The Effects of Sub-Faults Strike Direction and Landslide Energy on the Propagation of the 2011 Tohoku Earthquake and Tsunami


 We carried out a tsunami simulation of the 2011 (Mw 9.0) Tohoku earthquake. We analyze the tsunami run-up modeling by applying additional variables to seismic moment and moment magnitude equation to find out what extent it affects of sub-faults strike direction and landslide energy to tsunami propagation. To investigate the accuracy of run-up and inundation of the tsunami, we processed and analyzed the mainshock and aftershocks by applying scaling law method and inundation equation. We applied the aftershocks data to determine the wide area of the fault. The fault is divided into several sub-faults to make simulation design and scaling formulation adjustment. Each of sub-faults strike direction on simulation design has a different energy one another, which is determined by the strike direction of each fault position. Furthermore, we calculated the affects of submarine landslides on tsunami propagation. To obtain the variable of resultant energy of earthquake and landslide it performed by using the law of mechanical energy conservation. We applied both L-2008 and ComMIT tools for processing tsunami simulation modeling. The result presents that the sub-fault strike direction and landslide energy can increase the propagation energy of the tsunami waves.

These results were then processed to conduct an analysis of tsunami potential based on the condition of bathymetry.
The fault parameters are presented in Table 1 and the area of the fault is obtained based on the destruction of the earthquake (Fig. 1). This tectonic process causes the earth's crust in the Japanese region to move actively and dynamically (Seno et al. 1993). The wide area of epicenter of the earthquake along with the size of the fault based on the destruction is around 90.000 km 2 (Gusman et al. 2012). Seismic moment indicates the energy which is released when an earthquake occured (Hanks and Kanamori 1979). It can be calculated by using the moment magnitude formula. The calculation of moment magnitude formulated by Hanks and Kanamori is presented in Wells and Coppersmith equation (Wells and Coppersmith 1994).
We then applied seismic moment to measure the static displacement value (m) which represents the surface deformation due to earthquake. In general, the seismic moment is calculated by using the following Equation (1).
The fault-plane area (A) is a function of fault length (L) and fault width (W) describe in the previous study (Papazachos et al. 2004), as defined by Equations (2) and (3) : L is length of fault and W is width of fault.
The tsunami run-up and inundation are the propagation of tsunami wave triggered by earthquake in the seafloor. It can be estimated by using Equation (4), (5) and (6) as follows: V is tsunami wave velocity (m/ s ), g is gravitational acceleration (9,8 m/ s 2 ), H is earthquake source depth (m), and η is tsunami wave height (m). We applied the formula suggested by Hills & Mader method (Hills and Mader 1997) as presented in Equation (7) to calculate the tsunami inundation distance.
Xmax is Maximum inundation (m), Η is maximum run-up (m), k is a constant (0.06), n is Manning's n = 0.015 for very smooth terrain, 0.03 for building-covered areas, and 0.07 densely treed landscapes.
By applying the physical dimension equation of the earthquake and landslide energy, we obtained each value between earthquake and landslide energy to generate a tsunami propagation. We added landslide value to the resultant energy value of the deformation produced by the earthquake process of its potential or kinetic energy generated by the landslide movement from the sea floor. The deformation causes the earthquake which to triger landslides in the submarine and/or landslide in a coastline cliff. Furthermore, can disrupt the seawater mass volume. If it happens, the earthquake and landslide can cause the two resultant energy to generate a propagation tsunami.
To calculate tsunami affected by landslides, we estimated the physical dimension of ETotal that is the same as the addition of M0 from the seabed deformation and landslides, in which M0 is seismic moment. This formula was applied to calculate the total energy of the earthquake and landslide. The numerical modeling of tsunami is affected by the potential energy (Ept) of the sediment transport caused by landslides. We assumed that Ept is ρ = 1 g 3 for all coral reef material landslides. We then defined it as the new potential energy (Ept) (Ma et al. 2015) as presented in Equation (8): The changes in mean seal level can be approached using Equation (9) and (10): where Epw is potential energy, ρ is density, g is gravity and (ηha) is the height of bathymetry structure (Ma et al. 2015). The generation impulse waves by landslide is defined by using Equation (11): Potential energy will be maximum if Eps = 0. We applied the law of conservation mechanical energy as presented in Equation (12): Accordingly, we calculated the earthquake affected by the landslide in coastal cliff. In this hypothesis we assumed that the disturbance of the sea water column at the top may occur due to the landslides from coastal cliffs or shallow seas. This landslides are regarded as a sediment transport in the upper seawater column or the movement of material that has slipped due to the collapse of a cliff on the coast with a very large volume of soil material due to earthquakes.
Also, we assumed that an earthquake is affected by a landslide from the coastal cliff, so the resultant energy accumulation from the earthquake and landslide will occur in the propagation of the tsunami waves. The second assumption is the distance (h) from the cliff slide when the working kinetic energy is replaced by t.
Therefore, we applied the formula for the law of free-fall motion v = g * t or v 2 = (gt) 2 .
There are two types of energy at work when the material slips in the landslide process, i.e. the kinetic energy that is formed when the landslide cliff material reaches sea level so that it takes effect (Ekfall) and the potential energy that is formed when the landslide material begins to sink (Epsinks) so that the law of conservation of mechanical energy applies. Other studies include two simple examples of slope margins (Santos et al. 2010), block, and free fall. Landslide of material with mass m slides on an inclined surface of the beach slope. The landslide material will make a repulsive force from the volume of sea water as presented in Equation (13) and (14) : Annotation: Ek fall = Energy Kinetic when the cliff material fall.
Ep sinks = Energy Potential when the cliff material sinks.

