## 3 Structure  
Unlike the traditional information processing algorithm based on a data planning structure, an original time-frequency decomposition is proposed, which allows the preprocessing to have more information regardless of the scales. This proposal contemplates several steps that need to be described in detail in terms of the scalar elements processed and the results of the neural network, which, for our purposes, will be a _Self-Organizing Map_. Initially, the information is presented by forming various packages at multiple scales from an _information cube_, as shown in Figure 2. In this sense, the management of the indices generates the strict follow-up of the geometry of the information that leads us to provide an order of the same indexing without losing the relevant characteristics in local terms and their collateral effects with geometrically close regions (Figure 3).  
It is essential to establish that the scope of such a learning strategy by the Self-Organizing Map is a distribution of characteristics on a map of \(K\) neurons distributed so as to allow a stable representation construction. This is invariant for the type of information to be processed.  
As a second stage, the characterization of the rest of the information is based on the trained neurons and the generated map, where it is possible to determine common characteristics in the rest of the maps that, for the particular example, refer to the planes of the _information cube_. In Section 4, more details of the case studies are given.  
Based on these two stages, a stable notation must be generated that allows us to distinguish the processing of the information. For the case of Figure 2 the depth will be defined as \(\kappa\).  
The generated notation is as follows, let  
\[a^{\mu,\zeta}_{i,j,\kappa}\;d^{\mu,\zeta}_{i,j,\kappa} \tag{1}\]  
Figure 3: Diagram of the method in terms of information analysis. The stages of seismic data processing are shown to ultimately obtain a classification useful for the interpreter.  
where:  
\(a_{i,j,\kappa}^{n,\zeta}\): represents the element of the vector processed by the _Wavelet_, which we will call approximations;  
\(d\): represents the element of the vector processed by the Wavelet, which we will call details;  
\(\kappa\): represents the plane based on the _information cube_ to be processed, \(\kappa=1,\ldots,\theta\);  
\(j\): initial vector number, \(j=1,\ldots,n\);  
\(i\): number of elements in the vector, \(i=1,\ldots,m\);  
\(\mu\): number of applied Wavelet;  
\(\zeta\): level of applied Wavelet;  
\(\alpha\): original vector data bounded by the sliding window of \(\beta\) with \(\gamma\).  
Input vectors \(V_{j}\) correspond to the input plane with \(\kappa=1,\ldots,\theta\) and scalar value \(\alpha_{i,j}\).  
There are \(n\) input vectors of length \(m\)  
\[\begin{array}{|c|c|c|c|}\hline V_{1}&V_{2}&\ldots&V_{n}\\ \hline\alpha_{1,1}&\alpha_{1,2}&\ldots&\alpha_{1,n}\\ \alpha_{2,1}&\alpha_{2,2}&\ldots&\alpha_{2,n}\\ \alpha_{3,1}&\alpha_{3,2}&\ldots&\alpha_{3,n}\\ \ldots&\ldots&\ldots&\ldots\\ \alpha_{m,1}&\alpha_{m,2}&\ldots&\alpha_{m,n}\\ \hline\end{array} \tag{2}\]  
The idea of using _Wavelet decomposition levels_ for feature extraction is that a characteristic presented within the analyzed data is highlighted from the rest of the information for a given type of scale. This procedure occurs as many levels are selected, extracting information as an accurate and reproducible mechanism.  
This experimental process is a _Discrete Wavelet_ to the initial data, processed after separation through a sliding window. For this example, we will apply it such that depending on the number of levels, we will have an Information Distribution that will depend on the size of the initial _information cube_ and the initial sliding window \(WT_{1}\) in parallel with two levels to the initial data as shown below: