Figure 1 Predictions of (a) polar wander speed, (c) polar wander direction and (e) as a function of lower-mantle viscosity, in which an elastic lithosphere (infinite viscosity) is assumed (results denoted by ‘el’). Those for (b), (d) and (f) correspond to Earth models with a viscoelastic lithosphere of 10²⁴ Pa s (results denoted by ‘ve’). The upper-mantle viscosity and lithospheric thickness are 5 × 10²⁰ Pa s and 100 km, respectively. The ice model is ICE3G from Tushingham & Peltier (1991). The results denoted by ‘full’ (solid line) are based on the surface load distribution including ice and water loads. The contributions owing to ice (dashed line) and water loads (dotted line) are also depicted to understand the change of the polar wander direction. The shaded regions show the range of the observations for the polar wander (McCarthy & Luzum 1996) and (Nerem & Klosko 1996). From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 2 Predictions of (a) polar wander speed, (b) polar wander direction and (c) as a function of the lower-mantle viscosity and lithospheric thickness. The lithospheric thickness adopted here is 50, 100 and 200 km. The upper-mantle viscosity is 5 × 10²⁰ Pa s and the ice model is ICE3G. The results denoted by ‘el’ and ‘ve’ correspond to Earth models with an elastic lithosphere and viscoelastic lithosphere of 10²⁴ Pa s, respectively. The observations for polar wander (McCarthy & Luzum 1996) and (Nerem & Klosko 1996) are represented by shaded regions. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 3 Predictions of (a) polar wander speed, (b) polar wander direction and (c) as a function of the lower-mantle viscosity and the upper-mantle viscosity. The upper-mantle viscosity adopted here is 2 × 10²⁰, 5 × 10²⁰ and 10²¹ Pa s. The lithospheric thickness is 100 km and the ice model is ICE3G. The results denoted by ‘el’ and ‘ve’ correspond to Earth models with an elastic lithosphere and viscoelastic lithosphere of 10²⁴ Pa s, respectively. The observations for polar wander (McCarthy & Luzum 1996) and (Nerem & Klosko 1996) are represented by shaded regions. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 4 Predictions of (a) polar wander speed, (c) polar wander direction and (e) as a function of the lower-mantle viscosity and the Late Pleistocene ice models, in which elastic lithosphere is assumed (results denoted by ‘el’). Those for (b), (d) and (f) correspond to Earth models with a viscoelastic lithosphere of 10²⁴ Pa s (denoted by ‘ve’). The upper-mantle viscosity is 5 × 10²⁰ Pa s, and the lithospheric thickness is 100 km. The ice models adopted here are ICE3G by Tushingham & Peltier (1991), ARC3 + ANT4b (results denoted by AC3AT4b) by Nakada & Lambeck (1988), ARC4 + ANT4b (results denoted by AC4AT4b) by Lambeck (1995) and Nakada & Lambeck (1988) and ARC4 + ANT5 (results denoted by AC4AT5) by Lambeck (1995) and Nakada et al. (2000). The results denoted by ‘J92’ are based on the ice model J92 scenario describing the recent mass imbalance of the Antarctic ice sheets (James & Ivins 1995). The equivalent sea level rise is 0.45 mm yr⁻¹. The observations for polar wander (McCarthy & Luzum 1996) and (Nerem & Klosko 1996) are represented by shaded regions. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 9 Schematic figures showing the polar wander for solutions of (a) s1 and (b) s2 (see the text). The polar wander vectors arising from the recent mass imbalance of both polar ice caps are in opposite directions. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 8 Relationship between the present-day total ESL rise and the ESL rise of the Antarctic for models with the effect of internal processes. The polar wander direction and speed for (a) and (b) are 24°W and 0.37 deg Myr⁻¹, respectively, corresponding to the estimates by Steinberger & O'Connell (1997). Those for (c) and (d) are 60°W and 0.37 deg Myr⁻¹, respectively. The adopted ice model is shown in each figure. The upper-mantle viscosity is 5 × 10²⁰ Pa s and the thickness of the viscoelastic lithosphere (10²⁴ Pa s) is 100 km. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 7 Relationship between the present-day total ESL rise and the ESL rise of the Antarctic for ice models of ARC3 + ANT4b, ARC4 + ANT4b, ARC4 + ANT5 and ICE3G + MTGLA (see the text). The ice model MTGLA corresponds to the recent melting of mountain glaciers tabulated by Meier (1984). The upper-mantle viscosity is 5 × 10²⁰ Pa s and the thickness of a viscoelastic lithosphere (10²⁴ Pa s) is 100 km. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 6 As in Fig. 5, except for the case of a lithospheric thickness of 200 km. From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS

Figure 5 Solutions that give the minimum χ² residuals in eq. (20) (see the text) and also satisfy the observations of both polar wander (McCarthy & Luzum 1996) and (Nerem & Klosko 1996). The upper-mantle viscosity is 5 × 10²⁰ Pa s, the lithospheric thickness is 100 km and the ice model is ICE3G. (a), (b) Relationship between the present-day total ESL rise and the ESL rise of the Antarctic ; (c), (d) relationship between the and the location (E-longitude) of the Antarctic melted ice; and (e), (f) relationship between and the lower-mantle viscosity. Results for (a), (c) and (e) correspond to Earth models with an elastic lithosphere, and those for (b), (d) and (f) are for Earth models with a viscoelastic lithosphere of 10²⁴ Pa s. The results with ‘A1’ indicate the source area of 50°≤λ≤ 180° (E) for the recent melting of the Antarctic ice sheet. The areas denoted by ‘A2’ correspond to 180°≤λ≤ 290° (E), and those denoted by ‘A3’ are for 290°≤λ≤ 360° (E) and 0°≤λ≤ 50° (E). From: Perturbations of the Earth's rotation and their implications for the present-day mass balance of both polar ice caps Geophys J Int. 2003;152(1):124-138. doi:10.1046/j.1365-246X.2003.01831.x Geophys J Int | © 2003 RAS