that β is less than 45° for the hanging wall blocks of listric faults. Furthermore, the values of β are within the range calculated by the inequality (8). Finally, these results indicate that simple shear was nearly vertical throughout the section.
(b)
(c)
(d)
SW
Bedding
s ke Dy
R 15°
ipa
ult
l fa
T
l fa
48° 78°
Pri nci pa
inc
ult
45°
Pr
Fig. 7. Characteristics of the pyroclastic dykes near the observation point (C) marked in Fig. 1a. (a) and (b) Dykes display flow bands and have a high dip angle. (c) Stereographic projections of the dykes in the vicinity of fault 13. (b) Sketch explaining the Riedel fractures used to calculate the angle of shear direction of fault 13 (β = 3°). In this shear direction, the distribution of the dykes is consistent with the R shear fractures, with a dip of 78° synthetic to the main fault.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8
5. Emplacement of dikes in the secondary fractures The emplacement of the dykes is the result of a combination of fluid pressure Pf and normal stress (σn) on the fracture walls (Delaney et al., 1986; Jolly and Sanderson, 1997). Emplacement of a dyke is possible only if Pf > σn. According to this criterion, some orientation of the fractures would be preferred during dyke emplacement because such an orientation is favored under low normal stresses (e.g., Grosfils and Head, 1994; Rivalta and Dahm, 2004). The easiest filled fractures should be the tensional fractures (e.g., Pollard et al., 1982), followed by the R and R′ fractures and finally the P fractures (Bons et al., 2012) (Fig. 6a). The dips of the mapped dykes vary from 40° to 90°, with most of the dips belonging in the range 70°–90° (Fig. 4f). This distribution of dips can be compared to the secondary fractures formed within the fault-bounded blocks by an inclined simple shear. If the internal friction angle and the direction of the simple shear are known, the attitudes of the secondary fractures can be determined. For most rocks, the coefficient of the internal friction is 0.6–0.85 (e.g., Byerlee, 1978). We assume that the value of the internal friction angle (ϕ) is between 30° and 40°. The angular relationship between the secondary fractures and the shear direction is exemplified in Fig. 6 for β = 0° and ϕ =30°. The dips of the R, T and P fractures are 75° (clockwise), 45° and 75°, respectively. Another example is in Fig. 6c, where the angle of the shear direction is β = 30°, in which case, the dips of the R, R′, T and P fractures are 75° (counterclockwise), 45°, 75° and 45°, respectively. For further analysis, we studied three sites in detail. The first site is near fault 13 (point C in Fig. 1a). The pyroclastic dykes show flow and band structures (Fig. 7a, b). The dykes have an average attitude of 310°/79°SW, approximately in the same direction as the principal fault (Fig. 7c). Using an angle 3° for β, calculated from fault 13, the
(a)
7
dip of the R fractures is 78°, which is similar to the average dip of the dykes (Fig. 7d). The second site is in the vicinity of fault 12 (point A in Fig. 1a). The widest dyke has an attitude of 320°/72° NW and 30–40 cm of width (Fig. 8a). This dyke does not show bands. Using β = 30° (Table 1), we can obtain the angle of the R fractures (Fig. 8b). This value is consistent with the dips of pyroclastic dykes (72°). The third site is in the vicinity of fault 17 (point B in Fig. 1a). The widest dyke has an attitude of 300°/65° NE and 20–40 cm of width (Fig. 8c). The dykes show bands, which may indicate multiple dykefill. According to the bedding and fault dips, β in this fault block is 34° (Table 1). The angle of the R fractures is 71° (Fig. 8d). This value is consistent with the dips of the pyroclastic dykes (65°).
6. Discussion P and R fractures may develop at the same time (Bartlett et al., 1981; Gamond, 1983). Generally, R fractures first occur before the peak shear strength and continue after this point is reached. P fractures form during the post-peak state as Riedel fractures (R and R′ fractures) and are extended and rotated into a direction more parallel to the shear zone (Moore and Byerlee, 1992). R′ fractures may form synchronously with or after R fractures (Moore, 1979). When dilatation is inhibited, R fractures are more likely to develop than R′ fractures (Vialon et al., 1979). Few T fractures appear in the experiments (e.g., Bartlett et al., 1981; Ahlgren, 2001). Through analogue experiments and theoretical analysis, Misra et al. (2009) demonstrates that the development of Riedel fractures are related to the rheology and the mechanical properties of the materials, which are controlled by
SW
(b) Dip of Bedding = 10°
Attitude of pyroclasitc dyke 320°/72° NE
R
Princ ipal fa
ult
15°
75°
335°/71°SW
(d)
(c)
SW
15°
Attitude of pyroclasitc dyke 300°/65° NE
71°
Princ ip
al fau
R
lt
Dip of Bedding = 10°
345°/78°SW Fig. 8. (a) Pyroclastic dykes at the observation point (A) marked in Fig. 1a. (b) Sketch showing the orientation of Riedel fractures calculated for β = 30° at point A in fault 12. (c) Pyroclastic dykes at the observation point (B) marked in Fig. 1a. (d) Sketch showing the orientation of the Riedel fractures calculated for β = 34°, at point (B) in fault 17.
