joint velocity inversion for pp and ps prestack depth imaging - PGS

1
JOINT VELOCITY INVERSION FOR P-P AND P-S
PRESTACK DEPTH IMAGING
Yaohui Zhang*, Don Pham, Min Lou and Sheng Lee
PGS Geophysical, 10550 Richmond Avenue, Houston, Texas, 77042 USA
Summary
We present a new velocity updating method for anisotropic P-P and P-S prestack depth
imaging via prestack joint velocity inversion. The joint velocity update consists of the
estimation of vertical P- and S-wave velocities and anisotropic parameters in the transversely
isotropic media with vertical symmetry (VTI). The near offset data is used for depth
consistent joint velocity inversion to estimate vertical depth and vertical P- and S-wave
velocities. Integrating anisotropic parameters with depth consistent velocity model from
vertical velocities completes the anisotropic prestack depth migration procedure. The results
from synthetic data show that joint velocity update technique is an effective and practical
approach for multi-component depth imaging.
Introduction
Establishing and updating velocity models are two important steps for multi-component
prestack seismic depth imaging. Anisotropic prestack depth migration requires predetermination
of anisotropic parameters (Mikhailov etal. ,2001, Nolte etal, 1999, and Bale
etal. ,1998). The key step in determining the required anisotropic parameters is to estimate the
vertical velocities of P- and S-waves. There are two flows commonly used in conventional
multi-component depth migration. The first flow commonly used in P-S prestack depth
migration is to assume that the depth model obtained from P-P migration is correct. The
velocity updating is done only to the S-wave focusing velocity to flat the P-S events for
stacking. The results of migration will produce the same depth model. If there were an error in
the P-wave depth model, the initial P-S image gathers may be incoherent and the updating of
S-wave velocity field may be very difficult and unstable. The second flow takes the P-wave
velocity as its down-going velocity field and updates the depth model with upcoming S-wave
velocity field independent of P-wave model and velocity. Since the updating of depth model
and S-wave velocity is independent of P-wave data, the outcome of the depth migration will
show depth inconsistency between P-P and P-S images. In addition, both of these flows
require the well log data to provide the vertical velocity information for anisotropic prestack
depth migration. Neither flow offers a practical approach to address the need of anisotropic
depth migration.
In this paper, we extend the application of post stack joint velocity inversion (Zhang etal.
2001) to the velocity updating for multi-component seismic depth imaging. The joint velocity
inversion utilizes near offset data to estimate the vertical P- and S-wave velocities that are
critical in determining anisotropic parameters for P-P and P-S depth migration in presence of
VTI anisotropy. The combination of near and mid-offset data is used to estimate anisotropic
parameters. In this paper, we use synthetic modeling to demonstrate our joint velocity
inversion procedure. Finally, we will show the practical aspects of this procedure with a real
data example.
EAGE 64th Conference & Exhibition — Florence, Italy, 27 - 30 May 2002

2
Theory and Methodology
The proposed multi-component prestack depth migration flow is as following:
(1) Build initial P-P and P-S velocity models and perform isotropic prestack depth migration
for near offset P-P and P-S data.
(2) Perform joint inversion on the migrated data to derive the vertical velocities that tie the
depth of P-P and P-S images. The output from the inversion procedure will be the vertical
depth, Z 0 , vertical P-wave velocity, Vp 0 , and vertical S-wave velocities, Vs 0 .
(3) Update velocity model and re-run prestack depth migration for the same data. The
resulting images between P-P and P-S should be depth consistent.
(4) Use the velocity model obtained in step 3 to perform prestack depth migration for near to
mid-offset data. If all depth image gathers are flat, then the data is isotropic and anisotropic
processing is not required. If the image gathers are not flat, then anisotropy is implied.
(5) Perform anisotropic parameter estimation.
Vp 0 ,Vs 0 ,Z 0
Vp N,Z pp
Vp N,Vs N,Z ps
Vertical depth
∆Zpp
∆Zps
Isotropic P-P image
Figure 1. The mismatches between isotropic P-P and P-S images and vertical depth in the VTI
medium.
Our strategy for the anisotropic parameter estimation is depicted in Figure 1. We first perform
P-P isotropic velocity focusing using the velocity model derived in step 3. Second, we stack
the data and measure the depth, Z pp (see Figure 1). Third, we measure the depth difference
between the vertical depth (Z 0 ) and isotropic P-P depth (Z pp ). Finally, we use this information
to estimate the anisotropic parameter δ that can be expressed, to the first order approximation,
as
Z pp − Z 0 ∆Z
pp
δ ≈ = .
Z 0 Z 0
where Z 0 is the vertical depth given by joint velocity inversion in step 2. Similarly, for the P-S
anisotropic parameter, σ, we can approximate it by the following expression
∆Z
2 pp 2 γ ∆Z
0 pp
σ ≈ γ 0 ( ) [ + 1]
Z 2 Z
0
where γ 0 (=Vp 0 /Vs 0 ) is the ratio of the vertical P-wave velocity to the vertical S-wave
velocity. Once these anisotropic parameters are determined, we can perform the final
anisotropic prestack depth migration that requires Vp 0 , Vs 0 , δ, and σ.
In summary, the depth consistent joint velocity inversion provides three critical parameters for
the estimation of anisotropic parameters in presence of anisotropy: the vertical depth, Z 0 ,
vertical P-wave velocity, Vp 0 , and vertical S-wave velocities, Vs 0 .
0
Isotropic P-S image

