## 4 Case Study  
As mentioned above, the actual analysis of the data of an available data set will be a group of mechanical signals that we will call the _seismic cube_ (Figure 5). For data confidentiality reasons, this set of signals will be treated only as input data with characteristics of signals in the frequency domain, omitting data such as location, extension, etc. The study was carried out in an area of Mexico that corresponds to an oil field. Through field studies, seismic data were obtained, processed, and converted to a readable format representing a set of vectors and ultrasound signals with 1200 entries. The number of vectors is around 1500 planes, with 600 points per vector and 350 vectors per plane. Data were collected in the field. They were originally arranged three-dimensionally in a cube (seismic cube), in SEG-Y format, one of the various standard formats for this type of geophysical data. The seismic cube is made up of each of the ultrasound signals that travel through the subsurface and are captured at the surface. This process is explained in detail in [20]. These signals are the input data in our model and are convolved using a Wavelet decomposition strategy. This wavelet and the number of signal decomposition levels will be selected as parameters. The next parameters to be selected correspond to the Pooling, where we choose the size of the Pooling matrix, which helps us reduce the dimensionality of the data after convolution, as well as the step size of this matrix over the data path. This is followed by the use of the Euclidean norm for data normalization. The point of interest here is how the method classifies this data set according to the architecture's adaptation of the _Wavelet_. An An analysis of this same data set was previously conducted with SOM without taking Pooling and sliding window processing stages; however, we seek to contribute with this work to understanding the effects of _Wavelet_ coupling to a _Self-Organizing Map_ by a sliding window. In order to specify the experiments and compare them with several parameters, a valuable experiment is proposed, as shown in Figure 6. This particular result is presented in as _Case 1_ and is compared to several other experiments by the mean square error (MSE) from weight matrices (Equation (21)). MSE is a common comparison metric between vectors or matrices since the dimensionality is not lost and scaling is not a key factor in comparing values. MSE is used to compare matrices (weight matrices) since it is stable for defining the main differences between neurons. In this study, our objective is to obtain, through the proposed algorithm, a classification of the data that allows us to identify areas with possible geological and geophysical characteristics that allow the storage of hydrocarbons following [20]. These areas are identified through the algorithm and visible in the graphics obtained after training the neural network and classifying the data. The first step that has been performed is the identification of the input vectors, \(V_{1},V_{2},\ldots,V_{n}\), as described in Section 3. Each vector \(V_{i}\) represents data or a signal. The second step is to perform the algorithm, obtaining a particular weight matrix \(\Omega\) considered as a basis, where the rest of the cases are those to be compared and named \(\widehat{\Omega}\). To test this proposal, a case study published in [20] is used, based on a seismic analysis taking partial data called stacked traces, as observed in Figure 5. Therefore, significant effort is necessary to combine all the possible variables (Table 1) to build the best case study from the proposed methodology. Understanding the meaning of correctness is crucial to  
Figure 5: Study region based on the characteristics indicated about the experiment on accurate data following [20]. allow for a proper selection of the most appropriate parameters. Table 2 shows some of the most essential sensitive variables to be selected. These are presented in terms of a suitable combination of current results.