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the grain constituents; materials with more ductility prefer to form R fractures first. We believe that the order of formation of the fractures within a shear zone influences the type of fractures in which the dykes are most likely to be emplaced. Although the sequential development of the second order shears is poorly understood, most authors agree that R fractures predate all other types of fractures (Morgenstern and Tchalenko, 1967; Tchalenko, 1970; Bartlett et al., 1981; Naylor et al., 1986). This could explain why in blocks deformed by internal shear in the Sierra de San Miguelito, we found the pyroclastic dikes to be emplaced within the R fractures. 7. Conclusions The orientations of the pyroclastic dike swarm of the Sierra de San Miguelito were measured. Most orientations of the dikes do not coincide with the orientation of the T fractures. To explain this behavior of the dikes, we calculated the theoretical orientations of the secondary fractures. In the analysis, simple shear was assumed to be the mechanism of strain in the study area, as proposed in previous work. To that end, we obtained the equations to calculate the extension and direction of the simple shear for the case of reverse drag of normal faults. The extension e is expressed by the equation ðβ Þð1þ tanδ tanβÞ e ¼ sinθ cos . If the extension is known, the angle of shear tanδ cosðβþθÞ cotδ direction can be obtained from the equation β ¼ arctan e cotθ− . 1þe We calculated the angles of the shear direction, β, from the domino faults in the Sierra de San Miguelito, Mesa Central, México. The values of β vary from −29.2° to 34°, with an average value of 3.3°. With these values, we were able to ascertain the orientations of the secondary fractures in each of the fault-bounded block of the system. Comparing the shear fractures produced by an internal simple shear in the fault-bounded blocks, with the dike orientations in the Sierra de San Miguelito, we conclude that the pyroclastic dykes were emplaced mainly within the R shear fractures. Acknowledgements This work was supported by the PAPIIT project IN107610 and the Conacyt projects 08967 and 80142. We acknowledge Fernando Ornelas Marques for his comments and suggestions, which greatly improved the quality of the manuscript. References Ahlgren, S.G., 2001. The nucleation and evolution of Riedel shear zones as deformation bands in porous sandstone. Journal of Structural Geology 23, 1203–1214. Anderson, E.M., 1951. The Dynamics of Faulting. Oliver and Boyd, Edinburgh. 83 pp. Axen, G.J., 1988. The geometry of planar domino-style normal faults above a dipping basal detachment. Journal of Structural Geology 10, 405–411. Bartlett, W.L., Friedman, M., Logan, J.M., 1981. Experimental folding and faulting of rocks under confining pressure Part IX. Wrench faults in limestone layers. Tectonophysics 79, 255–277. Bons, P.D., Elburg, M.A., Gomez-Rivas, E., 2012. A review of the formation of tectonic veins and their microstructures. Journal of Structural Geology 43, 33–62. Byerlee, J.D., 1978. Friction of rocks. Pageoph 116, 615–626. Correa-Gomes, L.C., Souza Filho, C.R., Martins, C.J.F.N., Oliveira, E.P., 2001. Development of symmetrical and asymmetrical fabrics in sheet-like igneous bodies: the role of magma flow and wall-rock displacements in theoretical and natural cases. Journal of Structural Geology 23, 1415–1428. Delaney, P.T., Pollard, D.D., Ziony, J.I., McKee, E.H., 1986. Field relations between dykes and joints: emplacement processes and paleostress analysis. Journal of Geophysical Research 91, 4920–4938. Gamond, J.F., 1983. Displacement features associated with fault zones: a comparison between observed examples and experimental models. Journal of Structural Geology 5, 33–45. Grosfils, E., Head, J.W., 1994. The global distribution of giant radiating dyke swarms on Venus: implications for the global stress state. Geophysical Research Letters 21, 701–704.
Jolly, R.J.H., Sanderson, D.J., 1997. A Mohr circle construction for the opening of a preexisting fracture. Journal of Structural Geology 19, 887–892. Kerr, H., White, N., 1996. Application of an inverse method for calculation threedimensional fault geometries and slip vectors, Nun River field, Nigeria. American Association of Petroleum Geologists Bulletin 80, 432–444. Kerr, H., White, N., Brun, J.P., 1993. An automatic method for determining 3-D normal fault geometries. Journal of Geophysics Research 98, 17837–17857. Labarthe-Hernández, G., Jiménez-López, L.S., 1994. Geología de la porción sureste de la Sierra de San Miguelito. S.L.P. Universidad Autónoma de San Luis Potosí, Instituto de Geología, Folleto Técnico (Open File Report), 120. 34 pp. Labarthe-Hernández, G., Tristán-González, M., Aranda-Gómez, J.J., 1982. Revisión estratigráfica del Cenozoico de la parte central del Estado de San Luis Potosí. Universidad Autónoma de San Luis Potosí, Instituto de Geología y Metalurgia, Folleto Técnico (Open File Report), 85. 