for multicomponent seismic data Wave-equation angle-domain imaging

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1 Wave-equation angle-domain imaging for multicomponent seismic data Paul Sava and Sergey Fomel Bureau of Economic Geology University of Texas at Austin September 5, 2005 EAGE/SEG Research Workshop on Multicomponent Seismic

2 Message Depth imaging of multicomponent data is conceptually simple...if implemented in the angle domain EAGE/SEG Research Workshop on Multicomponent Seismic 1

3 Outline 1. Imaging conditions in wave-equation migration 2. Ray vector geometry and angle gather extraction 3. Two synthetic examples EAGE/SEG Research Workshop on Multicomponent Seismic 2

4 Imaging conditions in wave-equation migration I(x) = S(x, ω; s) R(x, ω; s) dω ds (1) x space location ω frequency s shot location I(x) image S(x, ω; s), R(x, ω; s) downward-extrapolated wavefields EAGE/SEG Research Workshop on Multicomponent Seismic 3

5 Imaging conditions in wave-equation migration I(x) = S(x, ω; s) = Gs(x, ω; s) R(x, ω; s) = Gr(x, ω; r) D(s, r, ω) dr Gs(x, ω; s) Gr(x, ω; r) D(s, r, ω) dω ds dr (2) r receiver location Gs(x, ω; s) and Gr(x, ω; r) wave extrapolation kernels D(s, r, ω) data EAGE/SEG Research Workshop on Multicomponent Seismic 4

6 Surface offset imaging condition I1(x, ĥ) = Gs(x, ω; y ĥ) G r(x, ω; y + ĥ) D(y, h, ω) dy dω (3) y surface midpoint ĥ surface half-offset D(y, h, ω) = D(y ĥ, y + ĥ, ω) EAGE/SEG Research Workshop on Multicomponent Seismic 5

7 Subsurface offset imaging condition I2(x, h) = Gs(x h, ω; s) Gr(x+h, ω; r) D(s, r, ω) dω ds dr (4) h subsurface half-offset Generalizes (Rickett and Sava, 2002) EAGE/SEG Research Workshop on Multicomponent Seismic 6

8 Subsurface angle imaging condition I3(x, θ) =??? (5) θ reflection angle EAGE/SEG Research Workshop on Multicomponent Seismic 7

9 Outline 1. Imaging conditions in wave-equation migration 2. Ray vector geometry and angle gather extraction 3. Two synthetic examples EAGE/SEG Research Workshop on Multicomponent Seismic 8

10 Ray vector geometry px = ps + pr = kx/ω ph = pr ps = kh/ω ps = ns pr = nr ps pr = ns nr cos (2 θ) EAGE/SEG Research Workshop on Multicomponent Seismic 9

11 Ray vector geometry px 2 = n 2 s + n2 r + 2 n s nr cos (2 θ) (6) ph 2 = n 2 s + n 2 r 2 ns nr cos (2 θ) (7) px ph = n 2 r n 2 s (8) For isotropic single-component waves, ns = nr = 1/VP. For isotropic converted waves, ns = 1/VP and nr = 1/VS. From three equations, exclude two unknowns to express θ. EAGE/SEG Research Workshop on Multicomponent Seismic 10

12 Excluding px ph tan 2 θ = (1 + γ)2 kh 2 (1 γ) 2 kx 2 (1 + γ) 2 kx 2 (1 γ) 2 kh 2 γ = nr/ns For γ = 1, tan θ = kh / kx kh = k h EAGE/SEG Research Workshop on Multicomponent Seismic 11

13 Excluding khz (2-D) (1 + γ) a tan θ = 2 γ kz + (9) 4 γ 2 k z 2 + (γ 2 1) a b a = (1 + γ) kh + (1 γ) kx b = (1 γ) kh + (1 + γ) kx For γ = 1, tan θ = kh/kz (Stolt and Weiglein, 1985; Sava and Fomel, 2003) EAGE/SEG Research Workshop on Multicomponent Seismic 12

14 Outline 1. Imaging conditions in wave-equation migration 2. Ray vector geometry and angle gather extraction 3. Two synthetic examples EAGE/SEG Research Workshop on Multicomponent Seismic 13

15 Model I (D. Rosales) EAGE/SEG Research Workshop on Multicomponent Seismic 14

16 PP Data EAGE/SEG Research Workshop on Multicomponent Seismic 15

17 PS Data EAGE/SEG Research Workshop on Multicomponent Seismic 16

18 PP Image EAGE/SEG Research Workshop on Multicomponent Seismic 17

19 PS Image EAGE/SEG Research Workshop on Multicomponent Seismic 18

20 PP Subsurface Offset Gather EAGE/SEG Research Workshop on Multicomponent Seismic 19

21 PS Subsurface Offset Gather EAGE/SEG Research Workshop on Multicomponent Seismic 20

22 PP Angle Gather EAGE/SEG Research Workshop on Multicomponent Seismic 21

23 PS Angle Gather (Uncorrected) EAGE/SEG Research Workshop on Multicomponent Seismic 22

24 PS Angle Gather (Corrected) EAGE/SEG Research Workshop on Multicomponent Seismic 23

25 Model II (R. Baina) EAGE/SEG Research Workshop on Multicomponent Seismic 24

26 PP Shot Gather EAGE/SEG Research Workshop on Multicomponent Seismic 25

27 PS Shot Gather EAGE/SEG Research Workshop on Multicomponent Seismic 26

28 PP Image EAGE/SEG Research Workshop on Multicomponent Seismic 27

29 PS Image EAGE/SEG Research Workshop on Multicomponent Seismic 28

30 PP Subsurface Offset Gathers EAGE/SEG Research Workshop on Multicomponent Seismic 29

31 PS Subsurface Offset Gathers EAGE/SEG Research Workshop on Multicomponent Seismic 30

32 PP Angle Gathers EAGE/SEG Research Workshop on Multicomponent Seismic 31

33 PS Angle Gathers (Uncorrected) EAGE/SEG Research Workshop on Multicomponent Seismic 32

34 PS Angle Gathers (Corrected) EAGE/SEG Research Workshop on Multicomponent Seismic 33

35 PS Image (RVA Gradient) EAGE/SEG Research Workshop on Multicomponent Seismic 34

36 Message Depth imaging of multicomponent data is conceptually simple...if implemented in the angle domain Looking for data and industrial partners Extensions: anisotropy, true-amplitude RVA, etc. EAGE/SEG Research Workshop on Multicomponent Seismic 35

37 Acknowledgments U.S. Department of Energy Mihai Popovici and Sean Crawley (3DGeo) Daniel Rosales (Stanford University) Reda Baina (OPERA) Bob Hardage and Exploration Geophysics Laboratory EAGE/SEG Research Workshop on Multicomponent Seismic 36