# Deep Learning Logging Sedimentary Microfacies via Improved U-Net
## 2 Materials and Methods
### Improved U-Net Architecture  
The two-dimensional images constructed from well logging data may have the same texture characteristics after mirror inversion in the formation depth direction, but the sedimentary characteristics they represent are completely different. For example, the value of the GR curve decreases first and then gradually increases from bottom to top, forming a bell shape. The sediment grain size has a combination of fine-coarse-fine characteristics, indicating that the hydrodynamic force changes from weak to strong and then weak. If the GR curve is reversed and becomes funnel-shaped, it represents a completely different regressive depositional environment. The shapes are similar, but the direction is different, as shown in Figure 2. Since the sedimentation is time-sequential, the logging data have a certain time-series feature, as the geophysical response of the sedimentary body. As the shape of the logging curve has \"vectoriality\", log curves with similar shapes but different directions represent different sedimentary facies features, so the morphological and structural features of the log curves are the key to identifying sedimentary microfacies. However, the continuous pooling layer in the U-net architecture increases the receptive field at the cost of losing spatial information, which may lead to the loss of the structural feature information of the log curve. In addition, the maximum pooling can maintain the scale invariance, rotation invariance and translation invariance of the features to a certain extent, which do not match the actual features of the logging data. Figure 1: The network architecture of U-net. Figure 2: The bell shape (**left**) and funnel shape (**right**) of the GR curve. Thanks to the particularity and complexity of the formation of geological bodies, influenced by the length of sedimentary cycle and the shape of sedimentary basins, the thickness of geological bodies formed in the same depositional environment can be different. This is due to periodic changes in the depositional environment caused by changes in crustal movement, sea level, climate and sediment sources. Some periods are longer and some are shorter, resulting in variations in sediment thickness in depositional cycles. In addition, in different geographical locations and under the same depositional environment, affected by depositional events and the shape of depositional basins, there are certain differences in the depositional thickness. In the form of well logging curves, this difference is manifested as the difference in the length and amplitude of the curves, but the overall morphological characteristics are similar, which means they are \"multi-scale\". However, in the original U-net architecture, the convolution operation in each layer of the downsampling and upsampling parts is composed of two 3 \(\times\) 3 convolutions, which cannot better extract important features of different scales on the logging curve information. In addition, the identification of sedimentary microfacies based on images composed of well logging curves only requires image segmentation in the depth direction. However, the resulting map of semantic segmentation using the U-net network is the result of the classification of each pixel in the image, so it cannot be guaranteed that the values of different logging types corresponding to the same depth have the same category. Therefore, while considering the characteristics of logging curves for sedimentary microfacies identification, we constructed a deep learning model that is more suitable for logging sedimentary microfacies identification on the basis of the original U-net framework. The characteristics of building a deep learning model are as follows:  
1. Considering that the rotation invariance and inversion invariance of feature extraction should be discarded when logging data are applied to deep learning network algorithms.