208 pp. Misra, S., Mandal, N., Chakraborty, C., 2009. Formation of Riedel shear fractures in granular materials: findings from analogue shear experiments and theoretical analyses. Tectonophysics 471, 253–259. Moore, J.M., 1979. Tectonics of the Najd transcurrent fault system, Saudi Arabia. Journal of the Geological Society 136, 441–454. Moore, D.E., Byerlee, J., 1992. Relationships between sliding behavior and internal geometry of laboratory fault zones and some creeping and locked strike-slip faults of California. Tectonophysics 211, 305–316. Morgenstern, N.R., Tchalenko, J.S., 1967. Microscopic structures in kaofin subjected to direct shear. Geotechnique 17, 309–328. Naylor, M.A., Mandl, G., Sijpesteijn, C.H.K., 1986. Fault geometries in basement-induced wrench faulting under different initial stress states. Journal of Structural Geology 8, 737–752. Nieto-Samaniego, A.F., Ferrari, L., Alaniz-Alvarez, S.A., Labarthe-Hernandez, G., RosasElguera, J., 1999. Variation of Cenozoic extension and volcanism across the southern Sierra Madre Occidental Volcanic Province, Mexico. Geological Society of America Bulletin 111, 347–363. Nieto-Samaniego, Á.F., Alaniz-Álvarez, S.A., Camprubí í Cano, A., 2005. La Mesa Central de Mexico: estratigrafía, estructura y evolución tectónica cenozoica. Boletín de la Sociedad Geológica Mexicana 57, 285–317. Nieto-Samaniego, A.F., Alaniz-Ávarez, S.A., Camprubí í Cano, A., 2007. Mesa Central of México: stratigraphy, structure, and Cenozoic tectonic evolution. In: Alaniz-Ávarez, S.A., Nieto-Samaniego, A.F. (Eds.), Geology of México: celebrating the Centenary of the Geological Society of México: Geological Society of America Special Paper, 422, pp. 41–70. Orozco-Esquivel, M.T., Nieto-Samaniego, A.F., Alaniz-Alvarez, S.A., 2002. Origin of rhyolitic lavas in the Mesa Central, Mexico, by crustal melting related to extension. Journal of Volcanology and Geothermal Research 118, 37–56. Pollard, D.D., Segall, P., Delaney, P.T., 1982. Formation and interpretation of dilatant echelon cracks. Geological Society of America Bulletin 93, 1291–1303. Rivalta, E., Dahm, T., 2004. Dyke emplacement in fractured media application to the 2000 intrusion at Izu islands, Japan. Geophysical Journal International 157, 283–292. Rykkelid, E., Fossen, H., 2002. Layer rotation around vertical fault overlap zones: observations from seismic data, field examples, and physical experiments. Marine and Petroleoum Geology 19, 181–192. Sibson, R.H., 1985. A note on fault reactivation. Journal of Structural Geology 7, 751–754. Takada, A., 1994. The influence of regional stress and magmatic input on styles of monogenetic and polygenetic volcanism. Journal of Geophysical Research 99, 13563–13573. Tchalenko, J.S., 1970. Similarities between shear zones of different magnitudes. Geological Society of America Bulletin 81, 1625–1640. Torres-Hernández, J.R., Labarthe-Hernández, G., Aguillón-Robles, A., Martín GómezAnguiano, M., José Luis Mata-Segura, J.L., 2006. The pyroclastic dykes of the Tertiary San Luis Potosí volcanic field: implications on the emplacement of Panalillo ignimbrite. Geofísica Internacional 45, 243–253. Tristán-González, M., 1986. Estratigrafía y tectónica del Graben de Villa de Reyes, en los estados de San Luis Potosí y Guanajuato, México. Universidad Autónoma de San Luis Potosí, Instituto de Geología, Folleto Técnico (Open File Report), 107. 91 pp. Tristán–González, M., Aguillón–Robles, A., Barboza–Gudiño, J.R., Torres–Hernández, J.R., Bellon, H., López–Doncel, R., Rodríguez–Ríos, R., Labarthe–Hernández, G., 2009. Geocronología y distribución espacial del vulcanismo en el Campo Volcánico de San Luis Potosí. Boletín de la Sociedad Geológica Mexicana 61 (3), 287–303. Twiss, R.J., Moores, E.M., 1992. Structural Geology. W.H. Freeman and Company, San Francisco, USA. 532 pp. Vialon, P., Ruhland, M., Grolier, J., 1979. Eléments de Tectonique Analytique. Masson, Paris. Westaway, R., Kusznir, N., 1993. Fault and bed “rotation” during continental extension: block rotation or vertical shear? Journal of Structural Geology 15, 753–770. White, N.J., Jackson, J.A., Mckenzie, D.P., 1986. The relationship between the geometry of normal faults and that of the sedimentary layers in their hanging walls. Journal of Structural Geology 8, 879–909. Woods, A.W., 1998. Observations and models of volcanic eruption columns. In: Gilbert, J.S., Sparks, R.S. (Eds.), The physics of explosive volcanic eruptions: Geological Society, London, Special Publication, 145, pp. 91–114. Xu, S.-S., Nieto-Samaniego, A.F., Alaniz-Álvarez, S.A., 2004. Tilting mechanism in domino faults of the Sierra de San Miguelito, Central Mexico. Geologica Acta 3, 189–201. Xu, S.-S., Nieto-Samaniego, A.F., Alaniz-Álvarez, S.A., in press. Origin of superimposed and curved slickenlines in San Miguelito range, Central Mexico. Geologica Acta.
