Modern Earthquake Simulators and Seismicity models: Investigating earthquake predictability and disaster response applications

Abstract

In this poster, we report recent progress on two projects: the Virtual Quake earthquake simulator and an ETAS type aftershock forecast. Virtual Quake (VQ) is a fault type, physics based earthquake simulator. Recent improvement to the VQ programmatic architecture make it much easier to use and more computationally efficient. VQ is Open Source and available for download via Computational Infrastructure for Geodynamics (CIG) or from GitHub. In this poster, we present highlights from recent papers (Yoder et al. 2015ab) in which we observe evidence of quantifiable precursors to large m>7 earthquakes and we show that while some faults in the system exhibit classic elastic rebound type behavior, with respect to the recurrence of large m>7 earthquakes, others exhibit a very different 'activation' type triggering and recurrence. We also briefly discuss an ETAS type aftershock model recently published by Yoder et al. (2015/2014 online) and show an example of a forecast that was provided to the recent 2015 Gorkha, Nepal m=7.8 event and accurately forecast the location of the large m=7.3 and m=6.3 aftershocks on 12 May 2015. The Virtual Quake (VQ) Earthquake Simulator: Two significant challenges to earthquake forecasting and predictability science are 1) the complex and multi-scale behavior of earthquakes and earthquake systems, and 1) the relatively short available history of events. We have reliable catalogs of on order 10 to 100 years (depending on one's specific requirements), and earthquake cycles of interest (m>7 or so) may easily require catalogs on the order of thousands or even tens of thousands of years. Simulators provide one tool to circumvent this challenge. The Virtual Quake (VQ) simulator is based on a set of mapped faults with estimated slip rates, a prescribed plate tectonic motion, earthquakes on all faults, and elastic interactions (Rundle, 1988; Rundle et al, 2001, 2004). Earthquake activity data and slip rates are obtained from geologic databases; loading of each VC fault segment occurs due to the accumulation of a slip deficit at the prescribed slip rate of the segment (" backslip model "); the vertical rectangular fault segments interact elastically. Earthquake initiation is controlled by friction coefficients along with the space-and time-dependent stresses on fault segments which are computed by means of boundary element methods. To prescribe the friction coefficients, historical earthquakes are used that have moment magnitudes m>6 in California during the last 200 years. The primary role of the simulator is to produce extended earthquake histories (catalogs) from which a region's seismicity can be both qualitatively and statistically better understood. From these extended catalogs, we can calculate robust recurrence interval and large-event waiting time statistics. Recent additions to the VQ software suite also include surface deformation and gravity change modeling capabilities which can be used to study pre-and post-seismic surface deformation and stress fields as well as long term surface deformation (see Fig. 3b below). Another important advantage of simulators is that we can arbitrarily partition by region, fault, fault section, or any arbitrary source parameterization. Preliminary analyses suggest evidence of an acceleration based precursor in the simulation (see Figs. 5 and 6 below, and also Yoder and Rundle 2014, Yoder 2014, Yoder et al. 2015). Fig 1: Fault segments included in the " Virtual EMC " simulation, the UCERF2 fault segments from the El Mayor-Cucapah (EMC) region, as implemented in a Virtual Quake simulation. Bands of parallel lines indicate normal or reverse faulting, where dip δ ≠ 90 o. The red star near fault segments 123-125 indicate the epicenter of the 2010 m=7.2 EMC epicenter. Fig. 3a, Left: Probability distribution of expected recurrence intervals between m>7 (simulated) earthquakes P(Δt m=7) for the EMC region fault model in VQ. Each curve shows probabilities for an m>7 event in the region (on any fault segment) given the observation that some time t 0 has elapsed since the previous m>7 event. The solid line-and-dots show observed data; the dashed (lines es show the best fit to a conditional (Baysean) Weibull distribution for that value of t 0 , and the dash-dot (- .