Plate-tectonic analysis of shallow earthquakes:Toward long-term seismic hazard models based

on tectonics

Peter BirdYan Y. Kagan

Zheng-Kang ShenZhen Liu

UCLA Department of Earth & Space SciencesOctober 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.

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.

The kinematic basis for the global calibration:

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 simpleimprovement:Recognition of aMariana plate (MA)which separates fromthe Philippine Seaplate (PS) by back-arc spreading:

Example of a complex improvement: The Banda Sea-New Guinea region (8 small plates):

Regions of non-rigidlithosphere(or very many small plates)are designated as “orogens”in which this model is notexpected 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 boundaryis classified as being oneof 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* frequencyas a function of distance to thenearest plate boundary:

[*shallow earthquakes of appropriate focal mechanism, excluding those in orogens]

Note that the distribution forSUBduction zones is asymmetrical:

Table 1. Estimates of Apparent Boundary Half-Width (in km) and CMT catalog statistics

CRB CTF CCB OSR OTF OCB SUB

land-ward

sea-ward

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 17-165

0-5 0-23 17-165

50-150

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 32-268

40-200

26-58 26-96 40-200?

70-260

~122-151

Empirical:

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

Selection:

selected half-width 154 257 189 132 128 186 220 135

We adopt a“two-sigma”rule for apparentboundary half-width.

This is generallygreater than orequal to thehalf-widthsexpected a priori.

This rule selects~95% of shallownon-orogenic EQsinto one boundaryor another.

Formal assignment of an earthquake to a plate boundary stepis by a probabilistic algorithm that considers all available information: step type, spatial relations, EQ depth, and focalmechanism:

The A factor takes into account the length, velocity, and inherentseismicity 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 mechanismson each plate boundary step. When the step is oblique to relativeplate motion (the general case), the Earth may produce either oblique-slip EQs, or sets of partitioned-slip EQs:

For SUB steps,the depth PDF function Dassociated with each“model earthquake” helpsto separate mechanismsexpected to be shallow(green curve)from those expected to be within the slab(blue curve, for case ofslab top at 25 km depth)and those thrust eventsexpected to lie along theslab-top plate interface(a Gaussian PDFcentered on this depth;not shown here).

The final classification factor (E) “grades” a possible match on theangular discrepancy between actual and model focal mechanism:

The result…

The frequency/moment distribution that we fit to these subcatalogs is the

Advantages ofthis distribution:

Simple (only one more parameter than G-R);Has a finite integrated moment (unlike G-R) for < 1;Fits global subcatalogs slightly better than the gamma distribution.

The maximum-likelihood method is used to determine theparameters of these tapered G-R distributions (and their uncertainties):

An ideal case(both parameters determined)

A typical case(corner magnitude unbounded

from above)

thresholdmagnitude

95%-confidencelower limit

95%-confidencelower limit

not to betaken literally!(“a largenumber”)

95%-confidenceupper limit

Review of results on spectral slope,

Although there are variations, none is significant with 95%-confidence.Kagan’s [1999] hypothesis of uniform 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 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 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.

KinematicModel

MomentRates

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-Nevadaorogen as represented by a2-D spherical cap of finiteelements.Grid GCN8.6 has:5,243 nodes, and10,233 spherical-triangleelements, with dimensions of:28 km in the interior;14 km in most of California;4 14 km along major faults.

Our data base currentlyhas 690 active(or potentially-active)faults in the region of this orogen.

(They include all faultsused in the seismichazard models of theCalifornia 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 literatureand combined to estimate neotectonic slip rateand its uncertainty.

As this is a type-“N” (Normal) fault, all Offset and Neo-Ratevalues refer to relative vertical offset, or throw.

Each fault has an assignedslip rate and uncertainty.

In this plot the horizontalcomponent (heave rate)is represented by the widthof the colored trace.

Some faults which lackoffset features have assignedslip rates of zero (thesedo not appear in this plot).

Many slip rates havelarge uncertainties(also not shown here).

Zheng-Kang Shenassembled these1,021 geodeticvelocities in 2002.

They include mostof the data usedin the SCECCrustal Motion Map,version 3[Shen et al., 2003].

The reference frameis attached to sites instable North America to the east.

These 963 indicatorsof the azimuth of themost-compressivehorizontal principal stressare from the World Stress Mapdata base project,as of 2000.

(Another ~1,000 indicatorsin surrounding regionswere also used ininterpolation of stress directions.)

Basic algorithm of NeoKinema:Unfaulted elements have a nominal strain-rate of zero, with an assigned uncertainty (e.g., 310-16/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 interpolatedstress-direction field:

For clarity, only half ofthe symbols are shown.

Yellow fans represent90%-confidence limits.

Where the yellow fanswould be unreasonably,broad, no symbol is plotted(and no constraint isapplied to the strainrate tensor).

The field of long-term-averagehorizontal velocitycomputed by NeoKinema:

Velocity vectors are shown at only 1/9 of the node points,for legibility.

(The thin red striparound the west sideof the Gorda plateis a continuationof the Pacific plate.)

Fault heave ratespredicted by theNeoKinema model.

Note the prediction ofup to 6 mm/a oblique slip (thrusting + dextral)on the Mesozoicplate boundary faultoffshore.

This is a map of thecommon logarithmof the total(anelastic,long-term-average)strain rate,including faulting,as predicted byNeoKinema.

Long-term-averageseismicity ratescan be predicted from these strain rates,if seismic couplingcoefficients and frequency/magnituderelations 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.