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.