Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jb004519, 2007 Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge Benjamin C. Horner-Johnson, 1 Richard G. Gordon, 1 and Donald F. Argus 2 Received 19 May 2006; revised 23 January 2007; accepted 5 February 2007; published 30 May [1] Previously, we estimated the angular velocity of the Nubian plate relative to the Somalian plate from an updated set of spreading rates and transform fault azimuths. We found that the Nubia-Somalia plate boundary intersects the Southwest Indian Ridge (SWIR) between 26 E and 32 E if both the Nubian and Somalian plates are rigid and if the boundary between them is narrow. These prior results are not completely satisfactory mainly for two reasons: (1) The four-plate circuit Somalia-Antarctica-Nubia-Arabia does not close. (2) The largest (M w 6.8) recorded African earthquakes that are near, but not along, the SWIR occur near 48 E, well east of the intersection with the Nubia-Somalia boundary. Here we investigate these problems through detailed analysis of plate motion data, especially those along the SWIR east of the Andrew Bain Transform Fault Complex. We find an improved fit to the data and improved plate circuit closure if a region of the African lithosphere is interpreted as a new component plate. This new plate lies between the Nubian and Somalian plates along the SWIR and is separated from the latter by a diffuse boundary that includes the locations of the largest off-ridge earthquakes. Following C. J. H. Hartnady, we call this new plate Lwandle. Use of this new plate geometry shifts the Nubia-Somalia pole of rotation northeastward to just south of South Africa and thus alters estimates of current India-Eurasia plate motion. Citation: Horner-Johnson, B. C., R. G. Gordon, and D. F. Argus (2007), Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge, J. Geophys. Res., 112,, doi: /2006jb Department of Earth Science, Rice University, Houston, Texas, USA. 2 Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA. Copyright 2007 by the American Geophysical Union /07/2006JB004519$ Introduction [2] In a prior study [Horner-Johnson et al., 2005] (hereinafter referred to as paper 1), we estimated the angular velocity of the Nubian plate relative to the Somalian plate from an expanded and updated data set of spreading rates (averaged over the past 3.2 Ma) and transform fault azimuths. We also found that the Nubia-Somalia plate boundary intersects the Southwest Indian Ridge (SWIR) between 26 E and 32 E if both the Nubian plate and the Somalian plate are rigid and the boundary between them is narrow near that triple junction (Figures 1 and 2). This location agrees well with that found by Lemaux et al. [2002] from an analysis of the locations of crossings of magnetic anomaly 5 flanking the SWIR. The Nubia-Somalia pole of rotation of paper 1 differs significantly from, and is located 31 southwest of, that found by Chu and Gordon [1999]. This large difference in pole position has several implications: one of which is that unlike many other diffuse plate boundaries, the Nubia-Somalia pole of rotation lies significantly outside the Nubia-Somalia plate boundary (cf. Royer and Gordon [1997]; Gordon [1998]; Chu and Gordon [1999]; Conder and Forsyth [2001]; Cande and Stock [2004]). [3] Nonetheless, the results from paper 1 are not completely satisfactory for several reasons: [4] 1. The four-plate circuit Somalia-Antarctica-Nubia- Arabia does not close. [5] 2. The largest (M w 6.8) recorded African earthquakes that are near, but not along, the SWIR occur near 48 E, well east of the indicated confidence limits on the intersection of the Nubia-Somalia boundary with the SWIR (e.g., compare Figure 2 with Figure 3). [6] 3. Displacements across the East African Rift inferred from Neogene plate reconstructions that incorporate this plate geometry [e.g., Royer et al., 2006] are larger than generally accepted. [7] 4. The indicated Nubia-Somalia angular velocity is not in ideal agreement with site velocities from space geodetic data [Horner-Johnson et al., 2005]. [8] 5. The distribution of small earthquakes in the oceanic portion of the African composite plate has been previously invoked [Hartnady, 2002] to infer the presence of several smaller plates within the Somalian plate geometry inferred by Lemaux et al. [2002] and Horner-Johnson et al. [2005]. 1of12

2 Figure 1. Map of the African composite plate, component plates, and surrounding plates. The NB-LW boundary is the same as the Nubia-Somalia boundary in model i. Open circles indicate spreading rate data. Open triangles indicate transform fault azimuth data. Bathymetry (light gray lines, 4000 m depth contour) [Smith and Sandwell, 1997]. ABTFC, Andrew Bain Transform Fault Complex; BTJ, Bouvet triple junction; RTJ, Rodrigues triple junction; CIR, Central Indian Ridge. Black dots indicate earthquake epicenters ( ) [Engdahl et al., 1998]. Lambert equal-area projection. [9] 6. If only spreading rates are analyzed along the Somalian-Antarctic portion of the SWIR, the pole of rotation obtained differs significantly from that obtained from only transform fault azimuths along the same portion of the SWIR [Horner-Johnson et al., 2005]. A similar, but slightly smaller, inconsistency occurs also for Nubia-Antarctica rates and transform fault azimuths. [10] Here we investigate these