Plate-tectonic analysis of shallow seismicity:
Apparent boundary width, beta, corner
magnitude, coupled lithosphere thickness, and
coupling in 7 tectonic settings
Peter Bird
Yan Y. Kagan
UCLA Department of Earth & Space Sciences
Dec. 10, 2003
presented to AGU, San Francisco, CA
Seismic coupling and frequency/magnitude
relations are best determined from global
statistics.
• Different kinds of plate boundary clearly have
different seismicity characteristics.
• But, no single subduction zone (etc.) has a
long enough seismic record to determine
corner magnitude and coupling reliably
[McCaffrey, 1997].
• We 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.
Every digitization step
(from 1-109 km long)
along every plate boundary
is classified as being one
of 7 types:
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:
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:
The final classification factor (E) “grades” a possible match on the
angular discrepancy between actual and model focal mechanism:
The result…
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
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).