1. A Migration Approach to Generating Continuous Images of Salt and Sediment Boundaries from Multi-Offset VSP Data
Jakob B.U. Haldorsen1, Nicholas Brooks1, Pat Donais2, Werner Heigl2, Fred Li3 1 2 3
Microview Technology Inc
Presented at 14th SBGf International Congress, Rio de Janeiro, Brazil, August 3-6, 2015

2. Salt-Proximity Survey – Conventional
Objective:
Sidetrack to tap oil trapped against salt flank
It is of utmost importance to know the exact location of the salt flank
Seismic Technique:
The objective is to find the location of a single - unknown but significant - formation interface
Position Seismic Source above salt
Shoot through salt to geophones near salt flank
Gyro and rigid interconnects gives the orientation of geophones
Hodogram analyses give arrival angles
Adjust salt to match angles and velocity
Gives scattered exit points
Expensive, risky and unreliable
No good alternatives until now
Tools, Rigid Interconnects and Gyro

3. Apache, Midway Dome, MS
Objective: Drill along the salt flank to produce attic oil trapped along the flank of the salt dome
Problem: where is the salt dome?
Surface-Seismic
Image

4. Salt-Flank Imaging
The objective is to find the location of a single - unknown but significant - formation interface
One can locate the salt flank by Full Vector Reverse-Time Migration
However, in the next few slides I will
develop a simple – and somewhat simplistic and simple-minded – fast process, a “Ray-Based RTM”
verify the process by applying it to synthetic data generated over a known, isotropic salt model
apply the process to field data acquired by Apache, near the Midway Dome, MS, US
Compare the results of applying the Full Vector Reverse-Time Migration with the much faster “Ray-Based RTM”

5. Continuous Salt Flank Imaging (CSFI)
The question asked is the same as the one asked for a traditional salt-proximity survey and the answer is constrained by the same physics
Measurements:
waveforms
travel times
polarization of the wave field arriving at the receivers
velocities on the two sides of the interface
Question:
what is the location of the interface such that much of this information make sense?

6. Two Basic Tools Migration Deconvolution
Migration operator sorts out the relationship between geometry (locations of source/receiver/scatterer) and time (this is what the wave equation is for…)
Allows a decomposition of the data into orthogonal, elemental wave-field components (compressional and two shears)
Allows the estimation of possible primary and scattered wave fields at each point in subsurface
Deconvolution
Imaging Condition for migration, requiring that the reconstructed source and scattered waveforms are
simultaneous
similar

7. “Ray-based RTM”
The process makes the following useful and simplifying assumptions:
The source function at a point (x,y) in image space can be approximated by the source signature convolved with a propagation operator
All propagation operators are simple delay operators
The sequence of multiples and other periodicity in the source wave field is invariant over the entire image space
Assumption 3) allows one to use the direct wave field, as estimated from the three-component VSP receiver array, as an approximation to the source signature
Assumptions 2) and 3) are not independent, as the source signature estimated from the VSP data will include some of the more complex components of the wave-field propagators. However, it could be argued that this will relax some of the impositions from assumption 2) and reduce some of the obvious multiples seen in the data

8. Vector Projections
P and S waveforms, scattered at a point x in space, and recorded at receiver n after a time tP,S(x,xn):
f P,S are the scattered wave fields
d are the recorded data and pS,V are the ray vectors at the receivers for the rays connecting the scattering point with the receiver
The scattered P is polarized along the ray, the scattered Sv and Sh are polarized perpendicular to the ray - and all are mutually orthogonal (Haldorsen et al., SBGf 2013)
scattering point

9. “Ray-Based RTM”, PP At any point x in image space:
propagate the source function f P(ω;x) forward in time through the source-side velocity model from the source location to x
propagate the P projection of the recorded signal backward in time from each receiver n through the receiver-side velocity model from the receiver location to x
correlate the source-side and the receiver-side estimates of the primary fields, f Ps(ω;x) and fnPr(ω;x), apply inverse FFT, keeping only the t=0 values (i.e., sum over ω), sum over all receivers

10. “Ray-Based RTM”, PP Substituting, and re-arranging terms
Semblance-weighted deconvolution (= energy-normalized correlation) should give better resolution
Total Travel Times
Deconvolved data
Projection Operator

11. Semblance-Weighted Deconvolution: Multi-Trace Optimal Filter (Haldorsen, Miller, and Walsh, Geophysics, 1994)
Processing model
Filter objectives
spike signal
minimize noise
Analytic Solution
The model that we use is the same that is underlying conventional processing. The recorded traces contain copies of an effective source field, shifted in time, plus some other stuff, which conveniently can be called noise. The least-squares estimate of f is the average of the traces after aligning the first brakes.
Rather than looking for the source signature by itself, we look for an estimate of an inverse filter with two objectives in mind. We want to spike the signal, and we want to minimize the noise terms. The least-squares solution is given here as the conventional inverse to f modified by the ratio of coherent to the incoherent energy, or the semblance. This filter is extensively treated by Haldorsen, Miller and Walsh in a paper published in Geophysics in 1994.
As we’ll see, this filter reduces the deconvolution to a hands-off process

12. Deconvolved Signal
The model that we use is the same that is underlying conventional processing. The recorded traces contain copies of an effective source field, shifted in time, plus some other stuff, which conveniently can be called noise. The least-squares estimate of f is the average of the traces after aligning the first brakes.
Rather than looking for the source signature by itself, we look for an estimate of an inverse filter with two objectives in mind. We want to spike the signal, and we want to minimize the noise terms. The least-squares solution is given here as the conventional inverse to f modified by the ratio of coherent to the incoherent energy, or the semblance. This filter is extensively treated by Haldorsen, Miller and Walsh in a paper published in Geophysics in 1994.
As we’ll see, this filter reduces the deconvolution to a hands-off process
The deconvolved estimated signal has the spectrum of the semblance!
The results are inherently stable