problems through further analysis of plate motion data, especially those along the SWIR east of the Andrew Bain Transform Fault Complex (ABTFC). [11] Initially we investigate whether the nonclosure can be explained by biases in the spreading rates caused by outward displacement of magnetic reversal boundaries [DeMets and Wilson, 2005]. The locations of magnetic anomalies due to seafloor spreading are affected by outward displacement. Because new magma is emplaced across a several-kilometer-wide zone centered on the spreading axis, magnetic anomalies tend to be located farther from the axis of spreading than expected if reversal boundaries were vertical and if new crust and uppermost mantle were emplaced in a zone of infinitesimal width. Moreover, reversal boundaries are not vertical but instead dip away from the axis of spreading, thus also causing an outward displacement of the vertically averaged location of the reversal boundary. The size of the outward displacement of active spreading centers has been recently investigated by DeMets and Wilson [2005], who find that the globally averaged outward displacement is 1.9 ± 0.2 km (all numbers following ± in this paper are 95% confidence limits) when the outward displacement on both sides of a spreading center are summed. Herein, to correct for assumed outward displacement, a constant value of 0.6 mm yr 1 (corresponding to an outward displacement of 1.9 km [DeMets and Wilson, 2005] divided by a time interval of 3.2 Ma) is subtracted from all spreading rates. The corrected data are then reinverted. [12] The main focus of the paper, however, is to investigate whether the data are better fit by assuming that not one, but two plates, spread away from the Antarctic plate east of the ABTFC. We refer to the eastern of the two plates as the Somalian plate, and following Hartnady [2002, also personal communication, 1999], we refer to the western plate as the Lwandlean plate (Figure 1). In our investigation, for reasons discussed below, we focus on four alternative models. Model i assumes a single Somalian plate east of the ABTFC, i.e., identical to the geometry inferred in paper 1. Model ii features a plate geometry with a Somalia- Lwandle-Antarctica triple junction about 100 km east of the Indomed transform fault. Model iii features a plate 2of12

3 Figure 2. Map showing the locations along the Southwest Indian Ridge of the spreading rates (open symbols) and transform fault azimuths (shaded inverted triangles) from ship and aeromagnetic surveys used in this study. The gray lines are the 4000 m depth contour from Smith and Sandwell [1997]. The region shaded with horizontal lines near 30 E is the Nubia-Lwandle plate boundary along the SWIR. The region shaded with vertical lines is the diffuse plate boundary along the SWIR between the Lwandlean and Somalian plates. geometry with a Somalia-Lwandle-Antarctica triple junction just east of the Atlantis II transform fault. Model iv features a plate geometry with the Lwandlean plate having an eastern limit about 100 km east of the Indomed transform fault and the Somalian plate having a western limit just east of the Atlantis II transform fault (i.e., with a wide or diffuse boundary between the Lwandlean plate and the Somalian plate near the SWIR). 2. Data and Methods [13] We retain the values and assigned uncertainties of rates and transform fault azimuths from paper 1. The data along the SWIR are documented in paper 1. The Nubia- Arabia data, which are from the Red Sea and consist of 45 spreading rates and no azimuths of transform faults, are from Chu and Gordon [1998]. The Somalia-Arabia data, which are from the Gulf of Aden and consist of 46 spreading rates and 5 azimuths of transform faults, are from Chu and Gordon [1999] and documented in the auxiliary material 1 ; we omit the seven azimuths from earthquake slip vectors used by Chu and Gordon [1999] because slip vectors are known to be biased indicators of the direction of plate motion [Argus et al., 1989]. Data locations in the Red Sea and Gulf of Aden are shown in Figure 1. Data locations along the SWIR are shown in Figures 1 and 2. [14] We use the term best fitting angular velocity to refer to an angular velocity determined only from data along the relevant plate boundary. For example, the Nubia-Antarctica best fitting angular velocity is determined only from 1 Auxiliary materials are available at ftp://ftp.agu.org/apend/jb/ 2006jb data along the Nubia-Antarctica plate boundary (the SWIR west of the ABTFC). We use the term closure-fitting angular velocity to refer to an angular velocity determined from a circuit and using none of the data used to determine the best fitting angular velocity. For example, a Nubia- Antarctica closure-fitting angular velocity can be determined by summing the Nubia-Arabia, Arabia-Somalia, and Somalia-Antarctica best fitting angular velocities. We distinguish between predicted and calculated values of a datum, both of which can be compared with the observed value. A predicted value is determined entirely from data along other plate boundaries. For example, we can predict spreading rates along the Nubia-Antarctica boundary from the Nubia-Antarctica closure-fitting angular velocity. In contrast, the calculated values of rates and transforms along the Nubia-Antarctica plate boundary are estimated from an angular velocity