GNGTS 2015 - Atti del 34° Convegno Nazionale

12 GNGTS 2015 S essione 3.1 (Mazzotti and Zamboni, 2003). In the last case, we considered either a linear or a non-linear model (Eberhart-Phillips et al., 1989). In the non-linear approach, many methods can be used to derive such rock-physics model. Neural networks (Saggaf et al., 2003) and stochastic optimizations (Aleardi, 2015) have received great attention. ������� ������������� ���� ��� Anyway, independently from the method used, there is no doubt that the quality and the reliability of available well-log data and/or core measurements play an essential role in defining a solid RPM. The aim of this work is to derive a reliable RPM used in conjunction with an AVA inversion for the characterization of a clastic reservoir located in offshore Nile delta. We have employed both theoretical and empirical approaches to derive the RPM. For what concerns the empirical approaches we used both a linear and two non-linear methods to define different rock-physics models. We obtained the linear model by applying a multilinear stepwise regression, whereas neural networks and genetic algorithms are used to derive non-linear transformations from petrophysical to elastic properties. The main difference among neural networks and genetic algorithms is that the former is a gradient-based method while the latter is a global, stochastic, optimization method. We start by introducing the different methods used to derive the theoretical and the empirical rock-physics models. Then, the detailed analysis of RPMs resulting from theoretical and empirical approaches let us to outline the benefits and the limits of each method. Moreover, in the empirical approaches we focus our attention on discussing the differences between linear and non-linear methods for the specific case under examination and on analyzing the drawbacks that characterize the neural network technique. The simplicity and the reliability of the empirical rock-physics model derived by applying multilinear stepwise regression and the optimal prediction capability of the theoretical rock-physics model enable us to consider these two RPMs in the petrophysical AVA inversion that is discussed in the companion paper titled “ Seismic reservoir characterization in offshore Nile Delta. Part II: Probabilistic petrophysical- seismic inversion ”. A brief introduction to the methods used for deriving the rock-physics models. In this chapter, we briefly describe the empirical and the theoretical methods used to derive the rock- physics models.We start with the multilinear stepwise regression followed by the neural network approach, and by the optimization of the genetic algorithm used in the empirical approach. Thereafter, we will introduce the theoretical approach based on rock-physics models. Multilinear stepwise regression (SR). Stepwise regression is a semi-automated process of deriving a linear equation by successively adding or removing variables in the regression procedure based solely on the t- statistics of their estimated coefficients ������� ��� ������ (Draper and Smith, 1985)� ����� ���� ���������� ��� �� ���� �� ���� ���������� ������� ������� ���������� . Three main approaches can be used in this regression method: forward selection, backward elimination and bidirectional elimination. The first approach starts with no variable in the model and proceeds forward (adding one variable at a time). The second approach starts with all potential variables in the model and proceeds backward (removing one variable at a time). In this study, we applied the third method, which is a combination of the approaches described above and is essentially a forward selection procedure but allows the elimination of a selected variable at each optimisation stage. Neural Network optimization (NN). A neural network is a mathematical algorithm inspired by an animal’s central nervous system and trained to solve problems that would normally require human intervention (Haykin, 1999). In particular, a supervised neural network corresponds to a problem in which a set of input data and their corresponding outputs are available; in this way, the network can attempt to infer a relation between the input and the output. In this work, we apply a multilayer feed-forward neural network in which the petrophysical rock properties define the input, whereas the elastic attributes are the output of the net. The architecture of the network we used consists of one input layer, one output layer, and one hidden layer. In this work, the hidden layer consists of 25 neurons, whereas the input has as many nodes as the petrophysical properties of interest. The nodes in each layer are characterized by a sigmoid