Earthquake Magnitude Scaling using Seismogeodetic Data
Brendan W. Crowell1, Diego Melgar, Yehuda Bock, Jennifer S. Haase, and Jianghui Geng
crowellb@uw.edu, dmelgarm@ucsd.edu, ybock@ucsd.edu, jhaase@ucsd.edu, jgeng@ucsd.edu
Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics
Scripps Institution of Oceanography, University of California San Diego
9500 Gilman Drive, La Jolla, CA, 92093-0225
1
Now at Department of Earth and Space Sciences, University of Washington, Seattle
GRL, 2013
Supplementary Material
S1. Overview of seismogeodetic analysis to produce displacement and velocity waveforms
The GPS data processing for the three largest events (Tokachi-oki, Tohoku-oki and El-Mayor
Cucapah) was performed using instantaneous relative positioning on triangulated subnetworks
and then combined and referenced to a single distant station (0848 – Tohoku-oki; 0247 –
Tokachi-oki; GNPS – El Mayor-Cucapah) through a network adjustment [Crowell et al., 2009].
Using this relative method causes any motions at the reference station to contaminate positions
over the entire network so the reference stations were selected at sufficient distances (several
hundred kilometers) such that no ground motion occurred prior to the time period of interest. For
the Brawley seismic swarm events, the precise point positioning with ambiguity resolution
method (PPP-AR) was utilized. It uses a continental-scale network for satellite clocks and
fractional-cycle biases well outside the region of interest, and then applies these corrections to
the PPP clients (stations) within California as described by Geng et al. [2013]. Both methods
provide comparable precision at the 5-10 mm level in the horizontal directions and a factor of 35 poorer in the vertical direction [Langbein and Bock, 2004; Geng et al., 2013].
Bock et al. [2011] described the algorithm to produce seismogeodetic waveforms by applying
a multi-rate Kalman filter to GPS and accelerometer data for a series of shake table tests and the
El Mayor-Cucapah earthquake. The Kalman filter doubly integrates strong motion data using
GPS displacements as a constraint based on the noise characteristics of each sensor. Between
GPS positions, the integration is performed using the equations of motion under the assumption
of constant acceleration between accelerometer sampling epochs. This method creates
displacement and velocity waveforms that are sensitive to both low and high frequencies at the
sampling rate of the seismic instrument. Melgar et al. [2013a] showed that this method is able to
better capture the true displacements than automated baseline correction methods currently
employed in seismology [Wang et al., 2013], and has the distinct advantage that it can be applied
in real time, whereas baseline correction methods require fitting arbitrary functions to the entire
velocity waveform up to the time when ground motion has stopped. Geng et al. [2013] improved
this method by utilizing the strong motion constraints during the GPS processing for more
reliable ambiguity resolution, termed the tightly-coupled PPP-AR Kalman filter, as opposed to
the loosely-coupled Kalman filter that operates after GPS processing has been completed as
described in Bock et al. [2011].
Further details on the GPS processing can be found in Crowell et al. [2009] (2003 Tokachioki), Bock et al. [2011] (2010 El Mayor-Cucapah), Melgar et al. [2013b] (2011 Tohoku-oki),
and Geng et al. [2013] (2012 Brawley seismic swarm).
S2. Scaling values for different time windows and displacement components
As indicated in the text, the scaling parameters were estimated by least squares to the model:
log(𝑃𝑑 ) = 𝐴 + 𝐵𝑀𝑤 + 𝐶 log(𝑅)
where R is the hypocentral distance and Mw is the moment magnitude estimate from the JMA
catalog or the Southern California Earthquake Data Center for the California events. For PGD,
we modify the equation to include magnitude dependence on the attenuation term such that
log(𝑃𝐺𝐷) = 𝐴 + 𝐵𝑀𝑤 + 𝐶𝑀𝑤 log(𝑅)
Table S1. Regression values and standard errors for Pd and PGD
Method
Pd, sg1, 5 s, hor
Pd, sg, 3 s, hor
Pd, sm2, 5 s, ver
Pd, sm, 5 s, hor
Pd, sm, 3 s, ver
Pd, sm, 3 s, hor
Pd, sg, 5 s, ver
Pd, sg, 3 s, ver
PGD, sg
PGD, GPS only
A
A error3 B
B error
C
C error
Mag Unc.
