A quantitative analysis of transtensional margin width

Earth and Planetary Science Letters 491 (2018) 95–108

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Earth and Planetary Science Letters www.elsevier.com/locate/epsl

A quantitative analysis of transtensional margin width Ludovic Jeanniot a,c,∗ , Susanne J.H. Buiter a,b a b c

Geological Survey of Norway (NGU), Trondheim, Norway The Centre for Earth Evolution and Dynamics, University of Oslo, Norway Now in Earth Sciences – Mantle Dynamics, Utrecht University, The Netherlands

a r t i c l e

i n f o

Article history: Received 13 June 2017 Received in revised form 21 December 2017 Accepted 2 March 2018 Available online xxxx Editor: R. Bendick Keywords: transtension oblique extension continental rifting rifted margins margin width plate reconstruction

a b s t r a c t Continental rifted margins show variations between a few hundred to almost a thousand kilometres in their conjugated widths from the relatively undisturbed continent to the oceanic crust. Analogue and numerical modelling results suggest that the conjugated width of rifted margins may have a relationship to their obliquity of divergence, with narrower margins occurring for higher obliquity. We here test this prediction by analysing the obliquity and rift width for 26 segments of transtensional conjugate rifted margins in the Atlantic and Indian Oceans. We use the plate reconstruction software GPlates (www. gplates.org) for different plate rotation models to estimate the direction and magnitude of rifting from the initial phases of continental rifting until breakup. Our rift width corresponds to the distance between the onshore maximum topography and the last identified continental crust. We find a weak positive correlation between the obliquity of rifting and rift width. Highly oblique margins are narrower than orthogonal margins, as expected from analogue and numerical models. We find no relationships between rift obliquities and rift duration nor the presence or absence of Large Igneous Provinces (LIPs). © 2018 Elsevier B.V. All rights reserved.

1. Introduction The relative motions of tectonic plates with respect to each other include oblique divergence or convergence. This is to be expected because of the spherical surface of the Earth and because large-scale rheological and structural heterogeneities within the lithosphere that are oriented oblique to the main plate movements can localise deformation. Based on obliquity measurements along the present-day plate boundaries, Philippon and Corti (2016) statistically show that oblique relative plate motion (obliquity degree between 10◦ and 80◦ ) represents about 80% of the plate boundaries. Analytical and 3D numerical models have also shown that transtension requires less work than orthogonal continental rifting (Withjack and Jamison, 1986; Brune et al., 2012). Based on these arguments, we can expect that many rifted margins experience oblique motions at some periods during their evolution from rifting to seafloor spreading. We here ask the question whether the obliqueness of rifting has statistically significant effects on the deformation character of rifted continental margins. To address this question, we analyse rifted margins of the Atlantic and Indian Ocean quantitatively, using plate reconstruc-

*

Corresponding author at: Geological Survey of Norway (NGU), Trondheim, Norway. E-mail address: [email protected] (L. Jeanniot). https://doi.org/10.1016/j.epsl.2018.03.003 0012-821X/© 2018 Elsevier B.V. All rights reserved.

tions, the present-day topography and continent-ocean boundaries. Continental rifted margins are the transition between a continental crust of approximately 30–40 km ‘normal’ thickness and a much thinner oceanic crust of ca. 6–7 km thickness (Christensen and Mooney, 1995). Seismic images of continental rifted margins have highlighted a broad range in margin nature and architecture, with variations in margin width (Davison, 1997), rift flank topography (Osmundsen and Redfield, 2011), volume of volcanic materials and amount of exhumed mantle (Boillot et al., 1987; Péron-Pinvidic and Manatschal, 2009). Different widths of rifted margins have been linked to differences in obliquity of divergence, extension rates, original thermal state of the lithosphere, presence of melt, mantle hydration, and inherited basement structures (Davison, 1997, and references therein). Based on the analysis of seismic profiles of the Atlantic margins, Mascle (1976) suggested that transform margins are strictly narrow with an abrupt transition between the continental and oceanic crust. On the other hand, orthogonal margins could be either narrow or wide based on complementary analysis of 11 Brazilian margin cross-sections (Davison, 1997). This agrees with numerical models of orthogonal extension that show wide or narrow margins for variations in crustal rheology and extension rate (Huismans and Beaumont, 2011; Brune et al., 2012, 2017). The analogue models of Clifton et al. (2000) show that rift features, such as fault length and azimuth, total number of faults, and the width of deformation (defined by the lateral fault

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Based on the previous studies discussed above, we would expect that highly oblique margins are narrow, while orthogonal margins can be wide or narrow (Fig. 1). We will define ‘narrow’ and ‘wide’ for our purposes in the next section as well as our scale of observation. We have measured rift obliquity and velocity magnitude of relative plate motion for 26 transtensional and orthogonal rifted margin segments along the Atlantic and Indian Oceans (Fig. 2) for possible relationships between rift obliquity on the one hand and rift width, onshore topography, rift duration, and the presence or absence of melt on the other hand. We find a weak positive correlation between rift obliquity and width only. 2. Measurements of rift obliquity and rift width Fig. 1. Theoretical expectation of rift width versus rift obliquity.

distribution along the rift axis), are influenced by the rift obliquity. In these models, deformation occurs over a wider area with reduced obliqueness. Also active rifts may show a correlation between rift obliquity and width. The Main Ethiopian Rift varies from orthogonal rifting in the south to oblique rifting by ca. 50◦ in the north, while its width decreases from over 100 km in the south to less than 60–70 km in the north (Corti, 2009). Although early active rift systems do not necessarily predict the styles of mature margins (Brune et al., 2017; Tetreault and Buiter, 2017), this example supports a relationship between rift obliquity and width also for early stages of continental rifting. Interestingly, the Main Ethiopian Rift also points to a possible relation between rift obliquity and rift maturity: the more oblique portion of the rift shows a more advanced rifting stage.

