# Bulk modulus

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One of the elastic moduli, sometimes called *incompressibility*, *volumetric modulus*, or *stiffness*.

## Contents

## Definition

## In terms of *V*_{P} and *V*_{S}

## Other expressions

*K* can also be expressed in terms of Young's modulus, *E*, and Poisson's ratio, *ν*. This could be thought of as 'the engineer's perspective':

The 'rock physics perspective' casts *K* in terms of the 1st Lamé parameter *λ* and shear modulus *μ*:

## Bulk modulus of effective media

Upper and lower bounds on the bulk modulus of mixtures of *n* materials can be obtained using Voigt–Reuss and Hashin–Shtrikman bounds.

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The elastic properties of homogeneous isotropic linear elastic materials are uniquely determined by any two moduli. Given any two, the others can thus be calculated. Key reference: Mavko, G, T Mukerji and J Dvorkin (2003), The Rock Physics Handbook, Cambridge University Press.
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P-wave velocity |
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S-wave velocity |
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Velocity ratio |
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1st Lamé parameter |
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Shear modulus |
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Young's modulus |
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Bulk modulus |
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Poisson's ratio |
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P-wave modulus |