Effect of Block Rotation on the Pitch of Slickenlines

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 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 There are two types of block rotation. (1.) During block and/or older faults within this fault block will rotate with rotation, the fault plane that bounds that block does not an equal angle and around the same axis of rotation. In rotate. An example is the listric normal fault whose hang- the case of simple shear (vertical shear or inclined shear), ing wall rotates as it moves along the ideally fixed fault the finite shear near the fault plane is larger than finite surface. (2.) In some cases the block rotation is produced shear far from the fault (Figure 1). Furthermore, the ro- by the rotation of faults that bound the block. When an ac- tation of the bed increases closer to the fault plane. As a tive fault rotates, smaller and older faults within the block 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 ver-

29 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 steepen- ing of antithetic smaller faults and in the progressive gen- tling 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 Figure 2. Sketch showing the change in fault type due to block ro- we describe a theory for how block rotation affects the tation. The fault plane is assumed to be of elliptical shape pitch of slickenlines in a pre-existing fault. The second with slip direction parallel to the short axis of the ellipse. part describes a model for formation of multiple slickenline One type of fault can be transformed into any other type by a certain angle of rotation. This example shows that a sets within an isolated, rotated fault plane. In the third normal fault in (a) can be changed into an oblique fault in part we present a case study of faults in the Tunich area (b), a right-slip fault in (c), a thrust fault in (d), etc. of the Gulf of Mexico.

Figure 3 explains in detail such a change of fault type 2. Change in the pitches of slicken- using a stereographic projection created by the program StereoWin [8]. In Figure 3a, a normal fault AB oriented lines during block rotation 060˚/30˚ clockwise rotates for 30˚ around a horizontal axis with a trend of 90˚. CD is the new plane after rota- When a fault rotates around a vertical axis, its strike will tion oriented 116.6˚/29˚. The slickenside line shown as change, whereas the dip does not change. In this way, point E has an original pitch angle (R) of 90˚, i.e. the the pitches of pre-existing slickenlines in the fault are fault was pure dip-slip normal fault. After rotation, point not changed. When a fault rotates about an oblique or E moves to F and has a pitch R = 26.4˚. Now, the lateral horizontal axis, its strike, dip angle, and the pitches of component of displacement (SL) is D·cos(R), whereas the slickenlines in the fault will change. In this way, after ro- dip component of displacement (SD) is D·sin(R), where D tation, an original dip-slip normal fault could have a lat- is the dip-slip component of displacement. Because R is eral component of displacement and appear as an oblique smaller than 45˚, the value of SL is larger than the value fault, or as a strike-slip fault, or as a thrust fault. Simi- of SD. Now the fault is an apparent strike-slip fault. In larly, a strike-slip or reverse fault can appear as any other Figure 3b, a strike-slip fault AB oriented 100˚/60˚ ro- type of fault by a certain block rotation. These eﬀects are tates for 50˚ in the indicated sense, around a horizontal

30 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 strikes of the smaller fault are constrained by the system. a new attitude of 140˚/45˚, which is shown in arc CD. In The value of γ may be larger than 90˚. 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˚. Simi- larly, 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.