2.1. Rift trend and rift obliquity The obliquity during continental rifting is the angle α between the normal to a rift trend and the displacement vector of the plate (Fig. 3). We classify orthogonal rifting as an obliquity less than 10◦ , transtensional rifting as obliquities between 10◦ and 80◦ , and strike-slip (transform) divergence as an angle larger than 80◦ . To estimate the obliquity during continental rifting, we use the GPlates software (www.gplates.org, Boyden et al., 2011) with the following global plate rotation models: Seton et al. (2012), Matthews et al. (2016) and Torsvik and Cocks (2016). The plate model of Matthews et al. (2016) merges 2 models: Domeier and Torsvik (2014) from 410 to 250 Ma and Müller et al. (2016) from 230 to present-day. Because plate rotation models imply choices for ages of onset of rifting and breakup, and therefore rift duration, the use of different plate rotation models allows us to evaluate some of the associated uncertainties for our measurements.

Fig. 2. The 26 conjugate rifted margin segments analysed in this study.

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Fig. 3. Rift obliquity is measured relative to the rift trend segment which is drawn approximately parallel to surrounding boundaries such as the onshore maximum topography, coast line or Continent–Ocean Boundary (COB). a) The Gulf of Aden rift trend follows the present-day trend of maximum topography, coast line, COB and mid-oceanic ridge. b) The rift trend for Greenland–Norway separation is more difficult to draw due to a long and complex rifting history: we favour the rift trend to follow as much as possible the present-day maximum topography and COB. Plate reconstruction shown in a and b uses the plate rotation model of Torsvik and Cocks (2016). The three shades of grey represent the plates for Africa and Greenland (dark grey), the plates for Arabia and Scandinavia (light grey), and the region in which the plates overlap (middle shade grey). This overlap occurs because the plate reconstructions do not take into account rift margin extension.

The first step in measuring the rift obliquity is to determine a rift trend. A rift trend is a rift segment that is more-or-less parallel to rift deformation limits, such as the conjugate continent-ocean boundaries (COB), coast lines and topography highs, and that is not varying during the overall time period of rifting. Note that a rift trend is not necessarily parallel everywhere to all those natural limits or to the present-day mid-ocean ridge, as illustrated in Fig. 3a and 3b. The presence of prominent rift features such as pull-apart basins or transform faults may affect the determination of the rift trend, which results in a varied number of rift trend segments along strike for different margins. For instance, in Fig. 3a, the Gulf of Aden has a single trend, whereas we identified 3 main trends for the Norway–Greenland separation (North, Central and South Norway–Greenland in Fig. 3b). Conversely for the Ghana–Maranhão segment in the Equatorial Atlantic Ocean, we preferred one rift trend segment ca. 1100 km long over several shorter segments, even though major transform faults are present in the area (Fig. A.1). This is also determined by data availability, where onshore data for short segments are in general less available than for long segments. Determining a rift trend segment is therefore dependent on the geodynamic and geological context, but fortunately only few margins raise intricacy (Ghana– Maranhão, North and Central Norway–Greenland, SW Australia). Eventually, the segments that we identified for the 26 rifted margins are between 300 and 1200 km long (Table A.1). We consider that short rift trend segments (<300 km) may mainly reflect lo-

cal rift features, making it difficult to extract data for our analysis. For long rift trends we verified that our results are not noticeably different if we would have broken the long segment up in smaller segments. Because determining the location of a rift trend has a certain component of human guesswork, we performed this task two times, once by the first author and once by the second author, in order to find a rift obliquity measurement error. Once the rift trend is determined, rift obliquities can be extracted from plate rotation models in GPlates. Rift obliquity is measured from the first plate movement in the plate rotation models at every 1 Myr until the model time of breakup, here defined as when the conjugate COBs of the two plates are no longer overlapping each other (no middle shade grey in Fig. 3). The early stage of rifting may be difficult to identify in geological and geophysical data as subsequent deformation phases may have overprinted the records of first extension-related deformations. Similarly, determining the age of breakup is hampered by uncertainties in the location of the COB and the identification of the first clear seafloor magnetic isochron. For example, the age of breakup for the South Atlantic Ocean is considered as Hauterivian–Barremian (130 Ma) at the level of the Walvis Ridge–Rio Grande Rise (Namibia–South Brazil/Argentina segment) followed by a northward propagation of breakup close to the Aptian/Albian boundary (112 Ma) for the Angola–São Paulo and Gabon–Bahia segments and then mid-Albian for the Cameroon–Alagoas segment (Nürnberg and Müller, 1991;

