7 Earthquake Mechanisms and Plate Tectonics Seth Stein and Eryn Klosko Northwestern University, Evanston, Illinois, USA 1. Introduction Thus, at spreading centers plates move away from the boundary, whereas at subduction zones the subducting plate Earthquake seismology has played a major role in the devel- moves toward the boundary. At the third boundary type, opment of our current understanding of global plate tectonics transform faults, plate motion is parallel to the boundary. The and in making plate tectonics the conceptual framework used slip vectors of the earthquakes on plate boundaries, which to think about most large-scale processes in the solid Earth. show the motion on the fault plane, re¯ect the direction of During the dramatic development of plate tectonics, discussed relative motion between the two plates. from the view of participants by Uyeda (1978, and this volume), The basic principle of plate kinematics is that the relative Cox (1973), and Menard (1986), the distribution of earthquakes motion between any two plates can be described as a rotation on provided some of the strongest evidence for the geometry of a sphere about an Euler pole (Fig. 2). Speci®cally, at any point plate boundaries and the motion on them (e.g., Isacks et al., along the boundary between plates i and j, with latitude and 1968). More than thirty years later, earthquake studies retain a longitude , the linear velocity of plate j with respect to plate i is central role, as summarized here. vji !ji  r 1 Because earthquakes occur primarily at the boundaries between lithospheric plates, their distribution is used to map the usual formulation for rigid body rotations in mechanics. plate boundaries and their focal mechanisms provide infor- The vector r is the position vector to the point on the boundary, mation about the motion at individual boundaries. Plate boundaries are divided into three types (Fig. 1). Z Oceanic lithosphere is formed at spreading centers, or mid- N ocean ridges, and is destroyed at subduction zones, or trenches. v12 Oceanic plate Ridge Trench Euler vector Greenwich r 12 Meridian Fracture zone Continental Transform Y plate fault Magnetic Euler pole Lithosphere anomalies X Asthenosphere FIGURE 2 Geometry of plate motions. At any point r along the boundary between plate i and plate j, with geopraphic latitude and FIGURE 1 Plate tectonics at its simplest. Plates are formed at ridges longitude , the linear velocity of plate j with respect to plate i is and subducted at trenches. At transform faults, plate motion is parallel vji !ji  r. The Euler pole at latitude and longitude is the to the boundaries. Each boundary type has typical earthquakes. intersection of the Euler vector !ji with the Earth's surface. INTERNATIONAL HANDBOOK OF EARTHQUAKE AND ENGINEERING SEISMOLOGY, VOLUME 81A ISBN: 0 -12- 440652-1 Copyright # 2002 by the Int'l Assoc. Seismol. & Phys. Earth's Interior Committee on Education. All rights of reproduction in any form reserved. 69 70 Stein and Klosko and !ji is the rotation vector or Euler vector. Both are de®ned and are thus spreading centers. Figure 3b shows an alternative from an origin at the center of the Earth. case. The pole here is for plate 1( j 1) with respect to plate 2 The direction of relative motion at any point on a plate (i 2), so plate 1moves toward some segments of the boundary is a small circle, a parallel of latitude about the Euler boundary, which are subduction zones. Note that the ridge pole (not a geographic parallel about the North Pole!). For and subduction zone boundary segments are not small circles. example, in Figure 3a the pole shown is for the motion of The magnitude, or rate, of relative motion increases with plate 2 with respect to plate 1. The ®rst-named plate ( j 2) distance from the pole, since moves counterclockwise about the pole with respect to the second (i 1). The segments of the boundary where relative jvjijj!jijjrj sin 2 motion is parallel to the boundary are transform faults. Thus, where is the angle between the Euler pole and the site (cor- transforms are small circles about the pole and earthquakes responding to a colatitude about the pole.) Thus, although all occurring on them should have pure strike-slip mechanisms. points on a plate boundary have the same angular velocity, the Other segments have relative motion away from the boundary, linear velocity varies. If we know the Euler vector for any plate pair, we can write Rotation pole the linear velocity at any point on the boundary between the plates in terms of the local E±W and N±S components by a coordinate transformation. With this, the rate and azimuth of 21 plate motion become q Plate 1 NS 2 EW 2 rate jvjij vji vji 3 ! NS Plate 2 v azimuth 90 À tanÀ1 ji 4 Spreading vEW ridge ji such that azimuth is measured in degrees clockwise from