GNGTS 2017 - 36° Convegno Nazionale

686 GNGTS 2017 S essione 3.3 proposed by Kirkpatrick (1983), and it is efficient also with a large number of variables (up to tens of thousands). The method is based on a properly dense sampling of the whole inversion domain. Corana et al. (1987) presented a simulated annealing scheme, based on the Metropolis Hastings algorithm (Metropolis, 1953; Hastings, 1970), able to perform a systematic but parsimonious sampling of the model space, driven by statistical considerations. The algorithm can be summarized in the following steps: 1. ���������� ��� ����� ����������� ��� ������ ����� ����� ��� ����� ������� ���� ��������� initialize the model parameters, and define their upper and lower limits. Each parameter is a coordinate of a multidimensional space; 2. ������� � ����� �� ������������ ���� ����� ��� ���������� ��������� ������ ����������� perform a cycle of randommoves, each along one coordinate direction (model parameter). Accept or reject each point according to the Metropolis criterion. Record the optimum point reached so far. The moves can reach a maximum step v , in general different for each direction, associated to the range of variation of the considered parameter and on a temperature value: the higher the temperature, the longer the step; 3. ������ � ����� ����� �� repeat N times point 2; 4. ������ ��� ������������ ��� �� ��� ������� ���� �� ��� ������ ����� ��� ������� �� reduce the temperature, and so the maximum step of the random move, and restart at point 2, from the model point with minimum residual (optimum). Repeat Nt times; 5. ����� stop. In the first iterations the vector of maximum steps v is adapted so to explore the whole Fig. 1 - Inversion result (red lines) over true data (blue), and inversion iterative evolution (gray).