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 eµλθδσ 2+=

Modern Global Seismology, P. 49-51

uuu ×∇×∇−⋅∇∇+= µµλρ )()2(

Modern Global Seismology, P. 53-69

Motion of particles

Snell’s Law

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.

Snell’s 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 θ=

12 /)cos(2)/( VhVXT crefr θ+=

In a graph

Graphical representation-I

Deep Earth Pseudo-analogy

Steven Dutch

PKP(AB,BC) direct waves

PKiKP Reflected wave

PKP(diff) Headwave

Complexities

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

*Noise

ρµ)34( += KVp

ρµ

=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

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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

Coincident source-receiver.

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

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

M.Lorentz, R. Bradley

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

Answer

Finding dip angle

44

Question -4

Do question 4 in your in-class work sheet.

Migrator’s Equation

)V(

)(

)('

1

1

1

xtarcSin

xtVSin

tVzSinTan

∆∆

=

∆∆

=

∆=∆=

α

α

αβ

True Coordinates

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

Hand Migration(HM)Before computerized migrationSeveral schemes

∆x & t’ require,t – readily measured v – from finite-offset θ - 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

−=

=∆

=θTuchel’s 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 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)

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 (D’Alembert)

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

2

22

2

2

zV

t ∂∂

=∂∂ ϕϕ

)()(),( 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 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

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

Other Kirchhoff approaches

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

Migration

Pre-Stack Migration

Post-Stack Migration

Pre-stack Migration

Migrate data before stacking sequence occurs.

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

velocity structure*Better results

Applications & Problems

# Complex subsurface structure

# Complex subsurface Velocity Structure

# Modeling salt diapirs

# Expensive

# Time consuming

Pre-stack final picture

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

Basis: All data elements-Primary Reflections-Diffractions

Applications/Problems# Low dip non-interfering events

# Faster data processing

# Low cost

# Resolution < pre-stack migration

Post-stack final Picture

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