## 4 Principles of Technical Methods
### SOM-Based Seismic Attribute Clustering Analysis  
Seismic attribute analysis can effectively predict sandbody distribution, but numerous studies have demonstrated that single seismic attributes exhibit low correlation coefficients with drilled sandstone thickness, making it challenging to achieve precise interpretations for thin-layer sandbodies. To address this limitation, an optimized fusion approach for seismic attributes is adopted to enhance their correlation with sandstone thickness [92]. The key to thin-layer sandbody characterization lies in effective sandbody identification. Self-Organizing Maps (SOM), an unsupervised neural network method, is widely utilized in seismic attribute analysis for feature extraction, clustering, and visualization. By extracting multiple attributes representing geological characteristics and applying SOM to cluster attributes with similar data features, a three-dimensional spatial visualization of  
Figure 7: Frequency component analysis and thin Layer identification workflow of Waveform Indication Inversion. attribute \"hollow maps\" can be generated, significantly improving sandbody boundary identification [93]. Combined with high-resolution seismic inversion techniques, this approach reduces the interpretative ambiguity in seismic inversion, thereby enhancing the precision of sandbody boundary delineation [94]. The primary workflow involves seismic attribute optimization and SOM network configuration. In this study, five interbedded seismic attributes were extracted from the 2 nd sand layer of the Dong'erxia Subsection in the Huanghekou Sag: Root Mean Square Amplitude (RMS), Total Energy (TE), Average Energy (AE), Amplitude Envelope (ENV), and Peak Amplitude (PA). These attributes exhibit strong correlations with sandstone thickness [95]. A rectangular network structure was selected for SOM, comprising two neural layers: an input layer and a competitive layer. The competitive layer adopted a 10 \(\times\) 10 grid structure, containing 100 neurons. Each neuron in the grid occupies a specific spatial position [96]. The five optimized attributes were assigned as inputs to the network, with each neuron receiving a five-dimensional input vector corresponding to the five seismic attributes. When an input is presented, the neuron with the smallest Euclidean distance to the input vector is designated as the winner (WTU) (Figure 8) [97]. This is determined by calculating the distance between the weight vectors (W) of all neurons and the input vector (X):  
\[dj=\sqrt{\sum_{i=1}^{N}{(Wji-Xi)}^{2}} \tag{2}\]  
_dj_: The distance between the weight vectors (_Wji_) and input vectors (_Xi_)  
_Wji = (W11, W22,..., Wynt), \(j\) = 1, 2,..., \(p\),\(i\)=1, 2,..., \(n\)_ (where p is the total number of neurons in the network) represents an ordered sequence of weight values, forming an internal representation of the neural network  
_Xi = (x1, x2,..., xnt),i=1, 2,..., \(n\)_ denotes an ordered input sequence, where each seismic attribute can be viewed as an independent coordinate axis in the data space. The competitive learning mechanism ensures that the winning neuron and its neighboring neurons adjust their weights iteratively, thereby preserving the topological relationships within the input data. The two-dimensional grid of the competitive layer represents the topological structure after dimensionality reduction, with _Wji_ serving as the corresponding image of _Xi_[98]. The winning neuron and its neighboring neurons adjust their weight vectors to approach the input data, a process controlled by a neighborhood function (typi  
Figure 8: The structure of a Self-Organizing Map (SOM) network [61; 86]. cally implemented using the Mexican Hat Wavelet, also known as the Ricker wavelet) [99]. The mathematical expression of this neighborhood function is as follows.