### 3.2 Averaging kernels

By substituting Equation (11) into the RHS of Equation (14) we obtain
where
is the averaging kernel for the location . The averaging kernels are independent of
the values of the data. However, because the uncertainties in the data are used to weight the
inversion calculation that generates the coefficients , as described below in Sections 3.4 and
3.5, these do enter indirectly into the averaging kernels. The averaging kernels also depend
on which modes are present in the input data set. They provide a useful tool for assessing
the reliability of an inversion inference from a particular mode set (see, for example, Schou
et al., 1992, 1994).