This thesis investigates the Ground Motion Model (GMM) for the Groningen Seismic Hazard & Risk Analysis. We look at various aspects of the model to see where improvements can be made. We start by looking at model calibration and validation, where we check to what extent the proposed model along with its parameter fits the data. Here we come to the conclusion that both the parameters and the model itself have room for further optimization to reflect the data set more accurately. In addition to this, a new model for correlations of site-response amplifications is presented. The topic of how the dependence of these quantities should be modeled is still unclear. The lack of coherent solution to this modeling problem makes the proposed model valuable, as it is simple in nature and reflects the data we have the best.
Lastly, the main improvements that come out of this research are in on the computational front, by finding a novel method for calculating average spectral accelerations, which is the main quantity used in risk assessment. This method generates the distribution of this quantity in one step using numerical integration rather than the previously used Monte Carlo method. The method speeds up computations by a factor of 550 times.

This thesis contains a rigorous derivation of the path integral formulation of the Isingmodel with multiple original proofs. Besides that, thesis also contains various resultsof simulations of the 2D square lattice Ising Model with nearest-neighbour interactionsusing the Swendsen-Wang algorithm. Using finite size scaling to find critical exponentγ, we reported a value of γ = 1.748 ± 0.004. After calculating the relaxation times τ forvarious thermodynamic variables, we found the value for the dynamic critical exponentz to be in the range of z = 0.180 ± 0.004 and z = 0.282 ± 0.005.