Anisotropy Estimation for Prestack Depth Imaging A Tomographic Approach Tony Huang, Sheng Xu, Yu Zhang, CGGVeritas, 10300 Town Park Drive, Houston, TX 77072, USA Summary Building an anisotropic velocity model from surface seismic data generally requires complete elastic wave records. P wave anisotropy parameter determination normally occurs in the frame work of high order moveout analysis of common offset gathers in the time domain. This is the conventional approach for vertical velocity analysis and effective estimation. In areas where well data (sonic logs, check shots et al) are available, we are able to get accurate vertical velocity by calibrating seismic migration velocity with check shot velocity. We present a method to accurately determine anisotropic parameters in transversely isotropic media without the weak anisotropy assumption. We test the algorithm on synthetic data and present a work flow to determine anisotropic parameters for prestack depth imaging in the Gulf of Mexico. Introduction In isotropic media, 3D tomography works well to give an accurate interval velocity for prestack depth imaging. Correct velocity field flattens gathers, and positions events correctly in depth. However, presence of seismic anisotropy adds difficulties for prestack depth imaging. Estimation of reliable anisotropy parameters remains a big challenge. There are a number of approaches developed to estimate anisotropy parameters. Anisotropic travel time inversion has been done for transversely isotropic media (Alkhalihah and Tsvankin, 1995; Grechka and Tsvankin, 1998). In this approach, non-hyperbolic moveout in the NMO equation is used to determine effective for time migration. To use this approach in prestack depth imaging we need to convert effective to interval , and convert rms velocity to interval velocity using the Dix formula. Krebs, et al (2003) present an integrated velocity estimation technique by fitting surface seismic data and well data in an appropriate data domain. This approach uses 1D update and global constraints to obtain anisotropic parameters at well locations and extrapolates parameters along geological horizons to areas outside the wells. We present an approach for anisotropy estimation in the areas where vertical velocity ( ) can be accurately obtained at well locations with vertical check shot surveys. Our procedure is to invert for

0v

and parameters with a joint tomographic inversion.

The work flow is as follows: Start with isotropic velocity Obtain from calibration with check shot velocity 0v Generate 3D migration mini volume (e.g.,

1000mx1000m) around wells using (==0) 0v Jointly invert for one , function per well Generate a & volume by hanging 1d function

from WB Run 3D anisotropic migration to generate CIGs for

3D tomographic velocity update ( only, fix & )

0v

Joint inversion of and For P wave imaging, the required anisotropic parameters are ,0v , and . When the input is restricted to P wave surface seismic, even in 1D case, an ambiguity exists in inverting all three parameters. For example, if the seismic event in CIG gather exhibits a hyperbolic moveout, we can not distinguish whether it is caused by velocity perturbation or by a perturbation of elliptical anisotropy ( = ) parameters. Either perturbation can flatten the gathers in the depth domain. When non surface seismic data (e.g., check shots) are used, we can accurately determine and

ambiguity is no longer a problem. Knowledge of allows us to invert for the anisotropic parameters

0v

0v and

simultaneously. After fixing , we migrate gathers around the well area, and pick actual curvature in common image gathers (CIG). An algorithm is developed to invert

0v

and simultaneously. We start from the Hamiltonian:

( ) (1) 14

)(),(

20 = G

vH

xpx

Under acoustic approximation for VTI media (Alkhalihah and Tsvankin, 1995), the eikonal G is defined as ( ) 1)(8)21()21(

21 2222222

+++++= zxzxzx ppppppG ,

Where , are the normalized slowness components (Zhou et al, 2003)

xp zp

,/,/ 00 vpvp zzxx pp ==

Anisotropic Estimation for Prestack Depth Imaging

Anisotropy Estimation for Prestack Depth Imaging

From equation (1), we derive the group momentum for the ray tracing,

( )

( )22

220

22

220

)(21)(21

)(21)(2)21(

zx

xz

zx

zx

ppppv

ddz

ppppv

ddx

=

+

= (2)

We derive equation (2) without weak anisotropy assumption (Thomsen 1986). Notice that if we introduce weak anisotropy assumption, the denominators of equation (2) turn to unit. As the ray momentum on both horizontal and vertical share the same denominator, the group direction of the ray would be the same with or without weakness anisotropy assumption:

