class watex.externals.z.ResPhase(z_array=None, z_err_array=None, freq=None, **kwargs)[source]#

Bases: object

resistivity and phase class - generates Resistivity and phase tensors object.

compute_resistivity_phase(z_array=None, z_err_array=None, freq=None)[source]#

compute resistivity and phase from z and z_err

property phase#
property phase_det#
property phase_det_err#
property phase_err#
property phase_err_xx#
property phase_err_xy#
property phase_err_yx#
property phase_err_yy#
property phase_xx#
property phase_xy#
property phase_yx#
property phase_yy#
property res_det#
property res_det_err#
property res_err_xx#
property res_err_xy#
property res_err_yx#
property res_err_yy#
property res_xx#
property res_xy#
property res_yx#
property res_yy#
property resistivity#
property resistivity_err#
set_res_phase(res_array, phase_array, freq, res_err_array=None, phase_err_array=None)[source]#

Set values for resistivity (res - in Ohm m) and phase (phase - in degrees), including error propagation.

Parameters

  • res_array (np.ndarray(num_freq, 2, 2)) – resistivity array in Ohm-m

  • phase_array (n_loggeingp.ndarray(num_freq, 2, 2)) – phase array in degrees

  • freq (np.ndarray(num_freq)) – frequency array in Hz

  • res_err_array (np.ndarray(num_freq, 2, 2)) – resistivity error array in Ohm-m

  • phase_err_array (np.ndarray(num_freq, 2, 2)) – phase error array in degrees

class watex.externals.z.Z(z_array=None, z_err_array=None, freq=None)[source]#

Bases: ResPhase

Z class - generates an impedance tensor (Z) object.

Z is a np.complex128 array of the form (n_freq, 2, 2), with indices in the following order:

  • Zxx: (0,0)

  • Zxy: (0,1)

  • Zyx: (1,0)

  • Zyy: (1,1)

All errors are given as standard deviations (sqrt(VAR))

Parameters

  • z_array (numpy.ndarray(n_freq, 2, 2)) – array containing np.complex128 impedance values

  • z_err_array (numpy.ndarray(n_freq, 2, 2)) – array containing error values (standard deviation) of impedance tensor elements

  • freq (np.ndarray(n_freq)) – array of frequency values corresponding to impedance tensor elements.

Attributes

Description

freq

array of frequencies corresponding to elements of z

rotation_angle

angle of which data is rotated by

z

impedance tensor

z_err

estimated errors of impedance tensor

resistivity

apparent resisitivity estimated from z in Ohm-m

resistivity_err

apparent resisitivity error

phase

impedance phase (deg)

phase_err

error in impedance phase

Methods

Description

det

calculates determinant of z with errors

invariants

calculates the invariants of z

inverse

calculates the inverse of z

remove_distortion

removes distortion given a distortion matrix

remove_ss

removes static shift by assumin Z = S * Z_0

norm

calculates the norm of Z

only1d

zeros diagonal components and computes the absolute valued mean of the off-diagonal components.

only2d

zeros diagonal components

res_phase

computes resistivity and phase

rotate

rotates z positive clockwise, angle assumes North is 0.

set_res_phase

recalculates z and z_err, needs attribute freq

skew

calculates the invariant skew (off diagonal trace)

trace

calculates the trace of z
Example
>>> import mtpy.core.z as mtz
>>> import numpy as np
>>> z_test = np.array([[0+0j, 1+1j], [-1-1j, 0+0j]])
>>> z_object = mtz.Z(z_array=z_test, freq=[1])
>>> z_object.rotate(45)
>>> z_object.resistivity
property det#

Return the determinant of Z

Returns

det_Z

Return type

np.ndarray(nfreq)

property det_err#

Return the determinant of Z error

Returns

det_Z_err

Return type

np.ndarray(nfreq)

property freq#

Frequencies for each impedance tensor element

Units are Hz.

property invariants#

Return a dictionary of Z-invariants.

property inverse#

Return the inverse of Z.

(no error propagation included yet)

property norm#

Return the 2-/Frobenius-norm of Z

Returns

norm

Return type

np.ndarray(nfreq)

property norm_err#

Return the 2-/Frobenius-norm of Z error

Returns

norm_err

Return type

np.ndarray(nfreq)

property only_1d#

Return Z in 1D form.

If Z is not 1D per se, the diagonal elements are set to zero, the off-diagonal elements keep their signs, but their absolute is set to the mean of the original Z off-diagonal absolutes.

property only_2d#

Return Z in 2D form.

If Z is not 2D per se, the diagonal elements are set to zero.

remove_distortion(distortion_tensor, distortion_err_tensor=None)[source]#

Remove distortion D form an observed impedance tensor Z to obtain the uperturbed “correct” Z0: Z = D * Z0

Propagation of errors/uncertainties included

Parameters

  • distortion_tensor (np.ndarray(2, 2, dtype=real)) – real distortion tensor as a 2x2

  • distortion_err_tensor – default is None

Return type

np.ndarray(2, 2, dtype=’real’)

returns

impedance tensor with distorion removed

Return type

np.ndarray(num_freq, 2, 2, dtype=’np.complex128’)

returns

impedance tensor error after distortion is removed

Return type

np.ndarray(num_freq, 2, 2, dtype=’np.complex128’)

Example
>>> import mtpy.core.z as mtz
>>> distortion = np.array([[1.2, .5],[.35, 2.1]])
>>> d, new_z, new_z_err = z_obj.remove_distortion(distortion)

remove_ss(reduce_res_factor_x=1.0, reduce_res_factor_y=1.0)[source]#

Remove the static shift by providing the respective correction factors for the resistivity in the x and y components. (Factors can be determined by using the “Analysis” module for the impedance tensor)

Assume the original observed tensor Z is built by a static shift S and an unperturbated “correct” Z0 :

  • Z = S * Z0

therefore the correct Z will be :

  • Z0 = S^(-1) * Z

Parameters

  • reduce_res_factor_x (float or iterable list or array) – static shift factor to be applied to x components (ie z[:, 0, :]). This is assumed to be in resistivity scale

  • reduce_res_factor_y (float or iterable list or array) – static shift factor to be applied to y components (ie z[:, 1, :]). This is assumed to be in resistivity scale

Returns

static shift matrix,

Return type

np.ndarray ((2, 2))

Returns

corrected Z

Return type

mtpy.core.z.Z

Note

The factors are in resistivity scale, so the entries of the matrix “S” need to be given by their square-roots!

rotate(alpha)[source]#

Rotate Z array by angle alpha.

Rotation angle must be given in degrees. All angles are referenced to geographic North, positive in clockwise direction. (Mathematically negative!)

In non-rotated state, X refs to North and Y to East direction.

Updates the attributes

  • z

  • z_err

  • zrot

  • resistivity

  • phase

  • resistivity_err

  • phase_err

property skew#

Returns the skew of Z as defined by Z[0, 1] + Z[1, 0]

Note

This is not the MT skew, but simply the linear algebra skew

Returns

skew

Return type

np.ndarray(nfreq, 2, 2)

property skew_err#

Returns the skew error of Z as defined by Z_err[0, 1] + Z_err[1, 0]

Note

This is not the MT skew, but simply the linear algebra skew

Returns

skew_err

Return type

np.ndarray(nfreq, 2, 2)

property trace#

Return the trace of Z

Returns

Trace(z)

Return type

np.ndarray(nfreq, 2, 2)

property trace_err#

Return the trace of Z

Returns

Trace(z)

Return type

np.ndarray(nfreq, 2, 2)

property z#

Impedance tensor

np.ndarray(nfreq, 2, 2)

property z_err#