Kraijenhoff#

class Kraijenhoff(n_terms=10)[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.

  • meanstress (float) – mean value of the stress, used to set the initial value such that the final step times the mean stress equals 1

  • cutoff (float) – proportion after which the step function is cut off. default is 0.999.

Notes

The Kraijenhoff van de Leur function is explained in Van de Leur (1958). The impulse response function may be written as:

\[\theta(t) = \frac{4}{\pi S} \sum_{n=1,3,5...}^\infty \frac{1}{n} e^{-n^2\frac{t}{j}} \sin (\frac{n\pi x}{L})\]

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.

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.

impulse

Method to return the impulse response function.

step

Method to return the step function.