North. Given a set of Euler vectors with respect to one plate, those with respect to others are found by vector arithmetic. For example, the Euler vector for the reverse plate pair is the Transform negative of the Euler vector (a) !ij À!ji 5 Rotation pole Euler vectors for other plate pairs are found by addition !jk !ji !ik 6 12 so, given a set of vectors all with respect to plate i, any Euler vector needed is found from Plate 1 Plate 2 !jk !ji À !ki 7 Subduction For further information on plate kinematics see an intro- zone ductory text such as Cox and Hart (1986). As discussed there, motions between plates can be determined by combining three different types of data from different boundaries. The rate of spreading at ridges is given by sea-¯oor magnetic anomalies, and the directions of motion are found from the orientations Transform of transform faults and the slip vectors of earthquakes on (b) transforms and at subduction zones. As is evident, earthquake slip vectors are only one of three types of plate motion FIGURE 3 Relationship of motion on plate boundaries to the Euler pole. Relative motion occurs along small circles about the pole; data available. Euler vectors are determined from the relative the rate increases with distance from the pole. Note the difference the motion data, using geometrical conditions. Since slip vectors and transform faults lie on small circles about the pole, the pole sense of rotation makes: !ji is the Euler vector corresponding to the rotation of plate j counterclockwise with respect to i. must lie on a line at right angles to them (Fig. 3). Similarly, the Earthquake Mechanisms and Plate Tectonics 71 rates of plate motion increase with the sine of the distance from Ridge the pole. These constraints make it possible to locate the poles. Strike-slip fault Determination of Euler vectors for all the plates can thus (left lateral) Normal be treated as an overdetermined least-squares problem, and fault the best solution found using the generalized inverse to derive global plate motion models (Chase, 1972; Minster and Jordan, Fracture zone 1978; DeMets et al., 1990, 1994). Because these models use magnetic anomaly data, they describe plate motion averaged Transform over the past few million years. New data have become available in recent years due to the No seismicity No seismicity rapidly evolving techniques of space-based geodesy. These techniques (Gordon and Stein, 1992) (very long baseline radio Transform interferometry (VLBI), satellite laser ranging (SLR), the global positioning system (GPS), and DORIS (similar to GPS, but using ground transmitters)) use space-based technologies Normal to measure the positions of geodetic monuments to accuracies fault of better than a centimeter, even for sites thousands of kilo- Strike-slip fault meters apart. Hence measurements of positions over time yield (right lateral) Ridge relative velocities to precisions almost unimaginable during the early days of plate tectonic studies. A series of striking FIGURE 4 Possible tectonic settings of earthquakes at an oceanic results, ®rst with VLBI and SLR (e.g., Robbins et al., 1993), spreading center. Most events occur on the active segment of the and now with GPS (Argus and He¯in, 1995; Larson et al., transform and have strike-slip mechanisms consistent with transform 1997), show that plate motion over the past few years is faulting. On a slow spreading ridge, like the Mid-Atlantic, normal generally quite similar to that predicted by global plate motion fault earthquakes occur. Very few events occur on the inactive fracture zone. model NUVEL-1A. This agreement is consistent with the prediction that episodic motion at plate boundaries, as re¯ec- ted in occasional large earthquakes, will give rise to steady north±south trending ridge segments, offset by transform motion in plate interiors due to damping by the underlying faults, such as the Vema Transform, which trend approxi- viscous asthenosphere (Elsasser, 1969). As a result, the mately east±west. Both the ridge crest and the transforms are earthquake mechanisms can be compared to the plate motions seismically active. The mechanisms show that the relative predicted by both global plate motion models and space-based motion along the transform is right±lateral. Sea-¯oor spreading geodesy. on the ridge segments produces the observed relative motion. For this reason, earthquakes occur almost exclusively on the active segment of the transform fault between the two ridge 2. Oceanic Spreading Center Focal segments, rather than on the inactive extension, known as a Mechanisms fracture zone. Although no relative plate motion occurs on the fracture zone it is often marked by a distinct topographic fea- Earthquake mechanisms from the mid-ocean ridge system ture, due to the contrast in lithospheric ages across it.