2024年3月24日发(作者：星勇军)

Velocity Dispersion and

Wave Attenuation (Q)

Stanford Rock Physics Laboratory - Gary Mavko

(1) Seismic velocities almost always increase with

frequency, and

(2) Seismic waves are always attenuated as they

travel through rocks.

These two observations are usually intimately related. Both usually

increase from dry to fluid saturated conditions, and both usually

decrease with increasing effective pressure.

These effects complicate the comparison of laboratory and field

data, but they also reveal details about the pore space and the pore

fluids it contains.

Stanford Rock Physics Laboratory - Gary Mavko

183

184

Kramers-Kronig Relations

Q

"1

(

#

)=

|

#

|

&

M

R

(

%

)"M

R

(0)d

%

$

M

R

(

#

)

"&

'

%%

"

#

"

#

&

Q

"1

M)"M=

(

%

)M

R

(

%

)d

%

R

(

#

R

(0)

$

"&

'

|

%

|

%

"

#

Causality leads to a very specific relation required between Q

and modulus dispersion

Stanford Rock Physics Laboratory - Gary Mavko

I.1

In most rocks and sediments, the velocity tends to increase with

frequency. This is accompanied by attenuation. Attenuation tends to

be highest in frequency range where velocity is increasing most

rapidly.

Stanford Rock Physics Laboratory - Gary Mavko

185

186

2024年3月24日发(作者：星勇军)

Velocity Dispersion and

Wave Attenuation (Q)

Stanford Rock Physics Laboratory - Gary Mavko

(1) Seismic velocities almost always increase with

frequency, and

(2) Seismic waves are always attenuated as they

travel through rocks.

These two observations are usually intimately related. Both usually

increase from dry to fluid saturated conditions, and both usually

decrease with increasing effective pressure.

These effects complicate the comparison of laboratory and field

data, but they also reveal details about the pore space and the pore

fluids it contains.

Stanford Rock Physics Laboratory - Gary Mavko

183

184

Kramers-Kronig Relations

Q

"1

(

#

)=

|

#

|

&

M

R

(

%

)"M

R

(0)d

%

$

M

R

(

#

)

"&

'

%%

"

#

"

#

&

Q

"1

M)"M=

(

%

)M

R

(

%

)d

%

R

(

#

R

(0)

$

"&

'

|

%

|

%

"

#

Causality leads to a very specific relation required between Q

and modulus dispersion

Stanford Rock Physics Laboratory - Gary Mavko

I.1

In most rocks and sediments, the velocity tends to increase with

frequency. This is accompanied by attenuation. Attenuation tends to

be highest in frequency range where velocity is increasing most

rapidly.

Stanford Rock Physics Laboratory - Gary Mavko

185

186