of 18
Geophysical Journal International
Geophys. J. Int.
(2018)
212,
725–742
doi: 10.1093/gji/ggx430
Advance Access publication 2017 October 9
GJI Seismology
FinDer v.2: Improved real-time ground-motion predictions
for M2–M9 with seismic finite-source characterization
M. B
̈
ose,
1
D.E. Smith,
2
C. Felizardo,
3
M.-A. Meier,
3
T.H. Heaton
3
and J.F. Clinton
1
1
Swiss Seismological Service (SED), ETH Zurich, CH-
8092
Zurich, Switzerland. E-mail:
mboese@sed.ethz.ch
2
US Geological Survey, Pasadena, CA
91106
,USA
3
California Institute of Technology, Pasadena, CA
91125
,USA
Accepted 2017 October 6. Received 2017 August 28; in original form 2017 June 6
SUMMARY
Recent studies suggest that small and large earthquakes nucleate similarly, and that they often
have indistinguishable seismic waveform onsets. The characterization of earthquakes in real
time, such as for earthquake early warning, therefore requires a flexible modeling approach that
allows a small earthquake to become large as fault rupture evolves over time. Here, we present a
modeling approach that generates a set of output parameters and uncertainty estimates that are
consistent with both small/moderate (
M6.5) and large earthquakes (
>
M6.5) as is required for
a robust parameter interpretation and shaking forecast. Our approach treats earthquakes over
the entire range of magnitudes (
>
M2) as finite line-source ruptures, with the dimensions of
small earthquakes being very small (
<
100 m) and those of large earthquakes exceeding several
tens to hundreds of kilometres in length. The extent of the assumed line source is estimated
from the level and distribution of high-frequency peak acceleration amplitudes observed in a
local seismic network. High-frequency motions are well suited for this approach, because they
are mainly controlled by the distance to the rupturing fault. Observed ground-motion patterns
are compared with theoretical templates modeled from empirical ground-motion prediction
equations to determine the best line source and uncertainties. Our algorithm extends earlier
work by B
̈
ose
et al.
for large finite-fault ruptures. This paper gives a detailed summary of
the new algorithm and its offline performance for the 2016 M7.0 Kumamoto, Japan and 2014
M6.0 South Napa, California earthquakes, as well as its performance for about 100 real-time
detected local earthquakes (2.2
M
5.1) in California. For most events, both the rupture
length and the strike are well constrained within a few seconds (
<
10 s) of the event origin. In
large earthquakes, this could allow for providing warnings of up to several tens of seconds.
The algorithm could also be useful for resolving fault plane ambiguities of focal mechanisms
and identification of rupturing faults for earthquakes as small as M2.5.
Key words:
Image processing; Spatial analysis; Earthquake early warning; Earthquake
ground motions; Earthquake hazards; Earthquake source observations.
INTRODUCTION
Earthquake early warning (EEW) systems must fulfill two tasks: to
quickly identify potentially damaging earthquakes, and to provide
accurate shaking predictions and robust warnings to end users, typ-
ically based on the exceedance of critical shaking levels (B
̈
ose
et al.
2016a
; Cauzzi
et al.
2016a
). With a few exceptions (e.g. Zollo
et al.
2010
; Hoshiba & Aoki
2015), EEW processing typically consists of
two steps: the first step is to determine the earthquake hypocentre
and magnitude and the second step is to use these parameters in
empirical ground-motion prediction equations (GMPEs) to predict
the shaking that an end user will experience when located several
tens of kilometres from the epicentre.
Speed is the most critical design target for EEW systems that re-
spond to small to moderate-sized earthquakes (
M
6.5), since the
strongest shaking occurs mostly in small areas around the epicentre
(e.g. Heaton
1985). In contrast, the accuracy of the shaking progno-
sis is most difficult in larger events (
M
>
6.5), since (1) magnitudes
calculated from seismic data tend to saturate (e.g. Bock
et al.
2011;
Melgar
et al.
