# HantushWellModel#

An implementation of the Hantush well function for multiple pumping wells.

Parameters
• up (bool, optional) – indicates whether a positive stress will cause the head to go up (True, default) or down (False)

• 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 impulse response function is:

$\theta(r, t) = \frac{A}{2t} \exp(-t/a - abr^2/t)$

where r is the distance from the pumping well to the observation point and must be specified. A, a, and b are parameters, which are slightly different from the Hantush response function. The gain is defined as:

$$\text{gain} = A K_0 \left( 2r \sqrt(b) \right)$$

The implementation used here is explained in Veling and Maas (2010).

## 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. numba_step numpy_step quad_step set_distances step Method to return the step function. variance_gain Calculate variance of the gain from parameters A and b.