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Table 1 Rift obliquity and width for the 26 rifted margin segments. Rifted margins

Observed time of rifting1

Rift

Rift obliquity (◦ )

width3

Seton et al., 2012 model time2

↔

Matthews et al., 2016

←

→

model time2

↔

Torsvik and Cocks, 2016

←

→

model time2

↔

←

→

km

West Greenland 1. Baffin Bay

220–63

117–83

25

27

26

119–79

40

32

51

124–83

27

30

26

447

2. Davis Strait

220–63

117–83

53

57

51

119–79

68

67

70

124–83

56

61

51

398

3. Labrador Sea

220–63

117–83

8

10

4

119–79

19

22

14

124–83

9

14

4

447

North Atlantic 4. Svalbard–Greenland

57

55–45

81

68

85

55–45

81

64

86

55–45

81

69

85

184

5. North Norway–Greenland

400(?)–55

219–56

54

81

42

410–58

29

22

42

219–56

49

81

43

693

6. Central Norway–Greenland

400(?)–55

219–56

51

57

52

410–58

25

19

43

219–56

43

57

52

406

7. South Norway–Greenland

400(?)–70

219–69

65

85

13

410–80

48

61

43

219–69

72

85

13

254

8. Iberia–Newfoundland

200–130

132–120

21

20

19

199–145

24

24

24

219–138

37

59

13

1010

Central Atlantic 9. Morocco–NE coast US

228–200

202–195

16

16

16

239–200

22

22

22

209–195

16

16

16

685

10. Mauritania–NE coast US

228–200

202–195

17

17

17

239–200

14

14

14

209–195

18

18

18

926

South Atlantic 11. Guinea–Guyana

150–115

160–112

38

42

34

144–117

27

22

28

131–112

36

38

34

583

12. Ghana–Maranhão

150–115

160–112

55

30

65

144–119

57

51

64

131–112

54

23

65

481

13. Cameroun–Alagoas

150–115

160–118

21

18

45

144–118

36

5

44

131–118

22

16

47

326

14. Gabon–Bahia

150–120

160–120

19

33

9

144–120

24

25

21

131–120

20

36

11

631

15. Angola–São Paulo

150–120

160–124

25

19

35

144–121

45

26

64

131–124

25

16

36

440

16. Namibia–S Brazil

150–135

149–132

15

15

15

144–138

18

18

18

149–132

15

15

15

619

17. Red Sea

30–15

20–18

24

24

25

19–15

23

16

15

32–20

10

9

18

369

18. Gulf of Aden

34–15

20–19

58

58

58

19–17

43

53

41

32–29

67

67

67

168

19. Madagascar–Somalia

205–157

159–158

14

14

14

176–173

20

20

20

159–158

14

14

14

549

West Africa

20. Ride Davie

205–157

159–158

76

76

76

176–173

76

76

76

159–158

76

76

76

246

21. Mozambique–Antarctica

205–157

159–158

23

23

23

176–173

18

18

18

159–158

23

23

23

619

22. West India–Madagascar

?–90

132–87

80

81

36

159–93

63

55

58

132–87

81

77

65

360

23. East India–Antarctica

145–132

145–136

40

40

40

159–150

23

23

23

145–136

40

40

40

586

Indian margins

South Australia 24. SW Australia–Antarctica

145–83

120–85

56

58

55

159–100

20

20

20

120–88

54

58

47

851

25. SE Australia–Antarctica

145–70

120–80

69

82

7

159–93

50

33

78

120–84

72

78

46

765

20(?)–0

5–0

72

72

72

29–1

52

11

74

6–0

75

75

75

195

Pacific margins 26. Gulf of California 1

The approximate observed time of rifting until breakup (Ma) is from literature: Baffin Bay, Davis Strait and Labrador Sea (Larsen et al., 2009; Oakey and Chalmers, 2012); Svalbard–Greenland (Faleide et al., 1996); North, Central and South Norway–Greenland (Fossen, 1992; Faleide et al., 2008); Iberia–Newfoundland (Peron-Pinvidic et al., 2007; Tucholke et al., 2007); Morocco–NE coast US and Mauritania–NE coast US (Laville et al., 2004; Schettino and Turco, 2009); Guinea–Guyana and Ghana–Maranhão (Nürnberg and Müller, 1991; Edwards et al., 1997); Cameroon–Alagoas, Gabon–Bahia–Angola–São Paulo and Namibia–S Brazil (Nürnberg and Müller, 1991; Karner and Driscoll, 1999; Kusznir and Karner, 2007); Red Sea (Bosworth and Burke, 2005; Makris et al., 1991); Gulf of Aden (Bosworth et al., 2005); Madagascar–Somalia, Ride Davie and Mozambique–Antarctica (Salman and Abdula, 1995; Torsvik et al., 1998); East India–Antarctica (Powell et al., 1988); West India–Madagascar (Subrahmanya, 1998); SW/SE Australia–Antarctica (Williams et al., 2011; Ball et al., 2013); Gulf of California (Saunders et al., 1982; Bryan et al., 2014). 2 Model time (Ma) corresponds to the time in the plate rotation models from the first motion until breakup. Rift obliquity for ↔ the overall plate motion until breakup, ← the first 40 km extension and → the last 40 km extension prior to breakup. 3 Rift width determined as in Fig. 5 using ETOPO1 (Amante and Eakins, 2009).

