Migration velocity analysis using multifocusing/crs attributes based on paraxial raytracing

Transcription

1 Migration velocity analysis using multifocusing/crs attributes based on paraxial raytracing Tijmen Jan Moser Fugro-Jason, The Netherlands 29 September 24 Charles University, Prague, Czech Republic

2 Biography masters degree Geophysics, State University of Utrecht, The Netherlands (Nolet) PhD, "Shortest path method for seismic ray tracing in complicated media" State University of Utrecht, The Netherlands (Helbig, Nolet) Postdoc Amoco, Tulsa, OK (Gray, Treitel) Institut Français du Pétrole and Institut de Physique du Globe, Paris (Lailly, Madariaga, Tarantola) Institute of Solid Earth Physics and Norsk Hydro (Hanyga, Pajchel) Alexander von Humboldt fellow -Karlsruhe (Hubral, Karrenbach, Shapiro) Geophysical Institute of Israel/Norsk Hydro (Landa, Keydar, Gelchinsky, Pajchel) 2-present - Fugro-Jason

3 . Prestack depth migration 2. Multifocusing/Common reflection surface stack 3. Migration velocity analysis 4. MVA using MF/CRS and paraxial raytracing

4 . Prestack depth migration Diffraction stack (A unified approach to 3-D seismic reflection imaging, Part II: Theory. [Geophysics 6, 759 (996)]. Tygel et al.) where V (x) image, x subsurface point x S, x R source, receiver points U(x S, x R, t) (prestack) seismic data A weighting factor V (x) = dx Sdx R AU(x S,x R,T(x S,x,x R )) T (x S, x, x R )(multivalued) traveltime from source to image point to receiver point in a presumed known Earth model Image formula from first Born approximation Background velocity model c(x), first order perturbation δ ( c(x) ). 2 ΣΣ A(x S, x, x R ) U(x S, x R, T (x S, x, x R )) V (x) = δ ( c(x) ) = x S xr 2 ΣΣ A(x S, x, x R ) 2 x S xr A(x S, x, x R )product of amplitudes from x S to x and from x to x R.

5 Marmousi model km/s Smoothed version for ray tracing km/s c(x, y, z) = ΣΣ i j Σ c ijk B i (x)b j (y)b k (z) k

6 Shot gather at 4 km offset(km) time(s) Near-offset (2m) gather time(s)

7 Green s functions at four different locations (color scale: cos(5t))

8 Marmousi prestack depth migrated image

9 2. Multifocusing (MF)/Common reflection surface (CRS) stack Purpose: optimal zero-offset stack in time domain by finding traveltime surface in supergather domain with highest stack/semblance + useful attributes Multifocusing (Landa et al., Applications of multifocusing method for subsurface imaging: J. Appl. Geoph., 42, , 99) S C G P β R N Multifocus move-out = traveltime difference SRG - CNC Traveltime difference SRP - CNP Traveltime difference PG - PC τ = τ + + τ - τ + = (R + ) 2 + 2R + X S sin β + XS 2 R + V τ - = (R - ) 2 2R - X S sin β + XG 2 R - V R + = + σ R N + σ, R NIP R - = σ σ R N R NIP σ = X S X G X S + X G + 2 X S X G R NIP sin β Exact for constant velocity and circular reflector

10 Common Reflection Surface stack (Jaeger et al., Common-reflection-surface stack: Image and attributes, Geophysics, 66, 97-9, 2) β β R NIP R N CRS move-out t 2 (x m, h) = (t + 2sin β (x V m x )) 2 + 2t cos 2 β ( (x m x ) 2 + h2 ) V R N R NIP Exact for constant velocity and planar reflector

11 x = (x S + x R )/2, h = (x R x S )/2 x h x S x R Second-order hyperbolic traveltime expansion in cdp x and offset h: T 2 (x, h) = T 2 + (T h) 2 T h + (T x) 2 T x + 2 ht (T hh)h 2 + x T (T xh)h xt (T xx)x 2 = Drop linear terms in h: T 2 + 2T T x T x + 2 ht (2T h T h T + 2T T hh )h + 2 xt (2T x T x T + 2T T xx )x = T h = and T x = p: T 2 + 2T p T x + T h T T hh h + x T pp T x +T x T T xx x = T hh = M NIP and T xx = M N : (T + p T x) 2 + T h T M NIP h + T x T M N x = 2D: (T + p x x) 2 + m NIP T h 2 + m N T x 2 β, R NIP, R N or p x, m NIP, m N are found by a 3-parameter optimisation of signal semblance along the surface T (β, R NIP, R N )ort(p x,m NIP, m N )-for each x and each T. supergather R NIP = R N diffractions!

