GNGTS 2017 - 36° Convegno Nazionale

GNGTS 2017 S essione 3.3 709 Particle swarm optimization of magnetotelluric data: from 1d to 2d solutions F. Pace 1 , A. Santilano 2 , A. Godio 1 1 Department of Environment, Land and Infrastructure Engineering (DIATI), Politecnico di Torino, Italy 2 Institute of Geosciences and Earth Resources- National Research Council (IGG-CNR), Pisa, Italy Introduction. The inversion of geophysical data requires the solution of ill-posed, nonlinear and multi-parameter problems. In recent decades, in order to estimate the model parameters, two main methods have been developed: local and global search techniques. The former (e.g. conjugate gradient) are fast as long as a good initial solution is given, the latter (e.g. genetic algorithm GA, particle swarm optimization PSO, etc.) have recently become of great interest due to their probabilistic approach to searching for the optimal solution. Optimization techniques such as GA and simulated annealing (SA) (Sen and Stoffa, 2013) have been widely investigated so far, while the PSO algorithm is emerging as a powerful tool to solve inverse problems because it exploits the principle of swarm intelligence. Up to now, PSO has been applied to the inversion of VES data (Fernández Martínez et al. , 2010) and MT data (Shaw and Srivastava, 2007; Godio et al. , 2016), but only for one-dimensional problems. The present work aims at implementing the two-dimensional inversion of MT synthetic data and overcoming the extremely time-consuming computation using the parallel tool of the PSO algorithm. The ensuing sections focus firstly on the theoretical background of the PSO method and then its application to the inversion of 1D field data and 2D synthetic data. Finally, significant results are illustrated and discussed. The Particle Swarm Optimization algorithm. PSO is a global search method based on the social behavior observed in animals that group together, such as birds or fish. The way they share information to provide food or maintain the best reciprocal distance has been successfully adopted in nonlinear problem optimization (Kennedy and Eberhart, 1995). The PSO algorithm acts on a set of particles, each representing a model of the geophysical problem and seeking the global optimum in a multidimensional search space. The optimization is carried out by means of the adaptive behavior of the swarm: every particle has a position and velocity dynamically adjusted according to both cognitive and social state (mode of behavior). At each iteration, the velocity of the i-th particle is adjusted according to Eq. (1) (Ebbesen et al. , 2012): (1) where: i = [1,…,N]; N is the population of the swarm; k is the current number of iteration; and are the current position and velocity of the i-th particle; is called the inertia weight, the particle momentum that has been set to linearly decrease from 0.9 to 0.4 (Shi and Eberhart, 1998); is the cognitive acceleration towards the best personal position P ; is the social acceleration towards the best global position G among all the particles up to the current generation; are uniformly distributed random numbers. Then, the particle position is updated using Eq. (2): (2) The specific values of the three parameters , and should be carefully set because they rule the balance between exploration and exploitation of the search space, as well as the convergence behavior of the whole swarm. The values of the three parameters play a key role especially when the swarm is highly populated, i.e. the problem has many unknowns. In order to reach fast convergence and to avoid to be trapped in local minima, a recent approach introduced the Adaptive PSO (APSO) with time varying acceleration coefficients and (TVAC) (Zhan et al. , 2009). In the present work, has been set to linearly decrease from 2 to 0.5 and increase from 0.5 to 2, with the aim of emphasizing the exploration behavior at the beginning of the search and the exploitation behavior at the end.