Figure 4. Systemic variation of the pitches of slickenlines due to block rotation. The original fault is a N-S trending strike- slip fault dipping at 60˚ to east. The rotation axes are hor- Figure 3. Two examples of stereographic projection (lower hemi- izontal. The rotations are clockwise. sphere) showing the effect of clockwise rotation on the pitches of slickenlines (see text for detailed data of rotation). 3. Model of generation of multiple For the same fault, the effect of clockwise rotation around an axis is usually different from that of anticlockwise rota- sets of slickenlines during block rotation. Table 1 shows a north-south trending and eastward tion dipping fault with a dip angle of 60˚ which experiences a series of rotations about a horizontal axis trending N30˚E. According to Bott (1959) [7], the pitch (R) of a set of slick- We analyze three parameters after the same clockwise enlines can be calculated by: and anticlockwise rotations: fault attitude, slickenline attitude, and pitch angle of the slickenlines. Three results n σ − σ R 3 n2 − − n2 3 1 are obtained. First, the fault strikes and dips are dif- tan = 2 1 3 (1) n1n2 σ2 − σ1 ferent for clockwise and anticlockwise rotations. Second, the trends of the slickenlines are opposite although the where ni are the direction cosines related to coordinate plunges are equal to each other in both cases of clock- axes Xi, and σ i, are the principal stresses, assuming that wise and anticlockwise rotation. Third, the pitches of the σ i are parallel to the coordinate axes Xi. When a plane slickenlines are also different for clockwise and anticlock- rotates, its direction cosines will change. In this way, wise rotation, respectively. if the fault remains active after the rotation, the newly- Systemic change of slickenline pitch due to block rotation formed slip direction of the plane in the new position will is shown in Figure 4. In this example, the pitch of the be different from that before the rotation. This process will original slickenline is zero. After rotation, the pitch angle produce more than one set of slickenlines in the plane dur- R of the slickenline ( ) increases with the angle of rotation ing the period of rotation. The model for this mechanism α γ ( ) and the intersection angle ( ) between the original is shown in Figure 5. strike of fault and trend of the rotation axis. One can The pitch of a set of slickenlines in a new position can be see that in Figure 4 the intersection points between line calculated if the pitch of the slickenlines at the previous AB and any curve indicate a pitch of 50˚. This indicates stage is known (Figure 5). We can obtain the following that the same pitch angle can be produced from different relationship combinations of the value of γ and the amount of rotation i i−1 Ri = Θi + Ri (2) (α). Note that in this example, the value of γ is smaller than 90˚. In practice, when pre-existing smaller faults where Θi is the angle of rotation of the (i-1)th fault strike th i th rotate because of the rotation along a larger fault, the on the i fault plane, Ri is the pitch of the i 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 7.6˚ 11.4˚ 17.2˚ 21˚ 26˚ Fault (stike/dip) 354˚/47.4˚ 347.2˚/39.6˚ 337.1˚/32.9˚ 322.2˚/27.9˚ 302.7˚/25.7˚ B Slickenline(trend/plunge) 0.9˚/7.4˚ 2.4˚/12.2˚ 4.7˚/16.7˚ 7.8˚/20.7˚ 11.7˚/24.2˚ Pitch of slickenline 9.8˚ 18.8˚ 32.1˚ 48.8˚ 70.8˚

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 Alaniz- Alvarez (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. Figure 5. Block diagram showing the change of pitch in slickenlines during rotation. R is the pitch angel of slickenlines that To test the effect of block rotations on paleostress deter- ranges from 0˚ to 180˚, and Θ ranges from -90˚ to 90˚ ac- minations, we present an example of fault-slip data anal- cording to the right-hand rule. (a) At stage 1, the fault has ysis from the Gulf of Mexico (Figure 6). Many works one set of slickenlines. (b) The second set of slickenlines forms due to block rotation and reactivation in the constant have been published regarding structural features in this stress field. (c) The third set of slickenlines appears with area [15]. There are three folds trending in the NNW- further block rotation. SSE 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 lineation on the (i+1)th fault plane. The value of R is Miocene. These beds are presented as evaporites, lime- between 0˚ to 180˚ according to the right-hand rule. The stones, dolomitic limestones, siltstone and sandstone. In value of Θ is from -90˚ to 90˚ according to the right-hand this area, layer-parallel faults are commonly observed. In rule. For example, in the case of Figure 5b the value of other words, faults are reactivated bedding planes. These Θ1 is negative. 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 4. Paleostress tensor from a field the growth lineation is developed. In silty beds, a quartz example lineation is usually observed. Systematic slickenlines within bedding planes are measured from the core samples of wells A and B (Figure 7). Paleostress tensors are often determined from the fault- 25 samples from the cores in wells A and B are observed. slip data [9, 10]. For the analysis of paleostress, the For each sample, the bedding planes are sub-parallel to parameters of fault attitudes, slip sense and pitch an- each other. In this way, according to Equation 1, slick- gle (or plunge angle) of slickenlines are required. For enlines should have the same direction in each bedding this determination, three prerequisite conditions are also plane. However, the results show that the slickenlines in needed. First, the maximum shear stress vector is parallel different bedding planes are different. Observed slicken- to the slickenlines in the fault plane. Second, slickenlines lines indicate that bedding planes present dextral-lateral, are assumed to be produced by the far-field stress, indi- sinistral-lateral and normal faults. For most samples only cating that faults do not interact, and that the regional one set of slickenlines can be observed, but two or three stress field is homogeneous in space and time. Third, sets of slickenlines can be observed in some samples. the slickenlines should be measured near the center of Traditional theory assumes that each set of slickenlines in the fault. These conditions are not always met. It has a single fault plane represents a distinct tectonic phase. been documented that the maximum shear stress calcu- According to this theory, more than ten tectonic phases

