Restoring tensor with noised AMT data

Gives a step-by-step guide for restoring Z tensors using real noised data containing missing and weak frequency signals.

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

This is an example of restoring tensors when data contains missing frequency. The data used for the demonstration is from Huayuan data, Hunan province, China. The survey is AMT and data is collected alongside two long lines E1 (2.5km) and E2 (1.8km) . Unfortunately, because of strong interferences and the human-made made noises (agglomerations, power lines) and many factories in this area, signals were strongly corrupted and greatly affected by strong interferences.

• Why recovering tensors is important?

Commonly, a missing and weak signal can just be removed from the whole data and keep only the valid signals from interpolation. However, in the area with strong interferences when data is too much noised, suppressing the weak signals and missing frequencies will greatly affect the quality of data thereby leading to a misinterpretation of the structures found in this area after inversion.

For demonstration, we collected 47 samples of raw data stored as an inner dataset and plot the raw data of impedance tensor z in TM mode to visualize the missing tensors. This is the code snippet:

import watex  as wx
from watex.methods import EMAP
from watex.view import plot2d
data = wx.fetch_data('huayuan', return_data =True, samples =47 ,
                     key ='raw', clear_cache=True) # clear watex cache data to save new EDIs
tro = EMAP().fit(data)

• Output the impedance tensor in TM mode (yx)

Here we output the modulus of the complex number of tensor Z. We can also output z as the complex number by setting out=z since the kind param is by default set to complex. Use 'real' or ’imag’ for the real and imaginary part instead. Refer to method documentation for more details.

z_yx = tro.make2d(out= 'zyx', kind ='modulus' )

• Visualize the plot using the template 2D from watex.view.plot2d().

plot2d(z_yx,
    y = tro.freqs_,
    to_log10= True,
    top_label='Stations',
    plt_style ='imshow',
    fig_size =(10, 4 ),
    font_size =7,
    ylabel ='Frequency[$H_z$]',
    cb_label ='TM mode: $Z_yx$',
    distance =50., # distance between stations
    cmap = 'terrain'
    )

<AxesSubplot:xlabel='Distance(m)', ylabel='Frequency[$H_z$]'>

As a comment: one can visualize the blank line in the data which indicates the missing signal at these points. If we try to remove from each missing signal data which corresponds to data at a certain frequency, we will lose a lot of useful information. Mostly the idea is to interpolate data. The strategy proposed by watex for restoring tensor consists to interpolate in two directions (along the x-axis and y-axis ) at the same time and decide the best value that approximatively fits the surrounding resistivity values( because the demonstration refers to resistivity tensor in TM mode.). This improves a bit the reality of the resistivity distribution of the area.

There is a way to do the quality control of the data before restoring using the quality control method watex.methods.em.Processing.qc() by specifying the tolerance parameter. By default, the data is considered good above 50%. Note that this threshold can be severe with 30%. Indeed, the control for data validity should be soft when the tolerance parameter is close to ‘1’ and hard otherwise. Here is an example to get the quality control of data.

tro.qc (tol =.4 , return_ratio = True ) # we consider good data from .60%

0.94

The output shows 94% of data goodness. This score can be improved if the recovers the losses signal is triggered. However, If the user approves this ratio, there is a possibility of outputting the valid tensors using the the method watex.methods.em.Processing.getValidTensors() and set the option parameter to write with the same tolerance parameters as:

>>> tro.getValidTensors (tol = .4 ) # uncomment this will output new edi with valid tensors

The next step consists to recover the missing signals since we assume that we are not satisfied with our qc value = 94%

# * Recovering missing signals
Z = tro.zrestore ( )

Note that Z is three dimensional array ( n_freqs, 2 , 2 ), we can collect the TM restoring tensors using the function watex.utils.get2dtensor()

z_yx_restored = wx.get2dtensor(Z, tensor ='z', component='yx')

The impedance tensor z in TM mode can also be output using:

>>> tro.component ='yx'
>>> z_yx_restored = tro.zrestore ( tensor ='z')

• Plot the recovering tensors

wx.view.plot2d(z_yx_restored,
               y = tro.freqs_,
               to_log10= True,
               top_label='Stations',
               plt_style ='imshow',
               fig_size =(10, 4 ),
               font_size =7,
               ylabel ='Frequency[$H_z$]',
               cb_label ='TM mode: $Z_yx$',
               distance =50.,cmap = 'terrain'
               )

<AxesSubplot:xlabel='Distance(m)', ylabel='Frequency[$H_z$]'>

The plot below indicates the full-strength amplitudes of restored data. Tensors are recovered at all frequencies.