determined, in whole or in part, from the data along the Nubia-Antarctica plate boundary itself. [15] We use statistical tests for missing plate boundaries and closure of plate circuits previously described by Stein and Gordon [1984], Gordon et al. [1987], and Gordon et al. [1990]. The first test we use is for the significance of assuming distinct Lwandlean and Somalian plates spreading away from the Antarctic plate across the SWIR east of the Nubian plate, which we assume ends along the SWIR near the middle of the ABTFC. Incorporating additional adjustable parameters always improves the fit. The purpose of the statistical tests is to examine whether the improvement in the fit is significantly better than the improvement expected by chance. Initially, the data east of the Nubian plate along the SWIR are hypothetically assumed to record the motion of a single Somalian plate relative to Antarctica and the best fitting angular velocity and associated value of chi-square 3of12

4 Figure 3. Locations and 95% confidence regions for (a) Nubia-Lwandle and (b) Somalia-Lwandle poles of rotation with motion constrained to consistency with the Somalia-Antarctica-Nubia-Arabia plate circuit. Black dots indicate earthquake epicenters ( ) [Engdahl et al., 1998]. In Figure 3a, white diamond and dashed ellipse indicate paper 1 Somalia-Nubia pole of rotation (model i). Light gray square and ellipse indicate model ii Lwandle-Nubia pole of rotation for a narrow Lwandle-Somalia plate boundary along the SWIR (at 47 E). Black square and ellipse indicate model iii Lwandle-Nubia pole of rotation for a narrow Lwandle-Somalia plate boundary along the SWIR (at 57.1 E). Dark gray square and ellipse indicate model iv Lwandle-Nubia pole of rotation for a diffuse Lwandle-Somalia boundary between 47 E and 57.1 E along the SWIR. (Table 4). In Figure 3b, light gray square and ellipse indicate model ii pole and 95% confidence region. Black square and ellipse indicate model iii pole and 95% confidence region. Gray diamond and ellipse indicate model iv pole and 95% confidence region (Table 4). White star indicates idealized pole that would be consistent with the distribution of deformation indicated by the earthquake mechanisms. Focal mechanisms are from the Harvard CMT catalogue and Shudofsky [1985]. (i.e., the sum-squared misfit normalized by the uncertainties assigned to the data) are estimated for this two-plate model. Next a three-plate model is constructed with a narrow boundary between Lwandle and Somalia assumed to lie between the two westernmost data east of the Nubian plate; chi-square is determined for this three-plate model by finding the best fitting angular velocities for both Lwandle and Somalia relative to Antarctica; the values of chi-square for each of these two best fitting angular velocities are summed to obtain chi-square for this assumed triple junction location. The assumed triple junction location is then shifted eastward along the SWIR by reassigning the westernmost remaining Somalian-Antarctic datum as the easternmost Lwandlean-Antarctic datum; chi-square for this three-plate model is determined. We repeat this process until all data are reassigned as Lwandlean-Antarctic data and chi-square has consequently been determined for N-1 three-plate models, where N is the number of data along the SWIR east of the Nubian plate. The hypothetical location of the Lwandle-Antarctica-Somalia triple junction that results in the lowest value of chi-square is taken to be the best estimate of the triple junction location. An F ratio test is used to determine if the best fitting three-plate model (with separate Lwandlean and Somalian plates spreading away from Antarctica) significantly improves the fit to the data compared with the two-plate model of a single Somalian plate spreading away from Antarctica. [16] A key test in paper 1, on which we build in this paper, is to assess whether the four-plate circuit Somalia- Antarctica-Nubia-Arabia is consistent with closure. To do so, we estimate chi-square in two different calculations. In one calculation, we sum chi-square for all four best fitting angular velocities in the circuit, i.e., Somalia-Antarctica, Antarctica-Nubia, Nubia-Arabia, and Arabia-Somalia. As each best fitting angular velocity is described by three parameters, there are a total of twelve adjustable parameters in this test. In another calculation we simultaneously invert all four sets of data, while forcing the angular velocities to consistency with closure. For this calculation there are nine adjustable parameters. Chi-square from the first calculation is always less than chi-square from the second calculation, and the difference, Dc 2, is expected to be chi-square distributed with three degrees of freedom (because there are three more adjustable parameters in the first calculation than in the second calculation). We use an F ratio test to assess whether the improvement in fit is statistically significant. If it is a significant improvement, then we infer that the circuit fails closure. [17] A useful measure of the size and orientation of nonclosure of a plate circuit is the angular velocity of nonclosure. Let A, B, C, and D be four distinct tectonic plates. We assume that plate motion data are available along the boundary between plates A and B from which their relative angular velocity ( A w B, the angular velocity of plate A relative to plate B) can be estimated. Similarly we assume that plate motion data are available along the boundary between plates B and C, between plates C and D, and between plates D and A. Let w NC = A w B + B w C + C w D + D w A be the angular velocity of nonclosure. If plates were rigid and if there were no errors in the data, one would expect 4of12