2015), and (2) finite-source dimensions must be known
to predict future shaking, because this shaking is controlled by the
rupture-to-site distance rather than by the hypocentral distance (e.g.
Bommer & Akkar
2012;B
̈
ose
et al.
2014).
While magnitude saturation in large earthquakes can be avoided
by employing geodetic algorithms based on real-time positioning
or displacement data (e.g. Yamada
et al.
2007;B
̈
ose
et al.
2013b
;
C

The Authors 2017. Published by Oxford University Press on behalf of The Royal Astronomical Society.
725
Downloaded from https://academic.oup.com/gji/article-abstract/212/1/725/4411810
by California Institute of Technology user
on 29 November 2017
726
M. B
̈
ose
et al
.
Minson
et al.
2014; Grapenthin
et al.
2014a
;Crowell
et al.
2016),
a fast detector is needed to provide real-time estimates of fault
rupture dimensions. In B
̈
ose
et al.
(2012a
), we propose a Finite-
Fault Rupture Detector (FinDer) algorithm to characterize the fault
rupture extent of an assumed line source for large earthquakes
(
>
M6.5) based on the level and distribution of high-frequency
acceleration peak amplitudes (PGA) observed in a seismic network.
High-frequency motions are suitable for this purpose since, apart
from the earthquake size, they are predominantly controlled by the
rupture distance and are less affected by seismic slip and rupture
directivity compared to mid- and long-period motions (Spudich &
Chiou
2008).
Typically, EEW algorithms provide either point-source solu-
tions, which are adequate to describe small-to-moderate-sized earth-
quakes (
M
<
6.5), or finite-source models to characterize large fault
ruptures (
M
>
6.5). Point-source algorithms are either single sensor
(e.g. Kanamori
2005;Wu
et al.
2007;B
̈
ose
et al.
2012b
; Meier
et al.
2015
) or multiple sensor-based (e.g. Cua
2005; Allen
2007;B
̈
ose
et al.
2008; Satriano
et al.
2011; Kuyuk
et al.
2014;Behr
et al.
2015
;Behr
et al.
2016), and provide rapid estimates of earthquake
magnitudes and hypocentres. Finite-source algorithms (e.g. Yamada
et al.
2007;B
̈
ose
et al.
2013b
; Minson
et al.
2014; Grapenthin
et al.
2014a
;Crowell
et al.
2016), on the other hand, determine finite-fault
models of large events, including, for instance, 2-D source dimen-
sions and slip distributions. None of the current EEW algorithms
is suited for application to both event classes. Recent studies (e.g.
Meier
et al.
2016), however, suggest that large finite-source earth-
quakes and smaller point-source events start similarly, implying that
we can determine only lower bound magnitudes and must update
source parameter estimates as long as fault rupture is occurring.
This underlines the need for a consistent modeling approach that
can be applied to both small earthquakes, which are typically mod-
eled as point sources, and large earthquakes, which are typically
modeled as finite-fault ruptures.
In this paper, we present a novel modeling approach that provides
robust and improved real-time ground-motion predictions for point
source as well as large finite-fault earthquakes. Our algorithm, called
FinDer version 2 (v.2), extends earlier work of B
̈
ose
et al.
(2012a
).
While the original algorithm, however, can be applied only to large
earthquakes (
M
>
6), FinDer v.2 is suitable for application to the
entire spectrum of earthquake sizes (M2–M9). Above all, the new
algorithm allows for the detection of an earthquake that starts as a
small (point source) event and then gradually develops into a greater
magnitude earthquake.
ALGORITHM
FinDer (and FinDer v.2) uses 2-D spatial template matching (e.g.
Gonzales
et al.
2004) to find the best line-source model to explain
the observed ground-motion pattern in a seismic network at a given
time. The algorithm compares an
image I
that represents the so far
observed spatial distribution of peak absolute ground acceleration
amplitudes with theoretical
templates T,
which are modeled from
empirical GMPEs for line sources of different lengths; templates
are rotated to determine the rupture strike. The line-source approxi-
mation is most appropriate for the case of a vertically dipping fault.
