watex.methods.em.EMAP.skew#

EMAP.skew(method='swift', return_skewness=False, suppress_outliers=False)[source]#

The conventional asymmetry parameter based on the Z magnitude.

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). It is generally considered that an electrical structure of \(skew < 0.4\) can be treated as a 2D medium.

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] & = & \text{Im} C_2*C_1^*\\\[C_1, C_2] & = & \text{Re} C_1 * \text{Im}C_2 - R_e(C_2)* \text{Im}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).

Parameters

  • data (str of path-like or list of pycsamt.core.edi.Edi) – EDI data or EDI object with full impedance tensor Z.

  • method (str) – Kind of correction. Can be swift for the remove distorsion proposed by Swift in 1967. The value close to 0. assume the 1D and 2D structures and 3D otherwise. Conversly to bahr for the remove distorsion proposed by Bahr in 1991. The latter threshold is set to 0.3. Above this value the structures is 3D.

  • return_skewness (str,) – Typically returns the type of skewness. 'skew' or mu for skew and rotation- all invariant values respectively. Any other value return both skew and rotational invariant.

  • suppress_outliers (bool, default=False,) –

    Remove the outliers (if applicable in the data ) before normalizing.

    New in version 0.1.6.

Returns

skw, mu –

  • Array of skew at each frequency

  • rotational invariant mu at each frequency that measures of phase differences in the impedance tensor.

Return type

Tuple of ndarray-like , shape (N, M )

See also

watex.utils.plot_skew

For phase sensistive skew visualization - naive plot.

watex.view.TPlot.plotSkew

For consistent plot of phase sensitive skew visualization. Allow customize plots.

watex.view.TPlot.plot_phase_tensors

Plot skew as ellipsis visualization by turning the tensor parameter to skew.

Examples

>>> from watex.methods.em import Processing
>>> edipath = 'data/edis'
>>> p = Processing().fit(edipath)
>>> sk,_ = p.skew()
>>> sk[0:, ]
... array([0.45475527, 0.7876896 , 0.44986397])

References

Bahr, K., 1991. Geological noise in magnetotelluric data: a classification

of distortion types. Physics of the Earth and Planetary Interiors 66 (1–2), 24–38.

Barcelona, H., Favetto, A., Peri, V.G., Pomposiello, C., Ungarelli, C., 2013.

The potential of audiomagnetotellurics in the study of geothermal fields: A case study from the northern segment of the La Candelaria Range, northwestern Argentina. J. Appl. Geophys. 88, 83–93. https://doi.org/10.1016/j.jappgeo.2012.10.004

Swift, C., 1967. A magnetotelluric investigation of an electrical conductivity

anomaly in the southwestern United States. Ph.D. Thesis, MIT Press. Cambridge.