5 Figure 4. Sum-squared normalized misfit for various assumed longitudes of a hypothetical narrow boundary between the Lwandlean and Somalian plates. Thin black line indicates results from spreading rate data; heavy gray line indicates results from transform fault azimuths; heavy black line indicates results from combined spreading rate and transform fault azimuth data. The dashed horizontal lines show the significance thresholds for boundaries hypothesized from independent data or reasoning; the thin dashed line is for rates only, and the thick dashed line is for rates plus transform fault azimuths. The gray diagonally striped shaded region shows the 95% confidence limits of the narrow Lwandle-Somalia boundary for the spreading rate data. The stippled region shows the 95% confidence limits for the narrow Lwandle-Somalia boundary for the combined spreading rate and transform fault azimuth data. The light gray vertical lines show the longitudes of the transform fault azimuths. w NC = 0. With real data, in general w NC 6¼ 0 and standard statistical tools (e.g., a chi-square test) can be used to test whether the value of w NC differs significantly from zero. In this paper, A, B, C, and D respectively are the Somalian, Antarctic, Nubian, and Arabian plates. 3. Results and Discussion [18] 1. Correcting spreading rates for assumed outward displacement leads to a slightly worse fit to the data and cannot explain any of the misfits discussed in the introduction. The correction does not affect the location along the SWIR of the best fitting Nubia-Somalia plate boundary and the revised Nubian-Somalian angular velocity is not significantly different from the result in paper 1. [19] Using the geometry of paper 1, the angular velocity of nonclosure about the Somalia-Antarctica-Nubia-Arabia plate circuit changes from ± Ma 1 about 15.5 S, 55.3 W to ± Ma 1 about 17.6 S, 54.8 W and c 2 increases by 0.8. Thus the outward displacement correction slightly worsens the nonclosure problem. [20] As the plate boundary locations did not change, the location of the largest off-ridge earthquakes near the SWIR Table 1. Goodness of Fit to Subsets of Our Data Along the Southwest Indian Ridge a Plate Pair Model c 2 N v 2 c v No Lwandlean Plate; All Antarctica-Somalia Spreading Antarctica-Somalia i Best Fitting (rates plus transforms) Antarctica-Lwandle ii, iv Narrow Boundary between Lwandle and Somalia near 47.0 E Antarctica-Somalia ii Best fitting (rates) Antarctica-Lwandle iii narrow boundary between Lwandle and Somalia near 51.1 E Antarctica-Somalia iii, iv a Plate pair identifies two plates in relative motion across the Southwest Indian Ridge. The Somalian plate of model i is the region north of the SWIR and from the southern part of the Andrew Bain transform fault complex (28 E) to the Rodrigues triple junction (70 E). Abbreviations are c 2, summed squared normalized misfit; N, number of data points; v, number of degrees of freedom (i.e., the number of data minus the number of adjustable parameters); c 2 v, c 2 divided by v. 5of12

6 Table 2. Statistics for Angular Velocities a 2 Model N N rates N TF c cl v cl 2 c sum v sum Dc 2 F p i ii iii, iv a Statistics for the angular velocity of nonclosure about the Somalia-Antarctica-Nubia-Arabia plate circuit (equal to the sum of the best fit angular velocities for each plate pair in the circuit) (Table 3) and the angular velocity for the same plate circuit when closure is enforced. Abbreviations are N, number of data; N rates, number of spreading rates; N TF, number of transform fault azimuths; c cl, summed-squared normalized misfit (c 2 ) when closure is 2 enforced; v cl, number of degrees of freedom when closure is enforced; c sum, sum of c 2 for the best fitting angular velocities; v sum, number of degrees of freedom for the sum of the best fitting angular velocities; Dc 2 = c 2 cl c sum ; F = Dc 2 /3; p, probability of F being as large or larger than observed with 3 versus v sum degrees of freedom. Figure 5. Comparison of observed seafloor spreading rates with those calculated or predicted from various models for the intersection of the Lwandle-Somalia boundary with the SWIR. Dotted curve over diagonal stripes indicates rates calculated from the angular velocity (0.183 ± Ma 1 about 13.0 S, 29.8 W) that best fits spreading rates and transform fault azimuths west of 28 E, corresponding to Nubia- Antarctica motion; diagonal stripes show 1s uncertainty. The other three curves for Nubia-Antarctica motion are predictions found by summing Nubia-Arabia, Arabia-Somalia, and Somalia-Antarctica best fitting angular velocities. They differ only in which Somalian-Antarctic data are used. Solid light gray curve over vertical stripe region (0.140 ± Ma 1 about 16.5 S, 18.5 W) indicates Somalia- Antarctica data east of 47 E along the SWIR (i.e., model ii); the vertical stripe region is the 1s uncertainty. Dashed curve (no confidence region shown) (0.150 ± Ma 1 about S, 23.4 W) indicates Somalia-Antarctica