Magnitude of disturbance from a seismic source

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Problem 2.3a

Firing an air gun in water creates a pressure transient a small distance away from the air gun with peak pressure of 5 atmospheres ( Pa). If the compressibility of water is /Pa, what is the peak energy density?

Background

Air guns (see problem 7.7) suddenly inject a bubble of high‐pressure air into the water to generate a seismic wave.

Stresses acting upon a medium cause energy to be stored as strain energy, because the stresses are present while the medium is being displaced. Strain energy density (energy/unit volume) is equal to [see Sheriff and Geldart, 1995, equation (2.22)]


(2.3a)

Solution

From problem 2.1c, we see that Pa. Also, for water, so . From equation (7,5) of Table 2.2a we find that when . Also, (see equation (2.1f)), so


Using equation (2.3a) we find that


[The dimensions of are the same as those of stress, since strains are dimensionless. Thus, stress units are .]

Problem 2.3b

If the same wave is generated in rock with Pa, what is the peak energy density? Assume a symmetrical -wave with for .

Solution

We have , , so equation (2.3a) becomes


Equation (9,3) in Table 2.2a gives so that


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