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Seismic Migration (SM)

Januka Attanayake GEOL 377 Center for Integrative Geosciences University of Connecticut 13th November 2006

Goals:1) What is SM? 2) Why is it used? 3) How is it used?

Couple of thingsFeel free to take notes References are given when ever possible 4 Simple in-class questions Home work assignment, e-mailed to you Migration: -concept, easy to understand -application in algorithms, TERRIBLE !!3

ContentBackground information-Refraction survey -Reflection survey

Seismic Migration-Principles, Fundamental concepts -Hand Migration -Different Approaches -Different techniques based on sequence4

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

Stress & Strain:

ij = ij + 2eijModern Global Seismology, P. 49-51

Equation of Motion:

u = ( + 2 )( u) uModern Global Seismology, P. 53-69

Motion of particles

Snells LawWillebrord van Roijen Snell (1580-1626)

ni sin(i ) = nr sin(r )University Physics p.644-646

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

Snells Law & Seismic waves

Some energy loss

Fundamental Observable

TRAVEL TIMEOur trusted friend !!

Do question 2 in the in-class exercise sheet

V2>V1

Time RelationshipsTdir = X /V1

Trefl = 2h /[cos( )V1 ] Trefr = ( X / V2 ) + 2h cos( c ) / V1

In a graph

Graphical representation-I

Deep Earth Pseudo-analogyPKP(AB,BC) direct waves PKiKP Reflected wave PKP(diff) Headwave

Steven Dutch

Complexities4 Vp = ( K + ) 3

Vs =

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

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 methods 1960/70 - Emergence of digital wave equation technique Oil industry 1970/90 and present

Key ContributorsPrinciple 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.

23

Seismic reflection survey1) 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-offsetCoincident 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 MigrationDip 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), StructureM.Lorentz, R. Bradley

BREAK

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

39

Basic Idea

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

Answer

42

Finding dip angle

Question -4Do question 4 in your in-class work sheet.

44

Migrators EquationTan = Sin z' = V1 (t ) t Sin( ) = V1 x t = arcSin(V1 ) x

True Coordinates

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

2d t= VTrue depth of reflector at point R

z = dCosLateral shift of true position

Vt x = dSin = Sin 2

It is conventional to write t in terms of 2-way vertical travel time t

2z t ' = = tCos VThus both vertical shift t-t and the horizontal shift x = 0 (when dip angle =0) Basic Earth Imaging- Claerbout

Hand Migration(HM)Before computerized migration Several schemes x & t require, t readily measured v from finite-offset - measurable as follows..

t p0 = yWhere; p0 - time dip of the event or simply dip of the event y - The midpoint coordinate, the location of source-receiver pairTuchels Law;

Vp Sin = 2 V2

0

x =

pt

4 V2

t'= t

1

p

2

4

HM ProblemsEquations not practical -tedious -error-prone Why? Calculating/Inputting P problematic e.g. crossing events 2 reflectors but same arrival times Summation of such a wavefield

What are these?

Diffraction & Distortion

True Point

Purpose of Migration1) Reposition reflections 2) Remove diffraction images

* General purpose migration

True Picture

Different ApproachesTime Reverse Migration Kirchhoff 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 timeLiterature: 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)

2 2 =V 2 2 t 2 z

Solution (DAlembert)

s( z, t ) = f (Vt z) + g (Vt + z)f,g twice differentiable arbitrary functions, holds true even if you substitute (-t)

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, but played 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 from the 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 - ModelFault bend fold

Fault propagation fold

Lines et.al. (2001)

Example - Interpretation

Zero-offset section

Migrated 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 unmigrated section #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 ReflectorDiffraction migrates into a point

Diffraction curve of an unmigrated reflector element

Array Reflector

Linear Reflector

NoiseBurst of noise in an unmigrated section

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 curve the summation should extend? General Rule: Aperture > 2x horizontal distance of width migration of the reflector having steepest dips

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

Migration

Pre-Stack Migration

Post-Stack Migration

Pre-stack MigrationMigrate 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