This page here has been created for the latest stable release of Salvus. You have chosen to view the documentation for another Salvus version. Please be aware there might be some small differences you have to account for.
There exists a whole zoo of different parameterizations to describe the acoustic or elastic properties of a medium.
Salvus offers a lot of flexibility and supports various parameterizations. Because conversion can be a tedious and error-prone task, we list several parameter options and how the translate into each other below.
Internally, Salvus uses an abstract formulation of the acoustic wave equation, that allows to treat different parameterizations within the same implementation:
Different choices of and lead to a different physical meaning of and .
parameter | symbol | unit | Salvus key |
---|---|---|---|
variable | M0 | ||
variable | M1 | ||
density | RHO | ||
velocity (sound speed) | or | VP | |
impedance | coming soon | ||
compressibility | coming soon |
Below, we list conversion formulas for a displacement potential .
Salvus can handle isotropic and anisotropic elastic media and supports different parameterizations.
In isotropic media, the elastic properties reduce to three parameters, which can either be expressed using the Lamé coefficients or by the velocities of compressional (P) and shear (S) waves.
parameter | symbol | unit | Salvus key |
---|---|---|---|
first Lamé coefficient | LAMBDA | ||
second Lamé coefficient, shear modulus | MU | ||
density | RHO | ||
P-wave velocity | VP | ||
S-wave velocity | VS |
Here, the following conversion formula apply.
Due to the symmtetry relations
the fourth-order elastic tensor reduces to at most 21 (in 3-D) or 6 (in 2-D) independent parameters. Using Voigt notation, these are fully specified by
parameter | symbol | unit | Salvus key |
---|---|---|---|
density | RHO | ||
Elastic tensor | Cij |
with 1
i
j
6
in 3-D, and with 1
i
j
3
in 2-D, respectively.
Tilted transversely isotropic material is an important special case of anisotropic media with are only two additional parameters compared to isotropic material that distinguish the wave speeds of horizontally and vertically traveling waves.
parameter | symbol | unit | Salvus key |
---|---|---|---|
first Lamé coefficient | LAMBDA | ||
second Lamé coefficient, shear modulus | MU | ||
density | RHO | ||
horizontal P-wave velocity | VPH | ||
vertical P-wave velocity | VPV | ||
horizontal S-wave velocity | VSH | ||
vertical S-wave velocity | VSV |