  Autoencoders are neural network formulations where the input and output of
the network are identical and the goal is to identify the hidden representation
in the provided datasets. Generally, autoencoders project the data nonlinearly
onto a lower dimensional hidden space, where the important features get
highlighted and interpretation of the data becomes easier. Recent studies have
shown that even in the presence of noise in the input data, autoencoders can be
trained to reconstruct the noisefree component of the data from the
reduced-dimensional hidden space.
  In this paper, we explore the application of autoencoders within the scope of
denoising geophysical datasets using a data-driven methodology. The autoencoder
formulation is discussed, and a stacked variant of deep autoencoders is
proposed. The proposed method involves locally training the weights first using
basic autoencoders, each comprising a single hidden layer. Using these
initialized weights as starting points in the optimization model, the full
autoencoder network is then trained in the second step. The applicability of
denoising autoencoders has been demonstrated on a basic mathematical example
and several geophysical examples. For all the cases, autoencoders are found to
significantly reduce the noise in the input data.
