Download Plate-tectonic analysis of shallow earthquakes: Toward seismic

Plate-tectonic analysis of shallow earthquakes:
Toward long-term seismic hazard models based
on tectonics
Peter Bird
Yan Y. Kagan
Zheng-Kang Shen
Zhen Liu
UCLA Department of Earth & Space Sciences
October 1, 2003
presented to USGS, Menlo Park, CA
Approaches to improving seismic
hazard models:
I.
Do a good job on the long-term-average
(Poissonian) hazard maps before tackling
time-dependence.
II. Base seismic coupling and frequency/
magnitude relations on global statistics.
III. Determine fault slip rates and anelastic
strain rates from unified kinematic models.
I. Do a good job on the long-term-average
(Poissonian) hazard maps before tackling
time-dependence.
• Conceptually simpler. Perhaps we can all
agree on basic principles.
• Needed for LONG-term planning (nuclear
waste repositories, dams, new Pantheons).
• A stable hazard map simplifies public
education.
• Supports studies of time-dependent hazard by
showing which clustering patterns are
permanent, and which are time-dependent.
II. Base seismic coupling and
frequency/magnitude relations on global
statistics.
• In continents, “characteristic earthquake”
sequences may be the exception, not the rule.
• Anticipating fault segmentation is subjective.
• Some recent large earthquakes have ignored
expected rupture segments (Northridge,
Landers, Denali).
• Instead, use the “ergodic assumption”: Global
data over one century may substitute for local
data covering thousands of years.
The kinematic basis for the global calibration:
Plate boundary model PB2002 has 52 plates and 13 orogens:
Bird [2003] An updated digital model of plate boundaries,
Geochemistry Geophysics Geosystems, 4(3), 1027, doi:10.1029/2001GC000252.
Source data for the PB2002 plate boundary model:
• Plate Tectonic Map of the Circum-Pacific Region [Circum-Pacific Map
Project, 1981; 1986];
• gridded topography/bathymetry from ETOPO5 [NOAA-NGDC, 1988];
• 14 Euler poles for large plates from NUVEL-1A [DeMets et al., 1994];
• 10 small plates, and orogen concept, from Gordon [1995];
• 1,511 subaerial volcano locations from the Smithsonian's Global
Volcanism Program [Simkin & Siebert, 1995];
• mid-ocean spreading ridge boundaries from Paleo-Oceanographic
Mapping Project [Mueller et al., 1997];
• gridded sea floor ages from the Paleo-Oceanographic Mapping
Project;
• Global Seismic Hazard Map [Giardini et al., 1999];
• 168 regional studies, including 32 using GPS;
• locations and nodal planes of ~15,000 shallow earthquakes from the
Harvard CMT catalog.
Example of a simple
improvement:
Recognition of a
Mariana plate (MA)
which separates from
the Philippine Sea
plate (PS) by
back-arc spreading:
Example of a complex improvement: The Banda Sea-New Guinea region (8 small plates):
Regions of non-rigid
lithosphere
(or very many small plates)
are designated as “orogens”
in which this model is not
expected to be accurate.
Here: the Philippines orogen.
Model PB2002 includes estimated Euler poles and velocities for each plate:
Relative plate velocities predicted by PB2002:
Every digitization step
(from 1-109 km long)
along every plate boundary
is classified as being one
of 7 types:
New work, to determine:
“For each of the 7 types of plate boundary,
• What is the average rate of damaging
earthquakes (above some magnitude
threshold, per unit boundary length)?
• How large might the largest event be (in
the next century, at a given confidence)?
• What fraction of low-temperature
(frictional) inter-plate slip is expressed as
earthquakes?”
Using the Harvard CMT catalog of 15,015 shallow events:
We study histograms of
earthquake* frequency
as a function of distance to the
nearest plate boundary:
[*shallow earthquakes of
appropriate focal mechanism,
excluding those in orogens]
Note that the distribution for
SUBduction zones is asymmetrical:
Table 1. Estimates of Apparent Boundary Half-Width (in km) and CMT catalog statistics
CRB
CTF
CCB
OSR
OTF
OCB
SUB
landward
seaward
A Priori:
half-width of fault set
15-35
8-220
0
0-15
0-30
?
0-240
~100
half-width of fault
dip
2-20
0-9
17165
0-5
0-23
17165
50150
2-20
boundary mislocation
15
15-25
15
5-15
5-15
15
9
9
earthquake
mislocation
18-30
18-30
18-30
25-40
25-40
18-30
18-30
18-30
(combined)
expectation
38-69
32268
40200
26-58
26-96
40200?
