1. Seismic Upgrade Risk versus Benefit Shawn Callahan Mike Pollard 5/31/11

2. Executive Summary Seismic upgrade is an insurance policy designed to minimize risk. Our goal is to determine the value of each option based on the seismic risk and benefit. In our WBS we calculated the cost of each option and the benefit to cost ratio (BCR). Conclusion: –12.3% in 50 year event (2006 sized event) BCR<1 for all current options. This is due to low probability and high cost to retrofit. –2% in 50 year event (collapse prevention). Option B (protects glass) BCR=16 Option D (protects against collapse) BCR>>1

3. Benefit cost ratio (BCR) (12.3% probability in 50 years) based on 2006 event Baseline loss (2006 event): $7.7M Estimate loss for each restraint design. Benefit=Loss reduction ( Baseline loss- Estimated Loss) USGS probability of 0.3g’s (2006 event) quake=12.3%. BCR= Benefit x Probability/Cost (want > 1)

4. Baseline loss: Cost of 2006 earthquake Lost ~5 weeks of science (100k/telescope/night): $7.0M Cost of repair (summit): $681K Total lost: $7.7M see:\TSD Planning\TSD Development Projects\Seismic Upgrade\2006 Quake Recovery Doc

5. Estimated loss with new restraints ( 12.3% in 50 yrs and 6.3% in 25 yrs)

6. Benefit (Loss reduction) Baseline loss- Estimated loss ( 12.3% in 50 yrs and 6.3% in 25 yrs)

7. USGS Probability Peak Ground Acceleration (PGA) in 50 years for Mauna Kea 10% probability of 0.4g PGA 2% probability of 1.2 g’ PGA Use Gutenberg-Richter recurrence relation, log(N)= a-b*M solve for a, b. Calculate 12.3% probability for 0.3 g PGA

8. Benefit to cost ratio ( 12.3% in 50 yrs and 6.3% in 25 yrs)

9. Probabilistic Seismic Hazard Analysis (a.k.a. limited liability clause) Probabilistic Seismic Hazard Analysis (PSHA) is a methodology that estimates the likelihood that various levels of earthquake-caused ground motion will be exceeded at a given location in a given future time period. Due to the infrequency of large seismic events, there is inherently a large uncertainty in USGS predictions. Estimates continually being improved by USGS.

10. Conclusion BCR<1for all current options. This is due to low probability and high cost to retrofit. Until we can achieve BCR>1 we do not recommend proceeding to PDR.

11. Accelerations vs. damage The damage should be roughly proportional to acceleration (assume constant duration).

12. Benefit cost ratio (BCR) based on 2% in 50 year (Restraints only prevent collapse) Baseline loss: Possible loss of life. Total loss of both telescopes. Estimate loss for each restraint design. Benefit=Loss reduction ( Baseline loss- Estimated Loss) USGS probability of 1.2g’s=2% BCR= Benefit x Probability/Cost (want > 1)

13. “Collapse prevention” Baseline 2% probability in 50 years The "value of a statistical life" is $6.9 million in today's dollars, the Environmental Protection Agency reckoned in May [2011] In a 24 hour period assume 10 people were at risk ($70M) Replacement cost for two telescopes in today’s dollars ($750M?) Total: $820M??? (The TMT telescope cost was estimated in 2009 to be $970 million to $1.2 billion)

14. Collapse prevention restraint 2% probability in 50 years Loss estimate Options A through C already include collapse restraints. Option D: Design K1-style restraints for K2. Include additional uplift restraint to meet zone 4 PGA for both telescopes. The damage of an earthquake is proportional to the energy release: Option B$7.7M x 4.46=$34M. Option D: add $85M for M1 and M2 replacement= $119M

15. Benefit (Loss reduction) 2% probability in 50 years from adding collapse prevention Benefit= Baseline loss-estimated loss Option B: Benefit=$820M-$34M=$786M Option D: Benefit =$820M-$119M=$701M

16. Cost Option B: $854k Option D: $120K= 16x $5k+50% (Needs refinement!)

17. BCR BCR= Benefit x Probability/Cost (want > 1) BCR Option B: $701M*.02/854,420= 16 Option D: $786M*0.02 /$120K= 131