velocity analysis
DESCRIPTION
Velocity Analysis. Introduction to Seismic ImagingERTH 4470/5470. Yilmaz, ch 3.1-3.3.2. Figs 3-1 to 3-3 Velocities of sediment and sedimentary and volcanic rocks increase with depth. For sediment this is due to compaction of pore space with increasing pressure. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/1.jpg)
Velocity Analysis
Introduction to Seismic Imaging ERTH 4470/5470
Yilmaz, ch 3.1-3.3.2
![Page 2: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/2.jpg)
Figs 3-1 to 3-3•Velocities of sediment and sedimentary and volcanic rocks increase with depth. •For sediment this is due to compaction of pore space with increasing pressure. •Increase in rock velocity is due to closure of cracks with increasing pressure.
![Page 3: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/3.jpg)
Normal Moveout (NMO) Correction for Flat Layers
![Page 4: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/4.jpg)
Sho tR R
tim e
Z
to
tr
t
x
Z = h
Vh
direct a
rrival t =x/v
d
reflected arrival t r
x/2
2(x /4 +h )2 2 1/2
Normal Moveout Correction (NMO)
v
ht
v
hx
t
o
r
2
42 2
2
2/12
22
2
2
2
2
22
1
4
oor
or
vt
xtt
tv
x
v
h
v
xt
plot of tr2 vs x2 is linear
using binomial expansion we get
4
81
2
211
ooor vt
x
vt
xtt
for o
orNMOo
tvxtttand
vt
xhx 2
2
21,2 (This is the NMO correction)
For single layer (Figs. 3-4, 3-6 and 3-8). NMO depends on {x2/v2}, so we need to know v(z) in order to flatten CMP gather before stacking. For brute stack we assume a constant velocity (e.g. water) for simplificity, while knowing that this will not give a good image for deeper structures.
![Page 5: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/5.jpg)
![Page 6: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/6.jpg)
• For multiple layers, t2 = t2(0) + x2/vrms
2, so plots of t2 vs x2 will give a straight line with slope of 1/vrms.
• The root-mean square velocity (vrms) is determined by eq. 3.4 in terms of the interval velocity (vi) and travel time (Δti) of each layer interval (i). (Figs. 3.9 to 3-11)
![Page 7: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/7.jpg)
![Page 8: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/8.jpg)
For “real” data, we expect moveout of reflectors to decrease with depth (=time) as velocity increases with depth due to compaction
![Page 9: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/9.jpg)
2t t v Vrms z Vavg0 0 0
0.4 0.2 2 1.6 2 0.4 20.8 0.4 2.5 4.1 2.263846 0.9 2.251.2 0.6 3 7.7 2.533114 1.5 2.51.6 0.8 3.5 12.6 2.806243 2.2 2.75
4
Various definitions of velocity (Box6.4)
•Notice difference between vrms and vav but it is small•Note also that vnmo = vrms only for the small offset (spread) approximation (Fig. 3-22). For larger spread offsets, the best fit to flatten the actual moveout is not the same.
![Page 10: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/10.jpg)
This results in non-linear expansion of the time axis, which is greater for larger x and smaller v. This changes the frequency of the arrivals. (Fig. 3-13 and Table 3-2). When this effect becomes too large (generally in the upper 1-2 sec TWTT), we need to mute the result (Fig. 3-12). This can be done automatically for stretching greater than a certain amount, or by picking the front mutes by hand as we did to remove the refraction arrivals. (Fig. 3-14).
For continuous data (not individual picks) we need to flatten arrivals (ie remove increase in t as function of x and v) by stretching the time axis.
![Page 11: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/11.jpg)
![Page 12: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/12.jpg)
Methods for Velocity Analysis
![Page 13: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/13.jpg)
Synthetic example with 4 layers showing CMP gather, velocity spectrum and t2-x2 plots.
Spectrum is unnormalized, cross-correlation sum with a gated row plot.
![Page 14: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/14.jpg)
Real example with 4 primary layers and multiple secondary layers. Spectrum is unnormalized, cross-correlation sum with contour plot.
![Page 15: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/15.jpg)
Use of constant-velocity gathers (CVG) for a single CMP gather at various velocities to help detail exact nature of stacking velocities
![Page 16: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/16.jpg)
![Page 17: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/17.jpg)
Use of constant velocity stack (CVS) for range of gathers at different stacking velocities. Helpful in sections of low signal-to-noise (e.g. at greater depths in the section)
![Page 18: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/18.jpg)
Limitations in accuracy and resolution of velocity estimates
![Page 19: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/19.jpg)
Synthetic examples of 4 layers showing various plots of velocity spectra.
Effect of spread (offset) length
![Page 20: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/20.jpg)
Lack of long offsets reduce resolution of lower (high velocity) layers with smaller moveout
![Page 21: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/21.jpg)
Lack of near-offsets reduce resolution of shallow layers
Partial stacking (using incomplete fold) can save money (computer time) but can result in reduced resolution
![Page 22: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/22.jpg)
Reduced resolution caused by decrease in signal-to-noise
![Page 23: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/23.jpg)
![Page 24: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/24.jpg)
Effect of dipping layer
![Page 25: Velocity Analysis](https://reader038.vdocuments.us/reader038/viewer/2022102801/56814e43550346895dbbb818/html5/thumbnails/25.jpg)
Effect of dip is only significant when dip angle is large (i.e. > 20o)