( )( )2

2

)(21)(2)21(tan

xz

zx

pppp

dzdx

+

== (3)

For tomography, the shot and receiver locations are invariants. We need to derive the travel time perturbation with respect to anisotropic parameter and in a condition of keeping group direction constant. Using eikonal equation and equation (3), we then derive the

derivative

,,, TT for and joint

travel time inversion. Synthetic Studies To check the inversion process, we perform analysis with modeling data. The velocity model consists of two layers: one water layer with velocity of 1500m/s, and another earth layer with velocity of 3000 m/s. There are two anisotropy models: one with weak parameter; and the other with strong parameter. There are 4 reflectors at depth of 1500m, 3000m, 45000, and 6000m, respectively. Table 1 describes the modeling parameters.

Table 1: 1D model parameters

Layer z (m) V0 (m/s) Delta Epsilon Epsilon

weak strong

1 0 1500 0 0 0

2 1500 3000 0.03 0.06 0.06

3 3000 3000 0.03 0.06 0.18

4 4500 3000 0.03 0.06 0.18

6000 We perform depth migration using two modeled input gathers, and pick curvatures in the common offset imaging gathers (CIG) to simulate the real case application. Figure 1 shows CIG gathers and curvature picks that went into the tomography inversion. Figure 2 shows inversion results for two models. The derived anisotropic parameters are within one percent off from the parameters of true models. We are able to distinguish weak and strong .

(a) Weak anisotropy) (b) Strong anisotropy

Figure 1: CIG gathers from migration using V0 for weak anisotropy (a) and strong anisotropy (b). Blue lines denote curvature picks.

Anisotropy Estimation for Prestack Depth Imaging

Gulf of Mexico Example The real data set is over marine sediment basins in the Gulf of Mexico. The objective of anisotropic depth imaging is to improve salt positioning, which is expected to give better subsalt imaging. There are sonic logs and check shots available. The vertical velocity ( ,0v and) is obtained by calibrating isotropic velocity with vertical check shot velocity. Anisotropic parameters are not expected to change greatly in the area. The objective is to derive a v(z) anisotropy function ( and ) using seismic and well data. We average and functions at well location, and extrapolate the functions along water bottom, which is consistent with compaction driven sediment (Figure 3).

Figure 4 shows the improvement of steeply dipping TOS imaging near a well. There are improvements in structural focusing and seismic/well mistie. Anisotropic imaging shows more details of small salt wings which is confirmed by well data.

2 Layers weak epsilon

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0 1000 2000 3000 4000 5000 6000 7000

Depth

2ly_eps_true2ly_del_true2ly_eps_tom2ly_del_tom

(a) Weak anisotropy

2 Layer strong epsilon

00.020.040.060.08

0.1

0.120.140.160.18

0.2

0 1000 2000 3000 4000 5000 6000 7000

Depth

2ly_eps_true2ly_del_true2ly_eps_tomo2ly_del_tomo

(b) Strong anisotropy

Figure 2: Inversion results of weak anisotropy (a) and strong anisotropy (b) model data. Delta and epsilon are very close to true model.

Conclusions We presented a tomographic approach to determine anisotropic parameters for transversely isotropic media. We tested the methodology in model data as well as real data in a marine sedimentary basin. Acknowledgments We would like to thank CGGVeritas for giving us permission to present the paper. We thank Mike Howard of BHPB for discussion of anisotropic work flow, and encouragement in the work. We also thank Bruce Ver West for generating the synthetics and discussion in the topics. Finally, we would like to thank David Sixtra and Arnold Rodriguez of Anadarko Petroleum Company, Judy Mooney and Clive Hurst of ENI Petroleum for providing check shots in the study area.

Anisotropy Estimation for Prestack Depth Imaging

(a) Isotropic sedimentary flood migration (b) Anisotropic sedimentary flood migration

Figure 4: Anisotropy prestack depth imaging improves definition of TOS, minimizes seismic/well mistie. (a) Isotropic sedimentary flood migration. (b) Anisotropic sedimentary flood migration.

(a) Isotropic CIG Gathers (b) Anisotropic CIG gathers

Figure 5: CIG depth gathers. Anisotropic imaging yields flatter gathers. (a) CIG of isotropic migration. (b) CIG of anisotropic migration.