Let there be Ai, any parameter of an actual earthquake, and Fi, the forecast that was made of the same parameter for the same earthquake, and N the number of (Ai, Fi) test pairs.
These objectives were attained by integrating all prediction algorithms in a Microsoft™ Excel®workbook called NCEL.
Worksheet “Main” is the only one where the user can input data: a series of up to 1000 records of four earthquake parameters, event time and magnitude, epicentral latitude and longitude. It should be stressed that input data must have some sort of pre-processing. In all the examples below, the series were truncated for the lower magnitude events (non-linear bottom part of the Gutenberg-Richter function). Also, as a crude rule-of-thumb method to filter off foreshocks and aftershocks only the strongest earthquake in each day was used. The user can also, if willing, hand-tune most of the parameters of the neural network: length of the training set, number of neurons in the middle layer, learning rate, learning momentum, limit target error and limit number of iterations. However, default values for all these parameters are supplied. Namely, in the earlier works, the length of the middle layer vector was chosen so that the total number of connections was of the same order of the number of training examples.
Worksheet “Monte Carlo” performs Monte Carlo forecasts based on the input data on worksheet “Main” . Worksheet “Previous” performs naïve forecasts based on the input data on worksheet “Main” : it forecasts, for the next earthquake, exactly the same parameters that are recorded for the last one (which is a significantly successful method for weather forecasts for about half of the year). Worksheet “Averages”, another naïve approach (or maybe not so much, as will be seen below), forecasts, for the next event, the average for each parameter of all the previous events.
Visual Basic module “NCEL” performs the neural network training and testing procedures. The training procedure is based on the algorithm provided by [19]. In its earlier versions, “NCEL” followed closely the previous method, with the exception of forecasting the epicentral co-ordinates. Several test runs made over well known datasets showed unexpected results: many times the forecasts that were made by the “Averages” naïve method produced the smallest errors, mainly in MAD. In order to quantify this result and to further automate the forecasting procedure, the current version of VB module “NCEL” was all included in a loop that stops on one of two conditions: a command that is entered by the user or [MAD(NN) < MAD(Averages)] for the time parameter. Worksheet “Error Analysis” keeps track of the number of times that the neural network performs better than the “Averages” algorithm.
Why are the results not always the same? The “Previous” and “Averages” spreadsheets, once initially computed are, of course, invariant. Differences arise on each new calculation of spreadsheets “Monte Carlo” (because of the intrinsically quasi-random nature of the method) and “NN”. In the NN case, the differences occur because of the randomly initiated connections’ weights. However, unlike in “Monte Carlo” , the final results of different network runs never differ by more than 5% (on 300 tested cases).