Transcript A proposed triggering/clustering model for the current WGCEP

A proposed
triggering/clustering model for
the current WGCEP
Karen Felzer
USGS, Pasadena
Seismogram from Peng
et al., in press
Terminology
• Aftershock = Any earthquake triggered
by another earthquake, over any time,
distance, magnitude difference.
• Background Seismicity = All nonaftershocks.
Outline
• Background: Triggering in WGCEP 2002
• Justification: Why aftershocks should be
given a larger role.
• The empirical ETES/Aftershock triggering
model.
• Comparison of ETES with the STEP model
• Preliminary results: ‘Forecasting’ the years
2000-2005.
• Preliminary results: Forecasting aftershock
scenarios for The Big One.
Background
Earthquake interaction modeling in
WGCEP 2002
• Only effects of the1906 and Loma Prieta
earthquakes were modeled.
• The effect of 1906 was modeled on all Bay
Area faults using BPT step (Brownian
Passage Time) and the Reasenberg et al.
(2003) empirical models.
• The effect of the Loma Prieta earthquake on
two neighboring sections of the SAF was
modeled using BPT step.
Proposed Change: Replace BPT step
with empirical aftershock statistics
• We propose to avoid the large uncertainties in
physical models and parameters by using
Omori’s Law and other empirical aftershock
statistics directly. The aftershock statistics we
use have been thoroughly tested against
California data.
Proposed Change: Model the
aftershocks of many more earthquakes
• WGCEP 2002 modeled the potential
earthquake interaction behavior initiated by
the 1906 and Loma Prieta Earthquakes only.
• We propose to forecast the stress triggering
effects of all catalog M≥2.5 earthquakes,
using an ETES-style model (Ogata 1988, Felzer et
al. 2002, Helmstetter et al. 2006). Because the
cumulative triggering effects of smaller
earthquakes are significant, using all M≥2.5
earthquakes should produce more accurate
results.
The Bay Area stress shadow
• WGCEP 2002 was greatly concerned with
accurately modeling of the post 1906 (or
post-1927!) Bay Area Quiescence.
• The empirical Bay Area quiescence models
employed by WGCEP 2002 can be
incorporated into our model by modifying the
background seismicity rate.
Justification
Why have such a large aftershock
component in the time-variable model?
A sample of large California aftershocks:
•
•
•
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Landers, M 7.3
Big Bear, M 6.4
Hector Mine, M 7.1
Superstition Hills, M
6.7
• Northridge, M 6.7
• Bakersfield, M 5.8
(1952)
• Morgan Hill, M 6.2
• Cape Mendocino, M
7.1 (1992,
aftershock of 1991
Honeydew
earthquake)
Detailed aftershock statistics, updated
daily, produce significantly better
forecasts than steady-state models
Helmstetter et al. 2006 forecast for 23 October, 2004.
Steady state on right, ETES on left. M≥2 events given
by black circles. ETES forecast agrees with
earthquakes 11.5 times better than Poissonian.
But daily forecasts aren’t practical for
WGCEP!
We propose forecasts updated yearly -- less
accurate, but better for WGCEP users and still
better than steady state.
Aftershock modeling also:
•
•
Allows determination of the full error range on the
expected annual number of earthquakes.
Allows the building of earthquake sequence
scenarios -- e.g. how frequently will the Big One
on the SAF trigger an M 7 in the LA basin?
The ETES earthquake and
aftershock triggering model:
The nuts and bolts
Basic Model Ingredients
We solve for the expected rates of all of the following
during the forecast period:
Aftershocks of preforecast period M≥ 2.5
earthquakes
Background
seismicity
Aftershocks of
earthquakes
occurring during
forecast period
QuickTi me™ and a
TIFF ( Uncompressed) decompressor
are needed to see thi s pi ctur e.
No physics added!
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Basic Procedure
• The mean, median, and full PDF of expected
behavior over a region are obtained by
running a large number of Monte Carlo trials
in which discrete earthquakes and
aftershocks are modeled.
• The final forecasted probability at points in
space is obtained by averaging and
smoothing the Monte Carlo catalogs with an
inverse power law kernel.
