Modeling crustal velocity using Artificial Neural Networks (Case study: Iran Geodynamic GPS Network)

Artifitial neural network (ANN) is an information processing system that is formed by a large number of simple processing elements, known as artificial nerves. It is formed by a number of nodes and weights connecting the nodes. The input data are multiplied by the corresponding weights, and the summation are entered into neurons. Each neuron has an activation function. Inputs are passed to the activation function, and the output of the neurons is determined. The number of neurons and layers could be obtained through trial and error according to a specific problem. The behavior of a neural network depends on the communication between nodes. Using the trained data, the designed ANN can be adjusted in an iterative procedure to determine optimal parameters of ANN. Then for an unknown input, we can compute corresponding output using the trained ANN. One of the simplest and effective methods to use in the modeling of real neurons is the multi-layer perceptron neural network. This model consists of one input layer, one or more hidden layers, and one output layer. In this structure, all the neurons in one layer are connected to all neurons in the next layer. An important issue in multi-layer artificial neural networks is the number of neurons. The neurons of input and output layers are determined according to the number of input and output parameters. The number of neurons in the hidden layer can be determined by trial and error through minimizing the total error of the ANN. For this minimization, each ANN parameter’s share in the total error should be computed which can be achieved by a back-propagating algorithm. There are many methods for training the network and modifications of the weights. One of the most famous and simplest methods is a back-propagation algorithm that trains the network in two stages: feed-forward and feed-backward. In the feed-forward process, the input parameters are moved to the output layer. In this stage, the output parameters are compared with known parameters and the errors are identified. The next stage is done feed-backward. In this stage, the errors are moved from the output layer to the input layer. Again, the input weights are calculated. These two stages are repeated until the errors reach a threshold expected for the output parameters. In this study, a 3-layer perceptron neural network was used with 28 neurons in a hidden layer for modeling the eastern component (VE) and 27 neurons in a hidden layer for modeling the northern component (VN) velocity field of the earth's crust in Iran. Evaluation of the neural network model has been applied using 11 stations of GPS, and the velocity fields are defined with respect to the Eurasian plate. The minimum relative error obtained from this evaluation for the eastern component was -3.57% and for the northern component was +0.16%: also the maximum relative error for the eastern component was +38.1% and for the northern component was +95.3%. In this study, a polynomial of degree 5 with 18 coefficients was used to model the east and north components for the evaluation of artificial neural networks in estimating the velocity rate of geodetic points. A comparison of the relative error from the polynomial model and the relative error from the neural network illustrated the superiority of the neural model with respect to the polynomial model in this region.