Kraijenhoff#

class Kraijenhoff(up=True, gain_scale_factor=1.0, cutoff=0.999, n_terms=10, **kwargs)[source]#

The response function of Van de Leur [1958].

Parameters:

up (bool or None, optional) – indicates whether a positive stress will cause the head to go up (True, default) or down (False), if None the head can go both ways.
gain_scale_factor (float, optional) – the scale factor is used to set the initial value and the bounds of the gain parameter, computed as 1 / gain_scale_factor.
cutoff (float, optional) – proportion after which the step function is cut off.
n_terms (int, optional) – Number of terms.

Notes

The Kraijenhoff van de Leur function is explained in Van de Leur [1958].

The impulse response function for this class can be viewed on the Documentation website or using latexify by running the following code in a Jupyter notebook environment:

ps.Kraijenhoff.impulse

The function describes the response of a domain between two drainage channels. The function gives the same outcome as equation 133.15 in Bruggeman [1999]. This is the response that is actually calculated with this function.

The response function has three parameters A, a and b:

A is the gain (scaled),
a is the reservoir coefficient (j in Van de Leur [1958]),
b is the location in the domain with the origin in the middle. This means that b=0 is in the middle and b=1/2 is at the drainage channel. At b=1/4 the response function is most similar to the exponential response function.

Attributes#

impulse

Methods#

`__init__`
`block`	Method to return the block function.
`gain`
`get_init_parameters`	Get initial parameters and bounds.
`get_t`	Internal method to determine the times at which to evaluate the step response, from t=0.
`get_tmax`	Method to get the response time for a certain cutoff.
`step`	Method to return the step function.
`to_dict`	Method to export the response function to a dictionary.