Annual Report 2000 - WIT
Annual Report 2000 - WIT Annual Report 2000 - WIT
20 INVERSION BY MEANS OF CRS ATTRIBUTES The inversion algorithm uses the CRS stack attributes to back-propagate the ray associated with these attributes. 0 4.5 0 5.5 −1 4 −1 5 4.5 3.5 −2 −2 4 z [km] −3 3 z [km] −3 3.5 2.5 3 −4 −4 2.5 2 2 −5 −5 3 4 5 6 7 8 9 x [km] (a) 3 4 5 6 7 8 9 x [km] (b) Figure 1: 2-D macro-velocity model derived from a real data-set. (a) shows a velocity model with constant layer velocity. It is the mean velocity that is obtained from many traces and its corresponding attributes associated with the same event. (b) shows layers with laterally inhomogeneous velocities. The half-space beneath the last interface was filled with a constant velocity. The colour corresponds to the layer velocities [km/s]. In addition, picked ZO times divided by two, are needed to find the endpoints of the rays of one event. We use the algorithm for horizon inversion of (Majer, 2000) for continuously layers separated by smooth curved interfaces. The emergence ¡ angle determines the take-off angle of the back-propagated ray. The velocity for each indi- `gihkjmlbno d vidual ray, , of the first layer is obtained pMq no#r by . With this velocity and the &fe known ZO traveltime, the endpoint is determined. All endpoints that correspond to one picked event are used to calculate a smooth interface by means of spline approximation. In this approach, ¢¥£ is not used for constructing the interfaces. The curvature of the interfaces is computed with spline approximation. The next layers are obtained by applying the transmission law and Snell's law to the back-propagated rays associated with the next event. Now, the macro-velocity model can be built up in two alternative ways: Firstly, it can consist of layers with mean constant velocities separated by the smoothed interfaces, see Figure 1 (a). Those mean constant velocities are the arithmetic mean of all interval velocities determined for all ray segments in a layer. Secondly, the layers can have laterally varying velocities. For the first layer, e.g., the velocities are given by sgihkjtl/no pMq &fe . The layer is then filled with these velocities, see Figure 1 (b). The half- no#r space beneath the last smoothed interface is filled with a constant velocity provided by
u u u u 21 the user. To obtain a macro-velocity model, we have to execute the following four steps: Pick seismic events, extract the corresponding CRS stack attributes, smooth the attributes, and perform the inversion. PICKING OF SEISMIC EVENTS 0 CMP 2000 4000 6000 8000 0 CMP 100 200 300 400 500 600 time [s] 1 2 some picked seismic events time [s] 0.5 1.0 1.5 2.0 3 2.5 3.0 4 (a) (b) Figure 2: Two examples of simulated ZO time sections as a result of the CRS stack: (a) Synthetic data with four interfaces and constant velocity layers. The section was generated by ray tracing using a zero-phase Ricker wavelet with a peak frequency of 15 Hz. (b) Real data scaled with automatic gain control. The arrows indicate some seismic events, which where picked by the picking program we used. Here, picking means to follow a seismic (primary) reflection event from trace to trace in the time domain. The time samples of one and the same event are found by comparing the phase of adjacent traces. We pick the maximum amplitude because robust CRS stack attributes are found by a coherence analysis that is more reliable at the extrema of the wavelet than at the zero-crossings.