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Emplacement of pyroclastic dykes in Riedel shear fractures: An example from the Sierra de San Miguelito, central Mexico S.-S. Xu ⁎, A.F. Nieto-Samaniego, S.A. Alaniz-Álvarez Universidad Nacional Autónoma de México, Centro de Geociencias, Boulevard Juriquilla No. 3001, Querétaro, Qro., 76230, Mexico
a r t i c l e
i n f o
Article history: Received 5 March 2012 Accepted 15 October 2012 Available online 23 October 2012 Keywords: Domino faults Simple shear Riedel fractures Pyroclastic dykes Mexico
a b s t r a c t Although magmatic dykes are considered to be emplaced at depth, there are very few studies about the emplacement of pyroclastic dykes. There are two commonly accepted mechanisms for dike emplacements; namely, formation of a hydraulic (tension) fracture and filling of pre-existing fractures. In the Sierra de San Miguelito, central Mexico, there is a dike swarm with orientations that do not concur with any of the above two cases. Instead, the dikes have orientations resembling some type of secondary fractures within the fault-bounded blocks. Within a fault-bounded block, the reverse drag of the normal faults can be explained by simple shear. Based on the simple shear mechanism, we establish a series of equations to calculate the extension and the direction of the simple shear within a fault-bounded block. As an application of our methodology, the value of β, which is the angle measured from the vertical to the direction of the simple shear, is calculated from the domino faults in the Sierra de San Miguelito, Mesa Central, Mexico. The results demonstrate that the absolute values of β for the inclined shear are smaller than 34°. The inclined shear can be antithetic (β > 0), synthetic (β b 0) or vertical (β ≈ 0). The pyroclastic dykes in the study area have most of the strikes between 300° and 330° and are sub-parallel to the major faults. The preferred dips of the pyroclastic dykes vary from 80° to 90°. The distribution of the pyroclastic dykes in the study area indicates that the dikes were primarily emplaced along the R fractures due to simple shear. These results are different from the traditional understanding, which assumes that the dykes were mainly emplaced within the tension fractures. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Different mechanisms of emplacement of dykes have been proposed and are mainly dependent on the relationship between a tectonic stress field and fluid pressure. Tension fracture is the most common mechanism and consists of the formation of type I fractures by hydraulic stress (e.g., Anderson, 1951; Takada, 1994). Another such mechanism is the emplacement of magma in a pre-existing fracture and it depends on the difference between the normal stress on the fracture walls and the fluid pressure of the magma (e.g., Delaney et al., 1986). A less well known mechanism is the injection of magma during the movement of a fault. This mechanism can be inferred from the asymmetric structures within a dyke. These structures record the relative movement between the walls and the magma flow. Existing studies involve magmatic dykes emplaced at depths where the velocities of the flow of the magma are approximately 1 m/s (Correa-Gomes et al., 2001). In contrast, there are very few studies about the emplacement of pyroclastic dykes that are formed in an episodic manner in very shallow environments, with injection velocities faster than the magmatic dykes and most likely comparable to velocities encountered in pyroclastic column models that range from 100 to 300 m/s (e.g., Woods, 1998). ⁎ Corresponding author. E-mail address: [email protected] (S.-S. Xu). 0377-0273/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jvolgeores.2012.10.010
The Sierra de San Miguelito, in central Mexico, presents an ideal example to study the emplacement of pyroclastic dykes. The rhyolitic ignimbrites and the pyroclastic rocks of the Sierra de San Miguelito are crosscut by the San Luis–Tepehuanes fault system. No calderas have been identified in the Sierra de San Miguelito as potential sources for the deposits. A possible eruption of the ignimbrites through fissures has been proposed by some authors based on the presence of numerous pyroclastic dykes that are parallel to the main faults (LabartheHernández et al., 1982; Tristán-González, 1986; Labarthe-Hernández and Jiménez-López, 1994; Orozco-Esquivel et al., 2002; TorresHernández et al., 2006). A detailed study of the composition and internal structure of the pyroclastic dykes of Sierra de San Miguelito was performed by Torres-Hernández et al. (2006). The authors proposed that the dykes were either emplaced through the formation of new fractures or by the injection of magma into pre-existing fractures. They observed that the dykes were located in the hanging wall of the major faults, but they did not discuss the type of structure that would correspond to the orientation of the dykes in the fault system. There are three main aspects of this paper. First, we present new structural data of the pyroclastic dykes and the normal faults in the Sierra de San Miguelito, Mesa Central of México. From these data, the relationship between the normal faults and the dykes is inferred. Second, assuming that vertical shear was the mechanism that deformed the fault-bounded blocks (Xu et al., 2004), we obtained the
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from the fault planes. The tilting of these beds was interpreted by Xu et al. (2004) to be produced by a vertical shear. Furthermore, there are numerous small normal faults in the area that also show domino style (Fig. 2a, b). We measured some parameters of the normal faults of different sizes. The results indicate that most of the faults have strikes between 290° and 340° (Fig. 3a). Comparing the dips of all the faults (Fig. 3b) with the dips of only the major faults (Fig. 3c), it is evident that the dips of the numerous small normal faults are greater than those of the large normal faults. In contrast, the dominant pitch of the slickenlines on the faults is in the range 80°–90° (Fig. 3d). The faults with small pitches were most likely either formed during a different set of tectonic events for the Mesa Central as proposed by Nieto-Samaniego et al. (2005) or were a result of fault interaction during a single tectonic event (Xu et al., in press).
