Fig. 4

Genetic algorithm. The V _p model obtained by the inversion using genetic algorithms. The thick black line labeled KOCGA is the obtained continuous V _p model of the outer 700 km of the core, which has four layers with uniform V _p gradients. Other details are the same as Fig. 3. The thickness of the deepest layer is fixed to 400 km and the V _p value at the bottom of the layer is fixed to that of PREM, so that there are seven parameters to be determined, each of which is described as a 6-bit binary number. Therefore, each gene has a length of 42 bits. The least bit for the V _p at the top of each layer corresponds to 0.003 km/s, while the least bit for the thickness corresponds to 2 km. The depth of the CMB is fixed to that of PREM, so the inversion is not entirely free from the reference model, but the effect is quite small insofar as the differential travel times of SmKS waves are concerned. The range of the V _p value sought by this parameterization covers about ±0.2 km/s relative to PREM, which is wide enough not to miss any successful models. First, the samples of V _p model of the first generation are constructed by randomly selecting the seven model parameters. Second, the misfit of the model predictions to the observations is computed, and each V _p model sample is selected with a probability proportional to the inverse of the squared sum of its misfit. After the selection, crossover of the genes between two randomly selected samples occurs with a given probability, followed by the mutation within each gene that occurs with a given probability, in order to generate the samples of the next generation. This process is iterated through the fixed number of generations. The total misfit over the entire samples usually converges rapidly enough. The parameters used in the inversion are as follows: both the mutation probability and the crossover probability are 0.2, and the numbers of sample and generation are 100 and 40, respectively