Supplementary materials

Supplementary Tables

Table S1: The effective vertical cutoff rigidity (in unit of GV) calculated using trajectory tracing from a combination of four global paleomagnetic field models, i.e., GGF100k, GGFSS70, LSMOD.2, and CALS10k.2 over the last 100 ka. Timing resolution is 200 year before 10 ka, and 50 year after 10 ka.

Table S2: The effective vertical cutoff rigidity (in unit of GV) calculated using the GGF100k model. Timing resolution is 200 year.

Table S3: The effective vertical cutoff rigidity (in unit of GV) calculated using the GGFSS70 model. Timing resolution is 200 year.

Table S4: The effective vertical cutoff rigidity (in unit of GV) calculated using the LSMOD.2 model. Timing resolution is 200 year.

Table S5: The effective vertical cutoff rigidity (in unit of GV) calculated using the CALS10k.2 model. Timing resolution is 50 year.

Movie S1. The effective vertical cutoff rigidity R_vc contour maps derived from (a) GGF100k, (b) GGFSS70, (c) LSMOD.2, (d) IMOLEe, (e) CALS10k.2, and (f) Rc100k. (g) The latitudinal structure of Rc100k. (h) The longitudinal structure of Rc100k. (i) the impact area derived from Rc100k. (Access here)

Movie S2. The geomagnetic field radial component Br from (a) GGF100k, (b) GGFSS70, (c) LSMOD.2, (d) IMOLEe, (e) CALS10k.2, and (f) the combined model used to calculated the Rc100k over the last 100 ka. (Access here)

Movie S3. The geomagnetic field intensity B_totai from (a) GGF100k, (b) GGFSS70, (c) LSMOD.2, (d) IMOLEe, (e) CALS10k.2, and (f) the combined model used to calculated the Rc100k over the last 100 ka. (Access here)

Movie S4. The cutoff rigidity difference between (a) GGF100k and GGFSS70, (b) GGFSS70 and LSMOD.2, (c) LSMOD.2 and IMOLEe, and (d) CALS10k.2 and GGF100k. (Access here)

Movie S5. The R_vc contour maps using models with maximum spherical harmonic (SH) degree (a) geocentric axial dipole (GAD), (b) 1, (c) 2, and (d) 3. The difference between Rc100k and cutoff rigidity results using model with maximum SH degrees (e) geocentric axial dipole (GAD), (f) 1, (g) 2, and (h) 3. (Access here)

Figure S1. Geomagnetic field radial component Br maps from different paleomagnetic field models at (a) 67.85 ka, (b) 49.95 ka, (c) 32.65 ka, (d) 17.55 ka, (e) 9.95 ka. The left and middle panels show the Br maps of the adjoining models. The differences between two models are shown in the right panels.

Figure S2. Geomagnetic field intensity Btotai maps from different paleomagnetic field models at (a) 67.85 ka, (b) 49.95 ka, (c) 32.65 ka, (d) 17.55 ka, (e) 9.95 ka. The left and middle panels show the Btotal maps of the adjoining models. The differences between two models are shown in the right panels.

Figure S3. Effective vertical cutoff rigidity Rvc contour maps derived from different paleomagnetic field models at (a) 67.85 ka, (b) 49.95 ka, (c) 32.65 ka, (d) 17.55 ka, (e) 9.95 ka. The left and middle panels show the Rvc maps derived from the adjoining models. The differences between two Rvc maps are shown in the right panels.

Figure S4. The global average of the value differences Dvc between different paleomag- netic field models. The difference between Rc100k and cutoff rigidity calculated using only the geocentric axial dipole (GAD) from the combined model is also shown for comparison.

Figure S5. (a) The global average of the value differences and (b) the global average of the percentage differences between Rc100k and cutoff rigidity calculated using the truncated paleomagnetic field model, up to spherical harmonic degree 3, 2, 1, and geocentric axial dipole (GAD).

Figure S6. Mean value of the cutoff rigidity at Earth’s equator versus dipole moment of the geomagnetic field over the last 100 ka.

Figure S7. Cosmic ray spectrum for protons at solar modulation parameter $ = 300, 400, 500 and 600 MeV.

© J. Gao et al., Published by EDP Sciences 2022