Spatial Variation of Seismic B-Values of the Empirical Law of the Magnitude-Frequency Distribution from a Bayesian Approach Based On Spline (B-Spline) Function in the North Anatolian Fault Zone, North of Turkey

In this study, A Bayesian approach based on Spline (B-spline) function is used to estimate the spatial variations of the seismic b-values of the empirical law (G-R law) in the North Anatolian Fault Zone (NAFZ), North of Turkey. B-spline function method developed for estimation and interpolation of b-values. Spatial variations in b-values are known to reflect the stress field and can be used in earthquake hazard analysis. We proposed that b-values combined with seismicity and tectonic background. β=b*ln(10) function (the derivation of the G-R law) based on a Bayesian approach is used to estimate the b values and their standard deviations. A homogeneous instrumental catalog is used during the period 1900-2017. We divided into ten different seismic source regions based on epicenter distribution, tectonic, seismicity, faults in NAFZ. Three historical earthquakes (1343, MS = 7. 5, 1766, Ms=7.3, 1894, MS = 7. 0) are included in region 2 (Marmara Sea (Tekirdağ-Merkez-Kumburgaz-Çmarcik Basins)) where a large earthquake is expected in the near future because of a large earthquake hasn't been observed for the instrumental period. The spatial variations in ten different seismogenic regions are estimated in NAFZ. In accordance with estimates, b-values are changed between 0.52±0.07 and 0.86±0.13. The high b values are estimated the Southern Branch of NAFZ (Edremit Fault Zones, Yenice-Gönen, Mustafa Kemal Paşa, Ulubat Faults) region, so it is related low stress. The low b values are estimated between Tokat-Erzincan region, so it is related high stress. The maps of 2D and 3D spatial variations (2D contour maps, classed post maps (a group the data into discrete classes), image maps (raster maps based on grid files), 3D wireframe (three-dimensional representations of grid files) and 3D surface) are plotted to the b-values. The spatial variations b-values can be used earthquake hazard analysis for NAFZ.