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

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.

• 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.

• 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:

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 landward
SUB seaward
A Priori: half-width of fault set 15-35 8-220 half-width of fault dip
2-20 0-9 boundary mislocation earthquake mislocation
0
17-
165
0-15
0-5
0-30
0-23
?
17-
165
0-240 ~100
50-
150
2-20
15 15-25 15 5-15 5-15 15 9 9
18-30 18-30 18-30 25-40 25-40 18-30 18-30 18-30
(combined) expectation
Empirical:
38-69 32-
268
40-
200
26-58 26-96 40-
200?
70-
260
~122-
151
We adopt a
“two-sigma” rule for apparent boundary halfwidth.
This is generally greater than or equal to the half-widths expected a priori .
75% of total count
90% of total count twice median distance twice mean distance twice RMS distance
Selection: selected half-width
72
127
55
103
154
154
158
247
116
185
257
257
106
158
116
146
189
189
50
93
53
83
132
132
49
97
53
83
128
128
91
151
84
130
186
186
120
179
154
179
220
220
60
92
60
90
135
135
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)

threshold magnitude
95%-confidence lower limit
95%-confidence upper limit not to be taken literally!
(“a large number”)
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] (m t

6.28);
 included events of 1900-1975 AD from catalog of
Pacheco & Sykes [1992] (m t

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 ( m t
= 7.1) makes b very hard to determine, and risks biasing m c values which are smaller.

We chose not to work with merged subcatalogs for OSR and
OTF/medium-fast, where we already know that m c
< 7.1.

We fix b at the value determined from the 1977-2002 Harvard
CMT catalog, and only optimize the corner magnitude m c
.

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

• 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.)


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.

• 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.