32 Shunshan S. Xu, Ángel F. Nieto-Samaniego, Susana A. Alaniz-Álvarez, Luis Germán Velasquillo-Martínez

Figure 7. Slickenlines measured in layer-parallel faults from core samples of wells A and B in Figure 6. 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. tinguish between different slickenline clusters. Based on this method, our data could be divided into three homogeneous clusters, each compatible with its distinct stress could be obtained from our data in Figure 7. This is tensor. For cluster 1 in Figure 8a, the orientation of σ not consistent with the known geological history in this the maximum principal compressive stress ( 1) is inclined area [15, 18]. Therefore, we consider that these multiple (64˚/66˚, trend/plunge). For cluster 2 in Figure 8b, the σ sets of slickenlines could have been produced in part by orientation of 1 is N22˚E (attitude 22˚/01˚,). On the block rotation. The rotation is attributable to two factors. other hand, for cluster 3 in Figure 8c, the orientation of σ One is folding due to N-E regional compressive stress. 1 is 287˚ (attitude: 287˚/2˚). Evidently, none of the σ Another is by the movement of major faults, most of which orientations of 1 for the three clusters is consistent with are parallel to the strike of the beds. the proposed regional stress field that caused the forma- The measured data shown in Figure 7 were used to calcu- tion of the Cantarell-Tunich anticlinorium, which is N45- late the paleostress direction under the method of Ange- 60˚E indicated in Figure 6. In other words, the calculated lier (1991) [19]. The software program of Angelier (1989, stress tensors cannot be explained by the regional struc- 1991) [19, 20] was then used to invert for the paleostress tures in this area. We also corrected the slickenline data direction. Generally, the deduced paleostress direction by geometrically restoring the beds into a perfectly hor- is the best fitting stress direction that explains the slip izontal state. According to the bed-tilting correction, the direction along most faults within accepted angular mis- axis of rotation is 345˚/0˚ (trend/plunge), and the amount fit [21]. Nemcok, et al. (1999) [22] propose a method of rotation is 20˚. The rotation direction is clockwise. σ which is based on cluster analysis, wherein an appropri- The corrected orientations of 1 for clusters 1, 2, 3 are ate stress state for the each cluster can be determined 99.4˚/84.8˚, 20.1˚/17.6˚ and 108.2˚/10.2˚, respectively. separately. For our data, in some samples two or three These results indicate that the restored data do not re- sets of slickenlines are observed, while only one set of flect the regional stress field. slickenlines is observed in the remainder. For this reason, It is more probable that the observed orientation of slick- the method of Nemcok, et al. (1999) was also used to dis- ensides in the bedding planes is related to block rota-