-0.893
0.191 0.562
0.037
-1.731
0.111
0.383
-1.072
0.226 0.458
0.044
-1.398
0.131
0.557
-0.182
0.304 0.487
0.059
-2.173
0.176
0.704
0.981
0.312 0.436
0.061
-2.416
0.181
0.807
-0.240
0.327 0.430
0.063
-2.114
0.189
0.858
0.629
0.332 0.394
0.064
-2.208
0.192
0.951
-0.781
0.358 0.231
0.069
-0.688
0.207
1.754
-0.761
0.385 0.152
0.074
-0.520
0.223
2.861
-5.013
0.211 1.219
0.046
-0.178
0.010
0.224
-4.675
0.226 1.158
0.049
-0.169
0.011
0.254
1
Seismogeodetic data
2
Strong motion data
3
Errors are one-sigma values
S3. Bootstrap tests of Pd and PGD scaling
In order to test the robustness of our results and to give equal weight to small and large
events, we perform the seismogeodetic scaling analysis on random samples of the two Japanese
earthquakes combined with all the data for the California events. We randomly sample 12
Tohoku-oki and 12 Tokachi-oki data points, use all the El Mayor-Cucapah and Brawley Swarm
data points, and perform the scaling analysis 100,000 times for 5 s horizontal Pd on the 42 data
points and solve for the coefficients as for the entire data set. The same procedure is followed for
seismogeodetic PGD. Figures S1 and S2 show histograms of the parameters A, B, C and
magnitude uncertainty for Pd and PGD respectively. Also shown on Figures S1 and S2 are the
values from the regression using all data points from Table S1.
Supplementary Figure Captions
Figure S1: Histograms of the 5 s horizontal seismogeodetic Pd scaling coefficients and the
magnitude uncertainty. The blue circles and error bars are the values from the analysis of the
entire data set in Table S1.
Figure S2: Histograms of the seismogeodetic PGD scaling coefficients and the magnitude
uncertainty. The blue circles and error bars are the values from the analysis of the entire data set
in Table S1.
References
Bock, Y., D. Melgar, and B.W. Crowell (2011), Real-time strong-motion broadband displacements
from collocated GPS and accelerometers, Bull. Seismol. Soc. Am., 101, 2904-2925,
doi:10.1785/0120110007.
Crowell, B. W., Y. Bock, and M. Squibb (2009), Demonstration of earthquake early warning using
total displacement waveforms from real time GPS networks, Seismol. Res. Lett., 80(5), 772782, doi: 10.1785/gssrl.80.5.772.
Geng, J., Y. Bock, D. Melgar, B. W. Crowell, and J. S. Haase (2013), A new seismogeodetic
approach to GPS and accelerometer observations of the 2012 Brawley seismic swarm:
Implications for earthquake early warning, Geochem. Geophys. Geosyst., 14,
doi:10.1002/ggge.20144.
Langbein, J. and Y. Bock (2004), High-Rate Real-Time GPS Network at Parkfield; Utility for
Detecting Fault Slip and Seismic Displacements, Geophys. Res. Lett., 31,
doi:10.1029/2003GL019804.
Melgar, D. Y. Bock, D. Sanchez, and B. W. Crowell (2013a), On robust and reliable automated
baseline corrections for strong motion seismology, J. Geophys. Res., 118, 1177-1187,
doi:10.1002/jgrb.50135.
Melgar, D., B. W. Crowell, Y. Bock, and J. S. Haase (2013b), Rapid modeling of the 2011 Mw
9.0 Tohoku-oki earthquake with seismogeodesy, Geophys. Res. Lett., 40,
doi:10.1002/grl.50590.
Wang, R., S. Parolai, M. Ge, M. Jin, T.R. Walter, and J. Zschau (2013), The 2011 Mw 9.0
Tohoku Earthquake: Comparison of GPS and Strong Motion Data, Bull. Seismol. Soc. Am.,
103, 1336–1347, doi: 10.1785/0120110264.