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Undoing convolution in nature

Prediction-error filtering is called ``blind deconvolution''. In the exploration industry it is simply called ``deconvolution''. This word goes back to very basic models and concepts. In this model one envisions a random white-spectrum excitation function $ \bold x$ existing in nature, and this excitation function is somehow filtered by unknown natural processes, with a filter operator $ \bold B$ producing an output $ \bold y$ in nature that becomes the input $ \bold y$ to our computer programs. This is sketched in Figure 1.

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Figure 1.
Flow of information from nature, to observation, into computer.
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[pdf] [png] [xfig]

Then we design a prediction-error filter $ \bold A$ on $ \bold y$ , which yields a white-spectrum residual $ \bold r$ . Because $ \bold r$ and $ \bold x$ theoretically have the same spectrum, the tantalizing prospect is that maybe $ \bold r$ equals $ \bold x$ , meaning that the PEF $ \bold A$ has deconvolved the unknown convolution $ \bold B$ .


next up previous [pdf]

Next: Causal with causal inverse Up: PREDICTION-ERROR FILTER OUTPUT IS Previous: The relationship between spectrum

2013-07-26