watex.utils.ohmicArea#

watex.utils.ohmicArea(data=None, search=45.0, sum=False, objective='ohmS', **kws)[source]#

Compute the ohmic-area from the Vertical Electrical Sounding data collected in exploration area.

Parameters
* data: Dataframe pandas - contains the depth measurement AB from current

electrodes, the potentials electrodes MN and the collected apparents resistivities.

* search: float - The depth in meters from which one expects to find a

fracture zone outside of pollutions. Indeed, the search parameter is used to speculate about the expected groundwater in the fractured rocks under the average level of water inrush in a specific area. For instance in Bagoue region , the average depth of water inrush is around 45m. So the search can be specified via the water inrush average value.

* objective: str - Type operation to outputs. By default, the function

outputs the value of pseudo-area in \(\Omega .m^2\). However, for plotting purpose by setting the argument to view, its gives an alternatively outputs of X and Y, recomputed and projected as weel as the X and Y values of the expected fractured zone. Where X is the AB dipole spacing when imaging to the depth and Y is the apparent resistivity computed

kws: dict - Additionnal keywords arguments from |VES| data operations.

See watex.utils.exmath.vesDataOperator() for futher details.

Returns
List of twice tuples:
  • Tuple(ohmS, error, roots):

    • `ohmS`is the pseudo-area computed expected to be a fractured zone

    • error is the integration error

    • roots is the integration boundaries of the expected fractured

      zone where the basement rocks is located above the resistivity transform function. At these points both curves values equal to null.

  • Tuple (XY, fit XY,XYohmSarea):
    • XY is the ndarray(nvalues, 2) of the operated of AB dipole

      spacing and resistivity rhoa values.

    • fit XY is the fitting ndarray(nvalues, 2) uses to redraw the

      dummy resistivity transform function.

    • XYohmSarea is ndarray(nvalues, 2) of the dipole spacing and

      resistiviy values of the expected fracture zone.

Raises
VESError

If the search is greater or equal to the maximum investigation depth in meters.

Notes

The ohmS value calculated from pseudo-area is a fully data-driven parameter and is used to evaluate a pseudo-area of the fracture zone from the depth where the basement rock is supposed to start. Usually, when exploring deeper using the Vertical Electrical Sounding, we are looking for groundwater in thefractured rock that is outside the anthropic pollution (Biemi, 1992). Since the VES is an indirect method, we cannot ascertain whether the presumed fractured rock contains water inside. However, we assume that the fracture zone could exist and should contain groundwater. Mathematically, based on the VES1D model proposed by `Koefoed, O. (1976)`_ , we consider a function \(\rho_T(l)\), a set of reducing resistivity transform function to lower the boundary plane at half the current electrode spacing \((l)\). From the sounding curve \(\rho_T(l)\), curve an imaginary basement rock \(b_r (l)\) of slope equal to 45° with the horizontal \(h(l)\) was created. A pseudo-area \(S(l)\) should be defined by extending from \(h(l)\) the \(b_r (l)\) curve when the sounding curve \(\rho_T(l)\) is below \(b_r(l)\), otherwise \(S(l)\) is equal to null. The computed area is called the ohmic-area \(ohmS\) expressed in \(\Omega .m^2\) and constitutes the expected fractured zone. Thus \(ohmS\) ≠ \(0\) confirms the existence of the fracture zone while of \(Ohms=0\) raises doubts. The equation to determine the parameter is given as:

\[ \begin{align}\begin{aligned}ohmS & = &\int_{ l_i}^{l_{i+1}} S(l)dl \quad {s.t.}\\\begin{split}S(l) & = & b_r (l) - \rho_T (l) \quad \text{if} \quad b_r (l) > \rho_T (l) \\ & = & 0. \quad \text{if} \quad b_r (l) \leq \rho_T (l)\end{split}\\b_r(l) & = & l + h(l) \quad ; \quad h(l) = \beta\\\rho_T(l) & = & l^2 \int_{0}^{\infty} T_i( \lambda ) h_1( \lambda l) \lambda d\lambda\end{aligned}\end{align} \]

where \(l_i \quad \text{and} \quad l_{i+1}\) solve the equation \(S(l=0)\); \(l\) is half the current electrode spacing \(AB/2\), and \(h_1\) denotes the first-order of the Bessel function of the first kind, \(\beta\) is the coordinate value on y-axis direction of the intercept term of the \(b_r(l)\) and \(h(l)\), \(T_i(\lambda )\) resistivity transform function, \(lamda\) denotes the integral variable, where n denotes the number of layers, \(rho_i\) and \(h_i\) are the resistivity and thickness of the \(i-th\) layer, respectively. Get more explanations and cleareance of formula in the paper of `Kouadio et al 2022`_.

. _Cote d’Ivoire: https://en.wikipedia.org/wiki/Ivory_Coast

Examples

>>> from watex.utils.exmath import ohmicArea
>>> from watex.utils.coreutils import vesSelector
>>> data = vesSelector (f= 'data/ves/ves_gbalo.xlsx')
>>> (ohmS, err, roots), *_ = ohmicArea(data = data, search =45, sum =True )
... (13.46012197818152, array([5.8131967e-12]), array([45.        , 98.07307307]))
# pseudo-area is computed between the spacing point AB =[45, 98] depth.
>>> _, (XY.shape, XYfit.shape, XYohms_area.shape) = ohmicArea(
                AB= data.AB, rhoa =data.resistivity, search =45,
                objective ='plot')
... ((26, 2), (1000, 2), (8, 2))