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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

    PKP(diff) Headwave

  • 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

    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.

  • 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