Karner and Driscoll, 1999; Torsvik et al., 2009). Torsvik et al. (2009) emphasise the implication in choosing a different COB location in the South Atlantic Ocean, which results in altered rotation angles and rift duration. This choice of marks the main difference between the plate rotation models of Müller et al. (2016) and Torsvik and Cocks (2016) for onset of rifting in areas north of the Florianopolis Fracture Zone, which is 150 and 130 Ma, respectively. Timing differences between plate rotation models also occur for the onset of rifting of Iberia–Newfoundland, Norway– Greenland, East Gondwana and South Australia–Antarctica (Table 1).

Rift obliquities can vary along a rift trend segment and during the entire time of rifting. First, at some fixed time during continental rifting, rift obliquity may vary along a rift trend segment due to plate rotations. This variation occurs essentially for highly oblique margins and is dependent on the segment length: the longer the segment length, the larger the variation. Considering the 26 margins analysed in this study, the average of this obliquity variation is 1.15◦ per 100 km. We measured the mean rift obliquity along rift segments every 1 Myr, but took into account the rift obliquity variation along each segment in the error estimate

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(error bar in the following figures). Second, the movement direction of plates and their magnitude may vary during the overall timing period of rifting. This is the case for several margins, such as Norway–Greenland (Fig. 4), but also Canada–Greenland, Iberia– Newfoundland, East and West Indian margins, and South Australia– Antarctica. As rifting is multiphase (Whitmarsh and Wallace, 2001; Péron-Pinvidic and Manatschal, 2009), this raises the question which stage of rifting may control deformation features related to transtension. The variations in rift obliquities with time also raise the issue of how we can compare all our data in a consistent manner. In our evaluation of transtensional margins, we use the average of the sum of the absolute values of rift obliquity: n  | V n .αn | i =1

n

V n is the magnitude of a movement vector with its associated obliquity αn , independently of whether the divergence is dextral or sinistral, and n is the number of 1 Myr time intervals. Rift obliquities are determined for three different time periods. The overall rift obliquity corresponds to rift obliquities from the first motion of the plate pair until model time of breakup. In addition, we compare rift obliquities for the first 40 km of extension and the last 40 km extension prior to model breakup, except for the margins where the model does not show more than 40 km of extension (Morocco/Mauritania–East coast US; Namibia–S Brazil; Red Sea; Gulf of Aden; East India–Antarctica). For instance, the South Norway–Greenland rift trend segment has an overall rift obliquity of 72◦ , 85◦ for the first 40 km extension and 13◦ prior to breakup (Fig. 4). Note that the time of the first plate motion and the time of breakup may differ depending on the plate rotation model that is used. Comparing our data using more or less extension, from 20 km to a third or the half of total extension, does not result in major differences. 2.2. Rift width A measure of rifted margin width requires the use of specific limits that can be measured on all margins from similar data. We also need to measure both conjugate margins due to their potential asymmetry (Ranero and Pérez-Gussinyé, 2010). However, existing datasets and the lack of conjugate rifted margins seismic profiles do not allow us, yet, to restore all conjugate rifted margins to their initial state. Therefore, we indirectly measure the rift width using boundaries that most rifted margins have. Onshore, the farthest rift-related topography (rift flanks) is the ideal limit to characterise the width of a rift system, if the deformed region was exempted of initial topography and inherited deformation. This is of course usually never the case on Earth. Riftrelated topography may in addition have been influenced by later tectonic processes leading to faults reactivation during or following rifting (Redfield et al., 2005a), such as, another rift in its vicinity or far-field stresses. Therefore, this limit cannot be measured accurately for all rifted margins. Instead we use another onshore limit, the location of the maximum topography (Fig. 5). According to Matmon et al. (2002), this limit is primarily controlled by deep crustal root structures, even after the effects of surface processes and climate (glaciers) which reshape topography after rifting (Gilchrist et al., 1994). The maximum topography can therefore be used to approximate the edge of the ‘normal’ non-deformed continental crust prior to extension. This is an accurate limit to identify along continental rifted margins thanks to detailed topographic models (here we use ETOPO1; Amante and Eakins, 2009).

Fig. 4. Relative plate velocity magnitude and rift obliquity for the South Norway– Greenland rift trend segment using the plate rotation model of Torsvik and Cock (2016). Positive velocities characterise divergence and negative velocities convergence. The average of the sum of the absolute values of rift obliquity gives 72◦ for the overall time of rifting, 85◦ for the first 40 km of extension and 13◦ for the last 40 km of extension prior to breakup.

