kitagawa (version 3.1.2)

alpha_constants: Calculate any constants depending on effective stress coefficient \(\alpha\)

Description

This function accesses the appropriate method to calculate the \(\alpha\)-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.

Usage

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

Value

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

Arguments

alpha

the constant alpha (see omega_constants)

c.type

the constant to calculate

Author

A. J. Barbour <[e-mail]>

Details

What is "alpha"?

The constant \(\alpha\) is a function of frequency \(\omega\) as well as aquifer and well parameters; it is formally defined as $$\alpha \equiv R_S \sqrt{\omega S / T}$$ 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 \(\Phi\) in Eqn. 10

Psi

Given as \(\Psi\) 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)

See Also

omega_constants, well_response

Other ConstantsCalculators: kitagawa-constants, omega_constants()

Examples

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)