Magnitude of disturbance from a seismic source
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Series | Geophysical References Series |
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Title | Problems in Exploration Seismology and their Solutions |
Author | Lloyd P. Geldart and Robert E. Sheriff |
Chapter | 2 |
Pages | 7 - 46 |
DOI | http://dx.doi.org/10.1190/1.9781560801733 |
ISBN | ISBN 9781560801153 |
Store | SEG Online Store |
Contents
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)]
( )
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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Interrelationships among elastic constants | Magnitudes of elastic constants |
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Introduction | Partitioning at an interface |
Also in this chapter
- The basic elastic constants
- Interrelationships among elastic constants
- Magnitudes of elastic constants
- General solutions of the wave equation
- Wave equation in cylindrical and spherical coordinates
- Sum of waves of different frequencies and group velocity
- Magnitudes of seismic wave parameters
- Potential functions used to solve wave equations
- Boundary conditions at different types of interfaces
- Boundary conditions in terms of potential functions
- Disturbance produced by a point source
- Far- and near-field effects for a point source
- Rayleigh-wave relationships
- Directional geophone responses to different waves
- Tube-wave relationships
- Relation between nepers and decibels
- Attenuation calculations
- Diffraction from a half-plane