This document discusses time-dependent probabilistic seismic hazard assessment (PSHA) and summarizes two case studies. It introduces the concepts of time-dependent PSHA and the epidemic-type aftershock sequence (ETAS) model for modeling short-term earthquake clustering. A case study on the Lower Rhine Embayment in Germany uses the ETAS model in PSHA and finds that neglecting aftershocks can underestimate hazard by up to 8%. Ongoing aftershock sequences from historic events contribute significantly to present hazard levels. The document concludes by proposing a time-dependent PSHA for Northeast India to evaluate underestimation from removing aftershocks.

1. TIME-DEPENDENT PROBABILISTIC SEISMIC
HAZARD ASSESSMENT
DEPARTMENT OF EARTHQUAKE ENGINEERING
GYANENDRA PRAKASH RAHUL
STRUCTURAL DYNAMICS
13526015

2. OBJECTIVE
• INTRODUCTION
• TIME-DEPENDENT PSHA
• BASIC CONCEPTS
• METHODOLOGY
• A CASE STUDY ON LOWER RHINE EMBAYMENT, GERMANY
• INTRODUCTION
• METHODOLOGY
• SHORT TERM CLUSTERING
• APPLICATIONS AND RESULTS
• CONCLUSIONS
• TIME-DEPENDENT PSHA OF NORTH-EAST INDIA

3. INTRODUCTION
• Earthquake sequences seem to be globally continuous over time.
• Earthquakes spark other earthquakes as tectonic stresses move around in the fault
network.
• This explains the complex physical progression of earthquakes.
• Despite knowing the time-dependence of earthquake occurrences, it is mostly
uncared for.
• It has been found that on average the theory of uncorrelated random earthquake
activity underestimates the hazard by 5–10 per cent.

4. TIME-DEPENDENT PSHA
BASIC CONCEPTS
• In the very common approach to seismic hazard assessment, the temporal
behaviour of earthquake is assumed to be based upon Poisson model.
• On the other hand recent studies show unambiguous perturbations from a
Poissonian occurrence in seismic catalogues, and the presence of cluster activity
after a mainshock and its influence is worldwide accepted.

5. METHODOLOGY
1. SHORT-TERM EARTHQUAKE PROBABILITY (STEP) MODEL
• Developed by USGS, it is a simple method of prediction of the rate of
aftershocks based upon statistical parameters of aftershock distribution.
• Main drawback of this model is that it does not predict time, magnitude and
location of aftershocks.
• Used to monitor aftershock activities in California, also for daily seismicity
forecasts in Italy.

6. 2. EPIDEMIC TYPE AFTERSHOCK SEQUENCE (ETAS) MODEL
• It is a multigenerational model in which aftershocks from one earthquake causes
their own aftershock sequences because of multiple generations of earthquakes.
• It forecasts magnitude, space and time dependence of observed seismicity above
some threshold magnitude.
• The major advantage of this model is that discrimination of events is not required
and consideration of seismic dependence of past events to present seismicity.

7. • Poisson process is used for background event modelling and succession of
aftershocks is described by modified Omori-Utsu law, which is given as
where, t = time since occurrence of the shock
K = aftershock productivity which depends upon lower bound of
magnitude of aftershocks counted in v (t)
p = power law exponent
c = artefact related to difficulties in detecting events shortly after
mainshock
푣(푡) = 퐾 푡 + 푐 −푝

8. CASE STUDIES
1. LOWER RHINE EMBAYMENT, GERMANY
1.1 INTRODUCTION
• It is a low seismicity region in North-
Western Germany.
• The two sites under study was Cologne and
Aachen.
• Seismicity data came from Leydecker
catalogue, 2005, which was complete for
ML ≥ 2.0 since 1974.

9. • Short term clustering was modelled through ETAS and via Monte Carlo
technique it was applied on timescales with 50 year of exposure time.

