automatic selection of reference velocities for recursive depth migration hugh geiger and gary...
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Automatic selection of reference velocities for recursive depth migration
Hugh Geiger and Gary Margrave
CREWES Nov 2004
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POTSI* Sponsors:
*Pseudo-differential Operator Theory in Seismic Imaging
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The problem:• Many recursive wavefield extrapolators require
a limited set of reference velocities for efficient implementation
• How should these reference velocities be chosen?
example velocity profiles
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Objectives:• Efficient computation
- a minimum number of reference velocities• Accurate wavefield extrapolation
- reference velocities ‘close’ to model velocities
too few reference velocities?
~3000 ms-1 (~230%)
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Some specific requirements• PSPI – lower and upper bounding velocities
(vmin,vmax)- ideally minimize large interpolations (wavefield is a weighted summation)
• Split-step – more accurate focusingwith a slower velocity
too many reference velocities?
~80 ms-1 (~ 5%)~70 ms-1 (~ 4%)~70 ms-1 (~ 4%)
~320 ms-1 (~ 17%)
~40 ms-1 (~ 2%)
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Basic approach 1: Linear progression• choose an approximate velocity spacing dV
nV=round((vmax-vmin)/dV)
vstep=(vmax-vmin)/nV• what is a good choice for dV?
- empirical testing required- reasonable for both low and high velocities?
~500 ms-1 (~20%)
~500 ms-1 (~10%)
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(detail forsubsequent figures)
Basic approach 2a: Geometric progression• choose an appropriate percentage step vprcnt
v(i) = (1+vprcnt)*v(i-1)- Kessigner (1992) recommends vprcnt=0.15
- start at vmin for profile?- start at vmin for complete velocity model?
(perhaps if using lookup tables)
~370 ms-1 (~15%)
~750 ms-1 (~15%)
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Statistical method of Bagaini et al (1995)• choose a preliminary dv (geometric?)• equally spaced bins over vmin:vmax (e.g. nBtemp = 6)
• bin the velocities to give probability density Pi, Pi = 1
• optimal number of bins by statistical entropy S= PilogPi
nBopt = round(exp(S)+0.5) (e.g. nBopt = 5)
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• calculate cumulative probability distribution Yi, Yi = Pi
• each optimal bin to hold 1/nBopt (e.g. 0.2)- start at vmin
- linearly interpolate from temporary bin boundaries (e.g. at 0.2, 0.4, 0.6, 0.8)
• Is this optimal? - bins not necessarily close to peaks
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New peak search method• cluster velocities
- new cluster where jump exceeds vprcntmax
• Now, within each cluster:
• use Bagaini method for optimal number of bins nBopt
• create a new probability distribution with finer bins
• descending sort of Pi’s, choose all Pi’s where Pi < 0.9
• place vtemp at all Pi’s, include vmin,vmax
• use ‘greedy search’ to combine closely spaced Pi’s
- start search at bin spacing of 1, then 2, etc.- weighted linear average to move vtemp
• stop when at vtemp= nBopt
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Marmousi bandlimited reflectivity
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PSPI with velocity clustering algorithm
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –60msshot: ricker fdom 24 ghost array phsrot –68 (to zp) whiten [4 16 35 60]
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Marmousi bandlimited reflectivity
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Marmousi shallow reflectivity
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Linear
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Geometric
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Bagaini
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Peak Search
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Modified Bagaini: clusters
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Marmousi shallow reflectivity
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Linear
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Geometric
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Bagaini
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Peak Search
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Modified Bagaini: clusters
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Static shifts – affect focusing
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a) source wavefield in (x,z,t) b) reflected wavefield in (x,z,t)
x
z
t
zx
z
t
c) direct + reflected arrival at z=0 d) another perspective of (c)
xz
t
xt
(figures courtesy J. Bancroft)
horizontal reflector (blue)
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z=0
z=2
z=3
z=4
z=1
x
t
reflector
With a static shift of the source and/or receiver wavefield,the extrpolated wavefields will not be time coincidentat the reflector, causing Focusing and positioning errors.
