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Seismic Migration (SM)
Januka AttanayakeGEOL 377
Center for Integrative GeosciencesUniversity of Connecticut
13th November 2006
1) What is SM?
2) Why is it used?
3) How is it used?
Couple of things
Feel free to take notesReferences are given when ever possible4 Simple in-class questionsHome work assignment, e-mailed to youMigration:
-concept, easy to understand-application in algorithms, TERRIBLE !!
Background information-Refraction survey-Reflection survey
Seismic Migration-Principles, Fundamental concepts-Hand Migration-Different Approaches-Different techniques based on sequence
Seismic WavesStretch, squeeze & Shear material(Earth Material = Sponge)
Stress & Strain:
Equation of Motion:
ijijij e 2+=Modern Global Seismology, P. 49-51
uuu += )()2(
Modern Global Seismology, P. 53-69
Motion of particles
Willebrord van Roijen Snell(1580-1626)
)sin()sin( rnin ri =
University Physics p.644-646
Question - 1Do question number 1 in the in-class exercise sheet.
Snells Law & Seismic waves
Some energy loss
Our trusted friend !!
Do question 2 in the in-class exercise sheet
])/[cos(2 1VhTrefl =
12 /)cos(2)/( VhVXT crefr +=
In a graph
Deep Earth Pseudo-analogy
PKP(AB,BC) direct waves
PKiKP Reflected wave
*Travel times (Velocity perturbations) *Ray paths are affected by the subsurface structures
)34( += KVp
Seismic MigrationMigration Moving from one place to
What is Seismic Migration?A data processing technique
-Reflection seismic surveys-Accurate imaging of earth structures
Coming Attraction! Proper Definition
SM History1921 First use, at the beginning of Seismic
Exploration (seismic exploration,p.6, fig-1.3b)
1920/40 Human computer based methods1960/70 - Emergence of digital wave
Oil industry 1970/90 and present
Principle ones: (Theoretical)F. Reiber, J.G. Hagedoorn, J.F. Claerbout
Others:C.H. Dix, M.M. Slotnick, H. Slattlegger, A.J. Berkhout, B Shneider, R. Stolt, Moore
Seismic reflection survey
3) Data processing system
Data processing system
Data Processing Sequence
Got a problem?
Each CDP stacked trace in a seismic section is plotted to show reflections in positions that correspond to vertical travel paths
CDP Common Depth Point
i.e. Location of the source is as same as the receiver.
Is this it?
Answer is ..
Inclined flat reflector problem
Basic Exploration p.188
Undulating reflector problem
Cause of distortionPlotting depths calculated from arrival times
in incorrect positions
*Not from incorrect travel times
Dip distortion Correction by moving reflection points away from their positions on vertical lines on to inclined lines that correspond to the travel paths.
Process of placing seismic reflection energy in its proper subsurface location.
Proper definitionSeismic migration involves the geometric repositioning of the return signals to show an event where it is being hit by the seismic wave rather than where it is picked up.
Event Boundary (layer), Structure
M.Lorentz, R. Bradley
I am tired ! Lets have a 10 minute BREAK !!
Question -3Do question 3 (a),(b) of in-class exercise
Finding dip angle
Do question 4 in your in-class work sheet.
2-way travel time w.r.t. normal ray length
True depth of reflector at point R
dCosz =Lateral shift of true position
It is conventional to write t in terms of 2-way vertical travel time t
tCosVzt == 2'
Thus both vertical shift t-t and the horizontal shift x = 0 (when dip angle =0)
Basic Earth Imaging- Claerbout
Hand Migration(HM)Before computerized migrationSeveral schemes
x & t require,t readily measured v from finite-offset - measurable as follows..
Where; p0 - time dip of the event or simply dip of the event
y - The midpoint coordinate, the location of source-receiver pair
HM ProblemsEquations not practical
Why? Calculating/Inputting P problematice.g. crossing events 2 reflectors but
same arrival timesSummation of such a wavefield
What are these?
Diffraction & Distortion
Purpose of Migration
1) Reposition reflections
2) Remove diffraction images
* General purpose migration
Time Reverse MigrationKirchhoff Migration
*In addition, there are many other approaches. (Exploration seismology p. 326-335)
Time Reverse MigrationDepropagate seismic waves to its origin. i.e. reverse the path of seismic reflections
back to the geologic reflector by reversing time
Literature: Hermon(1978), Baysal et.al.(1983), Loewenthal & Mufti(1983), McMechan(1983), Whitemore(1983,1986), Mufti et.al.(1996), Zhu & Lines (1998)
Principle-IWe live in 4-D (space & time)
Any one of them can be reversed !Time, not physically!
Principle-IIWave Equation (1-D homogeneous medium)
f,g twice differentiable arbitrary functions, holds true even if you substitute (-t)
)()(),( zVtgzVtftzs ++=
Experiment, Hello olleH ! Time-Reversed Acoustics; November 1999; Scientific American
Magazine; by Fink; 7 Page(s) In a room inside the Waves and Acoustics Laboratory in Paris is an
array of microphones and loudspeakers. If you stand in front of this array and speak into it, anything you say comes back at you, butplayed in reverse. Your "hello" echoes-almost instantaneously-as "olleh." At first this may seem as ordinary as playing a tape backward, but there is a twist: the sound is projected back exactly toward its source. Instead of spreading throughout the room fromthe loudspeakers, the sound of the "olleh" converges onto your mouth, almost as if time itself had been reversed. Indeed, the process is known as time-reversed acoustics, and the array in front of you is acting as a "time-reversal mirror."
Example - Model
Fault bend fold
Fault propagation fold
Lines et.al. (2001)
Example - Interpretation
Zero-offset sectionMigrated section
Kirchhoff (diffraction-stack) Migration
Concept : Hagedoorn (1954)Curve of maximum convexity (PMR)i.e. unmigrated diffraction curve
Kirchhoff Method#1 Calculate the diffraction curves for
each reflector point on the unmigratedsection
#2 Data on the unmigrated section lying along this curve summed up
#3 This gives the amplitude at the respective migrated point
If, Signal approprate value Noise (+) + (-) values (small sum)
Kirchhoff MethodEach element of an unmigrated reflection is treated as a portion of a diffraction.
i.e. Reflector sequence of closely spaced diffracting points
Diffraction migrates into a point
Diffraction curve of
NoiseBurst of noise in an unmigratedsection
Migrates in to a wavefront
NoteResults of wavefront smearing (previous
figures) are identical to Kirchhoff migration results (Sheriff, 1978).
More notesAmplitudes are adjusted for obliquity and
divergence before summing
Introduce a wavelet-shaping factor to correct amplitudes
(Schneider, 1979), (Berryhill, 1979)
Near-field terms are neglected for collapsing diffraction curves as wave propagation in spherical coordinates
Aperture Definition ProblemAperture: Range of data included in the
migration of each point
How far down the diffraction cu