By: Ali Misaghi
Why seismic processing ?
Processing Steps
By: Ali Misaghi
What’s a seismic trace?
Rf(t)
Sandstone
*
S(t)
*
R(t)
+
Noise (t) = Seismic trace
Deconvolution
Filtering
Coal
Carbonate
Stacking
.
Salt
Shale
.
.
By: Ali Misaghi
f(t)
g(t)
*
f(t)
g(t)
*
By: Ali Misaghi
Wave propagation
By: Ali Misaghi
By: Ali Misaghi
By: Ali Misaghi
Marine data
Land data
Split shot gather
By: Ali Misaghi
Seismic events
Non-primary events
X (m)
0
0.0
500
R1
1000
1500
2000
2500
R2
Direct
0.2
Primary
0.4
T (s)
First multiple
0.6
Ground roll
0.8
1.0
Head wave (refraction)
By: Ali Misaghi
Seismic events
Non-primary events
Ground roll
Direct P-wave
R1
S
Earth’s surface
R2
Subsurface reflector
First multiple
Primary
Head wave (refraction)
By: Ali Misaghi
Number of receivers x receiver interval
CDP Fold =
2 x shot interval
By: Ali Misaghi
CDP gather
NMO
Stack
By: Ali Misaghi
Migration
“The goal of migration is to make the
stacked section appear similar to the
geologic cross-section”
Oz Yilmaz
By: Ali Misaghi
A step in seismic processing in which reflections in seismic data
are moved to their correct locations in the x-y-time space of
seismic data, including two-way traveltime and position relative to
shotpoints
By: Ali Misaghi
By: Ali Misaghi
By: Ali Misaghi
By: Ali Misaghi
Zn
Zm
m
n
By: Ali Misaghi
By: Ali Misaghi
By: Ali Misaghi
Typical ProMax flow for velocity analysis.
By: Ali Misaghi
Examining the normal moveout equation, it is possible to
analyze NMO velocities by plotting reflections in T2 X2 space
By: Ali Misaghi
Concept of Constant Velocity Stack as an aid to stacking
velocity estimation.
By: Ali Misaghi
One method to determine stacking velocity is to use a
Constant Velocity Stack (CVS) for several CDP gathers
By: Ali Misaghi
Same CVS panel of traces as before switching to variable
density color for the traces to utilize dynamic range
By: Ali Misaghi
Same as previous color panels with velocity range now
halved to better pick correct velocities
By: Ali Misaghi
Another term for Normal Moveout Equation.
By: Ali Misaghi
Options in the ProMax Velocity Analysis Routine.
By: Ali Misaghi
Demonstration of the velocity spectra
By: Ali Misaghi
Options in the ProMax Velocity Analysis Routine.
By: Ali Misaghi
CDP gather with NMO applied (center) surrounded by panels
having progressively lower velocity (left) or higher velocity.
By: Ali Misaghi
Options in the ProMax Velocity Analysis Routine.
By: Ali Misaghi
Options in the ProMax Velocity Analysis Routine.
By: Ali Misaghi
From left to right are panels for Semblance, Gather, Dynamic
Stack, Flip Stacks, and Velocity Function Stack.
By: Ali Misaghi
The ProMax routine ‘Velocity Analysis’ has it all – from left to
right: velocity spectra, interactive cursor with CDP gather,
dynamic stack, and a variation on CVS
By: Ali Misaghi
The Semblance Panel shows the semblance plot, the picked
velocity function, guide functions, and the interval velocity
computed from the picked function.
By: Ali Misaghi
Dix equation converts stacking velocities to interval velocities.
By: Ali Misaghi
However, you get RMS velocities, one can continue to
calculate interval velocities, interval thicknesses, and average
velocities.
By: Ali Misaghi
Remaining three panels in Velocity Analysis routine.
By: Ali Misaghi
Use of ProMax routine Velocity Viewer and Editor