Generation of background
earthquakes
• Background earthquakes are placed
randomly according to seismicity rates
and magnitude distributions specified in
spatial grid cells.
• Background rates may be taken directly
from the time-independent WGCEP
forecast or altered to reflect long-term
trends.
Generation of Aftershocks
1. The number of aftershocks, N, triggered by an
earthquake of magnitude M10bM (Reasenberg and
Jones (1989); Felzer et al. 2004).
2. Aftershock rate = (kD10bM)/(t+cD)pD (modified Omori
Law) where kD, cD, and pD are direct sequence
Omori parameters.
3. Aftershock density varies with distance from the
mainshock fault plane, r, r-1.37 (Felzer & Brodsky 2006).
4. Aftershock magnitudes are chosen randomly from
the Gutenberg-Richter distribution.
5. M≥6.5 earthquakes are modeled as planes; smaller
earthquakes as point sources
Direct Omori Law parameters fit the
decay of direct aftershocks only
Propagating the direct aftershocks of the mainshock and
all aftershocks makes a full sequence
Benefits of using direct sequence
aftershock parameters
• More accurate modeling of average
aftershock sequence behavior,
especially over the long term.
• More accurate modeling of the possible
range of aftershock sequence behavior
• More accurate modeling of large
secondary aftershock sequences.
Direct vs. Total Omori law parameters
and large secondary sequences
Aftershocks w. large
secondary sequence
• If using total rather than
direct Omori law
parameters (like STEP)
when a large aftershock
occurs the total sequence
for the large aftershock
must locally replaces the
original sequence.
• In ETES, total sequences
are built by adding the
direct sequences of each
aftershock => large
secondary sequences are
modeled automatically.
Additional differences between STEP
& ETES
• STEP uses sequence-specific Omori law parameters
when possible. ETES uses generic parameters but
self adjusts to the activity level of the total aftershock
sequence.
• The STEP model uses spatially varying GutenbergRichter b value; ETES uses a uniform b value.
• STEP, run in real time, needs to guess at mainshock
fault planes; ETES has the luxury of using known
fault planes.
• Otherwise the two models are very similar!
Some Preliminary Results of
the ETES Modeling
ETES Forecast trials, Years
2000 - 2005
• 100 Monte Carlo trials done for each
forecast.
• Catalog mainshocks used are all
recorded M≥ 2.5 earthquakes from 1990
only.
• Background rate based on declustered
1932-2000 M≥4 earthquakes, Gaussian
smoothing.
1. Statewide simulations: PDF for total
number of M≥2.5 earthquakes
Simulations for the year 2001
ETES => More quiet years and more extreme years
ETES simulation agrees better with
real data
2. Statewide results: Median forecast
number of M≥2.5 eqs each year
Correlation Coefficient = 0.5
3. Spatially varying results
Testing the ETES vs. Poissonian
spatial forecasts
Map 2
Map 1
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1) Each map is divided into 0.1 by 0.1° cells and each
cell is ranked by its forecasted probability of containing
an earthquake: #1 = highest probability.
2) For each earthquake that occurs we calculate a Signed
Rank = Rank on Map 2 - Rank on Map 1
Map 2
Map 1
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Signed rank of the example earthquake = 4
3) The list of signed ranks is evaluated with the Wilcoxon
Signed Rank Statistic to see if Map 2 is statistically better
than Map 1.
Wilcoxon test results, Year 2000
ETES does better, >99.9% confidence
Wilcoxon Test Results, 2001-2005
SAF M 7.8 Earthquake
Scenario Simulations: Another
application of the ETES model
Quick Time™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Scenario #1: Aftershock Light
Scenario #2: A little more activity
Scenario #3: M 7.5 rips through
Disneyland 4 days after mainshock!
Conclusions
• Aftershocks are the only obvious time-variant
feature of seismicity -- thus should be a
central part of time-variable forecasting.
• Given lack of understanding of aftershock
physics, we propose a completely
empirical/statistical model for forecasting the
effect of aftershocks on the next year of
seismicity.
• Tests indicate that our model predicts
seismicity better than a steady state
Poissonian at high confidence.