  Subsurface imaging involves solving full waveform inversion (FWI) to predict
geophysical properties from measurements. This problem can be reframed as an
image-to-image translation, with the usual approach being to train an
encoder-decoder network using paired data from two domains: geophysical
property and measurement. A recent seminal work (InvLINT) demonstrates there is
only a linear mapping between the latent spaces of the two domains, and the
decoder requires paired data for training.
  This paper extends this direction by demonstrating that only linear mapping
necessitates paired data, while both the encoder and decoder can be learned
from their respective domains through self-supervised learning. This unveils an
intriguing phenomenon (named Auto-Linear) where the self-learned features of
two separate domains are automatically linearly correlated. Compared with
existing methods, our Auto-Linear has four advantages: (a) solving both forward
and inverse modeling simultaneously, (b) applicable to different subsurface
imaging tasks and achieving markedly better results than previous methods,
(c)enhanced performance, especially in scenarios with limited paired data and
in the presence of noisy data, and (d) strong generalization ability of the
trained encoder and decoder.
