  Full waveform inversion (FWI) commonly stands for the state-of-the-art
approach for imaging subsurface structures and physical parameters, however,
its implementation usually faces great challenges, such as building a good
initial model to escape from local minima, and evaluating the uncertainty of
inversion results. In this paper, we propose the implicit full waveform
inversion (IFWI) algorithm using continuously and implicitly defined deep
neural representations. Compared to FWI, which is sensitive to the initial
model, IFWI benefits from the increased degrees of freedom with deep learning
optimization, thus allowing to start from a random initialization, which
greatly reduces the risk of non-uniqueness and being trapped in local minima.
Both theoretical and experimental analyses indicates that, given a random
initial model, IFWI is able to converge to the global minimum and produce a
high-resolution image of subsurface with fine structures. In addition,
uncertainty analysis of IFWI can be easily performed by approximating Bayesian
inference with various deep learning approaches, which is analyzed in this
paper by adding dropout neurons. Furthermore, IFWI has a certain degree of
robustness and strong generalization ability that are exemplified in the
experiments of various 2D geological models. With proper setup, IFWI can also
be well suited for multi-scale joint geophysical inversion.
