Yin Huang s Thesis, and Computing Gradients. William Symes

Transcription

1 Yin Huang s Thesis, and Computing Gradients William Symes

2 Yin Huang PhD student in TRIP: Thesis: Born Waveform Inversion in Shot Coordinate Domain Currently: Amazon, Seattle

3 Chapter 2 Born waveform inversion via shot record extension, variable projection, differential semblance [SEG 2015]

4 Chapter 2 Task: estimate Marmousi from homog. initial guess

5 Chapter 2

6 Chapter 2

7 Chapter 2

8 Chapter 2

9 Chapter 2 Bottom line: works, but slow 18 VP its 50 CG iterations - way too much

10 Chapter 3 Flexibly Preconditioned Extended Least Squares Migration in Shot Record Domain Joint with Rami Nammour - in Geophysics

11 Chapter 3 Task: use ΨDO scaling to precondition inner problem

12 Chapter 3 ΨDO scaling - Nammour 09, uses Bao-S. 96 Estimate amplitude by 2 Hessian ops Flexibly Preconditioned CG

13 Chapter 3

14 Chapter 3

15 Chapter 3

16 Chapter 3 Bottom line: speedup by factor of 3-4 Much better inner solve with same effort

17 Chapter 4 Task: evaluate effect of FPCG/CG inner solve on gradient accuracy

18 Chapter 4 Fast lens over flat reflector Computed gradient at const background model

19 Chapter 4 Relative error in J[m + hδm] J[m hδm] 2h as approx to J[m], δm

20 Chapter 4

21 Chapter 4 Bottom line: not so hot Why? Look to nature of tomo op

22 Chapter 4 J[m] = min r 1 2 F [m[r] d 2 + α 2 Ar 2 J[m] = DF [m](f [m]r d, r) fact: DF [m] is badly scaled (unbounded)

23 Chapter 4

24 Chapter 4

25 Chapter 4

26 Chapter 4

27 Chapter 4

28 Chapter 4 Order of DF = Order of F + 1 Convergent inner solve not sufficient for convergent computed gradient

29 Convergent Gradients Key ingredients: parametrix = asymptotic inverse robust optimization

30 Convergent Gradients Computable parametrices exist - subsurface offset extn some source extns

31 Convergent Gradients Example: subsurface offset acoustic Born (Hou &S. Geophys. 15) F [v] = modeling op, velo v F [v] = asympt inverse = W m [v] 1 F [v] T W d [v]

32 Convergent Gradients Weight ops W m, W d are filters - cheap, no raytracing or PDE solves Makes F almost unitary in weighted norms

33 Convergent Gradients Modeled data d = F [v]r

34 Convergent Gradients Data residual F [v]f [v] d

35 Convergent Gradients means (roughly): F [v] F [v] = I + S[v], S[v] is smoothing (suppresses HF signal) of order -1

36 Convergent Gradients Ignoring regularization, α 0 limit is min J[v] = 1 2 Ar[v] 2 : subj F [v] F [v]r[v] = F [v] d some algebra (see paper in TRIP16)...

37 Convergent Gradients and ignoring second LS problem, J[v] = DF [v] (d, A Ar[v]) trouble: r[v] r approx

38 Convergent Gradients F [v] F [v]r[v] = r[v] + S[v]r[v] = F [v] d so r[v] = F [v] d S[v]r[v]

39 Convergent Gradients order +1/-1: J[v] DF [v] (d, A AF [v] d) +DF [v] (d, A AS[v]r approx ) First term: Jie s appinv gradient; second term: correction for inner inversion

40 Convergent Gradients can compute S[v] = I F [v] F [v]! [grad error] [error in r]

41 Convergent Gradients more huffing and puffing: [Error in J] [K error in normal eqn] more trouble: no explicit control of K

42 Convergent Gradients Heinkenschloss-Vicente 01: variant of trust-region qn step length control: short enough step is near steepest descent so always works

43 Convergent Gradients H-V01: converges with inexact grad, provided [grad error] K max( approx grad, step bound) our case: [error in normal eqn] max(...)

44 Convergent Gradients Upshot: assure convergence via parametrix control grad error couple grad error to step control

45 Conclusion Inversion: practical reliable, efficient Yin s thesis: shot record LSM accel., clarified reliability issues with EFWI for separable EFWI: critical requirement is computable parametrix couple accuracy and step control

46 Thanks to... our sponsors present and former TRIPpers many colleagues developers of SU, Madagascar TACC & RCSG