Cent. Eur. J. Geosci. • 3(1) • 2011 • 29-36 DOI: 10.2478/v10085-010-0031-6
Central European Journal of Geosciences
Effect of block rotation on the pitch of slickenlines Research Article
Shunshan S. Xu1∗ , Ángel F. Nieto-Samaniego1 , Susana A. Alaniz-Álvarez1 , Luis Germán Velasquillo-Martínez2 1 Universidad Nacional Autónoma de México, Centro de Geociencias, Apartado Postal 1-742, Querétaro, Qro., 76001, México 2 Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas No. 152, Col. San Bartolo Atepehuacan, C.P. 07730, México D.F., México
Received 29 July 2010; accepted 29 September 2010
Abstract: Rotation of faults or pre-existing weakness planes produce two effects on the slickenlines of fault planes. First, the rotation leads to changes in the pitch of slickenlines. As a result, the aspect of the pre-existing fault may change. For example, after rotation, a normal fault may show features of an oblique fault, a strike-slip fault, or a thrust fault. Second, due to rotation, stress states on the fault planes are different from those before the rotation. As a consequence some previous planes may be reactivated. For an isolated plane, the reactivation due to rotation can produce new sets of slickenlines. With block rotation, superimposed slickenlines can be generated in the same tectonic phase. Thus, it is not appropriate to use fault-slip data from slickenlines to analyze the stress tensor in a region where there is evidence of block rotation. As an example, we present the data of slickenlines from core samples in the Tunich area of the Gulf of Mexico. The results wrongly indicate that the calculated stress tensor deviates from the far-field stress tensor. Keywords: Block rotation • fault • pitch • slickenline • Mexico © Versita Sp. z o.o.
1.
Introduction
There are two types of block rotation. (1.) During block rotation, the fault plane that bounds that block does not rotate. An example is the listric normal fault whose hanging wall rotates as it moves along the ideally fixed fault surface. (2.) In some cases the block rotation is produced by the rotation of faults that bound the block. When an active fault rotates, smaller and older faults within the block
bounded by the active fault rotate passively [1, 2]. There are different mechanisms of rotation for an active fault [3]. For rigid-body rotation, the entire fault block is defined to have an equal degree of rotation. In this case, smaller and/or older faults within this fault block will rotate with an equal angle and around the same axis of rotation. In the case of simple shear (vertical shear or inclined shear), the finite shear near the fault plane is larger than finite shear far from the fault (Figure 1). Furthermore, the rotation of the bed increases closer to the fault plane. As a result, smaller and/or older faults that are located near an active fault will experience a greater amount of rotation.
∗
E-mail:
[email protected]
For fault-block rotations, the rotational axis can be ver29
Effect of block rotation on the pitch of slickenlines
shown in Figure 2. In this article, the rotated fault will be termed the “apparent fault”. For example, if a normal fault was changed into a strike-slip fault, the fault is named an “apparent strike-slip fault”.
Figure 1.
(a) The distribution of shear strain for a model of vertical simple shear. (b) The distribution of shear strain for inclined simple shear. (c) Symmetrical distribution of bed tilts in simple shear. (d) An asymmetrical distribution of bed tilts in simple shear.
tical, horizontal and/or inclined [4–6]. The rotation of a larger normal fault can result in the progressive steepening of antithetic smaller faults and in the progressive gentling of synthetic smaller faults. All smaller faults within a block rotate. On the other hand, the stress in a fault plane depends on the attitude of the fault [7]. As a result, for the smaller faults of different attitudes, the effects of rotation on the slickenlines are different from each other. Three parts are presented in this paper. In the first part we describe a theory for how block rotation affects the pitch of slickenlines in a pre-existing fault. The second part describes a model for formation of multiple slickenline sets within an isolated, rotated fault plane. In the third part we present a case study of faults in the Tunich area of the Gulf of Mexico.