We used Bamber et al. (2013) for free ice-sheet topography and crustal thickness of Greenland, and Fretwell et al. (2013) for free ice-sheet topography of Antarctica. Offshore, boundaries are more difficult to identify because of non-uniform data (seismic) coverage. We use here COBs. A COB can be the first identified oceanic crust or the last continental crust, as illustrated in Fig. 5. Those limits do not necessarily coincide because of the potential presence of exhumed mantle. For our study, we use the last identified continental crust. We use the COB compilation of Seton et al. (2012) for a first order prospect and for consistency as it covers all our margins. However, COBs of Seton et al. (2012) may represent the most distal COB at some locations and the most proximal in others (Eagles et al., 2015). Therefore, where seismic profiles are available, we checked whether COBs of Seton et al. (2012) correspond to the last identified continental crust and can thus be used for our measurements. If the COB from the compilation is different than the COB from our definition, one or more corrections are applied along the whole margin, depending on the availability of seismic data. For the South and Central Norwegian margins, a COB correction was applied after the analysis by Peron-Pinvidic and Osmundsen (2016) of seismic profiles from Faleide et al. (2008). Other corrections were applied for the Iberia–Newfoundland (Funck et al., 2003; Cowie et al., 2015), Angola–São Paulo (Zalán et al., 2011) and SW/SE Australia–Antarctica margins (Williams et al., 2011) (Table A.1). A limitation to our analysis resides in the fact that global plate models use the COB location and the initial plate position to determine movements. Ideally our analysis would have required its own plate model with consistent COBs worldwide, here represented by the last identified continental crust. According to Eagles et al. (2015), COB determinations mainly rely on interpretations.

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Fig. 5. Schematic cartoon of the architecture of two rifted margin architecture showing the boundaries used in this study to determine the rift width of conjugate rifted margins: maximum topography and COB. Here we show an example for two significantly different rifted margin architectures: a wide magma-poor margin (left) and a narrow volcanic margin (right). COBl stands for the last identified continental crust; COBf stands for first identified oceanic crust (OC).

In some regions the progradation of the shelf (e.g. Niger Delta – Mauritania/SE coast US) affects the gravity anomaly and therefore adds an uncertainty to the COB interpretation. Eagles et al. (2015) estimated a worldwide COB uncertainty (COBl and COBf – Fig. 5) ranging from 10 to 100 km, averaging at 50 km, based on an extensive examination of more than 150 COB publications. In summary, we measure rift width as the horizontal distance between the onshore location of maximum topography and the offshore last identified continental crust. 3. Results and discussion Table 1 summarises rift obliquity and width for the 26 rifted margin segments analysed in this study. We present here the rift obliquity frequency and correlations between rift obliquity and rift width for the plate rotation models of Seton et al. (2012), Matthews et al. (2016), and Torsvik and Cocks (2016). The results are for measurements taken every 1 Myr during the overall time period of rifting until the model time of breakup, the first 40 km extension and the last 40 km extension prior to breakup. 3.1. Frequency of rift obliquity Fig. 6 shows rift obliquity frequency for the three plate rotation models and three time periods using 10◦ bins. Rift obliquities are unevenly scattered between 0◦ and 90◦ . For non-orthogonal margins, there are in general somewhat more rifted margins with lower than with higher rift obliquities: for all plate models and time periods, between a third and a half of the rifted margins range between 10◦ and 30◦ rift obliquity, and the rest of the margins ranges between 30◦ and 90◦ rift obliquity. This result seems to differ from the obliquity evaluation for extensional plate boundaries by Philippon and Corti (2016) which shows a higher percentage of present-day high obliquity plate boundaries. The difference in our analysis is that we measured rift obliquity for a period during continental rifting, either the overall period of rifting, for initial extension, or final extension prior to breakup. Philippon and Corti (2016) in contrast consider present-day active rifting and sea-floor spreading centres. A question that arises is, if analogue and numerical modelling suggest that less work is required for oblique rifting, why do we not observe more highly oblique margins? The reason for this difference between numerical models and our measurements may lie in the setup of the analogue and numerical models, which often use constant extension rates with time, do

not consider complex plate tectonic interactions, and often do not include inherited rheological weaknesses in the rift zone. In addition, our analysis comprises 26 samples only, because rift trend segments are primarily first-order rift features, which may affect the correlation between the number of rifted margins and their rift obliquity. Conversely, orthogonal margins with rift obliquities between 0◦ and 10◦ are the least represented in our compilation with no or only one margin for the majority of the histograms shown in Fig. 6, except for the Seton et al. (2012) plate model prior to breakup. As already suggested, this may be simply related to a statistic bias due a low number of samples. Alternatively, based on numerical modelling of the opening of the Equatorial Atlantic Ocean, Heine and Brune (2014) suggest that when two rift systems compete at the same time, the most orthogonal rift system tends to fail, which would explain their low frequency. In addition, the spherical surface of the Earth, plate reorganisations, and the presence of large-scale rheological and structural heterogeneities within the lithosphere may also explain that few or no rifted margins are actually orthogonal, although they may have had an orthogonal component in their history. 3.2. Rift width versus rift obliquity We show in Fig. 7 the relationship between rift obliquity and rift width. The error bars shown for each margin segment correspond to the variation along strike of that segment in measured rift obliquity and rift width. The uncertainties of determining the rift trend and the location of maximum topography and COB are not shown because we consider them to be similar for each rift trend. The repeatability of measurement between the two authors for determining the rift trend gives us a rift obliquity uncertainty of 4◦ . We estimate topographic highs to be falling within a 20 km precision window, which represent between 2.5 and 10% of the measurement scale of rift widths. We refer to Eagles et al. (2015) for a COB uncertainty of 50 km. In order to quantify the first order correlation between rift width and rift obliquity, we show in Fig. A.2 the linear tendency associated with our measurement. The coefficient of determination R2 is of course irrelevant because of the nature of the result which is expected to be falling into a triangle (Fig. 1), although it is indicative of how scattered our data are. Note that we do not know what the supposed rift width for orthogonal margins is in the theoretical triangle of Fig. 1.

