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Seismic Migration (SM) Januka Attanayake GEOL 377 Center for Integrative Geosciences University of Connecticut 13 th November 2006

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Page 1: Seismic Migration

Seismic Migration (SM)

Januka AttanayakeGEOL 377

Center for Integrative GeosciencesUniversity of Connecticut

13th November 2006

Page 2: Seismic Migration

Goals:

1) What is SM?

2) Why is it used?

3) How is it used?

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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 !!

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4

Content

Background information-Refraction survey-Reflection survey

Seismic Migration-Principles, Fundamental concepts-Hand Migration-Different Approaches-Different techniques based on sequence

Page 5: Seismic Migration

Seismic WavesStretch, squeeze & Shear material(Earth Material = Sponge)

Stress & Strain:

Equation of Motion:

ijijij eµλθδσ 2+=

Modern Global Seismology, P. 49-51

uuu ×∇×∇−⋅∇∇+= µµλρ )()2(

Modern Global Seismology, P. 53-69

Page 6: Seismic Migration

Motion of particles

Page 7: Seismic Migration

Snell’s Law

Willebrord van Roijen Snell(1580-1626)

)sin()sin( rnin ri =

University Physics p.644-646

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

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Snell’s Law & Seismic waves

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Some energy loss

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Fundamental Observable

TRAVEL TIME

Our trusted friend !!

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Do question 2 in the in-class exercise sheet

V2>V1

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Time Relationships

1/VXTdir =

])/[cos(2 1VhTrefl θ=

12 /)cos(2)/( VhVXT crefr θ+=

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In a graph

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Page 16: Seismic Migration

Graphical representation-I

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Deep Earth Pseudo-analogy

Steven Dutch

PKP(AB,BC) direct waves

PKiKP Reflected wave

PKP(diff) Headwave

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Complexities

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

*Noise

ρµ)34( += KVp

ρµ

=sV

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Enviroscan, inc.

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Page 21: Seismic Migration

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”

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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

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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.

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Seismic reflection survey

1) Source

2) Detectors

3) Data processing system

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Source

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Detectors (Geophones)

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Data processing system

+ Seismologists

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Method

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Cross section

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

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Data Processing Sequence

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

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Final Picture

UNR – CEMAT

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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

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Zero-offset

Coincident source-receiver.

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

Is this it?

Answer is ……..

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Inclined flat reflector problem

Basic Exploration p.188

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Undulating reflector problem

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Cause of distortionPlotting depths calculated from arrival times

in incorrect positions

*Not from incorrect travel times

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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.

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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

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39

BREAK

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

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Basic Idea

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

sheet.

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42

Answer

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Finding dip angle

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44

Question -4

Do question 4 in your in-class work sheet.

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Migrator’s Equation

)V(

)(

)('

1

1

1

xtarcSin

xtVSin

tVzSinTan

∆∆

=

∆∆

=

∆=∆=

α

α

αβ

Page 46: Seismic Migration

True Coordinates

Page 47: Seismic Migration

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

Vdt 2

=

True depth of reflector at point R

θdCosz =Lateral shift of true position

θθ SinVtdSinx2

==∆

It is conventional to write t in terms of 2-way vertical travel time t’

θtCosVzt ==

2'

Thus both vertical shift t-t’ and the horizontal shift ∆x = 0 (when dip angle =0)

Basic Earth Imaging- Claerbout

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Hand Migration(HM)Before computerized migrationSeveral schemes

∆x & t’ require,t – readily measured v – from finite-offset θ - measurable as follows…..

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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

−=

=∆

=θTuchel’s Law;

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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

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What are these?

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Diffraction & Distortion

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True Point

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Purpose of Migration

1) Reposition reflections

2) Remove diffraction images

* General purpose migration

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True Picture

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Different Approaches

Time Reverse MigrationKirchhoff Migration

*In addition, there are many other approaches. (Exploration seismology p. 326-335)

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Time Reverse Migration“Depropagate” 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)

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Principle-IWe live in 4-D (space & time)

Any one of them can be reversed !Time, not physically!

why?

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Principle-IIWave Equation (1-D homogeneous medium)

Solution (D’Alembert)

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

2

22

2

2

zV

t ∂∂

=∂∂ ϕϕ

)()(),( zVtgzVtftzs ++−=

Page 60: Seismic Migration

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."

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Example - Model

Fault bend fold

Fault propagation fold

Lines et.al. (2001)

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Example - Interpretation

Zero-offset sectionMigrated section

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Kirchhoff (diffraction-stack) Migration

Concept : Hagedoorn (1954)Curve of maximum convexity (PMR)i.e. unmigrated diffraction curve

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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)

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Kirchhoff MethodEach element of an unmigrated reflection is treated as a portion of a diffraction.

i.e. Reflector – sequence of closely spaced diffracting points

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Point Reflector

Diffraction migrates into a point

Diffraction curve of

an unmigrated

reflector element

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Array Reflector

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Linear Reflector

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NoiseBurst of noise in an unmigratedsection

Migrates in to a wavefront

“A Smile”

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NoteResults of wavefront smearing (previous

figures) are identical to Kirchhoff migration results (Sheriff, 1978).

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More notes…Amplitudes 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

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Aperture Definition ProblemAperture: Range of data included in the

migration of each point

How far down the diffraction curve the summation should extend?

General Rule:Aperture > 2x horizontal distance of width migration of the reflector having

steepest dips

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Other Kirchhoff approaches

Kirchhoff integral:Find integral Solution to the wave equation (Schneider 1978)

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Migration

Pre-Stack Migration

Post-Stack Migration

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Pre-stack Migration

Migrate data before stacking sequence occurs.

*Pre-stack depth migration (PDM)*Require more knowledge about subsurface

velocity structure*Better results

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Applications & Problems

# Complex subsurface structure

# Complex subsurface Velocity Structure

# Modeling salt diapirs

# Expensive

# Time consuming

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Pre-stack final picture

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Post-stack MigrationSeismic data is migrated after stacking sequence occurs.

Basis: All data elements-Primary Reflections-Diffractions

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Applications/Problems# Low dip non-interfering events

# Faster data processing

# Low cost

# Resolution < pre-stack migration

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Post-stack final Picture

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Main References:*Basic Exploration Seismology, Robinson & Coruh*Modern Global Seismology, Lay & Wallace*Exploration Seismology, Sheriff & Geldart*http://sepwww.stanford.edu/sep/prof/index.html* Lines et.al.(2001), Depth Imaging “if we could turn back

time”, CSEG Recorder *http://www.geol.lsu.edu/Faculty/Juan/ReflectSeismol97/rc

bradley/WWW/rcbradley1.html*Bednar.,J.B.(2005), A brief history of seismic migration,

SEG digital library, doi:10.1190/1.1926579*University Physics, Sanny & Moebs