alpha_constants: Calculate any constants depending on effective stress...
In kitagawa: Spectral Response of Water Wells to Harmonic Strain and Pressure Signals

Description Usage Arguments Details Value Author(s) See Also Examples

This function accesses the appropriate method to calculate the α-dependent constant associated with the choice of c.type. There are currently four such constants, which correspond to Equations 10, 11, 18, 19 in Kitagawa et al (2011).

This function is not likely to be needed by the user.

alpha_constants(alpha = 0, c.type = c("Phi", "Psi", "A", "Kel"))

## Default S3 method:
alpha_constants(alpha = 0, c.type = c("Phi", "Psi", "A", "Kel"))

`alpha`	the constant alpha (see `omega_constants`)
`c.type`	the constant to calculate

What is `"alpha"`?

The constant α is a function of frequency ω as well as aquifer and well parameters; it is formally defined as

α \equiv R_S √{ω S / T}

where S is the storativity, T is the aquifer's effective transmissivity, and R_S is the radius of the screened portion of the well.

What is calculated?

The various constants which may be calculated with this function are

Phi: Given as Φ in Eqn. 10
Psi: Given as Ψ in Eqn. 11
A: Given as A_i, i=1,2 in Eqns. 18, 19
Kel: The complex Kelvin functions (see Abramowitz and Stegun, 1972)

Complex matrix having values representing the constant represented by c.type, as well as any other α-dependent constants which are needed in the computation.

A. J. Barbour <andy.barbour@gmail.com>

omega_constants, well_response

Other ConstantsCalculators: kitagawa-constants, omega_constants()

1
2
3

alpha_constants()   # kelvin::Keir gives warning
alpha_constants(1)  # defaults to constant 'Phi' (note output also has Kel)
alpha_constants(1:10, c.type="A")  # constant 'A' (again, note output)