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Fig. 6. Rift obliquity frequency of the 26 rifted margin segments analysed in this study using plate rotation models of Seton et al. (2012), Matthews et al. (2016), and Torsvik and Cocks (2016), for measurements taken during the overall plate motion until breakup, the first 40 km of extension and the last 40 km extension prior to breakup.

The 9 diagrams of Fig. 7 suggest that low rift obliquities result in a range of widths and high rift obliquities in narrow margins. However in detail, this tendency includes rather scattered data. For all plate models and time periods, the width of rifted margins ranges from ca. 300 km to 1000 km for rift obliquities smaller than 30◦ , but there are no distinctive patterns for rift obliquities larger than 60◦ . Using the Seton et al. (2012) or Torsvik and Cock (2016) plate models, high rift obliquities result in rift widths ranging from 180 km to 900 km for the overall time period of rifting or the first 40 km extension, whereas rifted margins width is between 180 km and 500 km for the model of Matthews et al. (2016). Prior to breakup, the rift width for all models are between 180 km and 500 km for obliquities larger than 60◦ , with the exception of the 750 km of SE Australia–Antarctica rift width for the plate model of Matthews et al. (2016). Our expectation was that highly oblique margins are narrow while orthogonal margins can be wide or narrow (Fig. 1). The best fit to this expectation is found using the model of Matthews et al. (2016) independently of the time period, or using the time period prior to breakup for all plate rotation models. The major differences between Matthews et al. (2016) on the one hand and Seton et al. (2012) and Torsvik and Cocks (2016) on the other hand, reside in the choice of the initial position prior to continental rifting of the Australian plate (SW/SE Australia– Antarctica), and the Iberian plate (Iberia–Newfoundland – Torsvik and Cocks, 2016). Williams et al. (2011), included in Matthews et al. (2016), interpreted the initial position of Australia further west than previously suggested, therein greatly diminishing the

high transtension component during the overall time of rifting or the first 40 km extension. However, our results suggest a better fit to our expectations for rift obliquities measured just prior to the model time of breakup, which raises the question about the stage(s) of rifting that may control the deformation of rifted margins. According to recently proposed models in which continental rifted margins architecture is set in multiple stages of rifting, the continental crust and lithosphere become weaker during the socalled stretching phase leading at some point to localised deformation (thinning) until breakup and seafloor spreading (Whitmarsh and Wallace, 2001). As a result, we would expect that the deformation prior to breakup, supposedly localised to a narrow region, would preferably impact the location of the COB, whereas the deformation during the early stages of continental rifting would primarily affect the onshore topography. There is also the question if deformation features of rifted margins can be preserved. Perhaps rifted margins set different widths for the proximal margin than for the distal margin. Osmundsen and Redfield (2011) delimit the proximal and distal margin by the taper break, where the continental crust thinned to 10 km or less, also corresponding to the outer limit of the necking zone (Péron-Pinvidic and Manatschal, 2009) (Fig. 5). Osmundsen and Redfield (2011) identified a relationship between the height of rifted margin escarpments and the distance between the maximum onshore topography and the taper break: the distance is inversely proportional to the height of the topography. The distance from the onshore maximum topography to the taper break may therefore better represent the

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Fig. 7. Rift width versus rift obliquity for measurements taken during overall plate motion until breakup (left column), the first 40 km of extension (middle column) and the last 40 km extension prior to breakup (right column), using plate rotation models of Seton et al. (2012) (bottom row), Matthews et al. (2016) (middle row), and Torsvik and Cocks (2016) (top row).

major deformation process prior to crustal separation without an over-estimation of the width due to hyper-thinned continental crust (e.g. mid-Norwegian margins). The location of the taper break, however, is not mapped worldwide, and thus could not be used in our analysis to distinguish rift widths against rift obliquities. In our analysis we assumed that the location of maximum onshore topography remains fixed over time (Matmon et al., 2002). However, it has been argued that retreat of a rift escarpment could occur at rates of 1 to 2 km/Myr (Gunnell and Harbor, 2010). We test the effect of rift escarpment retreat using the plate rotation model of Matthews et al. (2016) for selected margin segments with similar rift obliquities (Fig. A.3). We assumed that the location of the COB at a rifted margin did not change since breakup. We find a weak relationship between rift width and the age of rift initiation (i.e. period from rift initiation until present-day), which may suggest an impact of rift escarpment retreat on rift width. However, in Fig. A.3 we show that a retreat rate of 1 km/Myr does not strongly alter our overall result of a (weak) correlation of rift width with rift obliquity, suggesting that the use of maximum onshore topography in the calculation of rift width is a reasonable choice.