Total Energy of Seafloor Deformation Affected by Landslides
When the law of conservation mechanical energy is applied, the resultant energy from equations (12) and (14) becomes equations (15) and (16): E total = M 0 (seafloor deformation) + M 0 (submarine landslide) + M 0 (costal cliff landslide)

Results and Discussion
The tsunami modeling scenario is a tsunami model by using the mainshock magnitude classification (Nakamura 2006   Assume : 1 degree ~ 111 km from A to B is 660.0771 km, interveal is 6.60 km ( Fig. 2.a).
The modeling scenario-based sub-faults is determined by finding the combination between the slip and the fault length from the epicenter to the coordinates of the affected location by considering the strike direction, e.g. the modeling scenario for Sendai City (B) applied the second sub-fault. Other parameters, such as depth, dip and other parameters were estimated by using equation from the previous studies (Hanks and Kanamori 1979;Wells and Coppersmith 1994). Each sub-fault has different strike angle that corresponds to the main fault. The area of the sub-faults is based on the epicenter distribution of the foreshocks, mainshock, and aftershocks. We then divided the seismic moment (M 0 ) into several sub-moments based on the sub-fault segments. (16), result of ComMIT tools which it indicate landslide energy were affected to Tohoku tsunami propagation on the March 11, 2011. We may compare that tsunami with landslide it generate a higher tsunamis than those without the affect of landslide.

Fig. 2. b is represent of Equation
The assumption of the fault area parameter tsunami modeling is a rectangular shape although, in fact, the fault area is polyline or spiral following plate boundary topography. The sub-fault's numbers and dimensions affect strike accuracy. The smaller sub-fault dimensions will give more accurate strike direction in the result (table 3).   The modeling using the fourth sub-faults of L-2008 tools is presented in Fig. 3.  (Fig. 4), and sub-fault 2 can represent the result of run-up modeling in area B as well as the area closest to B (Fig. 5).
We divided the study area into several observation areas based on the strike direction of the sub-faults. Group A is the observation area that becomes the result of the run-up model that is suitable for sub-fault 1, i.e. Hachinohe and Kuji (Fig. 4), but Hachiohe has similar values and correlation with the distribution pattern. Goup B is the result of the run-up model that is suitable for sub-fault 2, i.e. Miyako, Kamaishi, Ofunato and Onagawa (Fig. 5). The run-up model that has similar values and correlation with distribution pattern are Ofunato and Onagawa. Group C is the result of run-up model that is suitable for sub-fault 3, i.e. Sendai and Soma (Fig. 6).
Both areas have similar values and correlation with the distribution pattern.
The results of the run-up modeling subtitute to Equation (7) and obtain inundation in the affected area (Fig. 7). Inundation calculations were carried out for the types of field areas, building areas, and forest areas. The results of the calculations were then verified using the results of the modeling and direct measurements carried out by (Løvholt et al. 2012;Lesley 2011). The results of the inundation calculations and their verification are listed in Table 4.
There was a conformity between the results of the inundation calculation and the model references. The lowest inundation is 722.52 meters that occurred in Asahi, Chiba Prefecture, a residential area surrounded by cliffs and trees. The highest inundation is 5600.36 meters that occurred in Ofunato, Iwate Prefecture.
The result of the comparison in inundation calculations among field area, building area, forest area, and field observation is presented in Fig. 7. It shows the effects of landslide energy on tsunami propagation.
The inundation model is more suitable for inundation calculation in the field area (n = 0.015) than that of the field observations. The inundation that occurrred in the is relatively high, while the building area has a lower inundation distribution in Onagawa, Miyako, Sendai, and Soma (Table 4).

Results of Earthquake Affected by Landslides
We applied ComMIT tools to simulate the earthquakes with or without the effect of landslides.
We did the same calculation of tsunami numerical modeling by using the Equation of Wells and Coppersmith. The aftershocks data-based area of fault was measured using the seismic fault field information. The simulation model was performed using six seismic fault planes based on the NOAA database (National Oceanic and Atmospheric Administration 2019) database with the area of the fault area reached 30000 km 2 in total. We determined the Mw = 9.0 Magnitude by using ComMIT to make this simulation, in which the vertical displacement (D) = 10 m (Fig. 8).
We then obtained the maximum fault area of A = 39747 km 2 .
The kinetic landslide of m is mass of slid cliff and the slide movement of free fall of vslope = g.t. The height of fall process (η -ha) = 4000 m is obtained if the cliff of falling kinetic energy is applied, in which h is replaced by t. Based on the free fall motion = g * t or 2 = (g * t) 2 , we assumed that the fall movement of t ~ 3600 s.

Mw = 9.2182 Magnitude
Total energy of seafloor deformation affected by landslides is Mw 9.2182 Magnitude.

Conclusion
This study conducted tsunami modeling simulation process of Tohoku Japan by using calculation of the propagation source originating from fault sources due to earthquakes and landslides through several equations and simulations. The results confirm that both of sub-fault strike directions and landslide energy affect tsunami propagation. It was validated by the results of other studies that the affected area which is directly opposite to the strike directions of the sub-faults will be affected by higher tsunami propagation run-up than the surrounding area. Meanwhile, the effects of the landslide can result in stronger tsunami propagation, thus the inundation range that occurs as a result of the tsunami waves measured from the coastline to the center of the land will be longer. In conclusion, the hypothesis of this study stating that the sub-fault strike direction and landslide can affect the propagation energy of tsunami waves is correct and we have validated it through comparisons using related research and some equations.