equations for the extension and simple shear direction of the hanging wall of the major fault. Third, using these equations, the type of fracture orientations that would concur with the pyroclastic dyke orientations was determined. 2. Geology of the Sierra de San Miguelito, México The Sierra de San Miguelito is located in the physiographic province of Mesa Central, in central México (Fig. 1a) (Nieto-Samaniego et al., 2007; Tristán–González et al., 2009). The Mesa Central (MC) represents an intense acid volcanism episode comprising a large volume of lava and domes that were emplaced over an area of ca. 10,000 km 2. The pyroclastic deposits are located in the upper part of the stratigraphic column. The study area mainly consists of lava and pyroclastic rocks and comprises seven Oligocene units (Fig. 1b) (Labarthe-Hernández and Jiménez-López, 1994). From the bottom to top, the units are as follows: Portezuelo Rhyodacite, San Miguelito Rhyolite, Cantera Ignimbrite, Zapote Rhyolite, Lower Panalillo Ignimbrite, La Placa Basalt and Upper Panalillo Ignimbrite. Additionally, there are two units that unconformably overlay the Oligocene volcanic rocks, namely, the Halcones conglomerate and the alluvial deposits of Quaternary age. The Lower Cantera Ignimbrite and the Lower Panalillo Ignimbrite have better stratification than the other units (Fig. 1c). Therefore, the two ignimbrites were used as markers to measure the bedding length, bed dip and fault displacement. In the Sierra de San Miguelito, a system of normal faults (Fig. 1a) developed coevally with the Oligocene volcanic field. The normal faults show domino style that produces the tilting of blocks in a direction opposite to that of the dip direction of the faults (Figs. 1 and 2). The dips of the beds vary from a few degrees to 30°. The variation in the dips occurs both along the fault strikes and in cross-sections, which depends on the fault dips, displacements and distance away
3. Pyroclastic dykes in the study area Many pyroclastic dykes emplaced along the NW–SE faults have sub-vertical dips (Torres-Hernández et al., 2006). The dykes consist of pumice and rhyolite fragments, and broken crystals of quartz, sanidine and biotite. Some dykes show banded structure (Fig. 4a, b). The bands have different fragments, color and size. Some bands consist of symmetric structures, with the axis located near the center and parallel to the contact of the dyke with the wall rocks (Fig. 4b). This feature indicates that the dykes with the bands were formed by multiple intrusions. A comprehensive description of these dykes can be found in TorresHernández et al. (2006). On the walls of some of the dykes, slickenlines with a high angle of pitch (Fig. 4c) were observed. We measured the size of the pyroclastic dykes. In general, the dyke length varies from a few meters to hundreds of meters and their thickness varies from 1 cm to 80 cm. The thickness of the pyroclastic dykes ranges largely
(a)
(b) 05
2
1
3(km)
A
10
Upper Panalillo ignimbrite (26.8 Ma) La Placa Basalt (26.9 Ma)
F15
Lower Panalillo ignimbrite
F14
El Zapote rhyolite (27 Ma)
F18 F19
C
Mexico
Cantera ignimbrite (29 Ma) F13
B
San miguelito rhyolite (30 Ma)
F17
Study area
Oligocene
1
10
22
0
F16
AF12 F11
22
05
Portezuelo rhyodacite (30.6 Ma) Mesozoic rocks
F10 F9
F20
Upper Cantera (Ignimbrite)
F8
(c)
F7 F6 F4
F5
10 1
05
1 10
F3
10
F2
5 1 10
0 22
Lower Cantera (Ignimbrite)
F1
A
N
10 Fig. 1. (a) Normal faults in the San Miguelito, Mesa Central, Mexico, display a domino style. The insert shows the location of the study area. AA′ line is the measured cross-section. Dotted lines are the outcrops of the pyroclastic dykes. Gray circles are points of detailed observation of the pyroclastic dykes. (b) Simplified column of the stratigraphic sequence. (c) Photograph of the Cantera Ignimbrite showing good stratification.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8
3
SW
(a)
(b)
SW
(c) Fig. 2. (a) Normal fault with a dip-direction opposite to that of the bedding. (b) Normal faults show domino style. (c) Large normal faults with the domino style and with a dip-direction opposite to that of the bedding.
dykes to have a close spatial relationship with the secondary faults. The following section addresses the origin of the secondary faults that were generated by simple shear in the hanging walls of the major normal faults.
between 1 cm and 10 cm (Fig. 4d). The dyke lengths are smaller than the major faults in the study area, have strikes that range largely between 300° and 330° (Fig. 4e), and are sub-parallel to the major faults (Fig. 3a). In contrast, the preferred dips of the pyroclastic dykes vary from 80° to 90° (Fig. 4f), which are greater than the dips of the large normal faults (Fig. 3c) but similar to the dips of the numerous minor faults (Fig. 3b). From the characteristics described above and because the dykes were emplaced within the fault-bounded blocks, we interpret the
4. Simple shear produced by the large normal faults Normal faults develop progressively and the dips diminish as the extension progresses (e.g., Sibson, 1985). As a consequence of fault
N
(b)
330°
30° 50°
lt
p di
70°
290°
u Fa
310°
Total number
90° 80° 70° = 120 50 60° 40 50° 40° 30 30° 20 20°
Number
(a)
10 90°
270°
(d)
80
7
75
Fault dip (°)
70
Fault 1
65
10 12
3
5 11
60 55
40 SW
13 14
9 8
50 45
Fault 15
Number
(c)
0
2
4
6 NE
40 35 30 25 20 15 10 5 0
10° 0
10
20 30 40 50
0°
Number
Total number = 99
10° 20° 30° 40° 50° 60° 70° 80° 90°
Angle of pitch
Fig. 3. (a) Rose diagram of the strikes of all the faults. (b) Rose diagram of the dips of all the faults. (c) Dips of the large faults measured along the A–A′ section shown in Fig. 1. (d) Histogram of the pitch angles measured on the small and large faults.
