Joint inversion of compressional and shear seismic data in native time domains
PP and PS seismic data are jointly inverted in a stratigraphic grid, using different time axes for PP and PS reflections. A ratio of PP and of PS waves'travel times inside a same layer cell maintained to be a function of a ratio of a P-wave propagation velocity and of an S-wave propagation velocity therein. Since PP and PS seismic amplitudes and travel times are due to elastic properties of the same structure, they can be inverted at the same time to provide better estimates of these elastic properties.
1. A seismic exploration method for simultaneously inverting PP and PS seismic amplitudes in native time domains with optimized registration through travel times' estimations, the method comprising:
obtaining PP and PS seismic data acquired during a seismic survey of a multi-layer structure; and
jointly inverting the PP and the PS seismic data in a stratigraphic grid defined by interfaces between layers, using different time axes for PP and PS reflections to obtain an image of the multi-layer structure usable to assess presence of oil and/or gas reservoir, wherein a ratio of PP and of PS waves travel times inside each layer cell is a function of a ratio of a P-wave propagation velocity and of an S-wave propagation velocity therein,
wherein the function takes into consideration that, for the PP waves travel time, an incident and a reflected P-wave have same P-wave propagation velocity and an incident angle substantially equal to a P-reflection angle, while, for PS waves travel time, the incident and a reflected S-wave have different propagation velocities and an S-reflection angle different from the incident angle.
2. The method of claim 1 , wherein the inverting includes:
producing test models of geophysical properties inside the multi-layer structure by perturbing a previous model according to predetermined rules;
generating synthetic data corresponding to the PP and to the PS seismic data, using each of the test models; and
selecting one of the test models that minimizes a cost function depending on differences in amplitudes and travel times between the seismic data and the synthetic data.
3. The method of claim 2 , wherein the cost function incorporates constraints on a distance between the previous model and a model for which the cost function is calculated, and on a spatial continuity of the model.
4. The method of claim 2 , wherein the geophysical properties include density, the P-wave propagation velocity and the S-wave propagation velocity.
5. The method of claim 2 , further comprising generating an initial model of the multi-layer structure.
6. The method of claim 5 , wherein, for the initial model, values of geophysical properties in each cell of the stratigraphic structure are obtained from well measurement and extrapolations of the well measurements.
7. The method of claim 6 , wherein, for the initial model, values of geophysical properties in each cell of the stratigraphic structure are based on results of a previous seismic survey.
8. The method of claim 2 , wherein PP and PS reflectivities are calculated as
R
PP
=
1
2
(
1
-
4
V
_
S
2
p
2
)
Δρ
ρ
_
+
1
2
cos
2
i
Δ
V
p
V
_
p
-
4
V
_
S
2
p
2
Δ
V
s
V
_
s
,
and
R
PP
=
-
p
V
_
p
2
cos
j
[
(
1
-
2
V
_
S
2
p
2
+
2
V
_
S
2
cos
i
V
_
p
cos
j
V
_
s
)
Δρ
ρ
-
4
V
_
S
2
(
p
2
-
cos
i
V
_
p
cos
j
V
_
s
)
Δ
V
s
V
_
s
]
where ρ , V p and V s are mean values of density, P and S wave propagation velocities above and below a layer interface, Δρ, ΔV p and ΔV s are the change of the density, P and S wave propagation velocities across the interface, i is the P-wave's incident angle on the interface, j is the S-wave's reflected angle and p is a ray parameter given by
p =sin i/ V p =sin j/ V s .
9. The method of claim 1 , wherein the ratio of PP and of PS waves travel times inside the same layer cell, ΔTWT ps /ΔTWT pp depends on the ratio of a P-wave propagation velocity and of an S-wave propagation velocity, V p /V s therein as
ΔTWT ps /ΔTWT pp =1/2( V p /V s +1).