By: Ali Misaghi
A common problem with stacking is residual NMO on the
CDP gathers resulting from imperfect velocity specification.
By: Ali Misaghi
Example of the data/velocity Interleave Display using
Landmark’s SeisCube program.
By: Ali Misaghi
Progressive Mute Analysis
By: Ali Misaghi
Prestack CDP gather with a horizon plotted along an event
that is not perfectly flattened by NMO; other causes might be
statics, noise, and/or lithology that is affecting the phase.
By: Ali Misaghi
By: Ali Misaghi
By: Ali Misaghi
ProMax routine CDP/Ensemble Stack vertically stacks
input ensembles of traces.
By: Ali Misaghi
Definition of multiplies as it applies to processing
seismic reflection data using ProMax.
By: Ali Misaghi
Example of a surface multiple on left in red and intrabed
multiple on the right in blue.
By: Ali Misaghi
Comparison of short-path and long-path multiples.
By: Ali Misaghi
Conceptual abstraction of the Tau – P domain
By: Ali Misaghi
Organizing seismic reflection data into ray-parameter domain
has certain advantages that are elaborated here.
By: Ali Misaghi
Working definition of the Radon Filter commonly
used for multiple suppression – working in the intercepttime (T) / ray parameter (p) or slowness domain.
By: Ali Misaghi
Use of the radon transform for the removal of multiples by
discriminating on the basis of moveout – here no rejection.
By: Ali Misaghi
Use of the radon transform for the removal of multiples by
discriminating on the basis of moveout – rejection shown.
By: Ali Misaghi
More on the use of the Radon Filter.
By: Ali Misaghi
By: Ali Misaghi
Migration
By: Ali Misaghi
Migration
“The goal of migration is to make the stacked section
appear similar to the geologic cross-section”
Oz Yilmaz
“Migration is an inversion operation involving
rearrangement of seismic information elements so that
reflections and diffractions are plotted at their true
locations.”
R.E Sheriff
Unmigrated
By: Ali Misaghi
Migrated
By: Ali Misaghi
By: Ali Misaghi
Migration
• Collapses diffractions
• Corrects for dip
– Moves dipping events in the updip direction
• Removes effects of surface curvature
– “unties the bowties”
By: Ali Misaghi
Reconstructing the wavefield
By: Ali Misaghi
Constant velocity migration
By: Ali Misaghi
Schematic that shows the imaging problem for a simple
anticline.
By: Ali Misaghi
Schematic that shows the imaging problem for a simple
syncline.
By: Ali Misaghi
Schematic that shows the imaging problem for a vertical fault.
By: Ali Misaghi
Schematic that shows the imaging problem for a 30-degree
fault.
By: Ali Misaghi
Schematic that shows the imaging problem for a reef model.
By: Ali Misaghi
Migration Methods
• Kirchoff migration (diffraction stacking)
– integral solution of wave equation
• Finite difference method
– derivative solution of wave equation
• F-K migration
– Fourier domain solution of wave equation
By: Ali Misaghi
Kirchoff Migration
(Diffraction Summation)
For every point (x,z), collapse all energy from
hyperbola with vrms
C x O
t 
B
t0
A
2
x
t 2  t02  4 2
vrms
By: Ali Misaghi
Kirchoff Migration
(Diffraction Summation)
Factors to consider before summing energy in
diffraction:
• Obliquity factor
– A  cos 
• Spherical divergence factor
– A  1/r
• Wavelet shaping factor
– phase correction
By: Ali Misaghi
Migration collapses diffractions to
