VẬT lý địa CHẤN 05 amplitudes

Reynolds, 1998Processes altering seismic amplitudes... Question 2:• Wave with λ=100 m propagates through homogeneous medium • Between two detectors at radial distances of 1 km and 2 km t

(Reynolds, 1998)

Processes altering seismic amplitudes

Seismic amplitudes

Affected by

• Reflection and transmission at an interface

• Geometrical spreading

• Absorption

• Receiver response

• Measurement system

r 1

r 2

Plane wave:

constant

Geometrical spreading

Energy proportional to:

Energy is proportional to (Amplitude) 2

Attenuation due to geometrical spreading: ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

) (

)

( log

*

10

2

1 10

r E r E

Transformation of Energy into Heat

Quality factor

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

Relation between Q and α

α = Absorption coefficient

αx

0e A

A = −

=

∆

=

∆

=

E

E E

E

/

2

π

αλ πf

αv Q

Absorption

Energy is proportional with A 2

Amplitude:

Absorption is frequency dependent

Qv πf

α =

Common Earth materials

0.25 < α < 0.75 (dB/λ)

300 > Q > 50

αλ π

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 10 log (A0/A)= 20 10 log (2)=6dB/ 1km

= 0.6 dB/ λ ⇒ absorption coefficient: 1-0.6=0.4 dB/ λ!