data east of 28 E along the SWIR (i.e., model i). Solid black curve over horizontal stripe region (0.150 ± Ma 1 about 4.9 S, 42.7 W) indicates Somalia-Antarctica data east of 57.1 E along the SWIR (i.e., models iii and iv); the horizontal stripe region is the 1s uncertainty. Dash-dotted curve over stippled region indicates rates predicted by the angular velocity (0.170 ± Ma 1 about 2.0 N, 44.0 W) calculated by summing the Somalia-Arabia, Arabia-Nubia, and Nubia- Antarctica best fitting angular velocities. The other three curves for Somalia-Antarctica are calculations based on the best fitting angular velocities for different Somalian-Antarctic data sets. Dashed curve over diagonal stripes (0.131 ± Ma 1 about 6.8 N, 42.5 W) indicates Somalia-Antarctica data east of 28 E (model i); diagonal stripes show 1s uncertainty. Light gray curve (no confidence region shown) (0.126 ± Ma 1 about 3.0 N, 36.9 W) indicates Somalia-Antarctica data east of 47 E along the SWIR (model ii). Solid black curve (no confidence region shown) (0.154 ± Ma 1 about 13.1 N, 60.2 W) indicates Somalia-Antarctica data east of 57.1 E along the SWIR (models iii and iv). Dotted line over dotted gray outline of confidence region calculated from the Lwandle-Antarctica best fitting angular velocity (0.138 ± about 0.2 N, 35.2 W) from data between 28 E and 47 E along the SWIR (model iv); the confidence region is the 1s uncertainty. 6of12

7 Figure 6. Comparison of observed transform fault azimuths with those calculated or predicted from various models for the intersection of Lwandle-Somalia boundary with the SWIR. Dotted curve over diagonal stripes indicates azimuths calculated from the angular velocity (0.183 ± Ma 1 about 13.0 S, 29.8 W) that best fits spreading rates and transform fault azimuths west of 28 E, corresponding to Nubia-Antarctica motion; diagonal stripes show 1s uncertainty. The other three curves for Nubia- Antarctica motion are predictions found by summing Nubia-Arabia, Arabia-Somalia, and Somalia- Antarctica best fitting angular velocities. They differ only in which Somalian-Antarctic data are used. Solid light gray curve over vertical stripe region (0.140 ± Ma 1 about 16.5 S, 18.5 W) indicates Somalia-Antarctica data east of 47 E along the SWIR (model ii); the vertical stripe region is the 1s uncertainty. Dashed curve (no confidence region shown) (0.150 ± Ma 1 about 11.7 S, 23.4 W) indicates Somalia-Antarctica data east of 28 E along the SWIR (model i). Solid black curve over horizontal stripe region (0.150 ± Ma 1 about 4.9 S, 42.7 W) indicates Somalia-Antarctica data east of 57.1 E along the SWIR (models iii and iv); the horizontal stripe region is the 1s uncertainty. Dash-dotted curve over stippled region indicates azimuths predicted by the angular velocity (0.170 ± Ma 1 about 2.0 N, 44.0 W) calculated by summing the Somalia-Arabia, Arabia-Nubia, and Nubia-Antarctica best fitting angular velocities. The other three curves for Somalia-Antarctica are calculations based on the best fitting angular velocities for different Somalian-Antarctic data sets. Dashed curve over diagonal stripes (0.131 ± Ma 1 about 6.8 N, 42.5 W) indicates Somalia-Antarctica data east of 28 E (model i); diagonal stripes show 1s uncertainty. Light gray curve over solid gray outline of confidence region (0.126 ± Ma 1 about 3.0 N, 36.9 W) indicates Somalia-Antarctica data east of 47 E along the SWIR (model ii); the confidence region is the 1s uncertainty. Solid black curve over solid black outline of confidence region (0.154 ± Ma 1 about 13.1 N, 60.2 W) indicates Somalia-Antarctica data east of 57.1 E along the SWIR (models iii and iv); the confidence region is the 1s uncertainty. Dotted line over dotted gray outline of confidence region calculated from the Lwandle- Antarctica best fitting angular velocity (0.138 ± about 0.2 N, 35.2 W) from data between 28 E and 47 E along the SWIR (model iv); the confidence region is the 1s uncertainty. remain well east of the confidence limits on the intersection of the Nubia-Somalia plate boundary with the SWIR. [21] The significant difference in the locations and 95% confidence limits for the poles of rotation obtained from analyzing only spreading rates and only the transform fault azimuths along the Somalian-Antarctic portion of the SWIR [Horner-Johnson et al., 2005] is also increased slightly when the outward displacement correction is applied. While the spreading rates alone are better fit when the outward displacement correction is applied, the pole of rotation moves 0.7 farther from the pole of rotation from only the transform fault azimuths. [22] Thus the outward displacement correction to the spreading rates, which has been established by DeMets and Wilson [2005], does not improve the misfit to the data: c 2 increases by 4.4 for the best fitting location of the intersection of the Nubia-Somalia plate boundary with the 7of12

