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

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 stress-strain properties of isotropic medium  Bulk moduluskvolume stress/strain  Shear modulusshear stress/strain  Poissons ratio transverse/longitudinal strain  Young’s modulusE longitudinal stress/strain

Bulk modulus Bulk modulus:  = compressibility

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

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

Young’s modulus L+

 = 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

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

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

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 P-wave velocities v p for different material in (km/s)

Igneous / Metamorphic rocks Granite Gabbro Ultramafic rocks Serpentinite Pore fluids Air Water Ice Petroleum Other materials Steel Iron Aluminium Concrete , P-wave velocities v p for different material in (km/s) Kearey and Brooks, 1991

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

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

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)

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