Geophysical Research Letters
Supporting Information for
Earthquake Magnitude Calculation without Saturation from the
Scaling of Peak Ground Displacement
Diego Melgar1, Brendan W. Crowell2, Jianghui Geng3, Richard M. Allen1, Yehuda Bock3,
Sebastian Riquelme4, Emma Hill5, Marino Protti6 and Athanassios Ganas7
1 Seismological
2 Department
3 Cecil
of Earth and Space Sciences, University of Washington, Seattle, USA
H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of
Oceanography, University of California San Diego, La Jolla, USA
4
5
6
Laboratory, University of California Berkeley, Berkeley, USA
Centro Sismologico Nacional, Universidad de Chile, Santiago, Chile
Earth Observatory of Singapore, Nanyang Technological University, Singapore
Observatorio Vulcanológico y Sismológico de Costa Rica, Universidad Nacional, Heredia, Costa Rica
7
National Observatoruy of Athens, Athens, Greece
Contents of this file
Figures S1 to S2
Table S1
Introduction
The figures shown in the supplement show the results of the PGD scaling (Figure S1)
and retrospective magnitude calculations (Figure S2) performed exactly as described in
the methods section but ignoring the vertical component of the time series. The
1
regression coefficients are A = -4.639 ± 0.170, B = 1.063 ± 0.039 and C = -0.137 ± 0.007
and the standard error in the magnitude residuals is 0.29 magnitude units.
We also tested the impact of removing each event from the regression, re-computing the
coefficients and then running the retrospective magnitude calculation without this event.
The results are shown in Table S1 and show that even when each event is removed the
magnitude computation is not adversely affected. There is no bias in the magnitude
solutions due toe ach event being included. We did not re-run the bootstrap test after
removing each event. Thus, we assume uncertainties remain roughly unchanged.
Figure S1. Scaling of peak ground displacement measurements (PGD) without
considering the vertical component of motion. The oblique lines are the predicted scaling
values from the L1 regression of the PGD measurements as a function of hypocentral
distance.
2
Figure S2. Retrospective analysis of the time evolution of magnitude using the scaling
law of Figure S1 without considering the vertical component of motion. Plotted are the
magnitude calculations using 3 travel time masks at 2, 3 and 4 km/s. The error bars are
determined using the uncertainties of the regression coefficients. The red dashed line is
the magnitude from the slip inversion (Table 1) for that event. The shaded pink regions
are the source time functions for the kinematic slip inversions.
3
Table S1. Results of magnitude determination when each event is disregarded in the
scaling coefficient regression
Event name,
country
Epicentral
time (UTC)
Moment
(N-m)
Tohoku-oki,
Japan
Maule, Chile
2011-03-11
05:46:24
2010-02-27
06:34:14
2003-09-25
19:50:06
2014-04-01
23:46:47
2010-10-25
14:42:22
2012-09-05
14:42:08
2010-04-04
22:40:42
5.51x1022
(Mw9.09)
2.39x1022
(Mw8.85)
3.05x1021
(Mw8.25)
2.49x1021
(Mw8.19)
4.60x1020
(Mw7.68)
2.93x1020
(Mw7.57)
7.60x1019
(Mw7.18)
9.29±0.31
2014-05-24
09:25:02
2014-08-24
10:20:44
2004-09-28
17:15:24
2.58x1019
(Mw6.87)
1.85x1018
(Mw6.11)
9.82x1017
(Mw5.92)
Tokachi-oki,
Japan
Iquique, Chile
Mentawai,
Indonesia
Nicoya, Costa
Rica
El
MayorCucapah,
Mexico
Aegean Sea,
Greece
Napa, USA
Parkfield,
USA
MPGD with
vertical
MPGD no
vertical
9.27±0.29
MPGD with
vertical
when event
is ignored
9.31±0.31
MPGD
no
vertical
when event
is ignored
9.33±0.29
9.04±0.32
9.06±0.24
9.10±0.32
9.04±0.24
8.31±0.32
8.30±0.29
8.18±0.32
8.16±0.29
8.02±0.31
7.96±0.15
7.96±0.31
7.92±0.15
7.41±0.24
7.49±0.22
7.48±0.24
7.46±0.22
7.50±0.24
7.57±0.27
7.44±0.24
7.56±0.27
7.39±0.25
7.35±0.23
7.37±0.25
7.39±0.23
6.51±0.22
6.58±0.23
6.49±0.22
6.55±0.23
6.11±0.17
6.07±0.15
6.16±0.17
6.23±0.15
5.92±0.13
5.97±0.14
5.94±0.13
6.01±0.14
4