-) lines show the expected Weibull distribution using the best-fit parameters for t 0 =0. Note that recurrence intervals for the aggregated catalog agree closely with Poissan statistics. Fig 3b, Right: Expected waiting times Δt w , the expected time until the next m>7 earthquake at time t 0 since the previous large event-again for the aggregate EMC region. The center line shows the 50% probability waiting time; the upper and lower bounds show the 25 th and 75 th percentile probabilities. Fig. 2A (left): Simulated relative seismicity in the El Mayor-Cucapah region using the VQ earthquake simulator. The simulation was run with a full California fault model; analyses are performed over the set of EMC region fault segments indicated by blue lines; see also Fig. 2. Magenta dots indicate the locations of earthquakes in the simulation; " off fault " earthquakes indicate (large) events (left side) that initiated on fault sections excluded from the EMC region as shown) faults but that propagated to one or more included section. Rate contours are calculated using an ETAS like spatial initial rate and spatial distribution (Yoder et al. 2015) with the time dependent component removed (Omori scaling exponent p=0). 2b, Right: VQ simulated surface deformation for EMC region. In this figure, deep aseismic slip is intentionally excluded to exaggerate the block-rotational motions between parallel faults. Fig. 5 A sample set of earthquake alerts on fault segment 16. The green bars (bottom of the plot and up) represent earthquake magnitudes (scale on right); the blue dot-line represents inter-occurrence intervals between the i th and (i − 1) th earthquake in the catalog, ∆t i =t i − t i-1. The magenta shaded area indicates durations where an " alert " was active, specifically the times for which the slope of the linear fit over the previous n f earthquakes is less than the optimized threshold value, b<b 0. This alert model is similar to a framework presented by Yoder and Rundle (2015) and Keilis_Borok (2002) ; see also Fig. 7 below.

Full text

“Mainshock”: Small earthquakes
overlap and merge to form one
large rupture
“Aftershocks”: Moment release
slows; large ruptures separate into
smaller, discrete events
Modern Earthquake Simulators and
Seismicity models: Investigating
earthquake predictability and disaster
response applications
Mark R. Yoder1, Kasey W. Schultz1, Eric M. Heien2, John B.
Rundle123, Donald L. Turcotte12, Jay W. Parker4, Andrea Donnellan4,
Margaret T. Glasscoe4
1 Dept. Of Physics, University of California Davis, Davis CA USA
2 Dept. Of Physics, University of California Davis, Davis CA USA
3 Santa Fe Institute, Santa Fe NM USA
4 NASA Jet Propulsion Laboratory, Pasadena CA USA
Abstract
In this poster, we report recent progress on two projects: the Virtual Quake earthquake simulator
and an ETAS type aftershock forecast. Virtual Quake (VQ) is a fault type, physics based earthquake
simulator. Recent improvement to the VQ programmatic architecture make it much easier to use
and more computationally efficient. VQ is Open Source and available for download via
Computational Infrastructure for Geodynamics (CIG) or from GitHub. In this poster, we present
highlights from recent papers (Yoder et al. 2015ab) in which we observe evidence of quantifiable
precursors to large m>7 earthquakes and we show that while some faults in the system exhibit
classic elastic rebound type behavior, with respect to the recurrence of large m>7 earthquakes,
others exhibit a very different 'activation' type triggering and recurrence.
We also briefly discuss an ETAS type aftershock model recently published by Yoder et al.
(2015/2014 online) and show an example of a forecast that was provided to the recent 2015
Gorkha, Nepal m=7.8 event and accurately forecast the location of the large m=7.3 and m=6.3
aftershocks on 12 May 2015.
The Virtual Quake (VQ)
Earthquake Simulator:
Two significant challenges to earthquake forecasting and
predictability science are 1) the complex and multi-scale
behavior of earthquakes and earthquake systems, and
1) the relatively short available history of events. We have
reliable catalogs of on order 10 to 100 years (depending on one's specific
requirements), and earthquake cycles of interest (m>7 or so) may easily require
catalogs on the order of thousands or even tens of thousands of years. Simulators
provide one tool to circumvent this challenge.
The Virtual Quake (VQ) simulator is based on a set of mapped faults with estimated
slip rates, a prescribed plate tectonic motion, earthquakes on all faults, and elastic
interactions (Rundle, 1988; Rundle et al, 2001, 2004). Earthquake activity data and
slip rates are obtained from geologic databases; loading of each VC fault segment
occurs due to the accumulation of a slip deficit at the prescribed slip rate of the
segment (“backslip model”); the vertical rectangular fault segments interact elastically.