3.3. Rift obliquity sensitivity to rift duration and volcanism The Main Ethiopian Rift seems to point to a relation between rift obliquity and rift duration, with more oblique rifts being more mature and requiring less time to breakup than more orthogonal rifts (Keir et al., 2015). Numerical and analogue modelling of continental rifting also predict more rapid breakup for oblique margins than orthogonal margins, since oblique rifting requires less work (Brune et al., 2012; Heine and Brune, 2014). Long, slow rift phases result in more thermal cooling, which causes the lithosphere to be more difficult to break, potentially leading to rift failure. Therefore, we could expect that the rift duration should be less for high oblique margins than orthogonal margins. However, our analysis does not show any evidence of that possible relationship (Fig. A.4). There may be several explanations to this. We recognise that relations found in early, active continental rifts, as the Main Ethiopian Rift, may not fully apply to mature rifted margins, as the style of a mature margin is not necessarily predicted by the style of the early rift (Brune et al., 2017; Tetreault and Buiter, 2017). Also, plate motions are influenced by additional changing forces due to a complex plate mosaic interaction, which may lead rift systems of varied rift obliquity to succeed within a similar timing period

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Fig. 8. Present-day geographic distribution of rift obliquities and width for the 26 rifted margin segments analysed in this study using the plate rotation model of Matthews et al. (2016) for the overall time of rifting until breakup. Topographic map is ETOPO1 (Amante and Eakins, 2009).

(e.g. Somalia–Madagascar and Ride Davie). In addition, volcanism may have an impact, as well as the presence or not of prominent inherited deformation features. We also evaluated whether the relation of rift width versus rift obliquity is influenced by the presence of Large Igneous Provinces (LIP). The heating caused by a LIP can reduce lithospheric strength which may impact a correlation, because a LIP could promote fast breakup independently of the rift obliquity. We expect that such faster breakup due to a LIP could be visible in the more orthogonal margins, since oblique margins already separate more easily. In addition, we would also expect that the margins which have not been influenced by a LIP may show a better correlation between rift obliquity and rift width. However, this is not shown in our analysis (Fig. A.5). It seems that LIP-margins show a better correlation between rift obliquity and width than for the margins not disturbed by a LIP. Besides the presence or absence of LIPs, evaluating for each rift segment whether the final conjugate rifted margin is magma-poor or volcanic, if the volcanism appeared prior to rifting or during early rifting, or only at the time of breakup, is not an easy task because of non-uniform seismic coverage and variations along strike. For example, the western part of the Gulf of Aden is more volcanic than in the east, due to the Afar plume (Tard et al., 1991). 4. Conclusion We show a weak correlation between rift obliquities and widths of 26 transtensional rifted margin segments. Despite some significant differences between the 3 plate rotation models that we

used, in initial plate positions and COB locations, we show that orthogonal margins tend to be wider than highly oblique margins. The width that we measured in our analysis corresponds to the horizontal distance between the onshore maximum topography and the last identified continental crust. The resulting relationship between rift width and obliquity considers the whole evolution of rifting as we were not able to analyse in further detail specific stages of rifting that may, more or less, control the architecture of rifted margins. In addition, we could not identify any relationships of rift obliquities with rift duration and the presence or absence of LIPs. To summarise, and with some reserve, we show in Fig. 8 the geographic distribution and frequency of rift obliquities for the overall time period of rifting using the plate model of Matthews et al. (2016), which is the model that matches at best our expectations based on previous modelling studies. Acknowledgements This study was supported by the Norwegian Research Council through NFR project 213399/F20. We appreciate the many constructive discussions with Gwenn Peron-Pinvidic, Tim Redfield, John Naliboff, Per Terje Osmundsen, and the great help of Robin Watson with GPlates (www.gplates.org). We greatly thank Giacomo Corti and an anonymous reviewer for their helpful reviews of the submission version of this manuscript. Appendix A

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Fig. A.1. The 3 steps followed in this study to determining rift trend segments and measuring rift obliquity and width. We show the example for the Equatorial Atlantic Ocean and the 3 rift trends of Guinea–Guyana, Ghana–Maranhão and Cameroon–Alagoas. The first plate movement initiating rifting is 130 Ma using the plate rotation model of Torsvik and Cocks (2016). Topography is from ETOPO1 (Amante and Eakins, 2009). The offshore boundary of ETOPO1 represents the COB according to the compilation of Seton et al. (2012).

Table A.1 Present-day rift trend segment coordinates and length, LIP influence and COB corrections. Present-day rift trend segment coordinates1 lat A

long A

lat B

long B

Segment length (km)

LIP

COB

influence2

correction3

↔

←

West Greenland 1. Baffin Bay 2. Davis Strait 3. Labrador Sea

75.0098 70.7132 66.3538

−64.9834 −55.5040 −57.3676

70.7638 66.4858 60.1518

−55.2872 −57.4772 −50.5521

550 480 770

North Atlantic 4. Svalbard–Greenland 5. North Norway–Greenland 6. Central Norway–Greenland 7. South Norway–Greenland 8. Iberia–Newfoundland

