-measurements) that we must compare the simulation outputs, :math:`\mathbf{x}^b`
-the background (*a priori* values, or regularization values) of searched
-parameters, :math:`\mathbf{x}^t` unknown ideals parameters that would give as
-output exactly the observations (assuming that the errors are zero and the model
-exact).
-
-In the simplest case, static, the steps of simulation and of observation can be
-combined into a single observation operator noted :math:`H` (linear or
-nonlinear), which transforms the input parameters :math:`\mathbf{x}` to results
-:math:`\mathbf{y}` to be compared to observations :math:`\mathbf{y}^o`.
-Moreover, we use the linearized operator :math:`\mathbf{H}` to represent the
-effect of the full operator :math:`H` around a linearization point (and we omit
-thereafter to mention :math:`H` even if it is possible to keep it). In reality,
-we have already indicated that the stochastic nature of variables is essential,
-coming from the fact that model, background and observations are incorrect. We
-therefore introduce errors of observations additively, in the form of a random
-vector :math:`\mathbf{\epsilon}^o` such that:
+measurements) that we must compare to the simulation outputs,
+:math:`\mathbf{x}^b` the background (*a priori* values, or regularization
+values) of searched parameters, :math:`\mathbf{x}^t` the unknown ideals
+parameters that would give exactly the observations (assuming that the errors
+are zero and the model is exact) as output.
+
+In the simplest case, which is static, the steps of simulation and of
+observation can be combined into a single observation operator noted :math:`H`
+(linear or nonlinear), which transforms the input parameters :math:`\mathbf{x}`
+to results :math:`\mathbf{y}` to be compared to observations
+:math:`\mathbf{y}^o`. Moreover, we use the linearized operator
+:math:`\mathbf{H}` to represent the effect of the full operator :math:`H` around
+a linearization point (and we omit thereafter to mention :math:`H` even if it is
+possible to keep it). In reality, we have already indicated that the stochastic
+nature of variables is essential, coming from the fact that model, background
+and observations are incorrect. We therefore introduce errors of observations
+additively, in the form of a random vector :math:`\mathbf{\epsilon}^o` such
+that: