Brian Jackson edited subsection_The_Pressure_Depth_Recovery__.tex  almost 9 years ago

Commit id: 186eb10cd41f7875c4d9497515e481a0c0ef43e9

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\begin{equation}  f \equiv A(P_{\rm act})/A(P_{\rm max}) = \left( \dfrac{\Gamma_{\rm act}(P_{\rm act})}{\Gamma_{\rm act}(P_{\rm max})} \right)^2 \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right).   \end{equation}  For now, we'll assume $\Gamma_{\rm act}$ is independent of $P_{\rm act}$, giving $f_{\Gamma_{\rm $f_{\left( \Gamma_{\rm  act} = {\rm const.}} const.} \right)}  = \left( \dfrac{P_{\rm act} - P_{\rm min}}{P_{\rm max} - P_{\rm min}} \right)$. As expected, the probability to detect a devil with $P_{\rm act} = P_{\rm min}$ is zero. Of course, the probability for detecting a devil with $P_{\rm act} = P_{\rm max}$ is not actually unity, just the relative probability. Calculating the actual probability would require us to define the total area of the arena over which observations were made, e.g. the area of the playa where the barometer was deployed.