Explicit Coordinate Encoding Matters: A Coordinate-Driven Framework for First-Arrival Picking in Microseismic Monitoring

Summary Automatic first-arrival picking is crucial for microseismic monitoring as it directly influences event location and focal mechanism calculation. Current deep-learning based methods typically predict first-arrival time using only temporal features from individual traces, while overlooking coherent features across traces. For industrial microseismic monitoring, dense and regular receiver arrays produce spatially distinctive first-arrival patterns. To capture these multidimensional spatial features, current studies tend to use more complex model architectures, which result in higher training costs but do not necessarily improve picking accuracy. To address this issue, we propose a coordinate-driven framework based on explicit coordinate encoding. Specifically, the seismogram of microseismic event is reorganized into 2-D image, and the X and Y coordinates of each pixel are extracted and concatenated to the waveform image as two additional channels. Then, the combined data tensor is fed into a U-Net-based model to predict first arrivals. This gives the network direct awareness of absolute spatial positions, breaking the translational invariance of standard CNNs. Thus, the network can capture both temporal characteristics and spatial continuity of first arrivals with negligible additional model complexity and computational cost. Tests on a real dataset show that the coordinate-driven models significantly outperform non-coordinate-driven counterparts in training performance and picking accuracy. The average minimum loss is reduced by ~54%, while the model parameters increase only ~0.015%. The average excellent rate of P-arrivals rises from 73.06% to 92.24%, and the average error drops from 9.51 to 3.36 ms. Ablation experiments show that coordinate convolution accounts for most improvement, whereas attention gates and residual connections provide only marginal refinements. Compared to a single-trace-based model (PhaseNet) retrained on the same dataset, our model achieves ~10% higher excellent rate and half the average error. These results demonstrate that explicit coordinate encoding substantially improves the extraction of complex spatial features with negligible additional model complexity and computational cost.