Earthquake initiation is controlled by friction coefficients along with the space- and
time-dependent stresses on fault segments which are computed by means of
boundary element methods. To prescribe the friction coefficients, historical
earthquakes are used that have moment magnitudes m>6 in California during the last
200 years.
The primary role of the simulator is to produce extended earthquake histories
(catalogs) from which a region's seismicity can be both qualitatively and statistically
better understood. From these extended catalogs, we can calculate robust recurrence
interval and large-event waiting time statistics. Recent additions to the VQ software
suite also include surface deformation and gravity change modeling capabilities which
can be used to study pre- and post-seismic surface deformation and stress fields as
well as long term surface deformation (see Fig. 3b below).
Another important advantage of simulators is that we can arbitrarily partition by region,
fault, fault section, or any arbitrary source parameterization. Preliminary analyses
suggest evidence of an acceleration based precursor in the simulation (see Figs. 5
and 6 below, and also Yoder and Rundle 2014, Yoder 2014, Yoder et al. 2015).
http://geodynamics.org/cig/software/vq/
Fig 1: Fault segments included in the “Virtual EMC” simulation, the UCERF2 fault segments from the El Mayor-
Cucapah (EMC) region, as implemented in a Virtual Quake simulation. Bands of parallel lines indicate normal or
reverse faulting, where dip δ ≠ 90o. The red star near fault segments 123-125 indicate the epicenter of the 2010
m=7.2 EMC epicenter.
Fig. 3a, Left: Probability distribution of expected recurrence intervals between m>7 (simulated) earthquakes P(Δtm=7) for the EMC
region fault model in VQ. Each curve shows probabilities for an m>7 event in the region (on any fault segment) given the
observation that some time t0 has elapsed since the previous m>7 event. The solid line-and-dots show observed data; the dashed
( - - ) lines show the best fit to a conditional (Baysean) Weibull distribution for that value of t0, and the dash-dot (-.-) lines show the
expected Weibull distribution using the best-fit parameters for t0=0. Note that recurrence intervals for the aggregated catalog
agree closely with Poissan statistics.
Fig 3b, Right: Expected waiting times Δtw, the expected time until the next m>7 earthquake at time t0 since the previous large
event -- again for the aggregate EMC region. The center line shows the 50% probability waiting time; the upper and lower bounds
show the 25th and 75th percentile probabilities.
Fig. 2A (left): Simulated relative seismicity in the El Mayor-Cucapah region using the VQ earthquake simulator. The
simulation was run with a full California fault model; analyses are performed over the set of EMC region fault segments
indicated by blue lines; see also Fig. 2. Magenta dots indicate the locations of earthquakes in the simulation; “off fault”
earthquakes indicate (large) events (left side) that initiated on fault sections excluded from the EMC region as shown) faults
but that propagated to one or more included section. Rate contours are calculated using an ETAS like spatial initial rate and
spatial distribution (Yoder et al. 2015) with the time dependent component removed (Omori scaling exponent p=0).
2b, Right: VQ simulated surface deformation for EMC region. In this figure, deep aseismic slip is intentionally excluded to
exaggerate the block-rotational motions between parallel faults.
Fig. 5 A sample set of earthquake alerts on fault segment 16. The green bars (bottom of the plot and up) represent earthquake
magnitudes (scale on right); the blue dot-line represents inter-occurrence intervals between the ith and (i − 1)th earthquake in the
catalog, ∆ti=ti − ti-1. The magenta shaded area indicates durations where an “alert” was active, specifically the times for which the
slope of the linear fit over the previous nf earthquakes is less than the optimized threshold value, b<b0. This alert model is similar
to a framework presented by Yoder and Rundle (2015) and Keilis_Borok (2002) ; see also Fig. 7 below.
