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• Seismic Migration (SM)

Januka AttanayakeGEOL 377

Center for Integrative GeosciencesUniversity of Connecticut

13th November 2006

• Goals:

1) What is SM?

2) Why is it used?

3) How is it used?

• 3

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 !!

• 4

Content

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

• Snells Law

Willebrord van Roijen Snell(1580-1626)

)sin()sin( rnin ri =

University Physics p.644-646

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Snell.htmlhttp://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Snell.html

• Question - 1Do question number 1 in the in-class exercise sheet.

• Snells Law & Seismic waves

• Some energy loss

• Fundamental Observable

TRAVEL TIME

Our trusted friend !!

• Do question 2 in the in-class exercise sheet

V2>V1

• Time Relationships

1/VXTdir =

])/[cos(2 1VhTrefl =

12 /)cos(2)/( VhVXT crefr +=

• In a graph

• Graphical representation-I

• Deep Earth Pseudo-analogy

Steven Dutch

PKP(AB,BC) direct waves

PKiKP Reflected wave

• Complexities

*Travel times (Velocity perturbations) *Ray paths are affected by the subsurface structures

*Noise

)34( += KVp

=sV

• Enviroscan, inc.

• Seismic MigrationMigration Moving from one place to

another

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

equation technique

Oil industry 1970/90 and present

• 23

Key Contributors

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

Bednar J.B.

• Seismic reflection survey

1) Source

2) Detectors

3) Data processing system

• Source

• Detectors (Geophones)

• Data processing system

+ Seismologists

• Method

• Cross section

http://www.litho.ucalgary.ca/atlas/seismic.html

• Data Processing Sequence

http://www.litho.ucalgary.ca/atlas/seismic.html

• Final Picture

UNR CEMAT

• 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

• Zero-offset

i.e. Location of the source is as same as the receiver.

Is this it?

• 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

• Seismic Migration

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

• 39

BREAK

I am tired ! Lets have a 10 minute BREAK !!

• Basic Idea

• Question -3Do question 3 (a),(b) of in-class exercise

sheet.

• 42

• Finding dip angle

• 44

Question -4

Do question 4 in your in-class work sheet.

• Migrators Equation

)V(

)(

)('

1

1

1

xtarcSin

xtVSin

tVzSinTan

=

=

==

• True Coordinates

• 2-way travel time w.r.t. normal ray length

Vdt 2=

True depth of reflector at point R

dCosz =Lateral shift of true position

SinVtdSinx2

==

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..

• ytp

=0

Where; p0 - time dip of the event or simply dip of the event

y - The midpoint coordinate, the location of source-receiver pair

41'

4

2

22

2

0

pVtt

ptVx

VpSin

=

=

=Tuchels Law;

• HM ProblemsEquations not practical

-tedious -error-prone

Why? Calculating/Inputting P problematice.g. crossing events 2 reflectors but

same arrival timesSummation of such a wavefield

• What are these?

• Diffraction & Distortion

• True Point

• Purpose of Migration

1) Reposition reflections

2) Remove diffraction images

* General purpose migration

• True Picture

• Different Approaches

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!

why?

• Principle-IIWave Equation (1-D homogeneous medium)

Solution (DAlembert)

f,g twice differentiable arbitrary functions, holds true even if you substitute (-t)

2

22

2

2

zV

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

• Point Reflector

Diffraction migrates into a point

Diffraction curve of

an unmigrated

reflector element

• Array Reflector

• Linear Reflector

• NoiseBurst of noise in an unmigratedsection

Migrates in to a wavefront

A Smile

• 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