Introduction to SeismicMigration - One way traveltime = / V 1 m s Homogeneous dipping planar reflector - One way traveltime = / V 1 m s Homogeneous dipping planar reflector - One way traveltime = / V 1 m s Homogeneous dipping planar reflector Homogeneous dipping planar reflector - One way traveltime = / V 1 m s = Stacked position reflection position = Migrated position true their subsurface location Dipping reflections More complex structure Definition Process which moves dipping reflections to their true subsurface position and collapes diffractions Process which reconstructs seismic image from stack section so that reflections and difractions are plotted at their true location Stacked section Migrated section Migration Operation Velocit y Objectives • Moves dipping reflections to their true dip (up dip) and subsurface location • Collapes diffraction • Un-tie bow-tie Seismic Velocity Seismic Velocity • Instantaneous • Represents actual velocity • Similar to the well log velocity • Interval • Instantaneous velocity over a defined interval • • Root mean square (RMS) • Used during NMO and diffraction modeling • • Average • Total distance with a total traveltime dt dz V ins · ( ) ( ) ( ) ( ) ∫ ∫ · · 2 1 2 1 2 2 , 1 2 , 1 2 2 , 1 2 , 1 1 1 T T ins ins T T ins ins dt t V T T V dt t V T T V ( ) ( ) ∫ · · · T t t ins rms dt t V T t V 0 2 2 1 ∫ · · · T t t ins ave dt t V T T V 0 ) ( 1 ) ( RMS and Average Velocity ∑ ∑ · · ∆ ∆ · n i i n i i n rms t t V V 1 1 2 int 2 , ∑ ∑ · · ∆ ∆ · n i i n i i n ave t t V V 1 1 int , R M S velocity Average velocity How to derive velocity Pre-stack seismic gather stacking velocity Velocity analysis RMS velocity ) cos(dip V V stack rms · Interval velocity Dix equation Dix Equation (Dix,1955) Assumption • Horizontal planar reflectors • Small offset 2 / 1 1 1 2 2 int ) 1 ( ) ( ) ( , ` . | − − − · − − n n n rms n rms t t t n V t n V n V Vint ( - ) Vrms n 1 ( ) Vrms n TWT - tn 1 tn CDP Exercise-1 Compute RMS and average velocities at reflector , ! B C and D = Z 1000 m = Z 2000 m B = / Vab 2000 m s = / Vcd 6000 m s = / Vbc 4000 m s C D A = Z 3000 m Solution-1 Depth Vint DTi V_ave V_rms 1000 2000 . 0 5 . 2000 0 . 2000 0 2000 4000 . 0 25 . 2666 7 . 2828 4 3000 6000 . 0 167 . 3272 7 . 3618 1 V_ave V_rms V_int [ / ] Velocity m s [ ] T W T s Exercise-2 Semicircle superposition Impulse response migration Diffraction summation Kirchhoff Migration Huygens’s secondary source Huygens traveltime curve Kirchhoff Summation ∑ ] ] ] ] ∆ · x in RMS out P t r V x P * ) ( cos 2 ρ θ π O bliquity Sphericalspreading W avelet shaping factor ) / , 0 , ( v r t z x P in − · ) 0 , 2 / , ( 0 · · t v z x P out τ ( ) 2 2 0 z x x r + − · Kirchhoff time and depth Kirchhoff migration parameters • Velocity • Aperture • Maximum dip Migration velocities Overmigrated Undermigrated ZO Desired migration / 2500 m s % 5 % 10 % 20 Test for velocity Test for velocity Migration velocities Tests for maximum dip to migrate . a Z O section . b D esired m igration . c / 4 m s trace . d / 24 m s trace Tests for maximum dip Undermigration Migration strategy (Yilmaz) 2D versus 3D migration Post- versus post- migration Time versus depth migration Case Migration Case Migration dipping event time migration strong lateral velocity variations associated with complex overburden structure depth migration conflicting dips with different stacking velocities prestack migration 3D behavior of fault planes and salt flanks 3D migration complex nonhyperbolic moveout prestack migration 3D structure 3D migration ZO versus stack /CMP stack section . 1 Complex structure nonhyperbolic moveout . 2 Conflicting dips - Pre stack migration Migration algorithm • Integral solution to the scalar wave equation • Finite-difference solution • Frequency-wavenumber implementation: Stolt, phase- shift/Gazdag . 1 Handle steep dips with sufficient accuracy . 2 Handle lateral and vertical velocity variations . 3 , Be implemented efficiently Kirchhoff depth migration