# Incompressibility

## Definition

Incompressibility (K) is an elastic property of a material which describes the measure of which the material resists change in volume (compression) when subjected to uniform pressure. it is also known as Bulk Modulus .

Incompressibilty is an elastic constant mathematically defined as the ratio of the applied pressure(stress) to the volume strain caused by the pressure. This is illustrated below:

${\displaystyle K={\frac {P}{\Delta V/V}}}$
     where P denotes pressure or stress
V denotes volume
The delta V (ΔV) denotes change in volume.


## Application in Geophysics

The incompressibilty of Earth materials (Rocks and Fluids) greatly determine their acoustic velocities (VP and VS). The elastic constant can expressed in terms of acoustic velocities as shown below:[1]

${\displaystyle K=\rho \left(V_{\mathrm {P} }^{2}-{\frac {4}{3}}V_{\mathrm {S} }^{2}\right)}$