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rec arraysource array
hard water bottom
free surface
Complications for Marmousi imaging:•free-surface and water bottom ghosting and multiples modify wavelet•source and receiver array directivity•two-way wavefield, one-way extrapolators•heterogeneous velocity
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220m
32m28m
0mx=400m
v=1500m/s ρ=1000kg/m3
v=1549m/s ρ=1478kg/m3
v=1598m/s ρ=1955kg/m3
v=1598m/s ρ=4000kg/m3
x=0m
Marmousi source array: 6 airguns at 8m spacing, depth 8m receiver array: 5 hydrophones at 4m spacing, depth 12m
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reflector
downgoing transmitted wave
upgoing reflected wave
receiver array @ 45ºreceiver array @ 0º
Modeled with finite difference code (courtesy Peter Manning) to examine response of isolated reflector at 0º and ~45º degree incidence
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normal incidence reflection
~45 degree incidence reflection
~60ms ~60ms
desired 24 Hzzero-phase Ricker wavelet
Marmousi airgun wavelet
After free-surface ghosting and water-bottom multiples, the Marmousi airgun wavelet propagates as ~24 Hz zero-phase Ricker with 60 ms delay.
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• The deconvolution chosen for the Marmousi data set is a simple spectral whitening followed by a gap deconvolution (40ms gap, 200ms operator)
• this yields a reasonable zero phase wavelet in preparation for depth imaging
Deconvolution
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• the receiver wavefield is then static shifted by -60ms to create an approximate zero phase wavelet
• if the receiver wavefield is extrapolated and imaged without compensating for the 60ms delay, focusing and positioning are compromised, as illustrated using a simple synthetic for a diffractor
diffractor imaging with no delay diffractor imaging with 60ms delay
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reflectivity x: 4000-6000 z: 0-1000
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PSPI whiten [4 16 35 60] cvel .2% clip 6
data: deconpr 50 13 .0002 whiten [4 16 35 60] static 0msshot: ricker fdom 24 ghost array phsrot –68 (to zp) unwhiten
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PSPI whiten [4 16 35 60] cvel .2% clip 6
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –16msshot: ricker fdom 24 ghost array phsrot –68 (to zp) unwhiten
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PSPI whiten [4 16 35 60] cvel .2% clip 6
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –32msshot: ricker fdom 24 ghost array phsrot –68 (to zp) unwhiten
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PSPI whiten [4 16 35 60] cvel .02% clip 6
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –56msshot: ricker fdom 24 ghost array phsrot –68 (to zp) unwhiten
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PSPI whiten [4 16 35 60] cvel .02% clip 6
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –56msshot: ricker fdom 24 ghost array phsrot –45 (to zp) whiten [4 16 35 60]
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Marmousi bandlimited reflectivity- shifted to match Zhang et al.
(2003)
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Zhang et al. (2003) – positioning not accurate
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PSPI reference velocities: peak search- shifted to match Zhang et al.
(2003)
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Marmousi bandlimited reflectivity (as before)
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Marmousi shallow reflectivity
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Marmousi target reservoir
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Marmousi target reservoir
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Marmousi target reservoir
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Marmousi target reservoir
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Marmousi target reservoir
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Marmousi target reservoir
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V=3000m/sV=2000m/s
cos taper 70°-87.5°
PSPI creates discontinuities at boundaries – smoothing may be good!
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Conclusions• Preprocessing to zero phase, shot
modeling, and correction of static shifts important for imaging
• Optimal selection of reference velocities desired to maximize accuracy and efficiency of wavefield extrapolation
• Linear or geometric progression does not take into account distribution of velocities
• Bagaini et al. method does not necessarily pick reference velocities close to model velocities
• New peak search method selects reference velocites close to model velocities
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Conclusions (cont)• However, Bagaini method performs well
on Marmousi!• Our PSPI implementation provides a good
standard for judging our other algorithms
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(-60ms static + 16.67m down)
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-56ms static + 8.33m down
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(-56ms static + 8.33m down)
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reflectivity x: 3000-8500 z: 0-3000
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Shift down 8.33m
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PSPI whiten [4 16 30 55] cvel .2% clip 4
data: deconpr 50 13 .0002 whiten [4 16 35 60] static –60msshot: ricker fdom 24 ghost array phsrot –68 (to zp) whiten [4 16 35 60]