# Elastic*

Elastic* is a rock physics app for Android OS. It was built in Google App Inventor and we are planning to make it available in the Android Market in May 2011. It was developed and tested on Android 2.3 (Gingerbread).

## Functionality

The app is a straightforward calculator. It accepts values for VP and/or VS, and density. Instead of one of the velocities, you can enter a VP/VS ratio if you prefer. The app returns values for all of the elastic moduli.

## Features

• Optionally enter VP/VS ratio instead of one of the velocities
• If you only provide VP and density, the app assumes a VP/VS ratio of 2.0
• Shake the phone to reset the form (note: some phones are quite sensitive and reset easily)
• Click on the star for 'about' info

## Parameters

The app computes elastic moduli according to the equations on Evan's rock physics cheatsheet.

## Bugs and deficiencies

• There is no way to use Imperial units of measure

## For future release

• Use km/s or m/s for velocities, and kg/m3 or g/cm3 for density
• Implement Imperial unit conversion

This lookup table contains the relevant equations for this App:

Conversion formulas
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.
${\displaystyle E}$ ${\displaystyle \nu }$ ${\displaystyle K}$ ${\displaystyle \mu }$ ${\displaystyle \lambda }$ ${\displaystyle V_{P}}$ ${\displaystyle V_{S}}$ ${\displaystyle V_{P}/V_{S}}$
Young's modulus, Poisson's ratio
${\displaystyle E,\nu }$
${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle {\tfrac {E}{3(1-2\nu )}}}$ ${\displaystyle {\tfrac {E}{2(1+\nu )}}}$ ${\displaystyle {\tfrac {E\nu }{(1+\nu )(1-2\nu )}}}$ ${\displaystyle {\sqrt {\tfrac {E(1-\nu )}{\rho (1-\nu )(1-2\nu )}}}}$ ${\displaystyle {\sqrt {\tfrac {E}{2\rho (1-\nu )}}}}$ ${\displaystyle {\sqrt {\tfrac {1-\nu }{{\tfrac {1}{2}}-\nu }}}}$
Bulk modulus, Shear modulus
${\displaystyle K,\mu }$
${\displaystyle {\tfrac {9K\mu }{3\kappa +\mu }}}$ ${\displaystyle {\tfrac {3K+2\mu }{2(3\kappa +\mu )}}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle \kappa -{\tfrac {2}{3}}\mu }$ ${\displaystyle {\sqrt {\tfrac {\kappa +{\tfrac {4}{3}}\mu }{\rho }}}}$ ${\displaystyle {\sqrt {\tfrac {\mu }{\rho }}}}$ ${\displaystyle {\sqrt {\tfrac {\kappa +{\tfrac {4}{3}}\mu }{\mu }}}}$
Shear modulus, 1st Lamé parameter
${\displaystyle \mu ,\lambda }$
${\displaystyle {\tfrac {\mu (3\lambda +2\mu )}{\lambda +\mu }}}$ ${\displaystyle {\tfrac {\lambda }{2(\lambda +\mu )}}}$ ${\displaystyle \lambda +{\tfrac {2}{3\mu )}}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle {\sqrt {\tfrac {\lambda +2\mu }{\rho }}}}$ ${\displaystyle {\sqrt {\tfrac {\mu }{\rho }}}}$ ${\displaystyle {\sqrt {\tfrac {\lambda +2\mu }{\mu }}}}$
P-wave velocity, S-wave velocity
${\displaystyle V_{P},V_{S}}$
${\displaystyle {\tfrac {\rho V_{S}^{2}(3V_{P}^{2}-4V_{S}^{2})}{V_{P}^{2}-V_{S}^{2}}}}$ ${\displaystyle {\tfrac {V_{P}^{2}-2V_{S}^{2}}{2(V_{P}^{2}-V_{S}^{2})}}}$ ${\displaystyle \rho (V_{P}^{2}-{\tfrac {4}{3}}V_{S}^{2})}$ ${\displaystyle \rho V_{S}^{2}}$ ${\displaystyle \rho V_{P}^{2}-2V_{S}^{2}}$ ${\displaystyle -}$ ${\displaystyle -}$ ${\displaystyle -}$