2. Change in the pitches of slickenlines during block rotation When a fault rotates around a vertical axis, its strike will change, whereas the dip does not change. In this way, the pitches of pre-existing slickenlines in the fault are not changed. When a fault rotates about an oblique or horizontal axis, its strike, dip angle, and the pitches of slickenlines in the fault will change. In this way, after rotation, an original dip-slip normal fault could have a lateral component of displacement and appear as an oblique fault, or as a strike-slip fault, or as a thrust fault. Similarly, a strike-slip or reverse fault can appear as any other type of fault by a certain block rotation. These effects are 30
Figure 2.
Sketch showing the change in fault type due to block rotation. The fault plane is assumed to be of elliptical shape with slip direction parallel to the short axis of the ellipse. One type of fault can be transformed into any other type by a certain angle of rotation. This example shows that a normal fault in (a) can be changed into an oblique fault in (b), a right-slip fault in (c), a thrust fault in (d), etc.
Figure 3 explains in detail such a change of fault type using a stereographic projection created by the program StereoWin [8]. In Figure 3a, a normal fault AB oriented 060˚/30˚ clockwise rotates for 30˚ around a horizontal axis with a trend of 90˚. CD is the new plane after rotation oriented 116.6˚/29˚. The slickenside line shown as point E has an original pitch angle (R) of 90˚, i.e. the fault was pure dip-slip normal fault. After rotation, point E moves to F and has a pitch R = 26.4˚. Now, the lateral component of displacement (SL ) is D·cos(R), whereas the dip component of displacement (SD ) is D·sin(R), where D is the dip-slip component of displacement. Because R is smaller than 45˚, the value of SL is larger than the value of SD . Now the fault is an apparent strike-slip fault. In Figure 3b, a strike-slip fault AB oriented 100˚/60˚ rotates for 50˚ in the indicated sense, around a horizontal
Shunshan S. Xu, Ángel F. Nieto-Samaniego, Susana A. Alaniz-Álvarez, Luis Germán Velasquillo-Martínez
axis with the trend of 135˚. After rotation, the plane has a new attitude of 140˚/45˚, which is shown in arc CD. In the original fault AB, the slickenline (point A) is horizontal, i.e. the fault is a strike-slip fault. During rotation, point A moves to E which has a new pitch R = 62˚. Similarly, because R is larger than 45˚, the lateral component of displacement is smaller than the dip component of displacement. Now the fault is an apparent normal fault with lateral displacement.
strikes of the smaller fault are constrained by the system. The value of γ may be larger than 90˚.
Figure 4. Figure 3.
Two examples of stereographic projection (lower hemisphere) showing the effect of clockwise rotation on the pitches of slickenlines (see text for detailed data of rotation).
For the same fault, the effect of clockwise rotation around an axis is usually different from that of anticlockwise rotation. Table 1 shows a north-south trending and eastward dipping fault with a dip angle of 60˚ which experiences a series of rotations about a horizontal axis trending N30˚E. We analyze three parameters after the same clockwise and anticlockwise rotations: fault attitude, slickenline attitude, and pitch angle of the slickenlines. Three results are obtained. First, the fault strikes and dips are different for clockwise and anticlockwise rotations. Second, the trends of the slickenlines are opposite although the plunges are equal to each other in both cases of clockwise and anticlockwise rotation. Third, the pitches of the slickenlines are also different for clockwise and anticlockwise rotation, respectively. Systemic change of slickenline pitch due to block rotation is shown in Figure 4. In this example, the pitch of the original slickenline is zero. After rotation, the pitch angle of the slickenline (R) increases with the angle of rotation (α) and the intersection angle (γ) between the original strike of fault and trend of the rotation axis. One can see that in Figure 4 the intersection points between line AB and any curve indicate a pitch of 50˚. This indicates that the same pitch angle can be produced from different combinations of the value of γ and the amount of rotation (α). Note that in this example, the value of γ is smaller than 90˚. In practice, when pre-existing smaller faults rotate because of the rotation along a larger fault, the
Systemic variation of the pitches of slickenlines due to block rotation. The original fault is a N-S trending strikeslip fault dipping at 60˚ to east. The rotation axes are horizontal. The rotations are clockwise.
