Fault Segmentation: User Perspective Norm Abrahamson PG&E March 16, 2006

Segmentation Approaches in Seismic Hazard Practice Pre ~1985 –Used 1/3 to 1/2 fault length for the characteristic (max) earthquake –Implies segmentation but unknown segmentation points –Geologist identified segmentation points –Used full length of segments for characteristic earthquake –Typically considered segmented or unsegmented cases through logic tree (e.g. epistemic uncertainty), but not aleatory variability in segmentation Current –Begin to include aleatory variability in segmentation (sometimes individual segment rupture, sometimes multi-segment ruptures

Unknown Segmentation Truncated exponential model for mag pdf is sometimes used as proxy for segmentation

Example: Effects of Segmentation Slip-rate=10 mm/yr

Deterministic Approach (Median Sa) MagnitudePGASa(T=3 sec) Segmented g.088g Unsegmented g0.108g

Example: Effects of Segmentation PGA: Site 1 (at segmentation point)

Example: Effects of Segmentation T=3: Site 1 (at segmentation point)

Example: Effects of Segmentation PGA: Site 2 (middle of a segment)

Example: Effects of Segmentation T=3: Site 2 (middle of a segment)

User Needs for Segmentation Fault Models –Need rates of ruptures on faults –Develop credible models of the fault behavior in terms of segmentation that are consistent with observations Avoid Bias –Should not include intentional conservatism Not clear what is conservative Uncertainty –Uncertainty in segmentation is handled using alternative models of fault behavior Should not just be single segments ruptures and all segment ruptures

Truncated Exponential Model for faults Hecker evaluated variability of surface slip at a point Found that the truncated exponential model will produce much larger variability than observed Concluded that truncated exponential model is not applicable to individual faults

User Needs Earthquake probabilities for ruptures are useful, but they need to be converted to PSHA inputs More useable information is the equivalent slip-rate that for each rupture (single segment or multi-segment) –Allows direct input into standard PSHA codes

Example from WG03 94% Moment in Char Eqk RuptureMean Characteristic Magnitude P(M>6.7) in 30 yrs Equivalent slip- rate (mm/yr) NH SH NH+SH RC RC+NH RC+NH+SH Floating

Coefficient of Variation of Surface Slip at at Point (from Hecker) Style-of-faultingCV Strike-slip0.38 (±0.04) Normal0.45 (±0.04) Reverse0.32 (±0.04)

Testing of Magnitude Recurrence Models Using C.V. Forward Modeling of expected observations of slip at a point –Prob (M) (from mag recurrence model) –Prob (rupture to surface given M) –Prob (rupture past site given Rup Length(M)) –Prob (amount of surface slip given M) –Prob (detection) including effect of adding slip from non-detected events to the detected events Magnitude recurrence models –Truncated exponential –Youngs & Coppersmith Characteristic –Max Mag = 7.5, MinMag = 6.0

Amount of Surface Slip Average Displacement –Use Wells and Coppersmith for all fault types –log(AD) = M ± 0.36 ( ± 0.82 ln units) Variation in Displacement along Strike –Use results from (ref?) –Sigma along strike approx 0.7 natural log units Total standard deviation of slip-at-a-point –Sqrt( )=1.07

C. V. from Modeling Results Case1: Using full Slip Variability for given M Slip with 50% chance of detection in next to last event Truncated Exponential Y&C Characteristic 0.1 m m m m m

C. V. from Modeling Results Case1: Using reduced Variability for given M (reduced to 0.3 natural log units) Slip with 50% chance of detection in next to last event Truncated Exponential Y&C Characteristic 0.1 m m m m m

Conclusions from Forward Modeling of Surface Slip Variability of slip at a point must be much smaller than expected using global models The Y&C mag recurrence model can give C.V. values similar to observed values if small variability in slip for given mag is used. The truncated exponential mag recurrence model gives much larger C.V. values than observed even with reduced variability in slip given mag. –The truncated exponential model is not consistent with the observed C.V. values.

Effect of Small Number of Events per Site Use Monte Carlo –Population C.V.=0.4 –Same sampling as in data set Result: –Average C.V.=0.41 (small bias toward larger CV)

Event Position of Smallest Slip Smallest slip is more often the most recent event Accommodate effect by overprinting Calibrate levels for overprinting (e.g. 40% of amplitude) using observed frequencies

Effect of Probability of Detection and Overprinting Example: mean slip is close to detection threshold result: Increase in C.V.

Effect of Probability of Detection Example: mean slip is 2.5 times detection threshold Result: Similar C.V.

Probability of Surface Rupture (modified from IGNS, 2003)