Magnitude
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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 | 3 |
Pages | 47 - 77 |
DOI | http://dx.doi.org/10.1190/1.9781560801733 |
ISBN | ISBN 9781560801153 |
Store | SEG Online Store |
Problem 3.10
Using equation (1,8) in Table 2.2a, show that the fractional change is not necessarily small when , , and are all small.
Solution
Equation (1,8) in Table 2.2a is
Because does not enter into this equation, it has no effect upon . The fractions , , and are of the form which suggests that we use logs [since . Taking logs of both sides of the above equation, we get
.
Differentiation gives
Thus,
Since , the product of the two -factors varies between (when ) and (when ). Therefore, even though is small (being the difference between two small quantities), the right-hand side can be large.
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Reflection/transmission coefficients at small angles and magnitude | AVO versus AVA and effect of velocity gradient |
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Theory of Seismic Waves | Geometry of seismic waves |
Also in this chapter
- General form of Snell’s law
- Reflection/refraction at a solid/solid interface and displacement of a free surface
- Reflection/refraction at a liquid/solid interface
- Zoeppritz’s equations for incident SV- and SH-waves
- Reinforcement depth in marine recording
- Complex coefficient of reflection
- Reflection and transmission coefficients
- Amplitude/energy of reflections and multiples
- Reflection/transmission coefficients at small angles and magnitude
- AVO versus AVA and effect of velocity gradient
- Variation of reflectivity with angle (AVA)