alpha_constants: Calculate any constants depending on effective stress...

In kitagawa: Spectral Response of Water Wells to Harmonic Strain and Pressure Signals

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"))

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

Arguments

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

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)

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.

Author(s)

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

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)

kitagawa documentation built on May 29, 2024, 4:21 a.m.