8 Figure 7. Location and three-dimensional 95% confidence ellipsoid for the angular velocity of nonclosure of the Somalia-Antarctica-Nubia-Arabia plate circuit (models iii and iv, Table 3). (a) Contours of the upper surface of the 95% confidence ellipsoid. The black square is the best fitting pole of nonclosure for model iii with narrow Lwandle-Somalia boundary at 57.1 E along the SWIR. The black cross is the location of the maximum rotation rate. (b) Contours of the lower surface of the 95% confidence ellipsoid. The black square is as in Figure 7a, and the rotation rate at the best fitting pole is Ma 1. The black cross is the location of the minimum rotation rate. The range of rotation rates at the best fitting pole is Ma 1 to Ma 1. SWIR and none of the other problems discussed in the introduction are resolved by this correction. [23] 2. Data along the SWIR east of the previously inferred Nubia-Somalia boundary are fit significantly better if it is assumed that the previously defined Somalian plate consists of two plates, which we term Lwandle for the western portion and Somalia for the eastern portion. If both rates and transform fault azimuths are analyzed, we find that the best fitting location for the intersection of the Lwandle-Somalia boundary with the Southwest Indian Ridge is between 46.7 E and 47.6 E, which is 100 km east of the Indomed transform fault. The 95% confidence limits on this location, assuming that the Lwandle-Somalia boundary is narrow where it intersects the SWIR, are from 46.5 E to 49.8 E (Figure 4). For this best fitting location, the statistic Dc 2 has a value of 24.2 with 4 degrees of freedom (Table 1). The statistic F is 5.9 with 4 versus 57 degrees of freedom; the probability, p, of obtaining a value of F this high or higher if there were a single rigid Somalian plate (and no separate Lwandle plate) is only Although the decrease in c 2 of 24.2 is large and highly significant, it is small compared with 275.4, the decrease in chi-square obtained when Nubia and Somalia are treated as distinct plates, instead of as a single African plate, spreading away from Antarctica along the SWIR [Horner-Johnson et al., 2005]. [24] If only transform fault azimuths are analyzed, we find that no location for the hypothetical intersections gives a significant improvement in the fit to the data (Figure 4). [25] If only spreading rates are analyzed, the best fitting location for the intersection of the Lwandle-Somalia boundary with the Southwest Indian Ridge is between 56.3 E and 57.4 E, an interval that includes the Atlantis II transform fault. The 95% confidence limits on this location, assuming that the Lwandle-Somalia boundary is narrow where it intersects the SWIR, also are from 56.3 E to 57.4 E (Figure 4). For this best fitting location, Dc 2 is 17.3 with 4 degrees of freedom. F = 5.4 with 4 versus 43 degrees of freedom (p = ). [26] 3. All four plate geometries along the SWIR discussed in the introduction result in significant nonclosure of the Somalia-Antarctica-Nubia-Arabia plate circuit, but the misfit is the largest for model ii, for which Dc 2 = 38.0 and smallest for models iii and iv, for which Dc 2 = 13.9 (Table 2). (Models iii and iv give identical results for this Table 3. Angular Velocity of Nonclosure for SM-AN-NB-AR Plate Circuit a Model Lat Long w w 95% Major Minor Azimuth i ii iii, iv a The angular velocity of nonclosure for the Somalia-Antarctica-Nubia-Arabia plate circuit is equal to the sum of the best fitting angular velocities for each plate pair in the circuit: Somalia-Antarctica, Antarctica-Nubia, Nubia-Arabia, and Arabia-Somalia. The only variation between models is which data along the SWIR are considered to be part of the Somalian-Antarctic plate boundary. Abbreviations are Lat, latitude in N; Long, longitude in E; w, angular speed in deg Ma 1 ; w 95%, 95% confidence limits on w; Major, major axis length in degrees of the 95% confidence ellipse for the angular velocity; Minor, minor axis length in degrees of the 95% confidence ellipse; Azimuth, azimuth of the major axis in degrees clockwise from north. 8of12

9 Figure 8. Location and three-dimensional 95% confidence ellipsoids for the Nubia-Somalia angular velocities from the Somalia-Antarctica-Nubia (black) and Somalia-Arabia-Nubia (gray) plate circuits. (a) Contours of the upper surfaces of the 95% confidence ellipsoids. The black triangle is the best fitting Nubia-Somalia angular velocity from data along the SWIR, assuming a diffuse Lwandle-Somalia boundary along the SWIR (i.e., model iv, our preferred model). The gray inverted triangle is the best fitting Nubia-Somalia angular velocity from data in the Red Sea and Gulf of Aden. (b) Contours of the lower surfaces of the 95% confidence ellipsoids. Symbols are as in Figure 8a. test and many other tests because they use identical data for estimating the angular velocity of the Somalian plate relative to the Antarctic plate.) Because the closure test for model ii uses only a subset of the data along the SWIR used in the closure test for model i, it was surprising to us that the misfit for model ii is larger than the misfit for model i, for which Dc 2 = 34.8 (Table 2). [27] The size of the difference between predicted and observed rates and transform azimuths varies from plate pair to plate pair. It is smallest when compared for the Nubian-Antarctic boundary for which rates are significantly misfit (Figure 5), but azimuths of transform faults are not significantly misfit (Figure 6). (Although the predicted transform azimuths differ by about 10 from the observed transform azimuths, the uncertainty in the prediction is so large that this difference is not significant.) If the misfit is caused by a bias in plate motion data, the rates along the Nubian-Antarctic boundary would be the most plausible suspects. [28] The