Transcript Document

Methods for isolating coherent
noise in the Radon domain
Shauna Oppert and R. James Brown
University of Calgary
•Coherent energy involved in
high-velocity layers
•The Radon transform
•Some new Radon variants
•Testing on synthetic data
Mode-converted reflections
Surface
P
High-velocity
salt
Radon Transform
One-sided CMP gather
x
Radon domain
p

t
 ( p, ) 
• • •
xmax
  ( x, t )dx,
xmin
Transform at slowness p
and zero-offset time 
CMP data
•Parabolic transform
t    px
2
•t2-stretched parabolic transform
Input =
t t
t   p x
2
2
2
2 2
•Hyperbolic multiple transform
t   p

( xk )  z  z
2
2

Castle (1994)
Dix hyperbola
Shifted hyperbola
Fourth-order non-hyperbolic NMO equation:
t  c1  c2 x  c3 x  ...,
2
c1  t ,
2
0
c2 
2
1
2
,
4
1 22  4
c3 
,
2 4
4 t0 2
N
j 
j


V
 kk
k 1
N
 
k 1
.
k
The CMP gather model
Mode-converted
reflection
Base-of-salt
multiple
Primary
Far-offset
smear
Near-offset
smear
p (x10-8 s/m)
Amplitude scale (x10-3)
 (s)
Parabolic Radon transform
Data weighting prior to a parabolic Radon transform
 (s)
Amplitude scale (x104)
p (x10-8 s/m)
Hyperbolic multiple transform
 (s)
Amplitude scale (x10-3)
p (x10-4 s/m)
t2-stretched parabolic transform
 (s)
Amplitude scale
p (x10-4 s/m)
Fourth-order non-hyperbolic transform
 (s)
Amplitude scale
p (x10-4 s/m)
•Tuned for mode-converted reflection
Fourth-order non-hyperbolic transform
 (s)
Amplitude scale
p (x10-4 s/m)
•Tuned for primary reflection
Fourth-order non-hyperbolic transform
Far offsets
 (s)
 (s)
Near offsets
p (x10-4 s/m)
p (x10-4 s/m)
•Tuned for mode-converted reflection
Some things to think about…
•Stretching and unstretching the data (t2) can
cause aliasing
•Tuned Radon transforms become expensive
when applied to real data
•Introducing a ‘fudge’ factor for 4 and t0 may
make the fourth-order algorithm more robust
Conclusions
•Data weighting prior to a Radon transform
may allow for discrimination of specific events
Aid in designing substantially more accurate
mutes for unwanted energy
•Focusing of all events was maximized when
using a t2-stretched parabolic or a fourthorder transform tuned for converted waves
Conclusions
•The removal of near-offset mode-converted
energy is possible using the hyperbolic
multiple or fourth-order non-hyperbolic
transform on near-offset data.
Mode-converted reflections can be diminished
with near-offset mutes and stacking
Future Work
•Improving a data-weighting function to account
for AVO affects in all types of reflections
•Develop a robust method for implementation
of a fourth-order or larger NMO-equation
transform
•Test all transforms with the high-resolution
Radon algorithm
Acknowledgements
Sponsors of
Dr. Mauricio Sacchi
Marco Perez
Xinxiang Li
Fourth-order non-hyperbolic transform
 (s)
Amplitude scale
p (x10-4 s/m)
•Tuned for multiple reflection