reveal structure
By: Ali Misaghi
Migration collapses diffractions to
reveal structure
By: Ali Misaghi
Finite Difference Migration
• Solving the wave equation by stepping down
discrete intervals from z=0
• Downward continue wavefield to “exploding
reflector”
• Define an angle for width of cone for to be
included in migration for each point
– wider cone  more accurate
– narrow cone  faster, better approximations
By: Ali Misaghi
By: Ali Misaghi
Migration steepens and moves
dipping reflectors
Apparent dip in time section is related to true
dip:
tan  a  sin  (migrator’s equation)
By: Ali Misaghi
Collapsing diffraction and relocating
dipping surface
Diffraction D  Apex P
Reflector B  A
By: Ali Misaghi
F-K Migration
• Events can be separated by
their dips in F-K space
• Transform according to
migrator’s equation
tan
a=sin 
• Advantage: very
computationally efficient!
• Disadvantage: only works for
constant velocity (without
modifications that
compromise its efficiency)
By: Ali Misaghi
By: Ali Misaghi
Migration removes multiplebranch reflections
• Synclines
get broader
• Anticlines
get narrower
By: Ali Misaghi
“Untying the bowties”
By: Ali Misaghi
Limitations of Migration
•
•
•
•
•
•
Insufficient spatial resolution will result in aliasing
2-D slice of 3-D wavefield (need 3-D migration!)
Edge effects
Coherent noise
Requires knowledge of velocity structure
Time migration methods assume lateral velocity varies
slowly (otherwise need depth migration)
By: Ali Misaghi
By: Ali Misaghi
3-D Processing
• Binning by common midpoints in cells on a
grid
• Migration can be two stage 2-D migration
(in-line direction, then cross-line direction)
or full 3-D wavefield solution
• Most other processing operations are
unchanged
• Display is more difficult (and more fun!)
By: Ali Misaghi
By: Ali Misaghi
Why Deconvolution?
• Decreases ringing
• Increases resolution
• Improves appearance of stacked section and
makes it easier to interpret
• Section is more like the earth and less like the
seismic source
• Can remove multiples
By: Ali Misaghi
Convolutional model of a
seismogram
s=w*e+n
source wavelet
(+noise)
Earth response function
seismogram
=
*
1v1
2v2
3v3
4v4
5v5
By: Ali Misaghi
Spiking Filter
• Take existing
wavelet and
transform to a unit
impulse (delta
function)
• Also called
“whitening” because
it aims to create a
white spectrum
By: Ali Misaghi
Predictive Deconvolution
• Deconvolution with a built-in time lag
• Use to remove
– Multiples
– Bubble pulse
By: Ali Misaghi
Deconvolution Example
By: Ali Misaghi
Raw gather
decon
autocorrelograms
Bandpass
filtered
By: Ali Misaghi
Raw
gathers
By: Ali Misaghi
After
decon
By: Ali Misaghi
By: Ali Misaghi
Deconvolution
•
•
•
•
•
•
Deterministic Inverse Filtering
Deghosting
Least Squares (Optimum) Filtering
Spiking filter
Wavelet shaping
Predictive Deconvolution
By: Ali Misaghi
Convolutional model of a
seismogram
s=w*e+n
One equation with 3 unknowns
How can we possibly find e?
We make assumptions:
– e, n are white (random)
– w is minimum phase
By: Ali Misaghi
w
e
s
Amplitude
Spectrum
Autocorrelation
Amplitude
By: Ali Misaghi
Earth response
Wavelet
Seismogram
By: Ali Misaghi
Deterministic Deconvolution
Assume that an operator f(t) exists such that
w(t ) * f (t )   (t )
In the Fourier domain:
W ( ) F ( )  1
so
and
F ( ) 
i w

