1. Modeling of free-surface multiples
Using the data as modeling operator:
Tutorial
Case study example
Discussion
Presented at SEP meeting, April 2001, Pajaro Dunes, CA

2. = shot = receiver sea surface reflector
Slide 2. Basic concept of surface multiple attenuation.
reflector

3. D() = P () + D () ( r W() -1 )P ()
 : frequency
D = Data
P = Primaries (data in experiment without free surface)
W = Acquisition wavelet
r = Reflection coefficient at free surface
The expression above holds for 1D vertical incidence plane wave data, after transform to frequency.

4. = shot = receiver sea surface reflector
Slide 2. Basic concept of surface multiple attenuation.
reflector

5. 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

6. Model of free-surface multiples at location SG
Prepare two-sided shot gathers at locations S and G
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
The model consists of a dipping seafloor and the free-surface.
The vertical axis is time in sec, the horizontal axis is in meters.

7. Model of free-surface multiples at trace GS
Prepare two-sided shot gathers at locations G and S
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
Overlay of two-sided shot gather, shot at location 1740.

8. Model of free-surface multiples at trace GS
Prepare two-sided shot gathers at locations G and S
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
Convolve the two-sided shot gathers trace by trace

9. Model of free-surface multiples at trace GS
Prepare two-sided shot gathers at locations G and S
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
Convolve the two-sided shot gathers trace by trace
Convolution is also correlation with time-reversed traces.

10. Model of free-surface multiples at trace GS
Prepare two-sided shot gathers at locations G and S
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
Convolve the two-sided shot gathers trace by trace
here convolution in x-t
other options after transforms
time to frequency
offset to ray-parameter
offset to wavenumber
Display of the convolved traces before summation.
In 3-D, the corresponding panel is a cube, typically irregularly and sparsely sampled cross-line.
Consider possibilities to use depth-velocity model for interpolation, mutes, etc.

11. Model of free-surface multiples at trace GS
Prepare two-sided shot gathers at locations G and S
interpolate gaps
use reciprocal traces from common receiver gathers at locations S and G
Convolve the two-sided shot gathers trace by trace
Apply tapers, mutes, interpolation, etc
Sum traces to obtain the multiple model trace
In red, trace from the data. In blue – result of summing the traces in the panel being displayed.
In green, the trace from Dephi’s itermul module.
Note that has narrower bandwidth than the data.

12. Model of free-surface multiples for shot gathers at location S
Repeat the previous procedure for all traces in the shot gather

13. Case study example – 2-D, East of Faroes Islands
Acquisition (1999):
Single vessel, towing 11.4 km long streamer
Shot interval 25 m
Group interval 12.5 m
10 sec records
Grid of eleven 2-D lines
One 120 km long line available at SEP
The gather displayed on the right is a CMP gather after pre-stack time migration. Note that P reflections energy from intra and base-basalt are recorded up to the maximum offset and provide valuable information for velocity analysis.
The maximum offset is 11.4 km. The data were acquired with a single vessel towing an 11.4 km long cable, shooting every 25 m. Group interval is 12.5 m and the record length is 10 sec.
The processing sequence includes several passes of multiple attenuation, several iterations of velocity analysis and pre-stack time migration.
The mute applied to the data selects pre-critical events only, with reflection angles up to about 30 degrees at the top basalt and progressively opening up to degrees at base basalt and below.

14. is an issue for SRME Feathering 3 km Source locations Receiver
We first look at the feathering.
On this map we see part of the grid of lines with receiver positions superposed.
We see a consistent feathering pattern across lines which also changes along the line.
A zoom on receiver position in the test area indicated that feathering is strong, up to 3 km cross-line at the far offsets and also among the strongest in the data.
Clearly the assumption of coincident source and receiver positions is not satisfied at the far offsets.
It seems this should be addressed during acquisition:
regional currents, tides, weather tolerances on maximum feathering,for instance by shooting 2-D swath acquisition with multiple cables and interpolation of traces, or by multiple acquisition passes.

15. 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.

16. Pre-stack time migration
12 km
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.

17. SRME applied to data from the 1999 survey (offsets up to 9 km)
Input
Model
Output
LMO
4 km/sec
The method being tested the Surface Related Multiple Attenuation method, developed at Delft University.
The reason for testing this method is that it models all free-surface multiples without input of interpreted horizons or velocities.
There are requirements on the geometry and quality of the data which we had considered in the survey design:
dense shot intervals,
shot interval an integer multiple of the receiver interval
small near offset gap.
I will show first shot gathers:
Input … Model … Output.
The near offset of the panel in the middle are reversed in order to
allow more direct comparison at the near offsets.
The maximum offset in this test is 9 km -- this is determined considering feathering, and will be discussed later.

18. 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

19. Requirement for sources and receivers at the same locations …
Heuristics:
Don’t convolve traces which are ``too far apart’’
Bandpass and dip-filter traces as function of their distance
Estimate ``plane-wave components” from the data and use these to compute the multiple model
Sx D(, s,x)P(,x,g) ~ Sp D(, s,p)P(,p,g)
x : space coordinate
p : spatial wavenumber or ray-parameter (ps or pg)

20. Gathers as function of offset (left) and ray-parameter (right)

21. Models before summation along offsets (left) and ray-parameter (right)

22. Further work
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
Display/Filter intermediate results when computing the multiple model
Investigate computing the multiple model by convolving plane wave components
Local plane-wave decompositions within CRG/CSG gathers?
Could handle also interpolation of missing near-offsets?