Propagation of the seismic wave Propagation of the seismic wave

Propagation of the seismic wave:
Seismic waves subjected to several phenomenon when travel
through the earth
The most important are:
1- Attenuation
2- Reflection
3- Refraction
4- Diffraction
5- Multiples
6- Generation of wave face
7- Change of velocity
8- Frequency filtering
1- Attenuation
There are two types of attenuation:
a- Geometrical spreading: Take place due to traveling certain amount of distance
Example: Find attenuation of a wave after a distance (r) from the source
α
I= I o * r o / r * e - α r
is absorption coefficient
I o , r o
r
I=?

- Intrinsic attenuation: loss of amplitude taken place due to dissipation of
energy into heat by friction
Io
e -œr
Distance
Note:
Higher frequencies attenuate over shorter distances due to their shorter wavelengths.
Therefore, high frequencies decay first leaving a low frequency signal remaining.
2- Reflection:
It is take place when a seismic wave hits an interface separating two media of
different elastic Properties (or different acoustic impedance, z)
Acoustic impedance: define as the product of velocity with density
Z = p * V

Z1 = p 1 * V1
Z2 = p 2 * V2

Reflection Coefficient: It is a ratio of reflected wave amplitude (Ar) to
incidence wave amplitude (Ai)
R = Ar / Ai = Z2 – Z1 / Z2 + Z1 = P2V2 – P1V1 / P2V2 + P1V1
Notes:
1- R is positive when Z2>Z1 and negative when Z1>Z2
2- R =+1 when Z1 = 0 and R = -1 when Z2 = 0
3- R is approach to unity in two cases:
a- When incidence angle = Critical incidence angle
b- Tangential (Grazing) incidence
(a)
(b)

3- Refraction : Apart of seismic wave is refracted when hits an interface
separating two media
Refraction depend on Snell’s law:
Notes:
1- When V 2 is smaller than V 1 so i 1 > i 2 , in this case
refraction will not take place, the wave will be
deflected.
2- When V 2 >V 1 , i 2 will be greater than i 1 , when i 2 =90
the
wave will travel along the interface and refraction will
take place,
So i 2 is called critical angle.
i1
Refraction not take place
Refraction not take place
Refraction will take place and i 1 is called
critical angle =i c , i 2 = 90, then sin 90 =1
i2
So Sin i c = V1 / V2

4- Diffraction:
it takes place when the seismic wave hits:
1- Irregularity
2- Abrupt discontinuity
3- Faults
In this case the irregular feature act as point source for radiating waves in all
directions.
Source
Surface
V1
V2
Faults
5- Multiple:
They are signals undergone more than one reflection, and they are of
small energy
There are two types of multiples:
1-Short path multiples : They are almost arrived with useful signals and form a tail to
them, such as
A- Ghost
B- Near-surface multiples
C- Peg-leg Multiples

2- Long path Multiples : They are arrived at a later time than primary
Such as
A- Simple multiples.
reflections, they appear as a separate signals.
B- Interformational multiples.
Primary
Reflection Ghost
Near
Surface
Peg-Leg
Simple
Multiple
Surface
Interformational
Short path Multiples
Long path Multiples

6- Generation of wave phase:
When P-wave hits an interface generate four types of the seismic waves:
Seismic Wave
Reflected S-Wave
Reflected P-Wave
Refracted P-Wave
Refracted S-Wave
Notes:
1- When the wave hits an interface vertically , does not generate other type of waves.
2- When the first medium is liquid, only three types will generate because S-wave does
not propagates through the liquid.