Multi-scale Dilated Residual Networks for Fast Forward Modeling of Airborne Transient Electromagnetics over Undulating Terrain

Summary Airborne transient electromagnetic (ATEM) inversion relies on efficient forward modeling, yet conventional numerical methods struggle to balance computational efficiency and accuracy when handling undulating terrain and large survey datasets. We present a fast forward modeling approach using multi-scale dilated residual networks that takes two-dimensional conductivity profiles with embedded terrain information as image inputs and directly predicts electromagnetic response tensors across multiple flight altitudes. The network architecture employs progressively increasing dilation rates to capture multi-scale geological features while preserving spatial resolution. A dual-domain loss function combining log-normalized and linear domains balances the fitting weights across electromagnetic responses spanning seven orders of magnitude. We trained and tested the model on 100,000 synthetic samples of random terrain and geoelectric structures generated with the SimPEG three-dimensional finite volume method. The network achieves mean absolute percentage errors (MAPE) of 2.24%-3.57% across four terrain types (flat, slope, peak, and valley). Spline interpolation enables accurate prediction at arbitrary flight altitudes not included in training, with errors of 1.69%-3.53%. On a 10 km survey profile, the method achieves approximately 2000-fold speedup compared to SimPEG. This approach provides a practical forward modeling solution for rapid ATEM inversion over complex terrain, and the proposed multi-scale feature extraction strategy and dual-domain loss function design offer transferable insights for other geophysical machine learning applications.