harmonica.filters.reduction_to_pole_kernel
harmonica.filters.reduction_to_pole_kernel¶
- harmonica.filters.reduction_to_pole_kernel(fft_grid, inclination, declination, magnetization_inclination=None, magnetization_declination=None)[source]¶
Filter for reduction to the pole in frequency domain
Return a
xarray.DataArray
with the values of the frequency domain filter for applying a reduction to the pole on magnetic data. The filter is built upon the frequency coordinates of the passedfft_grid
and is defined as follows:\[g(\mathbf{k}) = \frac{1}{\Theta_m \Theta_f}\]with
\[\Theta_m = m_z + i \frac{m_e k_e + m_n k_n}{|\mathbf{k}|}\]\[\Theta_f = f_z + i \frac{f_e k_e + f_n k_n}{|\mathbf{k}|}\]where \(\hat{\mathbf{f}} = (f_e, f_n, f_z)\) is a unit vector parallel to the geomagnetic field and \(\hat{\mathbf{m}} = (m_e, m_n, m_z)\) is a unit vector parallel to the magnetization vector of the source. The \(f_e\), \(f_n\), \(m_e\), \(m_n\) are the easting and northing components while the \(f_z\) and \(m_z\) are the downward coordinates. Each of these components can be obtained from the inclination and declination angles of the geomagnetic field (\(I\) and \(D\), respectively) and for the magnetization vector (\(I_m\) and \(D_m\), respectively):
\[\begin{split}\begin{cases} f_e = \sin D \cos I \\ f_n = \cos D \cos I \\ f_u = \sin I \end{cases}\end{split}\]\[\begin{split}\begin{cases} m_e = \sin D_m \cos I_m \\ m_n = \cos D_m \cos I_m \\ m_u = \sin I_m \end{cases}\end{split}\]- Parameters
fft_grid (
xarray.DataArray
) – Array with the Fourier transform of the original grid. Its dimensions should be in the following order: freq_northing, freq_easting. Usexrft.xrft.fft
andxrft.xrft.ifft
functions to compute the Fourier Transform and its inverse, respectively.inclination (float in degrees) – The inclination of the inducing Geomagnetic field.
declination (float in degrees) – The declination of the inducing Geomagnetic field.
magnetization_inclination (float in degrees or None) – The inclination of the total magnetization of the anomaly source. If None, the
magnetization_inclination
will be set equal to theinclination
, neglecting remanent magnetization and self demagnetization. Default None.magnetization_declination (float in degrees) – The declination of the total magnetization of the anomaly source. If None, the
magnetization_declination
will be set equal to thedeclination
, neglecting remanent magnetization and self demagnetization. Default None.
- Returns
da_filter (
xarray.DataArray
) – Array with the kernel for the reduction to the pole filter in frequency domain.
References
See also