Assessments of the Conditional Probability of Rupture of the Northwest Segment of the North Tabriz Fault, Considering Existing Uncertainties

There have been considerable studies in recent years about evaluating the long-term conditional probability of the next strong earthquake (Mw>7) occurring on specific faults or fault segments which have experienced strong shocks. Also in these researches different kinds of recurrence-time distributions have been utilized in order to estimate these probabilities. In the shortage of a long term historical strong earthquake catalog, likely paleoearthquake observations provide possibility that can be used for probabilistic forecasting. In this paper, in order to gain dates of known recent ruptures of the fault, Paleoseismological observations are used. Uncertainties in input data and model parameter values have often ignored in hazard assessment that consequently causes less accuracy in results. Furthermore paleoseismic observations almost miss enough events at a given site to determine directly a probability density function for earthquake recurrence. So in access to more accurate outcomes, here a common statistical method that takes account of uncertainties in data and model parameter values are applied to estimate the time-varying hazard of rupture of the considered fault segment.
The North Tabriz Fault is a major seismogenic fault in Northwest Iran where is defined by a high level of seismicity. This main right-lateral strike-slip fault with an average strike of Northwest-Southeast (NW-SE) has experienced strong and destructive earthquakes that the most destructive one is the 1780 AD. (Ms 7.4), rupturing the northwestern segment of the fault. Accordingly, the conditional probability of further rupture of the northwestern segment of this major fault is a significant subject. The recurrence interval of such earthquakes occurring on this fault segment based on paleosiesmological researches is 821±176year [1].
In order to evaluate the conditional probability, the basic statistical method adopted here is that of Rhoades et al. [2], with alterations clarified and applied by Rhoades & Van Dissen [3] and, recently, used by Van Dissen et al. [4].The purpose of this approach is to estimate the conditional probability of rupture of the fault as a single value which takes account of both input data and parameter uncertainties.  Here we consider two different recurrence-time distributions, exponential as a time-independent model and weibull as a time-dependent model. The Exponential recurrence- time distribution commonly assumed in probabilistic seismic hazard analysis is the model just with one parameter called seismicity rate (λ). This model corresponds to a stationary Poisson process. The Weibull distribution is extensively assumed in failure time modelling for manufactured items. This time-dependent model which has been proposed as a model of fault rupture recurrence has two parameters called shape parameter (c) and scale paramer (β) [5].
Input data assuming in this methodology are based on assessments of the average single-event displacement and its uncertainties, the long-term slip rate and its uncertainties and the dates of known recent ruptures of the fault segment and its uncertainties [3]. Where the values of average single-event displacement and dates of recent ruptures of the fault are gotten from Paleoseismological investigations done by Hessami et al. [1] and preferred long-term slip rate is adopted from Rizza et al. [6]. In order to survey the sensitivity of the northwestern segment of the North Tabriz Fault conditional probability results to the reformed slip rate, conditional probabilities are estimated again with long-term slip rate value extracted from Hessami et al. [1].
As mentioned above, the methodology used here is the same as that described by Rhoades & Van Dissen [3]. In this approach parameter values as well as input data values are entered into analysis as probability distributions for considering data uncertainties. Lognormal distribution is assumed for the average single-event displacement and long-term slip rate, too [3-4]. In order to gauge the sensitivity of the considerable fault segment conditional probability outcomes to dates of rupture distribution than our uniform distribution, results are evaluated again with assumption of normal distribution for each date of rupture. Also, it requires determining prior distributions for the parameters of the recurrence time model. The prior distribution for the parameters of the exponential and weibull models are produced in the same way as those elaborated by Rhoades & Van Dissen [3]. The prior distribution of the mean recurrence times is specified from the considered probability distributions of the average single-event displacement and the average slip rate. The prior distribution of the coefficient of variation is taken to be uniform on (0, 1). Eventually, prior distribution for the parameters of the chosen models is obtained based on these two constructed prior distributions and relations given by Rhoades & Van Dissen [3]. By using prior distribution of parameters and equations presented [3], this procedure is carried out to compute time-varying hazard and conditional probability of rupture of the considered fault segment.
By way of description [3], the above methods are performed to the northwestern segment of North Tabriz Fault, where strong events have been dated [1]. The mean hazard function under each of the models at any time between the year 2015 and 2330 , allowing for data and model parameter values uncertainties, has been figured. Over the 300 year, hazard rate under exponential model, although it is on decreasing tend, is almost static; whereas, the hazard rate under weibull is always increasing. The estimated conditional probabilities of rupture of northwestern segment of the North Tabriz Fault under the assumed models have been computed for time intervals 5, 10, 20, 50, 75, 100, 200 and 300 year. For the next 100 year the probability of rupture of the considered fault segment is15.88% and 10.28% under   the exponential and Weibull models, respectively. Compared with the exponential model the conditional probability of rupture under the Weibull model is lower. As for results, the estimated conditional probability under these models is not similar. Although the exponential model is commonly used in hazard analysis but it is not suggested to be applied as a recurrence-time model to the faults or fault segments where large shocks occur [7]. So here, for the northwestern segment of North Tabriz Fault, the outcomes under time-dependent weibull model are preferred.
Obtained results of the northwestern segment of North Tabriz Fault demonstrate that, assumption of the different types of prior distribution for dates of known ruptures has no significant effect on outcomes; however, these assessments are so sensitive to the values of the long-term slip rate and it’s uncertainties, causing in about 40% and 80% changes in values of probabilities for exponential and weibull recurrence-time distributions, respectively.
Reference

Hessami, K., Pantosti, D., Tabassi, H., Shabanian, E., Abbassi, M. R., Feghhi, K.H., and Solaymani, S. (2003) Paleoearthquakes and slip rates of the North Tabriz fault, NW Iran: Preliminary results. Ann. Geophysics, 46, 903-915.
Rhoades, D.A., Van Dissen, R.J., and Dowrick, D.J. (1994) On the handling of uncertainties in estimating the hazard of rupture on a fault segment. Journal of Geophysical Research, 99(7), 13,701-13,712.
Rhoades, D.A. and Van Dissen, R.J. (2003) Estimates of the time – varying hazard of rupture of the Alpine Fault, New Zealand, allowing for uncertainties. New Zealand Journal of Geology and Geophysics, 46, 479-488.
Van Dissen, R.J., Rhoades, D.A., Little, T., Litchfied, N., Carne, R., and Vilamor, P. (2013) Conditional probability of rupture of the Wairarapa and Ōhariu faults, New Zealand. New Zealand Journal of Geology      and Geophysics, 56(2), 53-67.
Hagiwara, Y. (1974) Probability of earthquake occurrence as obtained from a Weibull distribution analysis of crustal strain. Tectonophysics, 23, 318-323.
Rizza, M., Vernant, P., Ritz, J. F., Peyret, M., Nankali, H., Nazari, H., Djamour, Y., Salamati, R., Tavakoli, F., Chery, J., Mahan, S.-A., and Masson, F. (2013) Morphotectonic and geodetic evidence for a constant slip-rate over the last 45 kyr along the Tabriz fault (Iran). Geophys. J. Int., 193, 1083-1094.
Ogata, Y. (1999) Estimating the hazard of rupture using uncertain occurrence times of paleoearthquakes.  Journal of Geophysical Research, 104, 17995-18104.