1. Modeling of free-surface multiples - 2
Introduction
Long offset Faroes data: velocity analysis and demultiple
Modeling of free-surface multiple diffractions, 3D geometry
Further work
Presented at SEP meeting, April 2001, Pajaro Dunes, CA

2. East of Faroe Islands (ten 2-D lines, 1700 km total)
This map shows the location of the survey. In blue are the 2D lines acquired in 99, 5 lines in the North-South direction and 5 in the East-West direction. The line in red was acquired in 1998.
The overlay in green shows the location of the seismic data which will be displayed in the next few slides. The data consist of part of an east-west line about 70 km long and parts of north-south lines about 25 km long.

3. Pre-stack time migration
12 km
Top basalt
Intra basalt
Base basalt
This section of the 1999 data is about 60 km long. We see the main reflectors shown also on previous slides.
Next we will look closer at the area enclosed in the white rectangle and compare the 1999 to the 1998 data.
----
Locations used for depth migration: between 4000 and 6400 (these
annotations have a factor 2 with respect to slide 15)
West
East

4. Line 105 - 1999 data 7.5 km Top basalt Intra basalt Base basalt
These are the 1999 data, …. green line on the site map ….
Base basalt
7.5 km

5. Line 104 - 1998 data 7.5 km And these are the 1998 data ….
The 1998 was acquired with two boats each towing a 6 km long streamer. The shot interval for each boat was 100 m. One of the objectives of the survey was the study of locally converted PSP waves and therefore the survey acquired long offsets (up to 18 km) and long time records (up to 17 sec) .
The image displayed is obtained a post-stack migration of P-waves, from offsets in the range 0-12 km.
Toggle between slides 11 and 12:
point out different ridge structure at distance of 10 km in the North-West direction.
much improved continuity of events and resolution below basalt in the new data.
The 1998 data were considered last year as good quality data for this area.
The 1999 are significantly better. The main improvements are due to having optimized the acquisition (shot interval is 25 m in the 99 data) for multiple attenuation, velocity analysis and imaging of P-wave data.
7.5 km

6. Improved results from 1999 data
Better multiple attenuation and velocity analysis
Facilitated by small shot spacing, single cable
Pre-stack time migration
Tested on small area
Clayton’s migration-velocity analysis
Depth migration (coherency analysis and Kirchhoff)
Demultiple using Delft’s SRME

7. Clayton’s Migration-Velocity Analysis
Slant stack
Downward continuation of the wave field
Convergence criterion:
Input Velocity = Output image
Last velocity curve used to the Clayton’s migration. Allows to have events very flat.
But question : is it the real one or just one of the possible ones ?

8. Depth-Velocity model Top B Intra-B Base-B
We apply a “standard” depth imaging processing sequence.
An initial velocity model was built by depth conversion of horizons interpreted on the time section. The velocity model was iteratively refined first by coherency inversion and then by tomography, using a criterion of minimal curvature in CIP gathers.
The resulting velocity model for a section about 40 km long shows
very low velocities down to the top of the basalt ( m/sec)
a sharp increase in interval velocities within the basalt with velocities in the range of m/sec.
The velocity below basalt has been set to a lower constant velocity but has not been optimized.
The thickness of the basalt sequence in this part of the line is of the order of 3 km.
At this point there has been no geological control and interpretation of the depth model. Clearly it is necessary to continue work on the model with input from geologists in particular with respect to including faults in the model.
Base-B

9. SRME in Shot Gather Domain
TBM
WBM TB WB
WBM TB
WBM
TBM
WBM
Effects of SRME in CSG domain. The predicted multiples and the demultipled CSGs have been flipped to simplify the comparison at near offset with the raw data.
The maximum offset in this test is 9 km -- this is determined considering feathering, which is a topic that we will discuss later.
Main primaries and multiples can be seen in the input data.
Wave equation based multiple attenuation methods, like the one we have used here, are able to predict pre-critical and post-critical multiples, refracted and diffracted energy.
The data after multiple attenuation.
While a large part of the multiple energy has been suppressed, some multiple energy still present at the far offset requires a second pass of multiple attenuation (by PRT velocity filtering), before velocity analysis and imaging.
TBM
Input
Predicted multiples
Input-Predicted multiples

10. D() = P () + D () ( r W() -1 )P ()
Pi(,s,g) = D (,s,g) - ( r W() -1 ) Sx D(, s,x)P i-1(,x,g) x1
The expression above holds for 1D vertical incidence plane wave data, after transform to frequency. x2

11. Further work (from last week’s seminar)
Effect of position errors (non-coincident sources and receivers) on synthetics:
Use source and receiver positions from the field data;
Specifications for maximum feathering during acquisition
…..

12. Modeling, diffracted multiples, 3-D
Reference: Taylor & Johnston, Edinburgh Univ, SEG-99
``Fast 2-D synthetic seismograms for testing multiple removal’’

13. Modeling, diffracted multiples, 3-D
With free-surface multiples:

14. An su modeling program:

15. Test cases for the modeling program:
1 diffractor, no free-surface
1 diffractor, free-surface
2 diffractors, no free-surface
2 diffractors, free-surface

16. 1 diffractor, no free-surface

17. 1 diffractor, free-surface

18. 2 diffractors, no free-surface

19. 2 diffractors, free-surface

20. Further work
Investigate effect of feathering on demultiple for the long offset Faroes data
Corrections during computation of the multiple model
Tolerance on feathering
Look at interpolation of missing near offset traces using Radon transforms and SEP’s optimization libraries