## 1 Introduction  
Numerous earthquakes of varying magnitudes occur around the world along faults formed as a result of the movement of tectonic plates [1]. One of these regions is the Anatolian plate, which interacts with the African, Arabian, and Eurasian plates (Figure 1) [2, 3]. There are many fault lines on this plate that have the potential to generate earthquakes. The most important of these are the North Anatolian Fault and East Anatolian Fault [2, 4]. Many earthquakes of magnitude seven or greater have occurred on them [5, 6, 7]. Determining the annual slip of plate motion is of great importance in revealing the seismic potential. The amount of annual slip can be determined through the Global Navigation Satellite System (GNSS) with an accuracy of a millimeter or less [8, 9, 10, 11, 7, 12]. Accordingly, the Anatolian Plate is moving westward at a rate of about 25 mm per year. Moment magnitude (M\({}_{w}\)) \(\geq\) 7 earthquakes have been recorded along the North Anatolian Fault during the instrumental period. When we examine these earthquakes and their dates, there is a chain of earthquakes moving from east to west (Figure 2) [6, 13, 14]. The last of this series were the Duzce and Golcuk earthquakes in 1999. Therefore, studies have shown that the next earthquake will occur within the Main Marmara Fault (MMF), which is the main branch of the North Anatolian Fault in the Marmara Region [12, 15, 16, 17, 18, 19]. Analytical methods whose mathematical equations are well defined can be solved directly and have definite results. Numerical methods are based on solving the defined problem iteratively through developing various approaches, and the results obtained are not definitive compared to those obtained through the analytical method. The results obtained through analytical methods offer great advantages because they are precise, accurate, and reliable. However, they have almost no applicability in complex problems [20]. Therefore, the use of numerical methods provides great advantages for complex, non-linear engineering problems that involve many variables. Figure 1: Anatolian plate tectonics (active thrust faults at continental collision zones are shown as lines with filled triangles, active subduction zones are indicated as lines with open triangles, normal faults are indicated as lines with unfilled triangles, and arrows indicate the motion of the plates) [3]. Figure 2: Earthquake sequence of the North Anatolian Fault (the arrow indicate the earthquake east to west migration). In earth sciences, studies on determining deformation of the surface and interior parts of a homogeneous isotropic environment through elastic half-space modeling [21; 22] can be cited as an example of the analytical method [23]. However, dislocation models ignore some physical phenomena such as frictional fault surfaces, and material structure and parameters. The results obtained from dislocation models can also be obtained using numerical modeling [23; 24]. In addition, the dynamic approach can be used in numerical modeling. Many of the physical phenomena discussed in the field of engineering can be explained through partial differential equations. It is almost impossible to solve these equations using analytical methods when solving models with arbitrary shapes [25]. The finite element method (FEM) is one of the numerical methods that enables these partial differential equations to be solved approximately. Unlike FEM, the solutions estimated with analytical methods are valid for that specific region and the results obtained are the same at every point of that region. FEM can be used for analyses such as stress, strain, fluid dynamics, etc. The underwater part of the Main Marmara Fault has a more complex structure than other parts. Contrary to the fact that the fault in this section is stated to be a continuous and right-lateral slip fault [26], it is stated that it is discontinuous and has a pull-apart feature [27] (Figure 3). Also, this part is quite far from land.