- Page 1 and 2: Wave Inversion Technology WIT Annua
- Page 3: Wave Inversion Technology WIT Wave
- Page 7: Copyright c 2000 by Karlsruhe Unive
- Page 11 and 12: i TABLE OF CONTENTS Reviews: WIT Re
- Page 13 and 14: Wave Inversion Technology, Report N
- Page 15 and 16: 3 theory. It relates properties of
- Page 17: Imaging 5
- Page 20 and 21: 8 two hypothetical eigenwave experi
- Page 22 and 23: 7 ¢¥£§¦©¨ ; < calculate sear
- Page 24 and 25: 7 7 searches ¡ HNJOL for ¢IHNJML
- Page 26 and 27: 14 Trace no. 1000 1500 2000 0.5 1.0
- Page 28 and 29: 16 CDP number 3100 3000 2900 2800 2
- Page 30 and 31: 18 REFERENCES Höcht, G., de Bazela
- Page 34 and 35: 22 For synthetic data, it is easy t
- Page 36 and 37: — J J J J J J G J - J J G
- Page 39 and 40: Wave Inversion Technology, Report N
- Page 41 and 42: · · v 0 B 0 £ & Ä Ã & v
- Page 43 and 44: 31 Dürbaum, H., 1954, Zur Bestimmu
- Page 45 and 46: Ã Ø Ì 0 0 Ì 4 0 Ã 0 G ' 4
- Page 47 and 48: Wave Inversion Technology, Report N
- Page 49 and 50: 0 0 ˜ ” Z ˜ ” Z 4 4
- Page 51 and 52: 39 strategy by combining global and
- Page 53 and 54: 41 elled data is presented in Figur
- Page 55 and 56: 43 0.2 Distance [m] 1000 1500 2000
- Page 57 and 58: 45 In Figure 10 we have the optimiz
- Page 59: 47 Gelchinsky, B., 1989, Homeomorph
- Page 62 and 63: § ¢ ø ø for a paraxial ray, ref
- Page 64 and 65: Œ § … Z ‹ Z § õ ø \ ø §
- Page 66 and 67: 54 As stated in Hubral and Krey, 19
- Page 68 and 69: § ó § 56 sequence. We made tes
- Page 70 and 71: 58 precision of the modeled input d
- Page 72 and 73: 60 Cohen, J., Hagin, F., and Bleist
- Page 75 and 76: Wave Inversion Technology, Report N
- Page 77 and 78: £ 65 The details of the theory inv
- Page 79 and 80: 67 of the figure. On both sides, a
- Page 81 and 82: 69 (a) (b) Depth (m) 600 800 Depth
20<br />
INVERSION BY MEANS OF CRS ATTRIBUTES<br />
The inversion algorithm uses the CRS stack attributes to back-propagate the ray associated<br />
with these attributes.<br />
0<br />
4.5<br />
0<br />
5.5<br />
−1<br />
4<br />
−1<br />
5<br />
4.5<br />
3.5<br />
−2<br />
−2<br />
4<br />
z [km]<br />
−3<br />
3<br />
z [km]<br />
−3<br />
3.5<br />
2.5<br />
3<br />
−4<br />
−4<br />
2.5<br />
2<br />
2<br />
−5<br />
−5<br />
3 4 5 6 7 8 9<br />
x [km]<br />
(a)<br />
3 4 5 6 7 8 9<br />
x [km]<br />
(b)<br />
Figure 1: 2-D macro-velocity model derived from a real data-set. (a) shows a velocity<br />
model with constant layer velocity. It is the mean velocity that is obtained from many<br />
traces and its corresponding attributes associated with the same event. (b) shows layers<br />
with laterally inhomogeneous velocities. The half-space beneath the last interface was<br />
filled with a constant velocity. The colour corresponds to the layer velocities [km/s].<br />
In addition, picked ZO times divided by two, are needed to find the endpoints of<br />
the rays of one event. We use the algorithm for horizon inversion of (Majer, <strong>2000</strong>) for<br />
continuously layers separated by smooth curved interfaces. The emergence ¡ angle<br />
determines the take-off angle of the back-propagated ray. The velocity for each indi-<br />
`gihkjmlbno<br />
d vidual ray, , of the first layer is obtained pMq no#r by . With this velocity and the<br />
&fe<br />
known ZO traveltime, the endpoint is determined. All endpoints that correspond to one<br />
picked event are used to calculate a smooth interface by means of spline approximation.<br />
In this approach, ¢¥£ is not used for constructing the interfaces. The curvature of<br />
the interfaces is computed with spline approximation. The next layers are obtained by<br />
applying the transmission law and Snell's law to the back-propagated rays associated<br />
with the next event.<br />
Now, the macro-velocity model can be built up in two alternative ways: Firstly, it<br />
can consist of layers with mean constant velocities separated by the smoothed interfaces,<br />
see Figure 1 (a). Those mean constant velocities are the arithmetic mean of all<br />
interval velocities determined for all ray segments in a layer. Secondly, the layers can<br />
have laterally varying velocities. For the first layer, e.g., the velocities are given by<br />
sgihkjtl/no<br />
pMq &fe<br />
. The layer is then filled with these velocities, see Figure 1 (b). The half-<br />
no#r<br />
space beneath the last smoothed interface is filled with a constant velocity provided by
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