Regional Variation of the ω - Upper Bound Magnitude of GIII Distribution in and Around Turkey: Tectonic Implications for Earthquake Hazards

Abstract

Complete data set of earthquakes in Turkey and the adjacent areas has been used in order to compute the x values in 24 seismic regions of Turkey. The parameter is obtained through Gumbel's third asymptotic distribution of extreme values and is well known as upper bound magnitude. This is an interpretation that no earthquake magnitude greater than x can occur in a region. The results also estimate the most probable magnitude for a time period of 100 years. The estimates of x exceed the value of 7.00 in 20 of the 24 seismic regions. An effort is also made to find a relation between the magnitude and the length of a fault in the complicated tectonics of Turkey and the surrounding area. Earthquake hazard revealed as tables and maps are also considered for Turkey and the surrounding area.

Inference for the truncated exponential distribution

“…Later, the relation has been truncated (Cosentino et al 1977), which implies a TED. Furthermore, the GED or the extreme value distribution type III (equivalent to the GED with c \ 0) have been used to estimate the maximum magnitude (Nordquist 1945;Tuncel et al 1974;Dargahi-Nourbary 1983;Pisarenko et al 2008;Bayrak et al 2008) or have been discussed (Christopeit 1994). However, there is a basic problem besides the fact that T can only be estimated by (12) ifĉ \ 0: The sample seems to be of an exponential distribution without a truncation if the sample size is small and the largest observation X n is much smaller than T. Only if the sample size is large and (T -X n ) is small, then the methods of the extreme value theory seem to be appropriate.…”

Assessment of the Relative Largest Earthquake Hazard Level in the NW Himalaya and its Adjacent Region

“…The parameters of the GIII distribution allow for any detectable curvature to the upper bound magnitude. Both techniques of Gumbel's first and third distribution have been applied for earthquake hazard assessment by a number of researchers in different re-gions of the world (e.g., Yegulalp and Kuo (1974) for Pacific Ocean; Makropoulos (1978) for Greece; Burton (1979) for Europe to India; Makropoulos and Burton (1985) for Pacific rim; Tsapanos and Burton (1991) for the whole world; Tsapanos (1997) for circum Pacific belt; Shanker et al (2007) for Hindukush-Pamir Himalaya region; Bayrak et al (2008) for Turkey; Yadav et al (2012aYadav et al ( , 2013a for NW Himalaya; Tsapanos et al (2014) for Turkey; among others).…”

Regional Variations of the ω-upper Bound Magnitude of GIII Distribution in the Iranian Plateau

“…Seismic moment upper bound is considered by Kagan (2002) in order to discuss various theoretical distributions that can be used to approximate the seismic moment data. The Gumbel's third asymptotic distribution of extreme values (GIII) has also proved useful in estimating upper bound magnitude in different regions of the world (Makropoulos 1978, Burton 1979, Makropoulos and Burton 1983, Tsapanos and Burton 1991, Tsapanos 1997, Bayrak et al 2008, Yadav et al 2012bTsapanos et al 2014).…”

“…The theory of extreme values described by Gumbel (1958) has the advantage that it does not require analysis of the complete record of earthquake occurrence, but uses the sequence of earthquakes constructed from the largest values of magnitude over a set of predetermined intervals. Both first and third asymptotic distributions of extreme value have been proved useful in mapping seismic hazard (Nordquist 1945, Epstein and Lomnitz 1966, Yegulalp and Kuo 1974, Knopoff and Kagan 1977, Burton 1977, Makropoulos 1978, Makropoulos and Burton 1986, Tsapanos and Burton 1991, Bayrak et al 2008. The advantage of Gumbel's third asymptotic distribution (GIII) over first distribution (GI) is that it includes a parameter known as upper-bound magnitude (Ȧ).…”

“…Later, Tsapanos (1997) evaluated upper-bound magnitudes in the subduction zones of the Circum-Pacific region. Bayrak et al (2008) used this method for 24 seismogenic regions in Turkey and surroundings to estimate upper-bound magnitude. Yadav et al (2012b) applied this method in 28 seismogenic regions in the Hindukush-Pamir Himalaya to estimate upper-bound magnitude and 100-years magnitude.…”