13. Raw VSP Data
Raw data appear to be quite noisy
duration 14s
bandwidth?

14. Correlated VSP Data Field data, correlated with the reference signal
Excellent quality
duration 2s
bandwidth Hz

15. Deconvolved VSP Data
Excellent quality
duration 2s
bandwidth Hz

16. “Ray-based RTM”
The process makes the following useful and simplifying assumptions:
The source function at a point (x,y) in image space can be approximated by the source signature convolved with a propagation operator
All propagation operators are simple delay operators
The sequence of multiples and other periodicity in the source wave field is invariant over the entire image space
Assumption 3) allows one to use the direct wave field, as estimated from the three-component VSP receiver array, as an approximation to the source signature
As the weighted correlation (“semblance-weighted deconvolution”) does not suffer from the instabilities normally associated with a deconvolution process, this process is suitable for an automatic process

17. “Ray-based RTM” In a more complete, formal treatment,
The Green’s functions are not simple time delay operators
The reconstructed wave fields at a point x will have strong directional dependencies caused by
radiation patterns associated with the source and receivers
aperture effects from source and receivers
the distribution of sources and receivers …
The deconvolved data segment depends on the differences in wave number vectors between the reconstructed source and reconstructed scattered wave fields
Uneven distribution of these wave-number vector differences will strongly affect the ability to image a point as a point

18. 2D Synthetic Data of a Simple Salt Flank

19. *
source
Velocity Model
receivers

20. 2D Synthetic Data

21. Salt-flank Imaging
Here we aim at finding the location of a single - unknown but significant - formation interface, located transversally to the direct source/receiver ray path
We have to assume that we do not know a priory where the salt flank is!

22. Source-side Velocities, “Salt-Flood”

23. Receiver-side Velocities, “Sediment-Flood”

24. Ray-Based Image from Synthetics, Raw Data

25. Ray-Based Image from Synthetics, Deconvolved Data

26. Salt-Flank Model

27. Comments
Both the raw (“correlated”) and deconvolved synthetic data give the correct location of the salt interface
The deconvolved synthetic data give higher resolution - however with some artifacts related to the apparent “ringing” in the deeper part of the data.

28. Apache, Midway Dome, MS
The data acquired in a deep well near the Midway Dome, on land in Mississippi, USA
The survey included 3 source points
Salt-Image VSP, source offset such that rays were penetrating through the salt
Zero-Offset VSP
Fixed-Offset VSP
Source: 60,000 Ib vibrator, linear Hz sweep
Data: from 15,725 ft to MSL, at 50 ft interval
More than 250 levels for each source position

29. Apache, Midway Dome, MS
Objective: Drill along the salt flank to produce attic oil trapped along the flank of the salt dome
Problem: where is the salt dome?
Surface-Seismic
Image

30. Apache, Midway Dome, MS
The geometry of the well and the three shot points in relation to the assumed salt body
Surface-Seismic
Image

31. Original Model From Apache
PSDM Velocity Model Used for Initial Ray Tracing
Ray Tracing Model with updated salt flank (after first penetration) and top salt from well control

32. OVSP
In the following slides, we show the results of using the “fixed-offset” data and “Ray-Based RTM” to image the salt interface

33. OVSP: Stacked (Correlated) Data
East
North
Vertical

34. Deconvolution Process
Raw data
correlate with
nominal sweep
pick
break times
semblance-
weighted
deconvolution
final image
Deconvolution Process

35. Average Estimated Raw, Uncorrelated Down P

36. Average Amplitude Spectrum, Down P

37. Average Semblance Spectrum, Down P

38. Frequency-Time Analysis, Synthetic Signature

39. Frequency-Time Analysis, Estimated Signature
Harmonics
Primary signal

40. Stacked (Correlated) Data
East
North
Vertical

41. Deconvolved Total Data
Radial
Transverse
Vertical

42. Deconvolved, Residual Data
Radial
Transverse
Vertical

43. Two-Way-Time Corrected Data
Radial
Transverse
Vertical .
dipping
reflectors
P reflections, steep dips
Sv conversions,
steep dips

44. Comments
For the wave-field components presumably scattered off of the steeply dipping structures
P is on the horizontal components
Sv is on the vertical components
This is consistent with horizontally propagating wave fields

45. Full Vector Reverse-Time Migration
Gray background is surface-seismic image
Red 3D rendering of the salt-exit points is obtained by a Full Vector Reverse-Time Migration (not the fast ray-based method) from the “Salt-Image” VSP

46. “Ray-Based RTM”, PP Reflections
The multi-colored background image is obtained by “Ray-Based RTM” from the OVSP, assuming PP reflections

47. “Ray-Based RTM”, PS Conversions
The multi-colored background image is obtained by “Ray-Based RTM” from the OVSP, assuming PS conversions

48. ZOVSP
Orange insert is steep-dip image obtained by “Ray-Based RTM” from the ZOVSP data
Confirms and extends the Full Vector Reverse-Time Migration image to shallower depths

49. Conclusions
The Full Reverse-Time Migration locates the deeper section of the salt flank as a continuous 3D interface from the “Salt-Image” VSP dataset
Images obtained by applying the much faster, “Ray-Based, Reverse-Time Migration”, applied to the ZOVSP and FOVSP give additional information about
shallower part of salt flank
steeply dipping sediments adjacent to salt body
The resulting images are being used to enhance the processing and interpretation of the surface-seismic data and to reduce future drilling risk around the Midway Dome