Brad Artman Spring Review

Transcription

1 Brad Artman Brad Artman Spring Review 2005

2 Passive Spy vs. Spy 1

3 Passive Spy vs. Spy 2

4 Passive Spy vs. Spy SS2 Installation 3

5 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 100% accurate ω k propagator Combined Linear/Hyperbolic radon transforms brad@sep.stanford.edu 4

6 FDIC & aliasing I(x, h) ω,z = U(x + h) D (x h) Î(k x, k h ) ω,z = 1 2 Û ( ) kx + k h 2 ( ) ˆD kx k h 2 derivation brad@sep.stanford.edu 5

7 FDIC & aliasing Fourier domain Space domain 6

8 FDIC & aliasing Fourier domain Space domain 7

9 FDIC & aliasing Fourier domain Space domain 8

10 FDIC & aliasing shallow deep 9

11 FDIC & aliasing every 10 th shot all shots 10

12 FDIC & aliasing Î(k x, k h ) = 1 2 Û ( ) kx + k h 2 ( ) ˆD kx k h 2 k x 1 k h Û( 2 2 ) ˆD (0) Û( 1 2 ) ˆD ( 1 2 ) Û(0) ˆD ( 2 0 Û( 1 2 ) ˆD ( 1 2 ) Û(0) ˆD (0) Û( 1 2 ) ˆD ( 1 2 ) 2 ) 1 Û(0) ˆD ( 2 2 ) Û(1 2 ) ˆD ( 1 2 ) Û(2 2 ) ˆD (0) 2 Û( 1 2 ) ˆD ( 3 2 ) Û(2 2 ) ˆD ( 2 2 ) Û(3 2 ) ˆD ( 1 2 ) brad@sep.stanford.edu 11

13 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 12

14 Fourier domain time windowing 13

15 Fourier domain time windowing 14

16 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 15

17 Gather correlation shot-profile survey sinking passive imaging U z=0 (x r, x s, ω) D z=0 (x r, x s, ω) R z=0 (x r, x s, ω) T z=0 (x r, ω) T z=0 (x r, ω) SSR 1 SSR +1 DSR SSR 1 SSR +1 U z=1 (x r, x s, ω) D z=1 (x r, x s, ω) R z=1 (x r, x s, ω) Tz=1 (x r, ω) T z=1 + (x r, ω) brad@sep.stanford.edu 16

18 Gather correlation Shot-profile=Source-receiver migration R z+1 = DSR R z = DSR U z Dz = (1) = SSR U z SSR Dz = = SSR U z (SSR 1 D z ) = U z+1 Dz+1. brad@sep.stanford.edu 17

19 Gather convolution Image space SRME: M z+1 = DSR M z = DSR U z Uz = (2) = SSR U z SSR Uz = = SSR U z (SSR 1 U z ) = U z+1 Uz+1. brad@sep.stanford.edu 18

20 Migration 19

21 Image-space multiple model 20

22 Migration, subtraction 21

23 Subtraction, migration 22

24 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 23

25 Forward-scattered angle gathers 24

26 Forward-scattered angle gathers x (p r + p s ) + z (q r + q s ) h x (p r p s ) h z (q r q s ) = 0, z h x = tan γ and z x = tan α. x (p r p s ) + z (q r q s ) h x (p r + p s ) h z (q r + q s ) = 0, z h x = cot γ a and z x = cot α a. brad@sep.stanford.edu 25

27 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 26

28 Valhall 27

29 Valhall 28

30 2005a Valhall passive data Plan-wave decomposition & spectral analysis migrate P,Z, & S components Back-scattered Forward-scattered P-Z summation as U D separation vs. correlation Compare to best-case image Search for earth tremor brad@sep.stanford.edu 29

31 2005b Finish aliasing paper Finish image-space multiple modeling paper Direct migration of Long Beach VSP data Submit multi-offset GPR migration paper 30

32 Thanks contents 31

33 2004 Fourier domain imaging condition & migration aliasing Fourier domain time windowing Gather convolution Foward-scattered angle gathers Valhall data 32

34 Derivation 1 I(x, h) ω,z = U(x r h)d(x s + h) (1) Fourier transform D to ˆD Î(x, h) = U(x h) ˆD(k s )e ik s(x+h) dk s (2) FT all the x s Î(k x, h) = U(x h) ˆD(k s )e ik s(x+h) dk s e ixk x dx (3) brad@sep.stanford.edu 33

35 Derivation 2 Introduce (Sergey inspired) variable flip-flop/reorder Î(k x, h) = ˆD(k s )e ik sh U(x h)e ix(k x k s ) dxdk s Î(k x, h) = ˆD(k s )e ih(2k s k x ) U(x h)e i(x h)(k x k s ) d(x h)dk s (4) Note salient details: Inner integral is FT of U, Î(k x, h) = Û(k x k s ) ˆD(k s )e ih(2k s k x ) dk s (5) brad@sep.stanford.edu 34

36 knowing k h = 2k s k x, Î(k x, h) = 1 2 Derivation 3 Û( k x k h 2 ) ˆD( k x + k h )e ihk hdk h (6) 2 This we see is FT over offset, so the complete FT of the IC is Î(k x, k h ) = 1 x k h 2Û(k ) 2 ˆD( k x + k h ). (7) 2 return brad@sep.stanford.edu 35