10. The method of claim 2 , wherein traces extracted from seismic data are grouped in incidence angle bins.
11. A seismic data processing apparatus comprising:
a communication interface configured to obtain PP and PS seismic data acquired during a seismic survey of a multi-layer structure; and
a data processing unit configured to jointly invert the PP and the PS seismic data in a stratigraphic grid defined using interfaces between layers, using different time axes for PP and PS reflections to obtain an image of the multi-layer structure usable to assess presence of oil and/or gas reservoir, a ratio of PP and of PS waves travel times inside a same layer cell being a function of a ratio of a P-wave propagation velocity and of an S-wave propagation velocity therein,
wherein the function takes into consideration that, for the PP waves travel time, an incident and a reflected P-wave have same P-wave propagation velocity and an incident angle substantially equal to a P-reflection angle, while, for PS waves travel time, the incident and a reflected S-wave have different propagation velocities and an S-reflection angle different from the incident angle.
12. The apparatus of claim 11 , wherein the data processing unit jointly inverts the PP and the PS data by:
producing test models of geophysical properties inside the multi-layer structure by perturbing a previous model according to predetermined rules;
generating synthetic data corresponding to the PP and to the PS seismic data, using each of the test models; and
selecting one of the test models that minimizes a cost function depending on differences between the seismic data and the synthetic data.
13. The apparatus of claim 12 , wherein the cost function incorporates constraints on a distance between the previous model and a model for which the cost function is calculated, and on a spatial continuity of the model.
14. The apparatus of claim 12 , wherein the geophysical properties include density, the P-wave propagation velocity and the S-wave propagation velocity.
15. The apparatus of claim 12 , wherein the data processing unit is further configured to generate an initial model of the multi-layer structure, with initial values of geophysical properties in each cell of the stratigraphic structure, the initial values being based on measurements.
16. The apparatus of claim 12 , wherein the data processing unit calculates PP and PS reflectivities as
R
PP
=
1
2
(
1
-
4
V
_
S
2
p
2
)
Δρ
ρ
_
+
1
2
cos
2
i
Δ
V
p
V
_
p
-
4
V
_
S
2
p
2
Δ
V
s
V
_
s
,
and
R
PP
=
-
p
V
_
p
2
cos
j
[
(
1
-
2
V
_
S
2
p
2
+
2
V
_
S
2
cos
i
V
_
p
cos
j
V
_
s
)
Δρ
ρ
-
4
V
_
S
2
(
p
2
-
cos
i
V
_
p
cos
j
V
_
s
)
Δ
V
s
V
_
s
]
where ρ , V p and V s are mean values of density, P and S wave propagation velocities above and below a layer interface, Δρ, ΔV p and ΔV s are the change of the density, P and S wave propagation velocities across the interface, i is the P-wave's incident angle on the interface, j is the S-wave's reflected angle and p is a ray parameter given by
p =sin i/ V p =sin j/ V s .
17. The apparatus of claim 11 , wherein the ratio of PP and of PS waves travel times inside the same layer cell, ΔTWT ps /ΔTWT pp depends on the ratio of a P-wave propagation velocity and of an S-wave propagation velocity, V p /V s therein as
ΔTWT ps /ΔTWT pp =1/2( V p /V s +1).
18. A computer-readable recording medium non-transitorily storing executable codes which, when executed on a computer, make the computer perform a seismic exploration method for simultaneously inverting PP and PS seismic amplitudes, in native time domains with optimized registration through travel times' estimations, comprising:
obtaining PP and PS seismic data acquired during a seismic survey of a multi-layer structure; and
jointly inverting the PP and the PS seismic data in a stratigraphic grid defined using interfaces between layers, using different time axes for PP and PS reflections to obtain an image of the multi-layer structure usable to assess presence of oil and/or gas reservoir, a ratio of PP and of PS waves travel times inside a same layer cell being a function of a ratio of a P-wave propagation velocity and of an S-wave propagation velocity therein,
wherein the function takes into consideration that, for the PP waves travel time, an incident and a reflected P-wave have same P-wave propagation velocity and an incident angle substantially equal to a P-reflection angle, while, for PS waves travel time, the incident and a reflected S-wave have different propagation velocities and an S-reflection angle different from the incident angle.