## 3 MDCAE Feature Extraction Model
### MDCAE Model  
The characteristic that distinguishes MDCAE from the standard Convolutional Auto-Encoder [39,40] is that it integrates the design of multi-scale convolution layers and dilated convolution layers, optimizing the processing ability of time series data. Compared with traditional convolution layers, the introduction of multi-scale fusion convolution layers enhances the model's ability to extract features in different observation fields, allowing the model to pay attention to the information of nearby and distant points simultaneously. The dilated convolution layer aims to expand the perception range of the convolution without the need to increase the number of convolution layers, which significantly reduces the number of parameters of the model. In addition, causal convolution, as a special convolution method, is suitable for time series analysis, ensuring that the model output is only related to past inputs, avoiding the influence of future data, and maintaining the causal relationship of the time series.  
In this model, all convolution layers adopt a one-dimensional design, and the data dimensions processed include the number of variables and the corresponding waveforms. The overall structure of MDCAE is divided into four main parts: multi-scale fusion expanded convolution module, dilated convolution module, feature extraction module, and decoding module. The initial part of the multi-scale fusion expanded convolution module performs data extraction through four standard convolution blocks of convolution kernels of size 1; followed by three expanded convolution blocks using convolution kernels of sizes 3, 5, and 7; and a final maximum pooling layer. The convolution results of the four different scales are processed by the residual block and spectral regularization and then concatenated and output by columns. The dilated convolution module includes a dilated convolution layer, a residual block, a causal convolution layer with a stride of 2, and a spectral regularization layer. The feature extraction module is composed of three fully connected layers, of which the first layer contains 256 neurons, the second layer 50, and the third layer again 256. The features extracted by the second layer are the target features. The decoding module is composed of alternating causal convolution layers and upsampling layers, and finally, the dilated convolution layer is used to reconstruct the data waveform. The detailed network structure diagram is shown in Figure 1.  
The model consists of four main modules: the multi-scale fusion convolution block, the dilated convolution block, the feature extraction module, and the decoder. Each component is specifically designed to extract rich, robust features from microseismic time-series signals. The multi-scale convolution block utilizes kernels of various sizes (1, 3, 5, and 7) to capture both local and global information. The dilated convolution block expands the receptive field without increasing parameters. The feature extraction module compresses the data into a 50-dimensional latent space, which is then decoded to reconstruct the input waveform. Spectral normalization is incorporated in multiple layers to stabilize training and enhance generalization.  
Figure 1: Network structure of MDCEA-CSBD-Vol model.