1. David Brillinger and [Bruce Bolt]
Objective Estimates of the Seismic Intensity of the 1755 Lisbon Earthquake
David Brillinger and [Bruce Bolt]
University of California, Berkeley

2. Introduction.
Quantifying damage
Intensity scales ordinal-valued
Isoseismals
Probabilistic approach
Lisbon event
n = 810

5. Methods.
Grouped continuous model
Latent r.v.  , cutpoints j
 Y= II if  < II
 Y= j if j-1 < < j if j = II,…,IX
  = X if IX < 
j increasing.

6. Objectives.
1. Automatic modelling method for ordinal-valued data
Ordinal scale: “OK, good, very good, excellent”
Can merge adjacent categories
2. Chance model for probabilistic risk assessment
3. Treat ordinal values as numerical?

7. Including explanatory X
Spatial case
’X = (x,y),  smooth function
extreme value distribution
Prob{Y=j|(x,y)} =
exp{-exp{ j-1+(x,y)}}-exp{-exp{j+(x,y)}}
Generalized additive model

8. Results. Data: MSK intensity countsII
II+
III
III+ IV
IV+ V V+ VI 5 11 27
128
114
104 48
111
VI+
VII
VII+
VIII
VIII+ IX
IX+ X 59 84 27 29 17 13 11

10. Estimate of (x,y)

11. Estimate of j

12. - Assessment of fit. Prob{Y=j|Y>j-1,X} = 1 – exp{-exp{φj+ (x,y)}}
Proportion of successes on y-axis
vs.
cells for lp: φj+ (x,y) on x-axis

14. Prob{Y=j|(x,y)} for j = X, VII, II

17. Dependence on distance.

18. Joyner-Boore type attenuation
log(-log(1-Prob{Y=j|Y>j-1}))
= j + d + log(d)
d, distance

19. Difficulties for small d

20. Discussion and conclusions.
Empirical relations for intensity probability as function of location
Stochastic model – assessment, tests
Limitations – other variables, e.g. regional and local geology
Hypercenter error
Uncertainties
Other functional forms (small d’s)

22. REFERENCES.
Martinez-Solares, J. M., Lopez-Arroyo, A. The great historical 1755 earthquake, effects and damages in Spain, J. Seismology 8, pp
Mendes-Victor, L., Baptista, M. A., Miranda, J. M., Miranda, P. M., Can Hydrodynamic Modelling of Tsunami Contribute to Seismic Risk Assessment? Phys. Chem. Earth 24, pp
Brillinger, D. R. Earthquake risk and insurance, Environmetrics 4, pp

23. Acknowledgements.
J. M. Miranda
J. M. Martinez-Solares
The Organizers
Beverley Bolt
[Bruce Bolt]
Errors are mine