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Quantifying Seismic Intensity: 1755 Lisbon Earthquake Analysis

This study presents a probabilistic approach to estimate seismic intensity of the 1755 Lisbon Earthquake. The research aims to develop automatic modeling methods for ordinal data and assess the seismic risk quantitatively. The results involve employing a generalized additive model to analyze intensity counts and estimate parameters related to locational factors. The study discusses challenges associated with proximity-dependent attenuation and offers insights into empirical relations between intensity probability and geographical location.

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Quantifying Seismic Intensity: 1755 Lisbon Earthquake Analysis

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  1. 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

  3. 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.

  4. 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?

  5. Including explanatory X • = -’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

  6. Results. Data: MSK intensity counts

  7. Estimate of (x,y)

  8. Estimate of j

  9. - 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

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

  11. Dependence on distance.

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

  13. Difficulties for small d

  14. 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)

  15. REFERENCES. Martinez-Solares, J. M., Lopez-Arroyo, A. The great historical 1755 earthquake, effects and damages in Spain, J. Seismology 8, pp 275-294. 2004. 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. 139-144. 1999. Brillinger, D. R. Earthquake risk and insurance, Environmetrics 4, pp. 1-21. 1993

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

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