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P wave

It is also named primary (sonic) wave, compression wave, longitudinal wave. Generally it is an elastic space wave. During seismic events it is the fastest (and therefore primary) of the three generated seismic waves (besides, S wave and superficial wave) with a velocity vp of 5.5 to 7.2 km/s in the Earth’s crust and 7.8 to 8.5 km/s in the Earth’s mantle. Generally vp increases with density. It is called compression wave because particles move along (or longitudinally with) the direction of propagation leading to elastic compression and extension of a rock volume during an earth quake. In an isotropic medium the velocity of the P wave vp can be described by the following equation:

vp = 0.5*[{E*(1-ν)}/{ρ*(1-2ν)*(1+ν)}]

with E as Young’s modulus, ν as the Poisson’s ratio and ρ as density.

Poisson's ratio

The dimensionless ν describes the deformation behaviour of a rock body in terms of the negative ratio between radial strain ε33 and axial strain ε11:

ν = δε33/δε11.

Usually the Poisson's ratio is calculated as the ratio between the gradients of the load paths of the unload-load cycle for both, the radial and the axial ε-σ1 curves of a given uniaxial/triaxial test.

Generally ν ranges between 0.1 and 0.5. In rocks it rarely exceeds 0.3. Exceptions include weakly consolidated sandstone and very soft claystone where ν can reach a value of 0.45). Brittle rocks have a low Poisson’s ratio.

Pore pressure

Pp is the pressure exerted by the brine within the pore space of a rock which counteracts the applied (external) stress Sij.


The porosity of a specimen stands for the volume of all its voids (pores and open cracks) in relation to the total volume of the specimen. Using the bulk density ρb and the grain density ρg, the effective porosity φeff is calculated by the following equation:

φeff = 1 – (ρbg)



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