This is a guest post by WebHubbleTelescope.

I find it interesting that much of the mathematics of depletion modeling arises from considerations of basic time-series analysis coupled with useful transforms from signal processing. As a case in point, Khebab has postulated how the idea of loglet theory fits into multi-peak production profiles, which have a close relationship to the practical wavelet theory of signal processing. Similarly, the Oil Shock Model uses the convolution of simple data flow transfer functions that we can also express as cascading infinite impulse response filters acting on a stimulated discovery profile. This enables one to use basic time series techniques to potentially extrapolate future oil production levels, in particular using reserve growth models ala Khebab's HSM or the maturation phase DD. ^[1]

In keeping with this tradition, it turns out that the generalized Dispersive Discovery model fits into a classic canonical mathematical form that makes it very accessible to all sorts of additional time-series and spatial analysis. Actually the transform has existed for a very long while -- just ask the guy to the right.