Department of Geological Sciences, Faculty of Sciences
Masaryk University/Brno & Czech Geological Society
September 12-14, 2011
Short Course on Geological HazardsShort Course on Geological Hazards
Day 2Day 2 (Tue AM)(Tue AM), Lecture 3, Lecture 3::
(Combines Topics 2 and 3 of Original Announcement)
Basics of PSHA, with Examples for 2 USBasics of PSHA, with Examples for 2 US
BridgesBridges in Stable Continental Regions (SCR)in Stable Continental Regions (SCR)
Klaus H. JacobKlaus H. Jacob
Lamont-Doherty Earth Observatory
of Columbia University, NY
jacob@ldeo.columbia.edu
1990
1989
2004
McGuire 2004
PSHA appliesPSHA applies ProtocolsProtocols (e.g. in US:(e.g. in US: ““SSHACSSHAC””) for Soliciting) for Soliciting
““Expert OpinionsExpert Opinions”” that then are formally taken intothat then are formally taken into
account toaccount to quantify the combined effects ofquantify the combined effects of UUaa andand UUee
UUaa
UUee
McGuire 2004 •
(Natural Randomness)
(Modeling Uncertainties, Lack of Knowledge & Understanding)
Science Tasks for ProbabilisticProbabilistic Seismic Hazard Assessment (PPSHASHA)
• Create Cleaned-Up Earthquake CatalogCreate Cleaned-Up Earthquake Catalog
Translate Intensity ==> Magnitude
Translate Various Magnitudes ==> Uniform Moment Magnitude, Mw Preferred
Completeness Checks, Remove Aftershocks, Other Checks: Doubles, Blasts, ...
•• Choose Seismic Source ZonesChoose Seismic Source Zones
Gridded Seismicity: Grid Size and Smoothing Parameter (==> agrid , b)
Source Zone Geometry , Fit Rate Relation ==> n(Mw), a, b, Max, h?
Faults, their Slip- or Moment-Rates; Characteristic Earthquakes Mch?
•• Ground Motion Relations: Select from available (a,v,u, PSA,PSV,PGA)= f(M,d,h,Ground Motion Relations: Select from available (a,v,u, PSA,PSV,PGA)= f(M,d,h,εε))
PSHA Procedural StepsPSHA Procedural Steps::
Choose “SSHAC” (or equivalent) Project Level/Protocol & Assemble Expert Team
Choose PSHA Computer Algorithm
Assign Multiple Model Choices and Logic Tree with Branch Weights
Compute n(C≥c) per Site & for all Sources & for all Branches in Logic Tree
Plot Results as Hazard Curves (n=n(c)) for Spectral Frequencies fi; Mean, Median
Choose Probability Levels (Tr) and make respective Uniform Hazards Spectra
Perform Deaggregation for (M*,d*,ε) at Given Ground Motion Values c*
Obtain recorded or synthetic Ground Motions g(t) for M*,d* at given Tr
Modify Ground Motion g(t) to be spectrally compatible with UHS at given Tr
Hazard CurveHazard Curve
aleatoryaleatory
E(z) Expected number of exceedances of ground motion levels Z≥z during period t
αi is the mean rate of occurrence of earthquakes between lower and upper magnitudes (mo and mu )
for source I during period t; (e.g. given by the (truncated) G-R relation).
N is the number of source zones considered
fi(m) is the probability density distribution of magnitude (recurrence relationship) for source i;
fi(r) is the probability density distribution of epicentral or source distances for between the various
locations within source i and the site for which the hazard is being estimated;
P(z>z|m,r) is the probability that a given earthquake of magnitude m and epicentral distance r will
exceed the ground motion level z (related to the used ground motion relation, including itsincluding its
aleatory uncertainty).aleatory uncertainty).