angular velocity of nonclosure is roughly similar in rotation rate and rotation rate uncertainty for all four models. The pole of rotation for model i indicates nonclosure of 4 mmyr 1 if mapped to the Nubia-Antarctica boundary (Table 3 and Figure 5); we think it unlikely that systematic errors in estimated spreading rates are this large. On the other hand, the pole of rotation (of nonclosure) for models iii and iv lies relatively near the Nubia-Antarctica boundary (i.e., at 34.0 S, 12.0 E, just west of South Africa) and indicates a systematic misfit to the rates of only about 1.0 to 1.5 mm yr 1 (Table 3 and Figures 5 and 7), which Table 4. Preferred Angular Velocities and Their Covariance Matrices a Plate Pair Lat Long w w 95% Major Minor Azimuth xx xy xz yy yz zz AR-NB AR-SM LW-AN NB-AN SM-AN NB-LW SM-LW NB-SM a Angular velocity and covariance matrix elements for each plate pair assuming our preferred plate geometry (i.e., model iv), with the Nubian plate comprising the region north of the SWIR between the Bouvet triple junction on the west and the ABTFC on the east, the Lwandlean plate having a western limit including the ABTFC and an eastern limit about 100 km east of the Indomed transform fault, and the Somalian plate having a western limit just east of the Atlantis II transform fault (i.e., with a wide or diffuse boundary between the Lwandlean plate and the Somalian plate near the SWIR) and its eastern limit at the Rodrigues triple junction. The angular velocities are constrained to consistency with closure about the Somalia-Antarctica-Nubia-Arabia plate circuit. In each plate pair, the first plate moves anticlockwise with respect to the second plate. Units of the elements of the matrix are 10 8 sr Ma 2 ; x parallels 0 N, 0 E, y parallels 0 N, 90 E, and z parallels 90 N. Abbreviations: Lat, latitude in N; Long, longitude in E; w, angular speed in deg Ma 1 ; w 95%, 95% confidence limits on w; Major, major axis length in degrees of the 95% confidence ellipse for the angular velocity; Minor, minor axis length in degrees of the 95% confidence ellipse; Azimuth, azimuth of the major axis in degrees clockwise from north; xx, xy, xz, yy, yz, and zz are elements of a symmetric 3 3 covariance matrix; AN, Antarctica; AR, Arabia; LW, Lwandle; NB, Nubia; SM, Somalia. 9of12

10 Figure 9. Map of the African continent and surrounding region and selected poles of rotation and 95% confidence regions (Table 4). Various poles of rotation are labeled using the following abbreviations: NB, Nubian plate; SM, Somalian plate; LW, Lwandlean plate; AR, Arabian plate; BF, best fitting angular velocity; CF, closure-fitting angular velocity; CG99, result from diffuse plate boundary model of Chu and Gordon [1999]; H05, result from [Horner-Johnson et al., 2005] assuming a narrow Nubia-Somalia boundary along the SWIR at 28 E (equivalent to model i of this paper); from AR, estimated only from data in the Red Sea and Gulf of Aden; M03, estimated from GPS data [McClusky et al., 2003]; C06, estimated from GPS data [Calais et al., 2006]. Gray arrows indicate velocities of the Somalian plate relative to an arbitrarily fixed Nubian plate (model iv); numerals give selected rates in mm yr 1. Black arrows indicate velocities of the Lwandlean plate relative to an arbitrarily fixed Nubian plate (model iv). Bathymetry (light gray lines, 4000 m depth contour) [Smith and Sandwell, 1997]. ABTFC, Andrew Bain Transform Fault Complex; BTJ, Bouvet triple junction; RTJ, Rodrigues triple junction; CIR, Central Indian Ridge. Black dots indicate earthquake epicenters ( ) [Engdahl et al., 1998]. Lambert equal-area projection. could conceivably be due to a systematic error in estimating rates. Significant misfits of this size are not without precedent. For example, DeMets et al. [1990] found significant misfits amounting to several millimeters per year about the Bouvet triple junction and about the Galapagos triple junction. [29] Although the nonclosure is significant, the 95% confidence region for the Nubia-Somalia angular velocity estimated from data from the Red Sea and Gulf of Aden overlaps the 95% confidence region for the Nubia-Somalia angular velocity estimated from SWIR data corresponding to models iii or iv (Figure 8). For these reasons, models iii and iv seem more promising than models i and ii. In model iii the off-ridge earthquakes near 48 E occur in the interior of the Lwandlean plate, but in model iv these occur in the diffuse boundary between the Lwandlean and Somalian plates. Thus model iv is our preferred model (Table 4 and Figure 9). [30] 4. Models iii and iv indicate that the angular velocity of Nubia relative to Somalia is similar to that estimated by Chu and Gordon [1999], whereas the Nubia-Lwandle angular velocity is similar to the Nubia-Somalia angular velocity estimated by Horner-Johnson et al. [2005]. The new angular velocity of Nubia relative to Somalia (models iii and iv) is also oriented similarly to the most recently published Nubia-Somalia angular velocity estimated from GPS data, that of Calais et al. [2006] (Figure 9), whereas the Nubia-Somalia pole of paper 1 lies far to the west of the GPS pole (Figure 9). The rate of rotation of our new Nubia- Somalia angular velocity (0.092 ± Ma 1 ) overlaps 10 of 12