3. Model of generation of multiple sets of slickenlines during block rotation According to Bott (1959) [7], the pitch (R) of a set of slickenlines can be calculated by: tan R =
n3 n1 n2
n22 − 1 − n23
σ3 − σ1 σ2 − σ1
(1)
where ni are the direction cosines related to coordinate axes Xi , and σ i , are the principal stresses, assuming that σ i are parallel to the coordinate axes Xi . When a plane rotates, its direction cosines will change. In this way, if the fault remains active after the rotation, the newlyformed slip direction of the plane in the new position will be different from that before the rotation. This process will produce more than one set of slickenlines in the plane during the period of rotation. The model for this mechanism is shown in Figure 5. The pitch of a set of slickenlines in a new position can be calculated if the pitch of the slickenlines at the previous stage is known (Figure 5). We can obtain the following relationship Rii = Θi + Rii−1 (2) where Θi is the angle of rotation of the (i-1)th fault strike on the ith fault plane, Rii is the pitch of the ith slickenside 31
Effect of block rotation on the pitch of slickenlines
Table 1.
Comparison of the results between clockwise and anticlockwise rotation of a N-S trending strike-slip fault dipping at 60˚ to the east. The original slickenlines are horizontal. The rotation axis is horizontal, trending at 30˚. Case A-clockwise rotation; Case B-anticlockwise rotation.
Angle of rotation
15˚
25˚
35˚
45˚
55˚
Fault (stike/dip) 1.3˚/64.4˚ 3.1˚/73.2˚ 4.1˚/82.2˚ 184.3˚/82.2˚ 184.3˚/88.8˚ A Slickenline(trend/plunge) 180.9˚/7.4˚ 182.4˚/12.2˚ 184.7˚/16.7˚ 187.8˚/20.7˚ 191.7˚/24.2˚ Pitch of slickenline Fault (stike/dip) B Slickenline(trend/plunge) Pitch of slickenline
Figure 5.
7.6˚
11.4˚
21˚
26˚
0.9˚/7.4˚
2.4˚/12.2˚
4.7˚/16.7˚
7.8˚/20.7˚
11.7˚/24.2˚
9.8˚
18.8˚
32.1˚
48.8˚
70.8˚
Block diagram showing the change of pitch in slickenlines during rotation. R is the pitch angel of slickenlines that ranges from 0˚ to 180˚, and Θ ranges from -90˚ to 90˚ according to the right-hand rule. (a) At stage 1, the fault has one set of slickenlines. (b) The second set of slickenlines forms due to block rotation and reactivation in the constant stress field. (c) The third set of slickenlines appears with further block rotation.
lineation on the (i+1)th fault plane. The value of R is between 0˚ to 180˚ according to the right-hand rule. The value of Θ is from -90˚ to 90˚ according to the right-hand rule. For example, in the case of Figure 5b the value of Θ1 is negative.
