kitagawa (version 1.1-1)

alpha_constants: Calculate any constants depending on $\alpha$

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).

Usage

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

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.

Details

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

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.

The various constants which may be calculated are [object Object],[object Object],[object Object],[object Object]

References

Kitagawa, Y., S. Itaba, N. Matsumoto, and N. Koisumi (2011), Frequency characteristics of the response of water pressure in a closed well to volumetric strain in the high-frequency domain, J. Geophys. Res., 116, B08301, doi:10.1029/2010JB007794.

http://www.agu.org/pubs/crossref/2011/2010JB007794.shtml

Abramowitz, M. and Stegun, I. A. (Eds.). "Kelvin Functions." $\S 9.9$ in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 379-381, 1972.

See Also

omega_constants, well_response, kelvin

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)