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(a)
(b)
(c)
40
dyke
(d)
35
Total number = 95
Number
30
Slicklines
25 20 15 10 5 0
10
20
30
40
50
60
70
80
Thickness (cm) N 330°
310°
30°
90° 80° (f) 70° 50 60° 40 50° 40° 30 30° 20 20°
Total number = 90
Number
(e)
50°
70° 290°
10 270°
0
90°
Dyke dip 0
10
10°
20 30 40 50
0°
Number Fig. 4. (a) Example of a dyke with two bands and different sized fragments. (b) A dyke showing flow structures and bands. (c) Slickenlines on the dyke wall with a high angle of pitch. (d) Histogram of the dyke thicknesses. (e) Rose diagram of the dyke strikes. (f) Rose diagram of the dyke dips.
faults, the tilt angles of the beds and faults are equal to each other and there is no internal deformation in the fault-bounded blocks (e.g., Axen, 1988; Twiss and Moores, 1992, p. 94). The second mechanism is the vertical shear mechanism proposed in Westaway and Kusznir (1993), where it was argued that the internal deformation within a fault-bounded block is due to vertical shear. The third mechanism is the inclined shear model (White et al., 1986), wherein the internal deformation within the blocks is due to an arbitrary oblique shear, which is not necessarily parallel to the fault plane. We grouped the latter two under the “simple shear model”. Kerr and White (1996)
rotation, the beds in the fault-bounded blocks also tend to rotate. There are two viable mechanisms of bed rotation: 1) The normal rotation, or the normal drag, in which beds on the hanging wall dip in the same direction as the fault. 2) The reverse rotation, or reverse drag, in which beds on the hanging wall dip in a direction opposite to that of the fault (Rykkelid and Fossen, 2002). The reverse drags are formed because of the decrease in the displacement with distance along the fault plane. There are three main mechanisms for bed tilting in reverse drags. The first mechanism is based on the rigid body rotation model and assumes that the rigid blocks are bounded by normal
(a)
(b)
h
D´
C
Dt
D L0 90°+
B´
Lb A
90°- -
Fig. 5. Sketch showing the inclined shear (a) in the initial stage and (b) the geometrical configuration of the inclined shear after faulting.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8 Table 1 Values of β for the faults that crosscut the section A–A′ shown in Fig. 1a. The values were obtained by using Eq. (9) in the text. θ = average tilt of beds in the block; δ = fault dip. Fault number
1
2
3
4
5
θ (°) δ (°) β (°)
20 58 −6.3
22 62 −4.1
24.5 15 63 45 −5.5 −15
6
25 28 64 45 −4.9 −29.2
7
8
9
30 75 2.2
24 55 −13.8
18 58 3.2
Fault number or location
10
11
12
13
14
15
A
B
θ (°) δ (°) β (°)
18 75 13.7
22 65 −1.1
12 67 19.8
18 64 3.2
12 65 17.9
14 66 13.2
10 71 29.8
10 78 34
and Kerr et al. (1993) have used the inclined simple shear model on the hanging-wall of a fault to infer the geometry and slip vectors of listric normal faults. To study the relationship between the pyroclastic dykes and the large normal faults, it is necessary to know the direction of the simple shear in each fault-bounded block in the area. Although a vertical shear has been proposed by Xu et al. (2004), in this paper we re-
5
analyze the data of the faults and bed-tilting by using an inclined simple shear model. In the following section, the equations for the calculation of the angle of shear direction for the fault-bounded blocks are derived. 4.1. Theoretical angle of simple shear direction The definition of linear extension is e ¼ ðLf –L0 Þ=L0 ;
ð1Þ
where Lf is the final length and L0 is the initial length of a line. The sketch for a simple shear model of a normal fault-bounded block is shown in Fig. 5b. DB′ is the initial length of the bedding (L0). The length of the deformed bedding (Lb = AB′) is obtained from the triangle ADB′ using the law of sines:
Lb ¼ AB′ ¼
L0 sinð90 þ βÞ L cosβ ¼ 0 ; sinð90−β−θÞ cosðβ þ θÞ
ð2Þ
where β is measured from the vertical to the direction of simple shear and θ is the dip of the bed. Applying the law of sines to the
(a) R´
T R
P
45°
90°-
(b)
(c) R
R T
15
°
T
45°
15°
R´ R´
45°
15°
75°
45
°
45°
75°
P 15°
P 75°
45°
75°
Fig. 6. (a) Sketch map of the Riedel fractures. R fracture is synthetic to the movement of the principal shear plane. R′ fracture is antithetic to the movement of the principal shear plane. T fracture is the tensional fracture. P fracture is antithetic to the movement of the principal shear plane. φ is the angle of internal friction. (b) Assuming φ = 30° and β = 0°, the dips of the R, P and T fractures are 75°, 75° and 45°, respectively. (c) For β = 30°, the dips of the R, P and T fractures are 75°, 45° and 75°, respectively.
