Plot phase sensitive skew

shows the phase sensitivity Skew that represents a measure of the skew of the phases of the impedance tensor

# Author: L.Kouadio
# Licence: BSD-3-clause

Skew is a dimensionality tool or a conventional asymmetry parameter based on the Z magnitude. Indeed, the EM signal is influenced by several factors such as the dimensionality of the propagation medium and the physical anomalies, which can distort the EM field both locally and regionally. The distortion of Z was determined from the quantification of its asymmetry and the deviation from the conditions that define its dimensionality. The parameters used for this purpose are all rotational invariant because the Z components involved in its definition are independent of the orientation system used. The conventional asymmetry parameter based on the Z magnitude is the skew defined by Swift (1967) as follows:

\[skew_{swift}= |\frac{Z_{xx} + Z_{yy}}{ Z_{xy} - Z_{yx}}|\]

When the \(skew_{swift}\) is close to 0., we assume a 1D or 2D model when the \(skew_{swift}\) is greater than >=0.2, we assume 3D local anomaly (Bahr, 1991; Reddy et al., 1977).

Furthermore, Bahr (1988) proposed the phase-sensitive skew which calculates the skew taking into account the distortions produced in Z over 2D structures by shallow conductive anomalies and is defined as follows:

\[ \begin{align}\begin{aligned}skew_{Bahr} & = & \sqrt{ \frac{|[D_1, S_2] -[S_1, D_2]|}{|D_2|}} \quad \text{where}\\S_1 & = & Z_{xx} + Z_{yy} \quad ; \quad S_2 = Z_{xy} + Z_{yx}\\D_1 & = & Z_{xx} - Z_{yy} \quad ; \quad D_2 = Z_{xy} - Z_{yx}\end{aligned}\end{align} \]

Note that The phase differences between two complex numbers \(C_1\) and \(C_2\) and the corresponding amplitude products are now abbreviated by the commutators:

\[ \begin{align}\begin{aligned}\[C_1, C_2] & = & I_m C_2*C_1^*\\\[C_1, C_2] & = & R_e C_1 * I_m C_2 - R_e(C_2)* I_m C_1\end{aligned}\end{align} \]

Indeed, \(skew_{Bahr}\) measures the deviation from the symmetry condition through the phase differences between each pair of tensor elements, considering that phases are less sensitive to surface distortions(i.e. galvanic distortion). The \(skew_{Bahr}\) threshold is set at 0.3 and higher values mean 3D structures (Bahr, 1991).

In this demonstration, we will plot skew with a sample of 20 files and we start by importing the required modules

import watex as wx

• Barh method

edi_sk = wx.fetch_data ("edis", return_data =True , samples = 20 )
# we can set the Barh threshold line by setting the threshold line to 'Barh'
wx.utils.plot_skew (edi_sk, method ='bahr', threshold_line='bahr', fig_size = (11, 5), style ='classic')

<AxesSubplot:xlabel='Frequency ($H_z$)', ylabel='Skew($\\mu$)'>

• Swift method

wx.utils.plot_skew (edi_sk, method ='swift', threshold_line='swift', fig_size = (11, 5),
                    mode='periods')

<AxesSubplot:xlabel='Period ($s$)', ylabel='Skew($\\mu$)'>