Adaptive Convolution Neural Networks for Electrical Resistivity Inversion

Electrical Resistivity Inversion is an inverse problem that intends to infer the resistivity model from apparent resistivity data. The input and output have the format as the image but are with some unique characteristics that differ from the common natural images. The patterns in resistivity data are no longer spatial invariant. In this case, though the vanilla convolutional neural networks could build the mapping between images, their weight sharing kernels may cause ambiguous situations when coping with the resistivity data. To address this problem, in this work, we directly adapt convolutional kernels to fit for the electrical resistivity inversion task. By analyzing the resistivity data, we found the data patterns corresponding to the same abnormal body will vary with the vertical position change, correspondingly we learn extra offset and amplitude parameters for each vertical position the convolutional kernels applied, to make convolutional kernels transformed to capture the varying patterns. Unlike active convolution and deformable convolution, our learned offsets and amplitudes are sharing at each vertical position, which is neither too free nor too rigid. More importantly, it obeys the inherent characteristics of resistivity data. Finally, through adversarial training, the inversion results are more realistic as the resistivity model. From comprehensive comparisons and studies, our adaptive convolutional neural networks (ACN) outperform the baselines consistently, verifying our assumption and the effectiveness of our proposed method.