10. 1.2 METHODOLOGY
• 20,000 synthetic catalogues of time duration 50 years were generated for hazard
assessment.
• The probability of non-exceedance of a level A* ground motion at a particular
location in time t was computed by counting the intervals in which A* didn't
occur
푃(퐴 ∗; 푡) = lim
푁→∞
1
푁
푁
퐻(퐴 ∗ −퐴max,푖
푖=1
P(A* ; t) = probability that A* is exceeded at least once in time period t
N = number of catalogues of time duration t, H = Heaviside function
Amax,i = maximum ground motion value occurred at a location during the ith catalogue

11. 1.3 SHORT TERM CLUSTERING
ETAS MODELLING
• Aftershock activity was included in the analysis by ETAS modelling, which is a
point process for representing occurrence of events larger than or equal to a
minimum threshold magnitude.
• The background events representing tectonic loading were modelled by Poisson
modelling, and the succession of aftershocks were defined by Omori-Utsu law.
푣(푡) = 퐾 푡 + 푐 −푝

12. • The magnitude for tectonic and triggered events was randomly selected from a
G-R relation. The proportionality of sequence was taken proportional to K10αM,
with M magnitude and K & α as constants.
• By maximum-likelihood method; values obtained were (Hainzl et al,.2007)-
μ = 1.35 yr-1 , K = 0.0083 , α = 0.70 , p = 0.98 , c = 0.5310-5 yr. , b = 0.96 ± 0.03

13. 1.4 APPLICATION AND RESULTS
• PGA at the site of interest was calculated
for each Ms ≥ 4.0 by using the Berge-
Thierry et al. (2003). The log(PGA) value
was randomly chosen from Gaussian
density function. Standard deviation =
0.2923, truncated at three standard
deviations.
• The solid line signifies 50 % percentile and
the dashed line signifies 90 % percentile at
Cologne. Amax value of 0.036g and 0.09g
respectively for Cologne and 0.049g and
0.12g respectively for Aachen.

14. IMPACT OF SHORT-TERM CLUSTERING
• Two different approaches were used for
declustering-
Case 1: following the ETAS modelling, the main shock was
described as the first event irrespective of magnitude.
Case 2: main shock was considered as the largest event in
cluster (perfect declustering).
• The effect of the time-independent hypothesis were
evaluated for the two sites through ETAS
catalogues and their corresponding Poissonian
catalogues. The figure shows the impact of
Poissonian hypothesis at the two locations.

15. • For every percentile the difference between the PGA values for Poissonian
catalogues and ETAS catalogues were calculated and normalized over the value
of ETAS catalogue.
• Case2, which was referred as perfect declustering, yielded an impact equal to 8 at
90% probability of non-exceedance in 50 years. This implied that with perfect
declustering the seismic hazard was being underestimated by 8 %.

16. IMPACT OF HISTORIC EVENTS
• Düren earthquake, February’1756 with ML = 6.4 and Roermond earthquake,
April’1992 with ML = 5.9 were selected to quantify the effect of aftershock
sequences of larger historic events using Monte Carlo simulations.

18. • In previous figure, top graph shows the contribution of ongoing aftershock
sequences caused by the 1992 Roermond earthquake, for the location of Cologne
and Aachen. Lower graphs show the contribution of ongoing aftershock
sequences caused by the 1756 Düren earthquake.
• Uncertainty linked to the magnitude of Düren earthquake was considered by
assuming upper and lower estimates of ML =5.9 and ML= 6.9 which were
reported as dashed and dotted lines respectively.
• Because the location of 1756 event was close to Aachen, it was found that the
contribution to the hazard was still large for high probabilities of non-exceedance,
reaching 20 % maximum for Aachen and significantly less for
Cologne. Furthermore the Roermond event,1992 contributed more than
10%to the hazard at 90% probability of non-exceedance for next 50 years.

19. 1.5 CONCLUSIONS OF THE CASE STUDY
• Analysis showed that neglecting aftershocks led to an underestimation of the
hazard by 8 % at 90 % probability of non-exceedance in 50 years.
• Moreover, the ongoing aftershock sequence of the Roermond event, 1992
contributed 10-15% to the hazard at the level of 90% of probability of non-exceedance.
Even the Düren event, 1756 contributed about 20% to the present
hazard for the city of Aachen at the level of 95% probability of non-exceedance.

20. TIME-DEPENDENT PSHA OF NORTH-EAST INDIA
• Till now the probabilistic seismic hazard assessment of North-Eastern region has
been carried out in time-independent mode with declustering performed based
upon Poissonian process.
• The aim of this project is to assess the seismic hazard of North-East India
including the cluster activities to evaluate the underestimation of hazard due to
removal of aftershock events.

21. THANK YOU