3
Data Example
We applied the joint velocity update method to anisotropic synthetic data to demonstrate that
the vertical depth, P- and S-wave velocities can be determined within error tolerance. We
believe that the near offset data is sufficient for the estimation of the vertical velocities. We
used a ray-tracing method to create the synthetic data with the P- and S-wave velocity models
shown in Figure 2. We introduced anisotropic (VTI) in the first layer. Figure 3 shows the
initial depth migrated sections of the anisotropic P-P and P-S data before joint velocity
inversion. We migrated these images with the initial P-wave velocity model that has an error
of 12% and the initial S-wave velocity model that has error of 7.5%. We then measured the
depth mismatch for the joint inversion to determine the depth consistent velocity fields. The
estimated vertical velocities from the joint inversion are within 2% errors of the correct
velocities. With these velocities, we re-run the depth migration for the same input data. The
results are shown in Figure 4. There is an excellent tie in depth between P-P and P-S depth
migrated sections. The consistency between exact model (Figure 2) and the joint inversion
depth results (Figure 4) demonstrates that we can determine the vertical P- and S-wave
velocities from the near offset anisotropic data. Based on the estimated vertical parameters,
we proceed to estimate the anisotropic parameters as outlined above.
5.0KM
5.0KM
0.5
0.5
1.0
1.0
1.5
1.5
D
ep
th
(K
M)
2.0
2.5
3.0
D
ep
th
(K
M)
2.0
2.5
3.0
Figure 2. P- and S-wave synthetic models.
P-P
P-S
Figure 3. Initial depth images of near offset P-P and P-S data before joint inversion for VTI.
P-P
P-S
Figure 4. Final depth images of near offset P-P and P-S data after joint inversion for VTI.
EAGE 64th Conference & Exhibition — Florence, Italy, 27 - 30 May 2002

4
(a)
(b)
Figure 5. (a) Depth consistent P-P and P-S image gathers by joint inversion for vertical velocities; (b)
focused P-P and P-S depth images using mid-offset data.
Figures 5a shows the depth consistent P-P and P-S image gathers of the anisotropic data. The
flattened gathers are shown in Figure 5b. The depth consistency and focusing cannot exist
simultaneously from isotropic processing. We can use the depth mismatch between the
vertical depth and the isotropic P-P depth to estimate the anisotropic parameters from as
outlined above. The estimated values of δ and σ are 0.09 and 0.619 which have a 10% error
compared to the exact values of 0.1 and 0.693, respectively.
Conclusions
We present a practical approach for the joint velocity update method to estimate anisotropic
parameters for multi-component depth imaging. We use the near offset data to check for the
depth consistency and to estimate vertical velocities. We also use the mid-offset data for
focusing analysis to estimate the isotropic P-P depth. The combination of the joint velocity
inversion and the focusing analysis allows us to calculate anisotropic parameters directly in
the depth domain. As a consequence, it is more stable and easy to tie with well log data for
reservoir interpretation. Finally, using joint inversion to estimate the vertical P- and S-wave
velocities are very useful for anisotropic depth migration when well log data is not available.
Acknowledgements
We would like to thank Jerry Yuan for many useful discussions and suggestions. We thank
Hongwei Wang for creating synthetic data and Shelton Ma for helping with the anisotropic
ray tracing. Finally, we thank PGS for the permission to publish this work.
References
Bale, R. A., Farmer, P., Hansen, J. O., Nichols, D. E. and Palacharla, G. K., 1998, Prestack depth
migration of converted wave data in anisotropic media, 68th Ann. Internat. Mtg: Soc. of Expl.
Geophys., 1108-1111.
Mikhailov, O. V., Johnson, J., Shoshitaishvili, E. and Frasier, C., 2001, Practical approach to joint
imaging of multi-component data: The Leading Edge, 20, no. 9, 1016-1021.
Nolte, B., Bishop, K. and Sukup, D., 1999, Anisotropic prestack depth migration of converted-wave
data from the Gulf of Mexico, 69th Ann. Internat. Mtg: Soc. of Expl. Geophys., 691-694.
Zhang, Y., Pham, L. and Neves, F., 2001, Depth-consistent P-P and P-S seismic image via joint
velocity inversion, 71st Ann. Internat. Mtg: Soc. of Expl. Geophys., 841-844.