W
(

)

A
(

)
e
w


i f 
F
(

)

A
(

)
e

f

1
Aw ( )ei w
 A f ( )  1 / Aw ( )

 f ( )   w ( )
The inverse operator f(t) has opposite phase
and inverse amplitude spectrum from the
source wavelet w(t)
By: Ali Misaghi
Deterministic Deconvolution
• Assumptions:
1 source wavelet is minimum phase
2 noise is zero
3 wavelet is known
• Not true, especially 2
• In practice, the Fourier domain
implementation is not very good if
assumptions are not met
• Other methods are more stable
By: Ali Misaghi
Deghosting
• Eliminate source & receiver ghosts by
considering them as time delayed copies of
the source (and with known depths the time
delays are known)
• Alternatively, hydrophones and geophones
with different responses can be combined to
eliminate ghosting effects
By: Ali Misaghi
Correlation
Autocorrelation
1
rk ( x) 
N
N  k 1
x
t
t 0
xt  k
k  0,1, , N  1
Cross-correlation
1
g k ( x, y ) 
N
N  k 1
x
t 0
t
yt  k
k  0,1, , N  1
By: Ali Misaghi
Wavelet Estimation
• In general, the source wavelet is unknown
• Source wavelet can be estimated from
seismogram alone assuming:
– minimum phase wavelet
– white earth response spectrum
rx  rw * re
rx  r0 rw
autocorrelation
(with white earth response)
Autocorrelation of seismogram is the autocorrelation of
source wavelet (within a constant)
By: Ali Misaghi
Optimum Weiner Filters
Want to find the optimum filter components fi that minimize the error between
the desired and actual outputs in a least-squares sense:
L   (d t   f t xt  ) 2

t
By setting
L
 0,
f i
i  0,1, 2, , (n  1)
L


 2 d t xt i  2   f xt  xt i  0
f i
t
t  

so
or
f  x


t 
xt i   dt xt i
t
t
Recognizing the terms for auto- and cross-correlation,
f r   g


i
i
By: Ali Misaghi
Optimum Weiner Filters
f r   g


i
are called the normal equations
r1
r2
r0
r1
r1
r0


rn  2
rn 3
 rn 1   f 0   g 0 
 rn  2   f1   g1 
 rn 3   f 2    g 2 

 

       
 r0   f n 1   g n 1 
i
Or, in matrix form,
 r0
r
 1
 r2

 
rn 1
The autocorrelation matrix is a Toeplitz matrix, and can be
inverted by Levinson recursion
By: Ali Misaghi
Optimum Weiner Filters
 r0
r
 1
 r2

 
rn 1
r1
r2
r0
r1
r1
r0


rn  2
rn 3
 rn 1   f 0   g 0 
 rn  2   f1   g1 
 rn 3   f 2    g 2 

 

       
 r0   f n 1   g n 1 
The gi terms are the cross-correlation of the desired wavelet
with the input wavelet (seismogram).
In the case of spiking deconvolution, the normal equations
take the form
 r0
r
 1
 r2

 
rn 1
r1
r2
r0
r1
r1
r0


rn  2
rn 3
 rn 1   f 0  1
 rn  2   f1  0
 rn 3   f 2   0

  
      
 r0   f n 1  0
By: Ali Misaghi
Wavelet Processing
• Attempt to shift source wavelet to some
other known wavelet, to accomplish one or
more of:
• Reduce variation of source (between shots,
between receivers)
• Shift to another known wavelet
– e.g., hydrophone response to match
seismometer
• Separate wavelet and earth response more
clearly
By: Ali Misaghi
Wavelet Processing
By: Ali Misaghi
Wavelet Processing
Transform to zero phase and broaden spectrum
Increase resolution
By: Ali Misaghi
By: Ali Misaghi
o
91
Real data
7.5 m
8.5 m
25 m
12.5 m
1) Shots : 2 – 548
2) Minimum phase
3) Traces have been resampled (2ms >4ms) and decimated (384 > 192)
4) Fk filter
5) Geometry has been applied
6) Velocity file is available(By Geco)
By: Ali Misaghi
Real data
work flow
Sorting
Pick mute
True Amplitude Recovery
Deconvolution
Velocity Analysis
Check the mute
NMO
Demultiple
Stack
Velocity Manipulation
Migration
By: Ali Misaghi
Real data
Project results:
-A report:
-Explanation of the processing steps with proper
and related snap shots(Mute, TAR, Decon, NMO,
Demultipling, Stacking, Migration,etc
-Final results(a comparison study)
-Brute-stack section(s)
-Demultipled stack section(s)
-Migrated section(s)