11 (within one-dimensional 95% confidence limits) with that of Calais et al. [2006] (0.068 ± Ma 1 ). Thus our new model eliminates the prior discrepancy with the results from GPS. [31] Depending on the plate geometry assumed along the SWIR, the possible locations of the Lwandle-Somalia pole of rotation include points along the proposed Lwandle- Somalia diffuse plate boundary, giving rise to east-west convergence near the SWIR and east-west divergence along the southern East African Rift system (for example, the open star shown in Figure 3b). [32] 5. The angular velocity of nonclosure can also be interpreted as the difference between (1) the Nubia-Somalia angular velocity estimated from data along the SWIR and (2) the Nubia-Somalia angular velocity estimated from data in the Red Sea and Gulf of Aden (Figures 7 and 8). In the vicinity of the best compromise angular velocity that combines SWIR data with Red Sea and Gulf of Aden data, the rate of rotation estimated from the SWIR data is consistently higher than that estimated from Red Sea and Gulf of Aden data. The former rate of rotation is bounded (at 95% confidence in the three-dimensional confidence ellipsoid) between about and 0.14 Ma 1 and the latter is bounded between about and 0.09 Ma 1. This causes us to seek an explanation why data from the Red Sea and Gulf of Aden would indicate a lower rate of rotation than data from the Southwest Indian Ocean. Although we cannot categorically exclude it, we believe it is unlikely to be caused by systematic errors in the data. Instead, we speculate that the difference is caused, at least in part, by ongoing thermal expansion of previously old and cold lithosphere adjacent to the Red Sea and Gulf of Aden. It is widely accepted that there is a large-scale thermal anomaly in the Afar region that most workers ascribe to a deep mantle plume. Such thermal expansion would cause the rate of plate rotation inferred from spreading rates in the Red Sea and Gulf of Aden to be less than the rate of rotation inferred from the displacement rate field far from the Red Sea and Gulf of Aden. Thermal contraction of young oceanic lithosphere adjacent to the SWIR may also play a role. 4. Implications and Conclusions [33] 1. Although the correction for bias in the spreading rate data due to outward displacement of magnetic anomaly reversal boundaries reduces the misfit to a rates-only data set, it did not resolve any other plate motion inconsistency. [34] 2. A region of African lithosphere along the SWIR can be interpreted as a third component plate in the African composite plate. This third component plate, the Lwandlean plate, lies between the Nubian and Somalian plates along the SWIR. [35] 3. The resulting angular velocity of Nubia relative to Somalia lies 11 southwest of that found by Chu and Gordon [1999] and has an insignificantly faster rotation rate. Moreover, our new angular velocity of Nubia relative to Somalia is similar to, and differs insignificantly from, a Nubia-Somalia angular velocity recently estimated from GPS data [Calais et al., 2006]. [36] 4. Although the three-dimensional 95% confidence regions overlap, the angular velocity for Nubia-Somalia relative motion based only on data along the SWIR differs significantly from the angular velocity for Nubia-Somalia relative motion based on data from the Red Sea and Gulf of Aden (Figure 8). The main way that they differ is that the former has a higher rate of rotation than the latter. We speculate that this difference is caused by thermal expansion of African and Arabian lithosphere caused by the heat source associated with the Afar plume. Thermal contraction of young oceanic lithosphere adjacent to the SWIR may also play a role. [37] 5. We propose that a diffuse oceanic plate boundary separates the Lwandlean component plate from the Somalian component plate. The magnitude (M w ) 6.8 thrust event of 26 February 1998 (36.9 S, 48.0 E) and several other large events, the mechanisms of which indicate east-west shortening, occurred within this proposed diffuse oceanic plate boundary. [38] 6. The data are consistent with the pole of rotation for Somalia-Lwandle relative motion lying in the diffuse oceanic plate boundary between the Somalian and Lwandlean component plates. If so, its location is consistent with other diffuse oceanic plate boundaries [Gordon, 1998]. [39] 7. Many data used in prior studies to estimate the motion of the African plate relative to the Antarctic plate lie along the Lwandle-Antarctica portion of the SWIR. Thus published rotations of Africa-Antarctica motion need to be used with great caution as they represent neither Nubian- Antarctic motion nor Somalian-Antarctic motion. Moreover, prior estimates of Nubia-Somalia motion, including that of paper 1 and of Royer et al. [2006]aremorenearlyestimatesof Nubia-Lwandle motion and need to be reconsidered. This does not affect new estimates of Pacific-North America motion [Royer et al., 2006] but does affect estimates of Nubia-Somalia motion and estimates of India-Eurasia motion. [40] Acknowledgments. All figures were prepared using GMT [Wessel and Smith, 1998]. We thank Sara Cowles, Bill Holt, and Rupert Sutherland for helpful comments on the manuscript. This work was supported by National Science Foundation grants OCE and OCE Donald Argus s part of this research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. References Argus, D. F., R. 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