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triangle AD′B′, the total displacement AD′ can be deduced as follows: Dt ¼ AD′ ¼ L0
sinθ cos ðβÞ sin δ cos ðβ þ θÞ
ð3Þ
The value of the final horizontal length Lf = D′D + DB′ = D′C + CD + L0. D′C = Dt cosδ, where δ is the fault dip and CD = AC tanβ = D′C tanδ tanβ. Therefore, Lf = Dt cosδ (1 + tanδ tanβ) + L0. Substituting for Dt, we get the following: Lf ¼ L0
sinθ cosðβÞð1 þ tanδ tanβÞ þ1 : tanδ cosðβ þ θÞ
ð8Þ
This inequality indicates that the value of β has a limit, which depends on the value of θ. Generally, the bed dip (θ) is acquired during field work. 4.2. Application to the Sierra de San Miguelito
Lf −L0 sinθ cosðβÞð1 þ tanδ tanβÞ : ¼ tanδ cosðβ þ θÞ L0
ð5Þ
Applying cos(β+θ)=cosβ cosθ−sinβ sinθ to Eq. (5) and rearranging it, we obtain e¼
b b arcð1=tanqÞ:
ð4Þ
Substituting in Eq. (1)
e¼
obtained: 1 − tanθ tanβ > 0, and rearranging this expression, β satisfies the following:
tanθð1 þ tanδ tanβÞ : tanδð1− tanθ tanβÞ
To calculate the direction of the simple shear (β), we use the data published by Xu et al. (2004). According to the strain ellipsoid calculated by Nieto-Samaniego et al. (1999), Xu et al. (2004) estimated the extension in the measured cross-section A–A′ (Fig. 1) to be e = 0.18. Using that value for e, we calculated β for each fault block across the section. From Eq. (6),
β ¼ arctan
e cotθ− cotδ : 1þe
ð9Þ
ð6Þ
For the vertical shear (β = 0), the horizontal extension is tanθ : ð7Þ tanδ To determine the direction of the simple shear, Eq. (6) requires e > 0 for reverse drag of the beds. Consequently, the following inequality is
ev ¼
(a)
The calculated directions of the simple shear (β) vary from −29.2° to 34° (Table 1), with an average value of 3.3°. Our results are consistent with the argument of White et al. (1986), who proposed that β is less than 45° for the hanging wall blocks of listric faults. Furthermore, the values of β are within the range calculated by the inequality (8). Finally, these results indicate that simple shear was nearly vertical throughout the section.
(b)
(c)
(d)
SW
Bedding
s ke Dy
R 15°
ipa
ult
l fa
T
l fa
48° 78°
Pri nci pa
inc
ult
45°
Pr
Fig. 7. Characteristics of the pyroclastic dykes near the observation point (C) marked in Fig. 1a. (a) and (b) Dykes display flow bands and have a high dip angle. (c) Stereographic projections of the dykes in the vicinity of fault 13. (b) Sketch explaining the Riedel fractures used to calculate the angle of shear direction of fault 13 (β = 3°). In this shear direction, the distribution of the dykes is consistent with the R shear fractures, with a dip of 78° synthetic to the main fault.
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8
5. Emplacement of dikes in the secondary fractures The emplacement of the dykes is the result of a combination of fluid pressure Pf and normal stress (σn) on the fracture walls (Delaney et al., 1986; Jolly and Sanderson, 1997). Emplacement of a dyke is possible only if Pf > σn. According to this criterion, some orientation of the fractures would be preferred during dyke emplacement because such an orientation is favored under low normal stresses (e.g., Grosfils and Head, 1994; Rivalta and Dahm, 2004). The easiest filled fractures should be the tensional fractures (e.g., Pollard et al., 1982), followed by the R and R′ fractures and finally the P fractures (Bons et al., 2012) (Fig. 6a). The dips of the mapped dykes vary from 40° to 90°, with most of the dips belonging in the range 70°–90° (Fig. 4f). This distribution of dips can be compared to the secondary fractures formed within the fault-bounded blocks by an inclined simple shear. If the internal friction angle and the direction of the simple shear are known, the attitudes of the secondary fractures can be determined. For most rocks, the coefficient of the internal friction is 0.6–0.85 (e.g., Byerlee, 1978). We assume that the value of the internal friction angle (ϕ) is between 30° and 40°. The angular relationship between the secondary fractures and the shear direction is exemplified in Fig. 6 for β = 0° and ϕ =30°. The dips of the R, T and P fractures are 75° (clockwise), 45° and 75°, respectively. Another example is in Fig. 6c, where the angle of the shear direction is β = 30°, in which case, the dips of the R, R′, T and P fractures are 75° (counterclockwise), 45°, 75° and 45°, respectively. For further analysis, we studied three sites in detail. The first site is near fault 13 (point C in Fig. 1a). The pyroclastic dykes show flow and band structures (Fig. 7a, b). The dykes have an average attitude of 310°/79°SW, approximately in the same direction as the principal fault (Fig. 7c). Using an angle 3° for β, calculated from fault 13, the
(a)
7
dip of the R fractures is 78°, which is similar to the average dip of the dykes (Fig. 7d). The second site is in the vicinity of fault 12 (point A in Fig. 1a). The widest dyke has an attitude of 320°/72° NW and 30–40 cm of width (Fig. 8a). This dyke does not show bands. Using β = 30° (Table 1), we can obtain the angle of the R fractures (Fig. 8b). This value is consistent with the dips of pyroclastic dykes (72°). The third site is in the vicinity of fault 17 (point B in Fig. 1a). The widest dyke has an attitude of 300°/65° NE and 20–40 cm of width (Fig. 8c). The dykes show bands, which may indicate multiple dykefill. According to the bedding and fault dips, β in this fault block is 34° (Table 1). The angle of the R fractures is 71° (Fig. 8d). This value is consistent with the dips of the pyroclastic dykes (65°).