12 Semblance S S = N ΣU(x i, h i, T (β, R NIP, R N )) 2 i N N ΣU(x i, h i, T (β, R NIP, R N )) 2 i x i, h i all cdp s and offsets close to the central ray Properties. S 2. S = ifall U are equal. 3. the more random U, the closer S to. 4. S is singular for U. Typically, the result of MF/CRS optimisation is three attribute sections:. R NIP (x, T ) 2. R N (x, T ) 3. β (x, T ) Stacking over the optimal traveltime surfaces results in enhanced stack.

13 Marmousi supergather - S =. 9. trace # time(s)

14 3. Migration velocity analysis Common Image Gathers offset depth distance common offset gather common image gather h S2 S R R2 far z z z depth CIG offset Flatness of events in CIG Stacking power Σ V (x) 2 maximal image

15 offset(km) -2 - offset(km) x=4. km 3. x=6.4 km offset(km) -2 - offset(km) x=5.2 km 3. x=8. km

16 Practical aspects of migration velocity analysis layer stripping horizon/event picking local global CPU adequate parametrisation

17 4. Migration velocity analysis from CRS/MF attributes Invert {R N (x, t), R NIP (x, t), β (x, t)}-sections into a smooth velocity model c(x). Problems Theoretical relationship between c(x) and {R N (x, t), R NIP (x, t), β (x, t)}? Based on raytheory? Partial differential equation for c(x)? {R N (x, t), R NIP (x, t), β (x, t)}-sections contaminated with numerical noise Sharp focusing criterion for velocity/image quality + efficient way to compute it + efficient way to optimize it

18 Proposals combination of CRS/MF analysis and inversion into one step optimize focusing criterion for smooth velocity distributions using paraxial N and NIP rays. assumption: velocity contours are locally parallel to reflecting interfaces instead of picking, do this for each point of a raster

19

20 "rays.clip" "contourlines" "rays" "contourlines"

21 Initial conditions at a point x Central ray p = c c 2, x T = H p, p T = H x, Π= x x p x x p p p = I O O I. Velocity contour c(x) = c(x ) x = x + g u + 2 g 2u 2, where g unit vector perpendicular to c, and = g T c g + c T g 2. Paraxial NIP rays Q = (x u, x T ) = (, x T ), P = p u, p T = g, p T. Paraxial normal rays p(u) = Rx u c(x(u)) x u Q = (x u, x T ) = g, x T, P = p u, p T. "brute force" differentiation p u = u Rx u c(x(u)) x u + Rx u u c(x(u)) x u + Rx u c(x(u)) u x u better: define Then W: = p T g 2 g T p T P = Q T W g T p T x T T p T.

22 Observations accuracy is an issue in Marmousi model (for small degrees of smoothing) ray tracing algorithms preserving symplecticity (implicit Runge-Kutta) testing of paraxial quantities cumbersome automatic differentiation of computer code

23 "rays" "contourlines" time(s) "tt_nip_ray" "tt_nip_parax" log(time) log(offset) "tt_nip_parax-ray" "ttpow2" "ttpow3"

24 -.5 "rays" "contourlines" time(s) "tt_n_parax" "tt_n_ray" log(time) log(offset) "tt_n_parax-ray" "ttpow2" "ttpow3"

25 Marmousi supergather - S =. 53 -max. offset =.5 km trace # time(s)

26 Algorithm I. for each raster point, compute central ray from velocity contour to surface + M N + M NIP (diverging rays rejected). 2. collect all traces from the prestack data set with source and receiver point "around" the central ray emergence point. 3. construct MF/CRS traveltime surface 4. evaluate stack/semblance 5. compute "total" stack/semblance Algorithm II. generate velocity fields 2. apply Algorithm I to evaluate "total" stack/semblance 3. optimise stack/semblance

27 Average stacking power 3e+7 "REPORT_SMOOTHING_Stacking_power" 2.5e+7 2e+7.5e+7 e+7 5e Degree of smoothing Average semblance.2 "REPORT_SMOOTHING_Semblance" Degree of smoothing Average stacking power 3e+7 "REPORT_PERTURBATION_Stacking_power" 2.5e+7 2e+7.5e+7 e+7 5e % of perturbation Average semblance "REPORT_PERTURBATION_Semblance" % of perturbation