Seismic velocity tomography with co-located soft data

Transcription

1 Seismic velocity tomography with co-located soft data Bob Clapp Stanford University SCRF Affiliate Meeting May 2009

2 Motivation soft data constrains flow simulation model 2

3 Outline Introduction Seismic tomography Geological constraints for velocity analysis Cross Gradients Function Accuracy in different frequency intervals Results Future work: Western Geco Dataset: Seismic & Resistivity 3

4 Introduction

5 Schematic of seismic imaging s g Velocity Estimation Model: v, ρ Data Image 5

6 Tomography Problem Data Choice of constraints Soft data Velocity estimation Training images Image Smoothness Velocity update traveltimeslowness operator Constraints Inverse Problem 6

7 Magnetotellurics (MT) data Natural-source (electromagnetic method) Insight into the resistivity structure as the main parameter Frequency: Hz Insensitive to thin resistors Coils Hx Hy Hz Electrodes E-Lines Ex Ey Amplifiers, digitizers, etc. Computer GPS antenna 7

8 Field Data 3D cube inverted resistivity Seismic Data Courtesy of WesternGeco Co. 8

9 Seismic tomography

10 Tomography Relate travel times and slowness t = T nl (s) Operator is model dependent Initial guess s0 Ray paths are a function of slowness Courtesy of Bob Clapp. 10

11 Tomography Relate travel times and slowness t = T nl (s) Operator is model dependent Initial guess s0 Ray paths are a function of slowness Courtesy of Bob Clapp. 10

12 Linearization Linearize operator Using Taylor s expansion t T nl s 0 + T nl s t t 0 + T 0 s t T 0 s Iteratively update approximation of s s0 s 1 = s 0 + s. Linearize the operator around new s0 11

13 Tomography and null space shadow zones lack of illumination or poor illumination (especially sub-salt regions) source receiver limited angle coverage imposed by recording geometry resolution decreases with depth velocity information is revealed with reflection angle. under-determined problem Q( s) = t T 0 s 2 + ɛ 2 A s 2, 12

14 Cross-gradients function

15 Cross-gradients function Structural similarity measurement x t(x, y, z) = m r m s z simplified 2-D definition t(x, z) = ( m r z m s x ) ( m r x m s z ) m r : resistivity field m s : slowness field Considering the mesh below, we can linearize the crossgradients function t 4 ( mrc (m sb m sr ) + m rr (m sc m sb ) + m rb (m sr n sc ) ) x z Xc Xb Xr 14

16 Cross-gradients vs. Frequency range Accuracy for field properties in different frequency intervals: Difference in frequency Structural complexity? Velocity vs. resistivity smooth velocity as resistivity 15

17 Marmousi model 16

18 Auto cross-gradient Cross-gradient values 17

19 Cross-gradient values = 18

20 Cross-gradient values = 19

21 Velocity analysis with cross-gradient constraint Velocity analysis objective function Q( s) = t T 0 s 2 + ɛ 2 A s 2, P( s) = t T L s 2 + ɛ 2 1 A s 2 + ɛ 2 2 G(s 0 + s) 2, T L : linear approximation of tomography matrix A : regularization operator G : linear cross-gradients operator g : cross-gradients function s : seismic slowness r : resistivity t : travel time 20

22 Synthetic model with semi-circular fault V (Km/s) Velocity model 21

23 Initial velocity estimation V (Km/s) Initial velocity guess 22

24 Velocity estimation without soft data V (Km/s) Updated velocity 23

25 Velocity estimation with soft data V (Km/s) Updated velocity with soft data 24

26 Observations Steering filters Smooth and continuous velocity anomalies Cross-gradient functions Sharp boundaries Salt structures Faults 25

27 Next

28 Future work Improved velocity-resistivity relations Apply to field data Integrate training images as a constraint to tomography problem Integrate statistical uncertainty analysis? 27

29 Acknowledgements Biondo Biondi (Stanford Exploration Project) Tapan Mukerji (SCRF) Olav Lindtjorn (WesternGeco company) WesternGeco company 28

30 Thank you