Elevated hazard
mainshock
Reduced hazard
Fig. 6(Right): Detecting pre-seismic acceleration (PSA) precursory to the 2010 m=7.2 El Mayor-
Cucapah earthquake. For this analysis, a “regional” type catalog is used; the catalog includes all
earthquakes in an approximately 4ox4o square encompassing northern Baja California Norte, Mexico and
souther California, USA. The top pane uses an algorithm based on record-breaking statistics to detect
PSA precursory to and decelerating seismicity (aftershocks) following the mainshock. The center pane
show “Omori intervals”, or the mean rate of earthquakes over fixed length sequences, and the bottom
pane shows earthquake magnitudes (see Yoder and Rundle 2014 for details). Researchgate.net
Fig 4: Similar to Fig. 3b, except waiting times Δtw calculations are limited to specific fault segments – fault sections 123 (left) and 111
(right). Note that both cases differ significantly from Fig. 3b. Fault section 123 exhibits an intuitive “elastic-rebound” type behavior, in
which the expected interval between large events is largest immediately following a large earthquake. For fault section 111, however,
the interval between large events is shortest immediately following a large m>7 earthquake. Nominally, this distinction implies
significantly different post-seismic hazard assessments and disaster response protocols following a large earthquake on these
sections.
Scaling constraints:
N
Omori
=
∫
0
∞
dN
dt dt=t
0
1−p
τ( p−1)
log (L
r
)= m
2−Δ λ
A
r
=L
r
D
log (N
Omori
)=b(m−Δ m−m
c
)
N
Omori
=
∫
0
∞
dN
dr dr=r
0
1−q
χ(q−1)
log (Δ t
r
)= m
2−Δ τ
A
ms
=
∑
n
A
n
=
∫
A(n)dn
Δt
ms
=
∑
n
Δt
n
=
∫
Δt(n)dn
Accurately estimates initial rate-density of aftershocks
Now, aggregate ETAS rates for a large catalog over a study area. Gorkha
region, Nepal: Contours indicate the aftershock forecast as of 7 May 2015; the
forecast was made available the same day. Orange and yellow circles indicate
recent earthquakes (courtesy of USGS web services). Two primary regions of
high risk are shown, 1) to the NW, near the mainshock and 2) near the 12 May
M=7.3 and 6.3 aftershocks (annotated in this figure, but that had not yet
occurred at the time the forecast was issued). Preliminary analyses suggest that
forecasts can be further improved by using “large aftershock” variations of the
spatial distribution.
A new way to do ETAS:
Finite extents, scaling constraints, and fractal geometry (as
implemented for the 2015 m=7.8 Gorkha earthquake)
(See Yoder et al. 2015[2014 online] for details)
Rupture-sequence model: Finite extents, scaling constraints, and fractal
geometry
Acknowledgements
This research is supported by the NASA Earth and Space Science fellowship number NNX11AL92H, NASA grant
NNX08AF69G, and JPL Subcontract 1291967.
Primary References
1. Glasscoe, M., Wang, J., Pierce, M., Yoder, M., Parker, J., Burl, M., Stough, T., Granat, R., Donnellan, A., Rundle, J., Ma, Y., Bawden, G.: E-
decider: Using earth science data and modeling tools to develop decision support for earthquake disaster response. Pure Ap. Geophys.
(Published online) (2014). Topical Volume on Multihazard Simulation and Cyberinfrastructure
2. OGATA Y (1988) Statistical models for earthquake occurrences and residual analysis for point processes. J. Am. Stat. Assoc.
3. Yoder, M.R.: Record-breaking earthquake precursors. Ph.D. thesis, University of California Davis (2011)
4. Yoder, M.R., Rundle, J.: Record-breaking intervals: Detecting trends in the incidence of self-similar earthquake sequences. Pure Ap.
Geophys. (published online) (2014). DOI 10.1007/s00024-014-0887-7
5. Yoder, M.R., Rundle, J., Glasscoe, M.: Near-field etas constraints and applications to seismic hazard assessment. Pure Ap. Geophys.
(published online) (2014). DOI 10.1007/s00024-014-0785-z
6. MR Yoder,KW Schultz, EM Heien, JB Rundle, DL Turcotte, JW Parker, and A Donnellan: “Title: The Virtual Quake earthquake simulator: A
simulation based forecast of the El Mayor-Cucapah region and evidence of predictability in simulated earthquake sequences” (2015, in
production).
7. V. Keilis-Borko, Earthquake Prediction: State-of-the-art and Emerging Possibilities, 10.1146/annurev.earth.30.100301.083856