6. Discussion P and R fractures may develop at the same time (Bartlett et al., 1981; Gamond, 1983). Generally, R fractures first occur before the peak shear strength and continue after this point is reached. P fractures form during the post-peak state as Riedel fractures (R and R′ fractures) and are extended and rotated into a direction more parallel to the shear zone (Moore and Byerlee, 1992). R′ fractures may form synchronously with or after R fractures (Moore, 1979). When dilatation is inhibited, R fractures are more likely to develop than R′ fractures (Vialon et al., 1979). Few T fractures appear in the experiments (e.g., Bartlett et al., 1981; Ahlgren, 2001). Through analogue experiments and theoretical analysis, Misra et al. (2009) demonstrates that the development of Riedel fractures are related to the rheology and the mechanical properties of the materials, which are controlled by
SW
(b) Dip of Bedding = 10°
Attitude of pyroclasitc dyke 320°/72° NE
R
Princ ipal fa
ult
15°
75°
335°/71°SW
(d)
(c)
SW
15°
Attitude of pyroclasitc dyke 300°/65° NE
71°
Princ ip
al fau
R
lt
Dip of Bedding = 10°
345°/78°SW Fig. 8. (a) Pyroclastic dykes at the observation point (A) marked in Fig. 1a. (b) Sketch showing the orientation of Riedel fractures calculated for β = 30° at point A in fault 12. (c) Pyroclastic dykes at the observation point (B) marked in Fig. 1a. (d) Sketch showing the orientation of the Riedel fractures calculated for β = 34°, at point (B) in fault 17.
8
S.-S. Xu et al. / Journal of Volcanology and Geothermal Research 250 (2013) 1–8
the grain constituents; materials with more ductility prefer to form R fractures first. We believe that the order of formation of the fractures within a shear zone influences the type of fractures in which the dykes are most likely to be emplaced. Although the sequential development of the second order shears is poorly understood, most authors agree that R fractures predate all other types of fractures (Morgenstern and Tchalenko, 1967; Tchalenko, 1970; Bartlett et al., 1981; Naylor et al., 1986). This could explain why in blocks deformed by internal shear in the Sierra de San Miguelito, we found the pyroclastic dikes to be emplaced within the R fractures. 7. Conclusions The orientations of the pyroclastic dike swarm of the Sierra de San Miguelito were measured. Most orientations of the dikes do not coincide with the orientation of the T fractures. To explain this behavior of the dikes, we calculated the theoretical orientations of the secondary fractures. In the analysis, simple shear was assumed to be the mechanism of strain in the study area, as proposed in previous work. To that end, we obtained the equations to calculate the extension and direction of the simple shear for the case of reverse drag of normal faults. The extension e is expressed by the equation ðβ Þð1þ tanδ tanβÞ e ¼ sinθ cos . If the extension is known, the angle of shear tanδ cosðβþθÞ cotδ direction can be obtained from the equation β ¼ arctan e cotθ− . 1þe We calculated the angles of the shear direction, β, from the domino faults in the Sierra de San Miguelito, Mesa Central, México. The values of β vary from −29.2° to 34°, with an average value of 3.3°. With these values, we were able to ascertain the orientations of the secondary fractures in each of the fault-bounded block of the system. Comparing the shear fractures produced by an internal simple shear in the fault-bounded blocks, with the dike orientations in the Sierra de San Miguelito, we conclude that the pyroclastic dykes were emplaced mainly within the R shear fractures. Acknowledgements This work was supported by the PAPIIT project IN107610 and the Conacyt projects 08967 and 80142. We acknowledge Fernando Ornelas Marques for his comments and suggestions, which greatly improved the quality of the manuscript. References Ahlgren, S.G., 2001. The nucleation and evolution of Riedel shear zones as deformation bands in porous sandstone. Journal of Structural Geology 23, 1203–1214. Anderson, E.M., 1951. The Dynamics of Faulting. Oliver and Boyd, Edinburgh. 83 pp. Axen, G.J., 1988. The geometry of planar domino-style normal faults above a dipping basal detachment. Journal of Structural Geology 10, 405–411. Bartlett, W.L., Friedman, M., Logan, J.M., 1981. Experimental folding and faulting of rocks under confining pressure Part IX. Wrench faults in limestone layers. Tectonophysics 79, 255–277. Bons, P.D., Elburg, M.A., Gomez-Rivas, E., 2012. A review of the formation of tectonic veins and their microstructures. Journal of Structural Geology 43, 33–62. Byerlee, J.D., 1978. Friction of rocks. Pageoph 116, 615–626. Correa-Gomes, L.C., Souza Filho, C.R., Martins, C.J.F.N., Oliveira, E.P., 2001. Development of symmetrical and asymmetrical fabrics in sheet-like igneous bodies: the role of magma flow and wall-rock displacements in theoretical and natural cases. Journal of Structural Geology 23, 1415–1428. Delaney, P.T., Pollard, D.D., Ziony, J.I., McKee, E.H., 1986. Field relations between dykes and joints: emplacement processes and paleostress analysis. Journal of Geophysical Research 91, 4920–4938. Gamond, J.F., 1983. Displacement features associated with fault zones: a comparison between observed examples and experimental models. Journal of Structural Geology 5, 33–45. Grosfils, E., Head, J.W., 1994. The global distribution of giant radiating dyke swarms on Venus: implications for the global stress state. Geophysical Research Letters 21, 701–704.
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