For faults with smaller dips, the FinDer line source will usually
translate in the fault perpendicular direction by several kilometres
to reach a better match with the observed ground-motion pattern
(see Discussion section).
FinDer minimizes iteratively the misfit between the
T
and
I
to
recover the best
T
and its position in
I
, and thus determines the
centroid
X
=
{
latitude, longitude
}
, length
L
and strike
θ
of the cor-
responding line source. The earthquake magnitude
M
is estimated
from empirical rupture-length-to-magnitude relations (e.g. Wells &
Coppersmith
1994); the event origin time,
t
0
, is determined from
the arrival times of peak amplitudes at various sensors.
The image
I
is created from the spatially interpolated logarithmic
values of PGA observed in a seismic network at a given time; inter-
polation is done via Delaunay triangulation. PGA is determined at
each station from the maximum absolute amplitude, which is taken
over all three sensor components and over a configurable time win-
dow. Here, we choose a time window length of 120 s, correspond-
ing to the approximate shaking duration of an M7.8 earthquake; if
ground motions are still increasing, the time window is automat-
ically extended during an earthquake. Any specific value,
I
(
x
,
y
),
results from the projection of the interpolated PGA amplitudes onto
a Cartesian grid of height
H
, width
W
, and elements specified by
coordinates (
x
,
y
). In this study, we use a grid of 5
×
5 km spatial
resolution. The size of
I
is determined by the spatial extent of the
seismic network to which FinDer is applied, plus some boundary
which we set here as 1
. Site corrections can be applied, but they
are of secondary importance here, because our approach takes into
account ground motions at different stations deployed over large ar-
eas that usually encompass different site conditions (see Discussion
section).
We model each value in our template,
T
(
x
,
y
), from empirical
GMPEs. For the examples shown in this paper, we use PGA relations
of Cua & Heaton (
2009) in combination with magnitude-rupture
length relations of Wells & Coppersmith (
1994). We compute our
templates as
T
(
x
,
y
)
=
log
10
(
PGA
(
x
,
y
))
=
[
0
.
73
M
7
.
2
×
10
4
(
R
2
+
9
+
C
(
M
)
)
1
.
48 log
10
(
R
2
+
9
+
C
(
M
)
)
0
.
42
]
+
log
10
(
1
.
1
)
(1)
with
C
(
M
)
=
1
.
16 exp[0
.
96(
M
5)]
×
[arctan(
M
5)
+
π/
2],
where PGA is given in cm s
1
s
1
and distance
R
in km;
R
is the
epicentral distance for
M
<
5 and fault distance for
M
5tothe
assumed line source located in the centre of each template. The
length
L
[km] of this line source is modeled as (strike-slip rupture,
Wells & Coppersmith
1994)
log
10
(
L
)
=
(
M
4
.
33
)
/
1
.
49
(2)
The factor log
10
(1.1) in eq. (1) is used to convert PGA from the
root mean square of amplitudes to the maximum of each horizontal
component (max(E, N)) as is used in FinDer (follows table 5.1 in Cua
& Heaton
2009). We set the width
w
and height
h
of the templates
as
w
=
h
=
min [145 (30
+
70log
10
(
L
+
1)], that is the template
size grows logarithmically with rupture length
L
and linearly with
magnitude
M
.
Our algorithm is independent of a particular set of relationships
(in particular, the GMPEs and rupture length-to-magnitude conver-
sion), and templates can be easily replaced, for example, to enable
application to subduction-zone environments (B
̈
ose
et al.
2015).
The FinDer output depends on the GMPE selected for template
generation. We have tested FinDer in different regions around the
world, and we prefer the use of local relations whenever available.
The template set is created externally and loaded by FinDer at
Downloaded from https://academic.oup.com/gji/article-abstract/212/1/725/4411810
by California Institute of Technology user
on 29 November 2017