Static tests are performed on samples extracted during the dynamics tests and determine rupture stress, shear modulus, Poisson and Young modulus. The dynamic properties are usually evaluated many times each meter, and the static properties are rarely determined. To extract the samples we need to stop the dynamic test and this is very inconvenient, making limitations to the sampling process.

In this work the parameters database includes two types of litologies: sandstone and calcareous. Table 1 summarizes the considered static and dynamic properties.

Despite the fact that dynamic and static tests generate distinct parameters, it is possible to establish relationships between these different parameters, so that one can obtain the static parameters without carrying static tests and therefore derive elastic properties of the material, such as elastic and shear moduli, etc.

This is the main reason to try to establish precise tools to correlate them. Evolving neural network architectures it is possible to obtain very good estimators of static parameters derived from a dynamic parameter database.

Particularly, the neural model presents some characteristics that make it attractive in many different areas [5], such as: (a) it is a self-adaptive method directed by the data itself, where the knowledge is captured by the model through examples, in other words, learning by experience; (b) after the learning it presents generalization capacity; (c) it approaches any continuous function in the desired precision; (d) it is a non-linear model, thus much more generic.

During the training neural network task, four criteria were adopted to select the best NN:

• the correlation function was chosen as a performance measure of the networks related to the training and testing data
• the rupture stress NN model should presents an asymptotic behaviour when we plot this value against the static confined pressure.
• motivated by the small number of samples and irregular distribution the NN models that predict extreme values are preferred
• the NN results were compared with existing formulas from the literature,

More than 150 NN were generated and we can conclude that high correlated and small RMS was generated and they satisfied the different criteria that were proposed.

Table 1: Data Description

Name Type I/O Description Unit Well string   Well   Depth number   Depth m number I static confined pressure MPa number I dynamic confined pressure MPa number I shear wave velocity m/s number I shear wave velocity m/s number I dynamic density g/cc number I dynamic porosity % Lit number I Litology (sandstone and calcareous)   number O rupture stress MPa Poisson number O Static Poisson modulus GPa Young number O Static Young modulus GPa Shear number O Static Shear modulus GPa

1

U.M. Fayyad, G. Piatetsky-Shapiro, P. Smith and R. Uthurusamy, "Advances in Knowledge Discovery and Data Mining", MIT Press, 1996.

2

S. Haykin, "Neural Networks - A comprehensive Foundation", 2 ed., Prentice Hall, 1999.

3

P.D. Wasserman, "Neural Computing: Theory and Practice", New York: Van Nostrand Reinhold, 1989.

4

T.W. Lambe, R.V. Whitman, "Soil Mechanics", SI version, John Wiley & Sons, 1979.

5

Zhang, G., Patuwo, B.E. & Hu, M.Y., "Forecasting with artificial neural networks: The state of the art", International Journal of Forecasting, 14, pp. 35-62, 1998. doi:10.1016/S0169-2070(97)00044-7

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