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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

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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

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Physical quantities to describe stress-strain properties of isotropic medium Bulk moduluskvolume stress/strain Shear modulusshear stress/strain Poissons ratio transverse/longitudinal strain Young’s modulusE longitudinal stress/strain

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Bulk modulus Bulk modulus: = compressibility

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Shear modulus Shear modulus: The shear modulus is zero for fluids and gaseous media is the shear stress

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Poissons ratio Poisson’s ratio varies from 0 to ½. Poisson’s ratio has the value ½ for fluids -

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Young’s modulus L+

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= Shear modulus = Lame’s lambda constant Seismic Velocities in a homogeneous medium k = Bulk modulus = mass density Can be expressed as function of different combinations of K, , E, , , Often used expressions are: E = Young’s modulus = Poisson ratio

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Ratio V p and V s depends on Poisson ratio: where

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Seismic velocity Depend on Matrix and structure of the stone Lithology Porosity Porefilling interstitial fluid Temperature Degree of compaction ………

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Seismic Velocity depending on rock properties (Sheriff und Geldard, 1995)

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Measurements of velocities Laboratory measurements using probes Borehole measurements Refraction seismics Analysis of reflection hyperbolas Vertical seismic profiling

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Kearey and Brooks, 1991 Unconsolidated Material Sand (dry) Sand (water saturated) Clay Glacial till (water saturated) Permafrost Sedimentary rocks Sandstone Tertiary sandstone Pennant sandstone (Carboniferous) Cambrian quartzite Limestones Cretaceous chalk Jurassic oolites and bioclastic limestones Carboniferous limestone Dolomites Salt Anhydrite Gypsum 0.2 - 1.0 1.5 - 2.0 1.0 - 2.5 1.5 - 2.5 3.5 - 4.0 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 P-wave velocities v p for different material in (km/s)

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Igneous / Metamorphic rocks Granite Gabbro Ultramafic rocks Serpentinite Pore fluids Air Water Ice Petroleum Other materials Steel Iron Aluminium Concrete 5.5 - 6.0 6.5 - 7.0 7.5 - 8.5 5.5 - 6,5 0.3 1.4 - 1.5 3.4 1.3 - 1.4 6.1 5.8 6.6 3.6 P-wave velocities v p for different material in (km/s) Kearey and Brooks, 1991

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Interval-Velocity Instantaneous Velocity Average-Velocity Velocities t m : measured reflected ray traveltime m : one-way reflected ray traveltime only through m th layer

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V1, 1 v2, 2 v3, 3 RMS-velocity (root-mean-square) Several horizontal layers t1t1 t2t2 t3t3 Measured traveltimes

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Conversion from v rms in v int (interval velocities) Dix’ Formula n-1 n V rms 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)

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Fast Anisotropy Slow Anisotropy(seismic): Variation of seismic velocity depending on the direction in which it is measured.

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