Reflectorless tomographic migration

1
Reflectorless tomographic migration velocity
analysis
Weihong Fei and George A. McMechan
10/16/2004
2
Tomographic velocity analysis

• Introduction

• Algorithm

• Examples

• Conclusions

3
Introduction

• Traveltime tomography needs to pick the complete
  reflections over all
• offsets, which is very time-consuming,
  sometimes even not possible

• Migration-based tomography is computationally
  intensive, and need to pick
• depth residuals after each iteration

• The algorithm proposed here overcomes the
  disadvantages of these
• two methods

4
Algorithm

• Incident angle estimation and common-offset
  migration

• Ray-tracing to define the CRP gather

• Velocity update estimation for each CRP gather

• Composite velocity model update

5
Algorithm

• Step 1 Incident angle estimation and
  common-offset migration.

• 1. a common-offset section (any offset) is
  selected
• 2. time-position of the salient reflections on
  the selected section are picked
• automatically
• 3. p values at receiver positions are estimated
  by a local slant stack in the
• corresponding common-shot gather

6
Algorithm
After estimating the p values, the prestack depth
parsimonious migration is used to migrate the
picked events in the common-offset section.
The spatial location and orientation of each
reflection point is given by the parsimonious
migration.
7
Algorithm

• Step 2 Define and extract (CRP) gathers through
  ray tracing

• Shooting pairs of rays upward from the reflection
  point
• symmetrically around the local reflector normal

• On the basis of the surface intersection of the
  two rays,
• extract the corresponding CRP trace.

8
Algorithm
Only the reference finite-offset reflection
satisfies the imaging condition, the other
offsets along the same reflection in the CRP
gather will diverge in time from the reference
offset as they get farther from it. (The
difference between T and T)
9
Algorithm

• Step 3 Velocity update estimation for each CRP
  gather

• Perturb the local velocity at the reflection
  point from V0 to V1

• Calculate reflection point location perturbation
  ?l

• Update the traveltime for each ray pair in the
  CRP gather by

TnewT2?lsin(?)/v0

• Rescale the traveltime T?Tnewv1/v0

• Stack the amplitudes along traveltime trajectory
  T ?

• Repeat the perturbation

• The trajectory T?max that corresponds to the
  stacked maximum amplitude
• will be the reflection event traveltime on the
  CRP gather

• The V(T?max )-V0 will be the optimal velocity
  update for this CRP gather

10
Algorithm

• Step 3 illustration

Offset
1) TnewT2?lsin(?)/v0
2) T?Tnewv1/v0
Time
Position
sn
rn
T
T?
?
?l
Depth
11
Algorithm

• Step 4 Composite velocity model update

• The estimated velocity update for each CRP gather
  are backprojected
• along the ray path associated with the CRP
  gather

• Averaging of all the predicted updates in each
  pixel gives the update for
• that pixel for the current iteration

12
Synthetic example

• Synthetic velocity model

Correct velocity model
Estimated velocity model
Initial velocity model is constant with 1.8 km/s
everywhere
13
Synthetic example
The reflection points used to extract CRP gathers
(every fourth)
Ray density of the estimated velocity model
Low ray density zone
14
Synthetic example

• CIGs using the estimated velocity model

CIGs using initial velocity model
CIGs using estimated velocity model
15
Synthetic example
Reference common-offset section With offset 1.5
km/s
Prestack depth migration using the
estimated Velocity model
Low ray density zone
16
Field data example
Reference common-offset section with offset 313
meters
Estimated velocity, initial velocity is
constant with velocity 1.5 km/s
Prestack depth image using the estimated velocity
17
Field data example
CIGs from the position (1,2, and 3 in the
previous slide)
CIGs using initial velocity
CIGs using estimated velocity
18
Conclusion

• The traveltime picking is only limited to one
  common-offset section
• No need to pick depth residuals after each
  iteration
• Faster than migration-based tomography
• No need to define continuous analytic reflectors