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## Amplitude pitfall

In geophysics we often discuss signal amplitude versus offset distance. It sounds easy, but there are some serious pitfalls. Such pitfalls are one reason why mathematicians often use nonintuitive weasel words. The best way for you to appreciate the pitfall is for me to push you into the pit.

Suppose we are writing a seismogram modeling program and we wish to model an impulsive plane wave of unit amplitude. Say the signal seen at x is .At the plane wave is shifted in time so that the impulse lies half way between two points, say it is .The question is, what should be the value of a?'' There are three contradictory points of view:

1.
The amplitude a should be 1 so that the peak amplitude is constant with x.
2.
The amplitude a should be so that both seismic signals have the same energy.
3.
The amplitude a should be 1/2 so that both seismic signals have the same area.