I am trying to train an autoencoding neural network (autoencoder) to reconstruct seismograms. Previous studies employing this technique (e.g. Valentine & Trampert, 2012) used an L2 (mean squared error) loss function to assess the network's performance, but I'm wondering if there are better loss functions out there for this type of data. Seismograms are rather spurious, in the sense that the signal rapidly oscillates around zero, which makes it hard to get a good point-by-point comparison. For instance, if the reconstructed seismogram has a slight time lag but is otherwise a perfect reconstruction of the original input (see image), the L2 loss could be enormous due to this slight misalignment.
My question: how would you evaluate the quality of the reconstruction in terms of the approximate position, duration, amplitude, etc.?