4. Paleostress tensor from a field example Paleostress tensors are often determined from the faultslip data [9, 10]. For the analysis of paleostress, the parameters of fault attitudes, slip sense and pitch angle (or plunge angle) of slickenlines are required. For this determination, three prerequisite conditions are also needed. First, the maximum shear stress vector is parallel to the slickenlines in the fault plane. Second, slickenlines are assumed to be produced by the far-field stress, indicating that faults do not interact, and that the regional stress field is homogeneous in space and time. Third, the slickenlines should be measured near the center of the fault. These conditions are not always met. It has been documented that the maximum shear stress calcu32
17.2˚
354˚/47.4˚ 347.2˚/39.6˚ 337.1˚/32.9˚ 322.2˚/27.9˚ 302.7˚/25.7˚
lated from the far-field stress tensor is not always consistent with the maximum shear stress calculated from the local stress tensor [11–13]. Nieto-Samaniego and AlanizAlvarez (1997) [14] argued that multiple slip vectors on a fault may be due to fault interactions. They proposed that one of the slickenline sets in a single fault be taken as parallel to the intersection line between the fault and another weakness plane. To test the effect of block rotations on paleostress determinations, we present an example of fault-slip data analysis from the Gulf of Mexico (Figure 6). Many works have been published regarding structural features in this area [15]. There are three folds trending in the NNWSSE direction. The inferred maximum compressive stress from the axis of the anticlines is NE 45˚- 60˚ [16, 17]. The stratigraphic records in this region are Jurassic to Miocene. These beds are presented as evaporites, limestones, dolomitic limestones, siltstone and sandstone. In this area, layer-parallel faults are commonly observed. In other words, faults are reactivated bedding planes. These layer-parallel faults can be used as marker planes to study any systematic changes of slickenlines. In limestone beds, the common mineral in the faults is calcite, along which the growth lineation is developed. In silty beds, a quartz lineation is usually observed. Systematic slickenlines within bedding planes are measured from the core samples of wells A and B (Figure 7). 25 samples from the cores in wells A and B are observed. For each sample, the bedding planes are sub-parallel to each other. In this way, according to Equation 1, slickenlines should have the same direction in each bedding plane. However, the results show that the slickenlines in different bedding planes are different. Observed slickenlines indicate that bedding planes present dextral-lateral, sinistral-lateral and normal faults. For most samples only one set of slickenlines can be observed, but two or three sets of slickenlines can be observed in some samples. Traditional theory assumes that each set of slickenlines in a single fault plane represents a distinct tectonic phase. According to this theory, more than ten tectonic phases
Shunshan S. Xu, Ángel F. Nieto-Samaniego, Susana A. Alaniz-Álvarez, Luis Germán Velasquillo-Martínez
Figure 7. Figure 6.
Slickenlines measured in layer-parallel faults from core samples of wells A and B in Figure 6.
Structural sketch map of studied area in the southern Gulf of Mexico. Three folds are shown. Number 3 indicates the location of Cantarell-Tunich fold.
could be obtained from our data in Figure 7. This is not consistent with the known geological history in this area [15, 18]. Therefore, we consider that these multiple sets of slickenlines could have been produced in part by block rotation. The rotation is attributable to two factors. One is folding due to N-E regional compressive stress. Another is by the movement of major faults, most of which are parallel to the strike of the beds. The measured data shown in Figure 7 were used to calculate the paleostress direction under the method of Angelier (1991) [19]. The software program of Angelier (1989, 1991) [19, 20] was then used to invert for the paleostress direction. Generally, the deduced paleostress direction is the best fitting stress direction that explains the slip direction along most faults within accepted angular misfit [21]. Nemcok, et al. (1999) [22] propose a method which is based on cluster analysis, wherein an appropriate stress state for the each cluster can be determined separately. For our data, in some samples two or three sets of slickenlines are observed, while only one set of slickenlines is observed in the remainder. For this reason, the method of Nemcok, et al. (1999) was also used to dis-
tinguish between different slickenline clusters. Based on this method, our data could be divided into three homogeneous clusters, each compatible with its distinct stress tensor. For cluster 1 in Figure 8a, the orientation of the maximum principal compressive stress (σ1 ) is inclined (64˚/66˚, trend/plunge). For cluster 2 in Figure 8b, the orientation of σ1 is N22˚E (attitude 22˚/01˚,). On the other hand, for cluster 3 in Figure 8c, the orientation of σ1 is 287˚ (attitude: 287˚/2˚). Evidently, none of the orientations of σ1 for the three clusters is consistent with the proposed regional stress field that caused the formation of the Cantarell-Tunich anticlinorium, which is N4560˚E indicated in Figure 6. In other words, the calculated stress tensors cannot be explained by the regional structures in this area. We also corrected the slickenline data by geometrically restoring the beds into a perfectly horizontal state. According to the bed-tilting correction, the axis of rotation is 345˚/0˚ (trend/plunge), and the amount of rotation is 20˚. The rotation direction is clockwise. The corrected orientations of σ 1 for clusters 1, 2, 3 are 99.4˚/84.8˚, 20.1˚/17.6˚ and 108.2˚/10.2˚, respectively. These results indicate that the restored data do not reflect the regional stress field. It is more probable that the observed orientation of slickensides in the bedding planes is related to block rota33
Effect of block rotation on the pitch of slickenlines
stylolites, as seen in Figures 7 and 9. This model would predict progressive rotations of the bedding planes of the SW limb in Anticline 3 shown in Figure 6.