33 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 Figure 9. (a) Two sets of overburden stylolites are observed. (b)-(d) Explanation of formation of two sets of stylolites. In (b), many normal faults in the study area [15, 18]. Normal stylolites 1 formed due to overburden pressure when the faults can form at an angle larger than 45˚ and will ro- beddings were horizontal. In (c), stylolites 2 formed after rotation of the bedding planes. (d) shows present state of tate down to 30˚ during continuous activity [24]. With the block. 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. In summary, block rotation is a consistent hypothesis, hav- Once stress in the bedding initiates slip, there is interac- ing been caused during folding, and also during rotation tion between the normal faults and the reactivated bed- of normal faults. The layer-parallel slip is also seen as a ding [26]. It has been documented that near the inter- result of folding and the interaction between the normal section line of interacting faults, shear stress and rotation faults and bedding planes. The multiple sets of overbur- increase considerably in the stress field [27]. Slip direc- den stylolites formed due to block rotation. Progressive tion near an intersection line will be different from that rotations explain the observed slickenline orientation bet- far from an intersection line. Large normal faults in our ter than traditional paleostress analysis. 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 5. Conclusions faults. These are all indicators of fault interaction, which implies rotation. This effect was indeed observed in our Large faults can rotate during their activity. In addition, studied area (Figure 7). Third, multiple sets of overbur- small faults can also rotate due to block rotation near den stylolites can be observed in cores from the Cantarell larger faults. During the rotation, the apparent fault type oilfield (Figure 9). For layer-parallel solution surfaces, can change. Moreover, block rotation can reactivate pre- dissolution often starts along a bedding surface in un- existing planes of weakness due to changes of stress in a formed rocks, due to overburden pressure. This indicates fault plane. In this way, new sets of slickenlines in rotated that the amount of material removed at a pressure-solution faults can be produced. The effects of block rotation can contact by dissolution is a function of the normal stress lead to a series of superimposed slickenlines in a fault present [28, 29], although pressure involves many vari- during a single tectonic event. The fault-slip data from ables including grain size, grain shape, grain boundary the Tunich area of the Gulf of Mexico indicate that the characteristics, plus temperature, etc. It is possible to fa- stress tensor that activated the observed layer-parallel vor a rotation model based on the evolution of overburden faults are not consistent with the far-field stress tensor,

