flow on the lithospheric base may be a primary driver of plate motions 1-3 and thus directly link 55 surface tectonics to interior dynamics. We can exploit this link for past times by utilizing tectonic 56 reconstructions of plate motions, which are becoming increasingly better constrained 8,9 , to infer 57 patterns of past mantle flow. We achieve this by examining the net properties of plate motions, 58 which should reflect the "average" response of Earth's lithosphere to long-wavelength viscous 59 mantle flow. Previously, net rotation of the lithosphere (Fig 1a) has been linked to present-day 60 mantle flow 14 , but its utility for past times 8 may be limited because observations of net rotation 61 are highly dependent on the choice of mantle reference frame. By contrast, the relative motions 62 between plates are less dependent on reference frame and are of larger amplitude than net 63 rotation rates. To exploit these attributes, we define several new metrics of relative plate motions 64 that are useful for constraining the interaction between plate tectonics and mantle flow, and 65 apply them to published reconstructions of plate motions both for present and past times. 66
67We defined three new "net characteristics" of plate motions by performing different integrations 68 4 of the tectonic plate motion vector field over the surface of the earth (see methods). The plate 69 tectonic dipole vector D defines a "net convergence pole" toward which plates are moving in an 70 average sense away from an antipodal "net divergence pole" (Fig. 1b). The plate tectonic 71 quadrupole, defined by the quadrupole deformation matrix Q (see methods), describes a 2 nd 72 order pattern of net plate motions associated with net hemispheric convergence toward two 73 antipodal "positive" poles and divergence away from two antipodal "negative" poles located 90° 74 away from the positive quadrupoles (Fig. 1c). This quadrupole motion occurs as revolution about 75 two intermediate null poles (Fig. 1c). Plate tectonic net stretching, defined by deformation matrix 76 S (see methods), describes convergence toward the two null poles of the quadrupole and 77 divergence away from an equator midway between them (Fig. 1d). These net characteristics 78 describe plate motions at the largest scales; they are influenced by both rapid regional-scale (e.g., 79northwestern North American convergence) and gradual global-scale deformations (e.g., the 80 circum-Africa ridge system), but are dominated by the longest-wavelength large amplitude 81 deformations. 82
83We computed these net characteristics for present-day plate motions (Fig. 2a) and for vector 84 fields associated with two major plate-driving forces: slab pull and basal shear tractions (Fig. 85 2b). The relevant pole locations for all three net characteristics (D, Q, and S) are approximately 86 co-located for both plate motions and plate-driving forces. For example, dipole convergence of 87 plate tectonics occurs in eastern Asia, dominated by convergent motion of the Pacific, 88Australian,...