70260
~122151
75% of total count
72
158
106
50
49
91
120
60
90% of total count
127
247
158
93
97
151
179
92
twice median
distance
55
116
116
53
53
84
154
60
twice mean distance
103
185
146
83
83
130
179
90
twice RMS distance
154
257
189
132
128
186
220
135
154
257
189
132
128
186
220
135
Empirical:
Selection:
selected half-width
We adopt a
“two-sigma”
rule for apparent
boundary halfwidth.
This is generally
greater than or
equal to the
half-widths
expected a priori.
This rule selects
~95% of shallow
non-orogenic EQs
into one boundary
or another.
Formal assignment of an earthquake to a plate boundary step
is by a probabilistic algorithm that considers all available
information: step type, spatial relations, EQ depth, and focal
mechanism:
The A factor takes into account the length, velocity, and inherent
seismicity of each candidate plate boundary step.
The inherent seismicity levels of the 7 types of plate boundary
(obtained by iteration of this classification algorithm)
are valuable basic information for seismicity forecasts:
We allow for several different “model earthquake” focal mechanisms
on each plate boundary step. When the step is oblique to relative
plate motion (the general case), the Earth may produce either obliqueslip EQs, or sets of partitioned-slip EQs:
For SUB steps,
the depth PDF function D
associated with each
“model earthquake” helps
to separate mechanisms
expected to be shallow
(green curve)
from those expected to
be within the slab
(blue curve, for case of
slab top at 25 km depth)
and those thrust events
expected to lie along the
slab-top plate interface
(a Gaussian PDF
centered on this depth;
not shown here).
The final classification factor (E) “grades” a possible match on the
angular discrepancy between actual and model focal mechanism:
The result…
The frequency/moment distribution that we fit to these subcatalogs is the
Advantages of
this distribution:
Simple (only one more parameter than G-R);
Has a finite integrated moment (unlike G-R) for b < 1;
Fits global subcatalogs slightly better than the gamma distribution.
The maximum-likelihood method is used to determine the
parameters of these tapered G-R distributions (and their uncertainties):
An ideal case
(both parameters determined)
A typical case
(corner magnitude unbounded
from above)
not to be
taken
literally!
(“a large
number”)
threshold
magnitude
95%-confidence
upper limit
95%-confidence
lower limit
95%-confidence
lower limit
Review of results on spectral slope, b:
Although there are variations, none is significant with 95%-confidence.
Kagan’s [1999] hypothesis of uniform b still stands.
In many cases, subcatalogs obtained from the Harvard CMT
catalog for non-orogen regions are not large enough to define
95%-confidence upper limits on the corner magnitudes.
We next enlarged some of our subcatalogs in three ways:
included events of 1976 AD from catalog of Ekström &
Nettles [1997] (mt  6.28);
included events of 1900-1975 AD from catalog of
Pacheco & Sykes [1992] (mt  7.10);
included plate-boundary-associated events from within
the 13 orogens of PB2002:
But, it is necessary to be careful:
• Catalog data from 1900-1975 is less accurate in every way
(moment/magnitude, location, depth, focal mechanism-?),
and therefore these events are more likely to be misclassified.
• The high catalog threshold (mt = 7.1) makes b very hard to
determine, and risks biasing mc values which are smaller.
 We chose not to work with merged subcatalogs for OSR and
OTF/medium-fast, where we already know that mc < 7.1.
 We fix b at the value determined from the 1977-2002 Harvard
CMT catalog, and only optimize the corner magnitude mc.
IMPLICATIONS:
1. Now that we know the coupled thickness of
seismogenic lithosphere in each tectonic
setting, we can convert surface velocity
gradients to seismic moment rates.
2. Now that we know the frequency/magnitude
distribution in each tectonic setting, we can
convert seismic moment rates to earthquake
rate densities at any desired magnitude.
Kinematic
Model
Moment
Rates
Long-term-average
(Poissonian)
seismicity maps
III. Determine fault slip rates and
anelastic strain rates from unified
kinematic models.
• Use a 2-D F-E grid on the sphere to represent the
long-term-average horizontal velocity field in a wide
orogen (2300 km) with good resolution (4-14 km).
• Fit velocity field to all available data:
 plate-tectonic velocity boundary conditions
 geologic slip rates
 geodetic benchmark velocities
 horizontal principal stress directions
• Resulting models are easily tested by more geodesy.
The Gorda-California-Nevada
orogen as represented by a
2-D spherical cap of finite
elements.
Grid GCN8.6 has:
5,243 nodes, and
10,233 spherical-triangle
elements, with dimensions of:
28 km in the interior;
14 km in most of California;
4  14 km along major faults.