83.7320 79.6875 74.1405 70.5333 42.2788

−30.5433 −13.9010 −18.4346 −18.6867 −12.9917

81.6265 76.1774 70.6700 68.5407 35.6310

−11.1168 −16.4209 −18.8105 −23.8339 −13.4267

360 395 390 300 740

✓ ✓ ✓ ✓

Central Atlantic 9. Morocco–NE coast US 10. Mauritania–NE coast US

30.0650 22.3658

−12.7718 −17.9485

23.2748 12.5470

−17.7964 −17.7142

905 1090

✓ ✓

South Atlantic 11. Guinea–Guyana 12. Ghana–Maranhão 13. Cameroun–Alagoas 14. Gabon-Bahia 15. Angola–São Paulo 16. Namibia–S Brazil

8.0075 4.1322 4.1807 −1.9773 −11.3876 −17.3896

−14.3117 −7.3434

4.1015 5.8879 −1.0560 −10.8064 −15.0594 −23.0051

−8.1810 2.6287 9.2793 12.3602 10.2394 12.2967

805 1120 590 1040 475 645

✓ ✓

✓ ✓

✓ ✓

✓ ✓

10.0031 9.3880 12.4776 10.7385

✓

→

✓ ✓

✓ ✓ ✓ ✓

−50 km −50 km −50 km −250 km (S Iberia)

✓ ✓

−60 km (Santos basin)

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Table A.1 (continued) Present-day rift trend segment coordinates1 lat A

long A

lat B

long B

Segment length (km)

LIP

COB

influence2

correction3

↔

←

→

1200 730 1000 1130 800

✓ ✓ ✓ ✓

✓ ✓ ✓ ✓

✓ ✓

76.6953 88.3483

1155 1010

✓ ✓

✓

−35.0746 −40.0467

130.7610 140.8996

1195 940

23.6954

−108.4408

555

West Africa 17. Red Sea 18. Gulf of Aden 19. Madagascar–Somalia 20. Ride Davie 21. Mozambique–Antarctica

26.6463 12.1795 1.7108 −5.1406 −15.9015

35.2973 45.4286 46.6953 40.1495 41.6404

17.1865 14.2098 −4.5666 −15.1184 −20.4628

40.9137 51.83.66 40.2094 41.9009 35.7614

Indian margins 22. West India–Madagascar 23. East India–Antarctica

16.7375 14.6332

72.5992 80.5970

7.1571 19.9567

South Australia 24. SW Australia–Antarctica 25. SE Australia–Antarctica

−36.3633 −34.8772

117.6161 132.5235

Pacific margins 26. Gulf of California

27.7471

−111.6807

✓ −100 km

1

Present-day rift trend segment coordinates are from the first author analysis and are similar for all plate rotation models. The coordinates given here are located near the coast of one of the conjugate margins. 2 We evaluated for each rift segments if a Large Igneous Province (LIP) was present or not during the overall time period of rifting, or if its presence was early rifting or prior to breakup. Data are from Buiter and Torsvik (2014). 3 A COB correction (malus) is applied if the rifted margins include exhumed mantle (Iberia–Newfoundland, Santos basin, SW Australia–Antarctica) or if new rifted margin interpretations change the location of the last identified continental crust.

Fig. A.2. Rift width versus rift obliquity for measurements taken during overall plate motion until breakup (left column), the first 40 km of extension (middle column) and the last 40 km extension prior to breakup (right column), using plate rotation models of Seton et al. (2012) (bottom row), Matthews et al. (2016) (middle row), and Torsvik and Cocks (2016) (top row). In addition to Fig. 7, we show here the linear tendency indicating that orthogonal margins are preferably wider than high oblique margins. The coefficient of determination R2 is also shown as an indicator of how scattered are our data, although irrelevant due to the nature of the result which is expected to be falling into the theoretical triangle (grey area) expected based on observations, and numerical and analogue modelling. Note that we do not know what the supposed rift width for orthogonal margins is in the theoretical triangle.

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Fig. A.3. Test of the effect of rift escarpment retreat on rift width relationships. We analysed rifts of similar obliquities to avoid the effect that rift obliquity has on rift width. We used measurements for the Matthews et al. (2016) plate rotation model for rift obliquities between 18◦ and 29◦ , which includes 12 margin segments. We assume that the location of the COB is fixed. a) Rift width versus the approximate age of rift initiation (e.g. duration from initiation to present-day) (upper plot). The lower plot shows rift width corrected by a regression rate of 1 km/Myr. The solid black lines represent the best fit and indicate the possible effect of rift escarpment retreat over time. b) Rift width versus rift obliquity using Matthews et al. (2016) plate rotation model (upper plot), and the same measurements using a rift escarpment correction of 1 km/Myr (lower plot). This test shows that even though the location of the rift escarpment location may change because of retreat due to erosion, the overall (weak) correlation of rift width with rift obliquity remains. We would argue that the uncertainty generated by the use of the maximum escarpment elevation for determining rift width has a low impact on our overall results.

Fig. A.4. Rift obliquity and rift duration are not related.

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Fig. A.5. Evaluation between rift obliquity and the presence of Large Igneous Provinces (LIP). We evaluated for each rift segment if a LIP was present or not during the overall time period of rifting, prior to early rifting or prior to breakup.

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