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Our second observation is that all signals eventually attenuate,
and this attenuation (*Q*) is a function of frequency and media properties.
How much they attenuate is generally a function of the media, but
a decent first approximation is that after a certain number of
cycles, a given frequency attenuates a given
percentageKjartansson (1979).
Therefore, after a certain number of cycles, the wave components at
that frequency will no longer
be of usable strength so we can stop downward continuing it.
This observation nicely compliments the wavelet sampling observation that
higher frequencies will attenuate quicker in depth, reducing the
distance we need to downward continue them.
We can combine these two ideas and replace our original cost equation with,

| |
(3) |

where our number of depth steps *nz*(*f*) is a function of frequency.

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Stanford Exploration Project

6/8/2002