HantushWellModel#

class HantushWellModel(up=True, gain_scale_factor=1.0, cutoff=0.999, use_numba=False, quad=False, **kwargs)[source]#

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).
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.
use_numba (bool, optional) – Use the method ‘numba_step’ to compute the step_response.
quad (bool, optional) – Use the method ‘numba_quad’ to compute the step_response.

Notes

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.HantushWellModel.impulse

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.
`to_dict`	Method to export the response function to a dictionary.
`variance_gain`	Calculate variance of the gain from parameters A and b.