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Nomenclature a = output of the transfer function a j k = Jth element of the artificial neural network's output related with input vector Pk a q = network's output for p q a 0 = input of the first layer B = y intercept of the regression line in the scatter plot b = bias e j k = Jth element of the error ways of Fk = summation of the error in the Kth frequency f = transfer function of the layer M = regression line slope in the scatter plot perf = neural network's performance function (sum of squared error) P i = input vector of the network R = correlation coefficient between the artificial neural network's output and observation S L = number of neurons in layer L T i = target vector for input P i t j k = Jth element of the target vector related with input vector Pk ! = weight matrix of each layer Subscript J = Jth element of the answer network Superscript L = number of network layers