Seismic Velocities Important for : Conversion from traveltime to depth Check of results by modeling Imaging of the data (migration) Classification and Filtering of Signal and Noise Predictions of the Lithology Aid for geological Interpretation Seismic velocities • Can be written as function of physical quantities that describe stress/strain relations • Depend on medium properties • Measurements of velocities • Definitions of velocities (interval, rms, average etc.) • Dix formula: relation between rms and interval velocities • Anisotropy Physical quantities to describe stressstrain properties of isotropic medium • Bulk modulus k volume stress/strain • Shear modulus µ shear stress/strain • Poissons ratio σ transverse/longitudinal strain • Young’s modulus E longitudinal stress/strain Bulk modulus Bulk modulus: κ = compressibility P k= = κ ∆V / V Shear modulus ∆L F/A = ∆L/L Shear modulus: τ µ= tanθ τ is the shear stress The shear modulus µ is zero for fluids and gaseous media Poissons ratio - Poisson’s ratio varies from to ½ Poisson’s ratio has the value ½ for fluids 3k − 2µ σ= 2(3k + µ) Young’s modulus L+ 9kµ E= 3k + µ Seismic Velocities in a homogeneous medium Can be expressed as function of different combinations of K, σ, E, µ, ρ, λ Often used expressions are: k = Bulk modulus σ = Poisson ratio 4µ k+ λ + 2µ vp = = ρ ρ µ vs = ρ E = Young’s modulus µ = Shear modulus ρ = mass density λ = Lame’s lambda constant λ=k− µ Ratio Vp and Vs depends on Poisson ratio: Vs 0.5 − σ = Vp 1−σ where 3k − 2µ σ= 2(3k + µ) Seismic velocity Depend on • Matrix and structure of the stone • Lithology • Porosity • Porefilling interstitial fluid • Temperature • Degree of compaction • ……… Seismic Velocity depending on rock properties (Sheriff und Geldard, 1995) Measurements of velocities • • • • • Laboratory measurements using probes Borehole measurements Refraction seismics Analysis of reflection hyperbolas Vertical seismic profiling P-wave velocities vp for different material in (km/s) Unconsolidated Material Sand (dry) Sand (water saturated) Clay Glacial till (water saturated) Permafrost 0.2 - 1.0 1.5 - 2.0 1.0 - 2.5 1.5 - 2.5 3.5 - 4.0 Sedimentary rocks Sandstone Tertiary sandstone Pennant sandstone (Carboniferous) Cambrian quartzite Limestones Cretaceous chalk Jurassic oolites and bioclastic limestones Carboniferous limestone Dolomites Salt Anhydrite Gypsum 2.0 - 6.0 2.0 - 2.5 4.0 - 4.5 5.5 - 6.0 2.0 - 6.0 2.0 - 2.5 3.0 - 4.0 5.0 - 5.5 2.5-6.5 4.5 - 5.0 4.5 - 6.5 2.0 - 3.5 Kearey and Brooks, 1991 P-wave velocities vp for different material in (km/s) Igneous / Metamorphic rocks Granite Gabbro Ultramafic rocks Serpentinite 5.5 - 6.0 6.5 - 7.0 7.5 - 8.5 5.5 - 6,5 Pore fluids Air Water Ice Petroleum 0.3 1.4 - 1.5 3.4 1.3 - 1.4 Other materials Steel Iron Aluminium Concrete 6.1 5.8 6.6 3.6 Kearey and Brooks, 1991 Velocities Interval-Velocity Instantaneous Velocity VI = zm − zn zm − zn = tm − tn τm dz Vinst = dt n Average-Velocity Vav = n ∑ z ∑v τ i =1 n ∑τ i =1 i i = i =1 n i i ∑τ i =1 i tm : measured reflected ray traveltime τm : one-way reflected ray traveltime only through mth layer Several horizontal layers V1, τ1 t1 t2 v2 , τ2 Measured traveltimes v3 , τ3 n RMS-velocity (root-mean-square) v2 = rms t3 v ∑ i τi i =1 n ∑τ i =1 i Dix’ Formula Conversion from v rms in vint (interval velocities) ⎡ (VRMS , n )2 tn − (VRMS , n − 1)2 tn − ⎤ V int = ⎢ ⎥ n − tn − t ⎣ ⎦ VRMS , n − tn − tn VRMS , n n-1 V int n Vrms is approximated by the stacking velocity that is obtained by NMO correction of a CMP measurement (when maximum offset is small compared with reflector depth) Anisotropy Fast Slow Anisotropy(seismic): Variation of seismic velocity depending on the direction in which it is measured [...]... Brooks, 1991 Velocities Interval -Velocity Instantaneous Velocity VI = zm − zn zm − zn = tm − tn τm dz Vinst = dt n Average -Velocity Vav = n ∑ z ∑v τ i =1 n ∑τ i =1 i i = i =1 n i i ∑τ i =1 i tm : measured reflected ray traveltime τm : one-way reflected ray traveltime only through mth layer Several horizontal layers V1, τ1 t1 t2 v2 , τ2 Measured traveltimes v3 , τ3 n RMS -velocity (root-mean-square) v2... int = ⎢ ⎥ n − tn − 1 t ⎣ ⎦ VRMS , n − 1 tn − 1 tn VRMS , n n-1 V int n Vrms is approximated by the stacking velocity that is obtained by NMO correction of a CMP measurement (when maximum offset is small compared with reflector depth) Anisotropy Fast Slow Anisotropy(seismic): Variation of seismic velocity depending on the direction in which it is measured ...Seismic Velocity depending on rock properties (Sheriff und Geldard, 1995) Measurements of velocities • • • • • Laboratory measurements using probes Borehole measurements Refraction seismics Analysis of reflection ... Salt Anhydrite Gypsum 2.0 - 6.0 2.0 - 2.5 4.0 - 4.5 5.5 - 6.0 2.0 - 6.0 2.0 - 2.5 3.0 - 4.0 5.0 - 5.5 2. 5-6 .5 4.5 - 5.0 4.5 - 6.5 2.0 - 3.5 Kearey and Brooks, 1991 P-wave velocities vp for different... Granite Gabbro Ultramafic rocks Serpentinite 5.5 - 6.0 6.5 - 7.0 7.5 - 8.5 5.5 - 6,5 Pore fluids Air Water Ice Petroleum 0.3 1.4 - 1.5 3.4 1.3 - 1.4 Other materials Steel Iron Aluminium Concrete... 6.6 3.6 Kearey and Brooks, 1991 Velocities Interval -Velocity Instantaneous Velocity VI = zm − zn zm − zn = tm − tn τm dz Vinst = dt n Average -Velocity Vav = n ∑ z ∑v τ i =1 n ∑τ i =1 i i = i =1