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

Bases: object

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

compute_resistivity_phase(z_array=None, z_err_array=None, freq=None)

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)

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)

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)

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)

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)

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