Basic Equation for Probabilistic Seismic Hazard Assessment, PSHABasic Equation for Probabilistic Seismic Hazard Assessment, PSHA
before Consideration ofbefore Consideration of Epistemic UncertaintiesEpistemic Uncertainties
Reiter 1990
Example of multiple GMPEsExample of multiple GMPEs
How to treatHow to treat epistemicepistemic (model) uncertainties U(model) uncertainties Uee??
==> Logic Trees==> Logic Trees
Rules for Logic Trees:Rules for Logic Trees:
Each Node has different Model Branches for theEach Node has different Model Branches for the
same topical Object (e.g. different Ground Motionsame topical Object (e.g. different Ground Motion
Prediction Equations)Prediction Equations)
Each Branch emerging from a Node has a weightEach Branch emerging from a Node has a weight
ww assigned. Theassigned. The SumSum of the Branch Weights atof the Branch Weights at
each Node must be 1 !each Node must be 1 !
The end weightsThe end weights WW at the ends of each branchat the ends of each branch
sequence, i.e. at the localsequence, i.e. at the local ““toptop”” of the tree,of the tree, is theis the
ProductProduct WW of all branch weightsof all branch weights ww, running from, running from
the trunk to thethe trunk to the lastlast branch orbranch or ““twigtwig”” at the top ofat the top of
the tree.the tree.
When youWhen you add upadd up all theall the end weightsend weights WW, located at, located at
the tops of the tree, thethe tops of the tree, the SumSum must add up to 1 !must add up to 1 !
Example of 2 different Expert Teams coming up with 2 differentExample of 2 different Expert Teams coming up with 2 different
Seismic Source Zone models.Seismic Source Zone models.
xx
xx xx
M* = 6.9M* = 6.9
d*d* ≤≤ 12.5 km12.5 km
Note large differences in PGA for the various
confidence fractions. From 15 to 85% level of
confidence the PGA varies from ~160 to ~920
cm/sec^2 for EP = 10^-5/y
NYCNYC
1Hz1Hz
ChicagoChicago
5Hz5Hz
NYCNYC
ChicagoChicago
Deaggregation of Hazard at given PE
Ratio R = (Sa 5Hz / Sa 1Hz)R = (Sa 5Hz / Sa 1Hz)
for P = 2% in 50 yr
Questions?
2d
GMPE
Hazard Curves
1 Hz
Hazard Curves
10Hz
Response Spectra for all branches in the Logic Tree
Response Spectra for all branches in the Logic Tree
Steps for Translating Probabilistic Ground Motion Spectra into Hazard-Compatible Ground
Motion Records in the Time Domain for Engineering Use:
1. Deaggregate PSHA Results (for 2 given probabilities 5 and 2% in 50 years; and for 2 discrete
frequencies 1Hz and 10Hz) into one or more discrete (M*, d*) pairs, depending on mode
topography.
2. Obtain the seismic parameters for the model of the regional crust through which seismic
waves propagate.
3. Choose regionally appropriate stress drop values (100 bar) and source depths hh for the
sources, and use focal mechanisms (reverse faulting or oblique SS with reverse components of
slip).
4. Find a regionally appropriate “scattering function” that complements the viscoelastic
(intrinsic) damping (Qα* and Qβ*) for the layers of the seismic model of the regional crust.
5. Compute Synthetic Ground Motion Records ( 3 components: Z, R, T) with full wave theory.
6. Convolve the Synthetic Seismograms with the Scattering Function to obtain the appropriate
ground motion duration and “coda-fall-off”.
7. Optional: Make the records in the time domain spectrally compatible with UHS for the
corresponding probabilities (2 and 10% in 50 years).
M*, d*M*, d*
M*, d*M*, d*
.
Questions?
2d
Example for Hybrid, Constant Recurrence Period (CRP) Method.Example for Hybrid, Constant Recurrence Period (CRP) Method.
This isnThis isn’’t a PSHA and does not accountt a PSHA and does not account forfor uncertaintiesuncertainties UaUa andand UeUe,,
but allows to model hazard-consistent ground motions for specifiedbut allows to model hazard-consistent ground motions for specified TrTr..
Questions?
2d