deletions | additions       diff --git a/section_Formulating_the_Recovery_Biases__.tex b/section_Formulating_the_Recovery_Biases__.tex  index d6bc21e..51e5944 100644  --- a/section_Formulating_the_Recovery_Biases__.tex  +++ b/section_Formulating_the_Recovery_Biases__.tex 
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With these assumptions, we can relate the geometry of an encounter directly to the observed profile parameters, and Figure \ref{fig:encounter_geometry} illustrates a typical encounter. As a devil passes the barometer, it will have a closest approach distance $b$. If the dust devil passed directly over the sensor, i.e. $b = 0$, the radial distance evolves as $r(t) = \upsilon t$, with time $t$ running from $-\infty$ to $+\infty$, and the devil passes directly over at $t = 0$. If $b \ne 0$, then $r(t) = \dfrac{b}{\cos\left[ \arctan\left( ^{\upsilon t}/_{b} \right) \right]}$. Figure \ref{fig:compare_profiles} compares profiles for $b = 0$ and $b = \Gamma_{\rm act}$. The deepest point observed in the pressure profile $P_{\rm obs}$ is given by   \begin{equation}\label{eqn:Pobs_from_Lorentz_profile}  P_{\rm obs} = \dfrac{P_{\rm act}}{1 - +  \left( \dfrac{2 b}{\Gamma_{\rm act}} \right)^2}. \end{equation}  Clearly, unless $b = 0$, $P_{\rm obs} < P_{\rm act}$, and, it turns out, the profile width observed in the time series $\Gamma_{\rm obs}^\prime > \Gamma_{\rm act}^\prime$. These effects represent the signal distortion induced by the miss distance effect. 
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