## 3 Earthquake Modelling
### Modelling Strategy: Fault Geometry and Slip Distribution  
Regarding the fault geometry (Table 3), this study was based on the previous model designed by [PERSON] [14; 17] and adjusted in accordance with the more recent literature as described in the introduction. Reference [14] is in agreement with the geologically constrained fault model of [PERSON] [33]. Mainly the decollement subfault was adjusted: especially the depth and dip and the rakes of each sub-fault according to the inversion of our data sets. The decollement was fixed arbitrarily to be wide enough so that insignificant slip occurred at one edge of it. Furthermore, for segments 2 and 3, we tried to avoid as many gaps and overlaps as possible. The purpose of the study was to test gABIC on a complicated but known case including several data sets, not to determine the most precise fault geometry. However, for more precision and physical reality a triangular dislocation model would be necessary. Poly3d will be used in a future work [34].  
Under the assumption of an elastic homogeneous half-space, the fault geometry and the slip distribution are determined following a 2-step approach using the Particle Swarm Optimization and OKada INVersion package (PSOKINV). It is a geodetic inversion package [35] developed in Matlab which can solve linear and nonlinear problems. Multiple geodetic data sets can be handled by the program.  
First, a nonlinear inversion is performed to determine the fault parameters (location, strike, dip, rake, length, width, depth and slip) minimizing the square misfit under the hypothesis of a uniform slip on a rectangular fault using the multi-peak particle swarm optimization (M-PSO) [36], a non linear algorithm approach based on the elastic Okada dislocation models [26]. The slip distribution is then determined as a linear problem, and optimally-smoothed parameters are obtained. This is an iterative technique for estimating optimal dip angle and smoothing factors based on a conjugate gradient least square method. When all the parameters are optimally determined, the fault plane was discretized into rectangular sub-patches of 2 km \(\times\) 2 km (see Figure 7).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**This Study** & **Length** & **Width** & **Depth** & **Dip** & **Strike** & **Rake** \\ \hline Segment 1 & 71.45 km & 30 km & 0 km & 23\({}^{\circ}\) & 3.3\({}^{\circ}\) & 62\({}^{\circ}\) \\ Segment 2 & 10 km & 10 km & 0 km & 22\({}^{\circ}\) & 50\({}^{\circ}\) & 90\({}^{\circ}\) \\ Segment 3 & 15 km & 20 km & 0 km & 24\({}^{\circ}\) & 88\({}^{\circ}\) & 90\({}^{\circ}\) \\ Segment 4 & 70 km & 34 km & 11.7 km & 5.7\({}^{\circ}\) & 3.3\({}^{\circ}\) & 54\({}^{\circ}\) \\
**[14; 17]** & & & & & & \\
**(SRCMOD)** & & & & & & \\ Segment 1 & 70 km & 30 km & 0 km & 23\({}^{\circ}\)[22; 23; 24; 25; 26; 27; 28; 29; 30; 31] & 3.3\({}^{\circ}\) &? \\ Segment 2 & 8.6 km & 30 km & 0 km & 23\({}^{\circ}\)[13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30] & 35\({}^{\circ}\) &? \\ Segment 3 & 27 km & [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 72; 75; 77; 78; 79; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94] &? \\ Segment 4 & 70 km &? & [5.8–8.6] km & [0–7]\({}^{\circ}\) & 88\({}^{\circ}\) &? \\ \hline \hline \end{tabular}
\end{table}
Table 3: Fault geometry parameters used in this study and the ones from Reference [14]. [SRCMOD: Earthquake Source Model Database ([[http://equake-rc.info/srcmod/](http://equake-rc.info/srcmod/)]([http://equake-rc.info/srcmod/](http://equake-rc.info/srcmod/)))].