ANALYSIS OF SPATIAL AND TEMPORAL VARIATION OF EARTHQUAKE HAZARD PARAMETERS FROM A BAYESIAN APPROACH IN AND AROUND THE MARMARA SEA

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1 ANALYSIS OF SPATIAL AND TEMPORAL VARIATION OF EARTHQUAKE HAZARD PARAMETERS FROM A BAYESIAN APPROACH IN AND AROUND THE MARMARA SEA Y. Bayrak 1, T. Türker 2, E. Bayrak 3 ABSTRACT: 1 Prof Dr. Geophysical Engineering, Karadeniz Technical University, Trabzon 2,3 Research Assn. Geophysical Engineering, Karadeniz Technical University, Trabzon tturker@ktu.edu.tr In this study, we used a Bayesian approach based on spline smooth (B-spline) function to estimate the spatial and temporal distribution of the earthquake hazard parameters in and around the Marmara Sea, the western of the North Anatolian fault zone (NAFZ). A homogenous and complete earthquake catalog during the period with magnitude Ms 4.0 is utilized to estimate the spatial and temporal variation. There were two ways to perform spline smooth. Firstly, estimated parameters were expanded and secondly, these parameters were recalculated. In the study, it was proposed that earthquake hazard parameter combined with seismicity and tectonic background. As a result, the high β and b values has appeared in the southern branch of the North Anatolian Fault region. Also, the low β and b values were observed in between the İzmit-Sakarya region and between the Sakarya-Düzce region. The high activity rate values were estimated in the Marmara Sea region. While the high Mmax values were estimated in between the İzmit-Sakarya region, the low Mmax values were estimated in the southern branch of the North Anatolian Fault region. Furthermore, spatial variations were plotted 2D contour maps, classed post maps (a group the data into discrete classes), shaded relief maps (raster maps based on grid files), 3D wireframe (three-dimensional representations of grid files) and 3D surface. It has been observed that the temporal and spatial method can be used to determine earthquake hazard analysis of a region. KEYWORDS: Spatial and Temporal Variation, A Bayesian Approach, Spline Smooth (B-spline) Function, the Marmara Sea. 1. INTRODUCTION The NAFZ were one of the most important major continental strike-slip fault zones about 1200-km-long in the world. Westward escape of the Anatolian plate produces large earthquake series on the right lateral North Anatolian Fault Zone (NAFZ). The last ones are the Kocaeli and İzmit-Düzce (1999) earthquakes. Their fault ruptures was delineated on land, however, its westernmost part is mainly under the sea. Bayrak and Türker (2017) were estimated earthquake hazard parameters with Bayesian method for different regions in the North Anatolian Fault Zone. In addition to, it were researched earthquake hazard parameters for the Marmara Sea in western branch of the NAFZ. İt were founded high seismicty of the Marmara Sea.

2 Figure 1. Epicenter distribution of earthquakes in and around the Marmara Sea. Epicenters of M s 4.0 events between The earthquakes are divided into 6 different seismic source regions with epicenter distribution of formed earthquakes in the instrumental period, focal mechanism solutions, and existing tectonic structures (Bottom figuresand maps plotted for 1/ scales). The Marmara Sea is demonstrated on Turkey map (Top figure and map plotted for 1/ scale). 2. METHOD In this study, we use free-knot spline functions to estimate and interpolate b-values in space. Since many parameters are required for the spline function, we maximize the log-likelihood function which measures data fitting to obtain parameter estimations. On the other hand, we adopt the objective Bayesian method to avoid unnecessary fluctuation of the estimated spline surface. A Bayesian approach with smoothness prior was suggested by Ogata et al. (1991) as an alternative approach to obtain the b-value, and it performs significantly better than the maxsimum likelihood estimate (MLE) approach. The smoothing spline is a method of fitting a smooth curve to a set of noisy observations using a spline function. Ever since Gutenberg and Richter (1944) observed the empirical law of the magnitude frequency distribution: (1)

3 where N is the cumulative number of earthquakes with magnitude M, the coefficient b has been playing a central role in earthquake hazard models. The Gutenberg Ritcher s law indicates the probability density function of the earthquakes with magnitude M as below: Since we assume that b is dependent on the location of the space, the current likelihood function can be rewritten as: (2) The parameterization of the function b(x,y): (3) 2-D B-spline function: (4) B-spline (DeBoor 1978): (5) (6) The local variation of a surface: (7)

4 The penalized log-likelihood function (Ogata et al. 1991): (8) The data set: (9) In order to obtain the optimal weights, we introduce the Bayesian Likelihood (Akaike 1980; Good 1965) into method. Bayesian Likelihood: (10) To obtain w1, w2, and cp, we need to maximize the Bayesian Likelihood. Log Bayesian Likelihood approach (Ogata et al. (1991): (11) Figure 2. A flow chart of the steps used to calculate the b-value.

