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:
m0ββt2βΟβββ (m1ββΟ)=f.
Different choices of m0β and m1β lead to a different physical meaning of Ο and f.
parameter
symbol
unit
Salvus key
m0β
m0β
variable
M0
m1β
m1β
variable
M1
density
Ο
kgmβ3
RHO
velocity (sound speed)
vpβ or c
msβ1
VP
impedance
I
kgmβ2sβ1
coming soon
compressibility
Ξ²
ms2kgβ1
coming soon
Below, we list conversion formulas for a displacement potential Ο.
the fourth-order elastic tensor C 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
Ο
kgmβ3
RHO
Elastic tensor
cijβ
Cij
with 1β€iβ€jβ€6 in 3-D, and with 1β€iβ€jβ€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.