Earthquake detection and seismic phase picking are fundamental yet challenging tasks in seismology due to low signal-to-noise ratios, waveform variability, and overlapping events. Recent deep-learning models achieve strong results but rely on large datasets and heavy backpropagation training, raising concerns over efficiency, interpretability, and sustainability. We propose GreenPhase, a multi-resolution, feed-forward, and mathematically interpretable model based on the Green Learning framework. GreenPhase comprises three resolution levels, each integrating unsupervised representation learning, supervised feature learning, and decision learning. Its feed-forward design eliminates backpropagation, enabling independent module optimization with stable training and clear interpretability. Predictions are refined from coarse to fine resolutions while computation is restricted to candidate regions. On the Stanford Earthquake Dataset (STEAD), GreenPhase achieves excellent performance with F1 scores of 1.0 for detection, 0.98 for P-wave picking, and 0.96 for S-wave picking. This is accomplished while reducing the computational cost (FLOPs) for inference by approximately 83% compared to state-of-the-art models. These results demonstrate that the proposed model provides an efficient, interpretable, and sustainable alternative for large-scale seismic monitoring.