VẬT lý địa CHẤN 05 amplitudes

Processes altering seismic amplitudes

(Reynolds, 1998)


Seismic amplitudes
Affected by
• Reflection and transmission at an interface
• Geometrical spreading
• Absorption
• Receiver response
• Measurement system


Geometrical spreading

Energy proportional to:
r1
Plane wave:

constant

Cylindrical wave:

~ 1/r

Spherical wave:

~ 1/r2

r2

Energy is proportional to (Amplitude)2

⎛ E (r1 ) ⎞
⎟⎟
Attenuation due to geometrical spreading: 10* log⎜⎜
⎝ E (r2 ) ⎠
10


Absorption
Transformation of Energy into Heat

Amplitude:

A = A0e

− αx

α = Absorption coefficient

Energy is proportional with A2
Quality factor
Q=

2π
E
= 2π
=
∆E / E

∆E

2π
Part of energy, that is lost in a cycle

Relation between Q and α

1 αv αλ
=
=
Q πf
π


Absorption is frequency dependent

πf
α=
Qv


Common Earth materials
0.25 < α < 0.75 (dB/λ)
300 > Q > 50

π
Q=
αλ

Note: exp(-αx)

Question 1:
•
•
•
•
•

20 Hz seismic wave
Travels with 5 km/s
Propagates for 1000 m. through
Medium: absorption coefficient 0.25 dB/λ
What is the wave attenuation in dB due
solely to absorption?????
Answer:

λ=v/f= 250 m: absorption: 4*0.25=1 dB


Question 2:
• Wave with λ=100 m propagates through
homogeneous medium
• Between two detectors at radial distances of 1 km
and 2 km the wave amplitude is attenuated by 10
dB.
• Calculate contribution of geometrical spreading to
this value of attenuation and, thus, determine the
absorption coefficient of the medium in dB/ λ.
10 dB in 1000 m: 1 dB/ λ

Geometrical spreading: 20 10log (A0/A)= 20 10log (2)=6dB/ 1km
= 0.6 dB/ λ ⇒ absorption coefficient: 1-0.6=0.4 dB/ λ!