  Physicists routinely need probabilistic models for a number of tasks such as
parameter inference or the generation of new realizations of a field.
Establishing such models for highly non-Gaussian fields is a challenge,
especially when the number of samples is limited. In this paper, we introduce
scattering spectra models for stationary fields and we show that they provide
accurate and robust statistical descriptions of a wide range of fields
encountered in physics. These models are based on covariances of scattering
coefficients, i.e. wavelet decomposition of a field coupled with a point-wise
modulus. After introducing useful dimension reductions taking advantage of the
regularity of a field under rotation and scaling, we validate these models on
various multi-scale physical fields and demonstrate that they reproduce
standard statistics, including spatial moments up to 4th order. These
scattering spectra provide us with a low-dimensional structured representation
that captures key properties encountered in a wide range of physical fields.
These generic models can be used for data exploration, classification,
parameter inference, symmetry detection, and component separation.