5 3. RESULTS The spatial-temporal variations are estimated for the six different seismogenic regions in and around The Marmara Sea. Table 1. 6 different seismic source region divided into in and around the Marmara Sea. Region No 1 Between Saroz Gulf-Ganos Regions 2 Marmara Sea (Tekirdağ-Merkez-Kumburgaz-Çınarcık Basins) 3 İzmit Gulf (Gölcük-Tepetarla-Arifiye-Dokurcun Basins) 4 Hendek Fault, Karadere-Düzce Basins 5 The Southern Branch of NAF (Edremit Fault Zones, Yenice-Gönen, Mustafa Kemal Paşa, Ulubat Faults) 6 The Southern of Marmara(Taşkesti Basin, Geyve-İznik, Mekece, Gemlik Faults ) Table 2. Estimate of temporal variations in 6 different seismic source regions. Regions Longitude Latitude Year Month Day Magnitude Depth b- value Region 1 26,12 40, ,9 33 0,92 26,08 40, ,9 18 0,92 26,12 40, ,6 14,97 0,72 26,131 40, ,9 9,48 0,92 Region 2 29,09 40, ,4 40 0,85 Region 3 29,99 40, ,8 18 0,62 30,1 40, ,8 19 0,95 Region 4 31,21 40, ,2 17,73 0,62 30,69 40, ,1 0,24 0,63 30,75 40, ,3 9 0,86 Region 5 27,4 40, ,8 12 1,45 28,99 40, ,3 13 1,42 Region 6 28,199 40, ,9 33,83 1,01 27,21 40, ,1 14,97 0,90 26,116 39, ,9 9,78 0,92

6 Figure 3. Temporal variations of b-values in all regions. Yellow line indicates the occurrence time of the 1999, M=7.8 İzmit earthquake. Red graph line was applied spline smooth function. Blue garph line was original estimates. Black points was estimated b-values for all regions. The maps of 2D and 3D spatial variations of the b-values are plotted. These were 2D contour maps, classed post maps (a group the data into discrete classes), shaded relief maps (raster maps based on grid files) and image maps, 3D wireframe (three-dimensional representations of grid files) and 3D surface. For example: Spatial variations of estimates of earthquake hazard parameters (maximum regional magnitude (Mmax), coefficient of G-R relationship (β value), seismic activity (λ value)) in Region 1 observed Figure 4, 5, 6 and 7. Figure 4. Spatial variations of M max mapped for Region 1.

7 Figure 5. Spatial variations of β mapped for Region 1. Figure 6. Spatial variations of λ mapped for Region 1.

8 Figure 7. 2D İmage maps of spatial variations of b-values for 6 different seismogenic source regions. We estimated earthquake hazard parameters in and around the Marmara Sea. Ogata et. al. (1991) estimated only b-values using b- spline function, but we estimated different hazard parameters Mmax, β ve λ etc. We applied spline smooth (b-spline) function for earthquake hazard parameters. In addition to, we observed spatial-temporal variations of earthquake hazard parameters. In the study, method was proposed that earthquake hazard parameter combined with seismicity and tectonic background. As a result, the high β and b values has appeared in the southern branch of the North Anatolian Fault region. Also, the low β and b values were observed in between the İzmit-Sakarya region and between the Sakarya-Düzce region. The high activity rate values were estimated in the Marmara Sea region. While the high Mmax values were estimated in between the İzmit-Sakarya region, the low Mmax values were estimated in the southern branch of the North Anatolian Fault region. The analysis shows that spatial-temporal variations of the b-values can be provided insight into the study of earthquake hazard models.

9 REFERENCES Akaike H (1980) Likelihood and the Bayes procedure. Trabajos de estadı stica y de investigacio n operativa 31(1): Bayrak Y, Türker T (2017) Evaluating of the earthqauke hazard parameters with Bayesian method for the different seismic source regions of the North Anatolian Fault Zone, Natural Hazards, 85, Good IJ (1965) The estimation of probabilities: an essay on modern Bayesian methods. MIT Press, Cambridge, MA. Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seismol Soc Am 34(4): Ogata Y, Imoto M, Katsura K (1991) 3-D spatial variation of b-values of magnitude frequency distribution beneath the Kanto District, Japan. Geophys J Int 104(1): doi: /j x.1991.tb02499.x.