Our data base currently
has 690 active
(or potentially-active)
faults in the region of
this orogen.
(They include all faults
used in the seismic
hazard models of the
California Geological Survey
[Petersen et al., 1996]
and USGS/1996 edition
[Frankel et al., 1996].)
Sample entry from the data base,
showing how data are assembled from the literature
and combined to estimate neotectonic slip rate
and its uncertainty.
As this is a type-“N” (Normal) fault, all Offset and Neo-Rate
values refer to relative vertical offset, or throw.
Each fault has an assigned
slip rate and uncertainty.
In this plot the horizontal
component (heave rate)
is represented by the width
of the colored trace.
Some faults which lack
offset features have assigned
slip rates of zero (these
do not appear in this plot).
Many slip rates have
large uncertainties
(also not shown here).
Zheng-Kang Shen
assembled these
1,021 geodetic
velocities in 2002.
They include most
of the data used
in the SCEC
Crustal Motion Map,
version 3
[Shen et al., 2003].
The reference frame
is attached to sites in
stable North
America to the east.
These 963 indicators
of the azimuth of the
most-compressive
horizontal principal stress
are from the
World Stress Map
data base project,
as of 2000.
(Another ~1,000 indicators
in surrounding regions
were also used in
interpolation of
stress directions.)
Basic algorithm of NeoKinema:
Unfaulted elements have a nominal strain-rate of zero, with an assigned
uncertainty (e.g., 310-16/s).
Horizontal principal stress directions are interpolated to every finite element
by the method of Bird & Li [1996]. The results are used to constrain the
orientation of distributed strain in unfaulted elements.
Faults with positive target slip rates contribute to the target strain rates of
all elements they cut through.
Uncertainties in fault slip rates contribute to anisotropic compliance of all
elements that the faults cut through.
Velocity boundary conditions around the edges of the orogen (within the
rigid parts of surrounding plates) are computed from global model PB2002.
Geodetic benchmarks are treated as internal point constraints on the
velocity field (with associated uncertainties).
The program attempts to balance all these requirements in a maximum
likelihood (weighted least squares) solution for the long-term-average velocity
field.
Some details of NeoKinema:
One may choose to permit a proportional amount of strike-slip on all faults
that are nominally pure dip-slip. This increases flexibility and usually
improves the fit to data.
The stress-direction interpolation method of Bird & Li [1996] has two
variants. We use the more conservative clustered-data method.
If a full covariance matrix for geodetic velocity components is available, it is
used in the maximum likelihood inversion. We minimize (m-g)T N (m-g),
where m is the vector of model velocity components, g is the vector of geodetic
velocity components, and N is the normal matrix (inverse of the covariance
matrix).
The reference frame of the geodetic velocities may be fixed, or floating.
Geodetic velocities are “corrected” for temporary locking of faults, using the
current model estimates of the fault slip rates, locking depths assigned a
priori, and analytic solutions for rectangular dislocations in a uniform elastic
half-space. This requires iteration of the solution, which is typically done 10
times.
Results are somewhat dependent on two “tuning” parameters:
*the relative weight of geodetic data
*the a priori allowance for strain rate in unfaulted elements.
Sample of the interpolated
stress-direction field:
For clarity, only half of
the symbols are shown.
Yellow fans represent
90%-confidence limits.
Where the yellow fans
would be unreasonably,
broad, no symbol is plotted
(and no constraint is
applied to the strain
rate tensor).
The field of long-term-average
horizontal velocity
computed by NeoKinema:
Velocity vectors are
shown at only 1/9
of the node points,
for legibility.
(The thin red strip
around the west side
of the Gorda plate
is a continuation
of the Pacific plate.)
Fault heave rates
predicted by the
NeoKinema model.
Note the prediction of
up to 6 mm/a
oblique slip
(thrusting + dextral)
on the Mesozoic
plate boundary fault
offshore.
This is a map of the
common logarithm
of the total
(anelastic,
long-term-average)
strain rate,
including faulting,
as predicted by
NeoKinema.
Long-term-average
seismicity rates
can be predicted
from these strain rates,
if seismic coupling
coefficients and
frequency/magnitude
relations are known.
Major tasks remaining:
• Convert the (anelastic, long-term-average) strain rate
in each finite element to a predicted local frequency/
magnitude curve.
• Test the resulting set of SHIFT seismicity maps
(both retrospectively and prospectively).
• Apply engineering “attenuation” relations to predict
shaking. (Use OpenSHA of SCEC/ITRP/CME?)
• Apply same techniques to Alaska & Caribbean.
• Develop and compare both kinematic and dynamic
strain-rate models for the eastern United States.
• Compare/contrast results with official NSH Maps.