# omega_constants: Calculate any constants that depend on angular frequency... In kitagawa: Spectral Response of Water Wells to Harmonic Strain and Pressure Signals

## Description

This function accesses the appropriate method to calculate the ω-dependent constant associated with the choice of c.type.

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

## Usage

 1 2 3 4 omega_constants(omega = 0, c.type = c("alpha", "diffusivity_time"), ...) ## Default S3 method: omega_constants(omega = 0, c.type = c("alpha", "diffusivity_time"), ...) 

## Arguments

 omega frequency, [rad/sec] c.type the constant to calculate ... additional params passed to calculator. In the case of ctype="alpha", set S., T., Rs.; and, in the case of ctype="diffusivity_time", set D. or S., T..

## Details

#### What is "omega"?

The name is in reference to radial frequency ω, which is defined as

ω \equiv 2 π / τ

where τ is the period of oscillation.

#### What is the "alpha" calculation?

The parameter α is defined as

α \equiv r_w √{ω S / T}

where r_w is the radius of the well, where S is the storativity, and T is transmissivity. See the parameter ... for details on how to pass these values.

This definition is common to many papers on the topic. For example, it corresponds to Equation 12 in Kitagawa et al (2011). Because the computation of α depends also on physical properties, additional parameters can be passed through (e.g. the transmissivity).

#### What is the "diffusivity_time" calculation?

This is a similar calculation to omega_norm. It uses the effective hydraulic diffusivity D, which is defined in this case as the ratio of transmissivity to storativity:

D \equiv \frac{T}{S}

## Value

Values of the constant represented by c.type for the given parameters

## Warnings Issued

In the case c.type='alpha', the parameters S., T., and Rs. should be passed; otherwise, values are assumed to ensure the calculation does not fail, and the results are essentially meaningless.

Warnings will be issued if any necessary parameters are missing, indicating default values were used.

## Author(s)

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

alpha_constants, well_response, and kitagawa-package for references and more background.
Other ConstantsCalculators: alpha_constants(), kitagawa-constants
  1 2 3 4 5 6 7 8 9 10 # alpha omega_constants() # default is alpha, but will give warnings about S., T., Rs. omega_constants(T.=1,S.=1,Rs.=1) # 0, no warnings omega_constants(1:10) # sequence, with warnings about S., T., Rs. omega_constants(1:10,T.=1,S.=1,Rs.=1) # sequence, no warnings # diffusivity time omega_constants(c.type="diffusivity_time", D.=1) # 0, no warnings omega_constants(c.type="diff", D.=1) # 0, no warnings (arg matching) omega_constants(c.type="diff") # 0, warnings about S., T. because no D. omega_constants(c.type="diff", S.=1) # 0, warnings about T. because no D. or S.