34 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 [12] Tikoff B., Wojtal S.F., Displacement control of geo- the observed deviation of the stress field could be block logic structures, J. Struct. Geol., 1999, 21, 959-967 rotation. [13] Cashman P.H., Ellis M.A., Fault interaction may gen- erate multiple slip vectors on a single fault surface, Geology, 1994, 22, 1123-1126 Acknowledgement [14] Nieto-Samaniego A.F., Alaniz-Alvarez S.A., Origin and tectonic interpretation of multiple fault patterns, This work was supported by the projects D.01003 of the Tectonophysics, 1997, 270, 197-206 Instituto Mexicano del Petróleo, 049049 and 80142 Cona- [15] Angeles A.F.J., Reyes N.J., Quezada M.J.M., Meneses cyt project of Mexico. R.J., Tectonic evolution structural styles and oil habi- tat in the Campeche Sound, Mexico, GCAGS Trans- actions, 1994, XLIV, 53-62 References [16] Bartolini C., Buffler R.T., Blickwede J.F., The circum- Gulf of Mexico and the Caribbean: hydrocarbon habi- tats, basin formation, and plate tectonics, AAPG Dat- [1] Jackson J., Mckenzie D., The geometrical evolution of apages, 2003, 178 normal fault systems, J. Struct. Geol., 1983, 5, 471- [17] Mandujano V.J.J., Keppie M.J.D., Cylindrical and con- 482 ical fold geometries in the Cantarell structure, south- [2] Sharp I.R., Gawthorpe R.L., Armstrong B., Under- ern Gulf of Mexico: implications for hydrocarbon ex- hill J.R., Propagation history and passive rotation ploration, J. Petrol. Geol., 2006, 29, 215-226 of mesoscale normal faults: implications for synrift [18] Mitra S., Figueroa G.C., Hernandez-Garcia J., Al- stratigraphic development, Basin Res., 2000, 12, 285- varado A.M., Three-dimensional structural model of 305 the Cantarell and Sihil structures, Campeche Bay, [3] Xu S-S., Nieto-Samaniego A.F., Alaniz-Álvarez S.A., Mexico, AAPG Bulletin, 2005, 89, 1-26 Tilting mechanism in domino faults of the Sierra de [19] Angelier J., Programmes de Jacques Angelier: Tec- San Miguelito, Central Mexico, Geol. Acta, 2004, 3, tonique Quantitative (version 5.45), 1991 189-201 [20] Angelier J., From orientation to magnitudes in pale- [4] Smith D.K., Escartín J., Schouten H., Cann J.R., Fault ostress determinations using fault slip data, J. Struct. rotation and core complex formation: Significant pro- Geol., 1989, 11, 37-50 cesses in seafloor formation at slow-spreading mid- [21] Angelier J., Determination of the mean principal ocean ridges (Mid-Atlantic Ridge, 13˚–15˚N), Geo- directions of stress for a given fault population, chemistry Geophysics Geosystems, 2008, 9, Q03003, Tectonophysics, 1979, 56, T17-T26 DOI: 10.1029/2007GC001699. [22] Nemcok M., Kova’c D., Lisle R.J., A stress inversion [5] Ron H., Nur A., Vertical axis rotation in the Mojave; procedure for polyphase calcite twin and fault/slip evidence from the independence dike swarm, Geology, data sets, J. Struct. Geol., 1999, 21, 597-611 1996, 24, 973-976 [23] Chapple W.M., Spang J.P., Significance of layer- [6] Weinberger R., Agnon A., Ron H., Garfunkel Z., Rota- parallel slip during folding of layered sedimentary tion about an inclined axis - 3-dimensional matrices rocks, GSA Bulletin, 1974, 85, 1523-1534 for reconstructing paleomagnetic and structural data, [24] Sibson R.H., A note on fault reactivation, J. Struc. J. Struct. Geol., 1995, 17, 777-782 Geol., 1985. 7, 751-754 [7] Bott M.H.P., The mechanics of oblique slip faulting, [25] Ferrill D.A. Morris A.P., Jones S.M., Stamatakos J.A., Geol. Mag., 1959, 96, 109-117 Extensional layer parallel shear and normal faulting, [8] Allmendinger R.W., 2002. StereoWin for Windows: J. Struc. Geol., 20, 1998, 355-362 ftp://www.geo.cornell.edu/pub/rwa [26] Fossen H., Rykkelid E., The interaction between [9] Gauthier B., Angelier J., Fault tectonics and defor- oblique and layer-parallel shear in high-strain zones: mation: a method of quantification using field data, observations and experiments, Tectonophysics, 1992, Earth Planet. Sci. Lett., 1985, 74, 137-148 207, 331-343 [10] Fleischmann K.H., Nemcok M., Paleostress inversion [27] Maerten L., Variation in slip on intersecting normal of fault-slip data using the shear stress solution of faults: Implications for paleostress inversion, J. Geo- Means (1989), Tectonophysics, 1991, 196, 195-202 phys. Res., 2000,105, 2553-2565 [11] Pollard D.D., Saltzer S.D., Rubin A.M., Stress inver- [28] Lehner F.K., A model for intergranular pressure so- sion methods: are they based on faulty assumptions? lution in open systems, Tectonophysics, 1995, 245, J. Struct. Geol., 1993, 15, 1045-1054

35 Eﬀect of block rotation on the pitch of slickenlines

153-170 tacts, Geology, 1998, 26, 663-665 [29] Gal D., Nur S., Elastic strain energy as a control in the evolution of asymmetric pressure-solution con-