Figure 8.
The paleostress inferred from the data in Figure 7. Three clusters of slickenline sets are distinguished, which are shown in (a), (b), and (c), respectively.
tion of the beds. The rotation of the beds can be documented in three aspects. First, there is folding. Figure 7 shows that slickenlines measured parallel to the strike of the bedding planes can be observed from the core samples. As is known, layer-parallel slip can occur in layered sedimentary rocks [23]. Folding in the studied area appears as buckling [18], so the pitch of slickenlines during folding should be 90˚. Therefore, layer-parallel faults that have a high pitch angle for slickenlines in the studied area can be attributed to folding. Second, there are many normal faults in the study area [15, 18]. Normal faults can form at an angle larger than 45˚ and will rotate down to 30˚ during continuous activity [24]. With progressive rotation of normal faults, bedding rotates to steeper dips [25]. As this occurs, the resolved shear stress in bedding increases and the tendency for slip enhances. Once stress in the bedding initiates slip, there is interaction between the normal faults and the reactivated bedding [26]. It has been documented that near the intersection line of interacting faults, shear stress and rotation increase considerably in the stress field [27]. Slip direction near an intersection line will be different from that far from an intersection line. Large normal faults in our study area have different attitudes, slickenlines on bedding planes near different large faults are different, and more than one set of slickenlines form on layer-parallel faults. These are all indicators of fault interaction, which implies rotation. This effect was indeed observed in our studied area (Figure 7). Third, multiple sets of overburden stylolites can be observed in cores from the Cantarell oilfield (Figure 9). For layer-parallel solution surfaces, dissolution often starts along a bedding surface in unformed rocks, due to overburden pressure. This indicates that the amount of material removed at a pressure-solution contact by dissolution is a function of the normal stress present [28, 29], although pressure involves many variables including grain size, grain shape, grain boundary characteristics, plus temperature, etc. It is possible to favor a rotation model based on the evolution of overburden 34
Figure 9.
(a) Two sets of overburden stylolites are observed. (b)-(d) Explanation of formation of two sets of stylolites. In (b), stylolites 1 formed due to overburden pressure when the beddings were horizontal. In (c), stylolites 2 formed after rotation of the bedding planes. (d) shows present state of the block.
In summary, block rotation is a consistent hypothesis, having been caused during folding, and also during rotation of normal faults. The layer-parallel slip is also seen as a result of folding and the interaction between the normal faults and bedding planes. The multiple sets of overburden stylolites formed due to block rotation. Progressive rotations explain the observed slickenline orientation better than traditional paleostress analysis.
5.
Conclusions
Large faults can rotate during their activity. In addition, small faults can also rotate due to block rotation near larger faults. During the rotation, the apparent fault type can change. Moreover, block rotation can reactivate preexisting planes of weakness due to changes of stress in a fault plane. In this way, new sets of slickenlines in rotated faults can be produced. The effects of block rotation can lead to a series of superimposed slickenlines in a fault during a single tectonic event. The fault-slip data from the Tunich area of the Gulf of Mexico indicate that the stress tensor that activated the observed layer-parallel faults are not consistent with the far-field stress tensor,
Shunshan S. Xu, Ángel F. Nieto-Samaniego, Susana A. Alaniz-Álvarez, Luis Germán Velasquillo-Martínez
even with bedding-tilt corrections. One of the reasons for the observed deviation of the stress field could be block rotation.
Acknowledgement This work was supported by the projects D.01003 of the Instituto Mexicano del Petróleo, 049049 and 80142 Conacyt project of Mexico.
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