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

Transcription

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

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

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

4 Content Background information -Refraction survey -Reflection survey Seismic Migration -Principles, Fundamental concepts -Hand Migration -Different Approaches -Different techniques based on sequence 4

5 Seismic Waves Stretch, squeeze & Shear material (Earth Material = Sponge) Stress & Strain: σ = λθδ + 2µ e ij ij ij Modern Global Seismology, P Equation of Motion: ρ u = ( λ + 2µ ) ( u) µ u Modern Global Seismology, P

6 Motion of particles

7 Snell s Law Willebrord van Roijen Snell ( ) ni sin( i) = n r sin( r) University Physics p

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

9 Snell s Law & Seismic waves

10 Some energy loss

11 Fundamental Observable TRAVEL TIME Our trusted friend!!

12 Do question 2 in the in-class exercise sheet V2>V1

13 Time Relationships T dir = X /V 1 T refl = 2h /[cos( θ) V ] 1 T refr = ( X / V V 2 ) + 2h cos( θc ) / 1

14 In a graph

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16 Graphical representation-i

17 Deep Earth Pseudo-analogy PKP(AB,BC) direct waves PKiKP Reflected wave PKP(diff) Headwave Steven Dutch

18 Complexities V p = ( K µ) ρ V s = µ ρ *Travel times (Velocity perturbations) *Ray paths are affected by the subsurface structures *Noise

19 Enviroscan, inc.

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21 Seismic Migration Migration 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

22 SM History 1921 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

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. 23

24 Seismic reflection survey 1) Source 2) Detectors 3) Data processing system

25 Source

26 Detectors (Geophones)

27 Data processing system + Seismologists

28 Method

29 Cross section

30 Data Processing Sequence

31 UNR CEMAT Final Picture

32 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

33 Zero-offset Coincident source-receiver. i.e. Location of the source is as same as the receiver. Is this it? Answer is..

34 Inclined flat reflector problem Basic Exploration p.188

35 Undulating reflector problem

36 Cause of distortion Plotting depths calculated from arrival times in incorrect positions *Not from incorrect travel times

37 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.

38 Proper definition Seismic 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!! 39

40 Basic Idea

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

42 Answer 42

43 Finding dip angle

44 Question -4 Do question 4 in your in-class work sheet. 44

45 Migrator s Equation Tan β = Sin α z' = V 1 ( t) t Sin( α ) = V 1 x α = arcsin(v 1 t ) x

46 True Coordinates

47 2-way travel time w.r.t. normal ray length True depth of reflector at point R 2d t = V z = dcosθ Lateral shift of true position x = Vt dsinθ = Sinθ 2 It is conventional to write t in terms of 2-way vertical travel time t z t '= 2 = tcosθ V Thus both vertical shift t-t and the horizontal shift x = 0 (when dip angle =0) Basic Earth Imaging- Claerbout

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

49 y t p = 0 Where; p 0 - time dip of the event or simply dip of the event y - The midpoint coordinate, the location of source-receiver pair 4 1 ' p V t t pt V x Vp Sin = = = θ Tuchel s Law;

50 HM Problems Equations 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

51 What are these?

52 Diffraction & Distortion

53 True Point

54 Purpose of Migration 1) Reposition reflections 2) Remove diffraction images * General purpose migration

55 True Picture

56 Different Approaches Time Reverse Migration Kirchhoff Migration *In addition, there are many other approaches. (Exploration seismology p )

57 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)

58 Principle-I We live in 4-D (space & time) Any one of them can be reversed! Time, not physically! why?

59 Principle-II Wave Equation (1-D homogeneous medium) 2 ϕ = V 2 t 2 2 ϕ 2 z Solution (D Alembert) s ( z, t) = f ( Vt z) + g( Vt + z) f,g twice differentiable arbitrary functions, holds true even if you substitute (-t)

60 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."

61 Example - Model Fault bend fold Fault propagation fold Lines et.al. (2001)

62 Example - Interpretation Zero-offset section Migrated section

63 Kirchhoff (diffraction-stack) Migration Concept : Hagedoorn (1954) Curve of maximum convexity (PMR) i.e. unmigrated diffraction curve

64 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)

65 Kirchhoff Method Each element of an unmigrated reflection is treated as a portion of a diffraction. i.e. Reflector sequence of closely spaced diffracting points

66 Point Reflector Diffraction migrates into a point Diffraction curve of an unmigrated reflector element

67 Array Reflector

68 Linear Reflector

69 Noise Burst of noise in an unmigrated section Migrates in to a wavefront A Smile

70 Note Results of wavefront smearing (previous figures) are identical to Kirchhoff migration results (Sheriff, 1978).

71 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

72 Aperture Definition Problem Aperture: 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

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

74 Migration Pre-Stack Migration Post-Stack Migration

75 Pre-stack Migration Migrate data before stacking sequence occurs. *Pre-stack depth migration (PDM) *Require more knowledge about subsurface velocity structure *Better results

76 Applications & Problems # Complex subsurface structure # Complex subsurface Velocity Structure # Modeling salt diapirs # Expensive # Time consuming

77 Pre-stack final picture

78 Post-stack Migration Seismic data is migrated after stacking sequence occurs. Basis: All data elements -Primary Reflections -Diffractions

79 Applications/Problems # Low dip non-interfering events # Faster data processing # Low cost # Resolution < pre-stack migration

80 Post-stack final Picture

81 Main References: *Basic Exploration Seismology, Robinson & Coruh *Modern Global Seismology, Lay & Wallace *Exploration Seismology, Sheriff & Geldart * * Lines et.al.(2001), Depth Imaging if we could turn back time, CSEG Recorder * bradley/www/rcbradley1.html *Bednar.,J.B.(2005), A brief history of seismic migration, SEG digital library, doi: / *University Physics, Sanny & Moebs