harmonica.filters.derivative_northing_kernel

harmonica.filters.derivative_northing_kernel(fft_grid, order=1)

Filter for northing derivative in frequency domain

Return a xarray.DataArray with the values of the frequency domain filter for computing the northing derivative. The filter is built upon the frequency coordinates of the passed fft_grid and is defined as follows:

\[g(\mathbf{k}) = (i k_n)^n\]

where \(\mathbf{k}\) is the wavenumber vector (\(\mathbf{k} = 2\pi \mathbf{f}\) where \(\mathbf{f}\) is the frequency vector), \(k_n\) is the northing wavenumber component of \(\mathbf{k}\), \(i\) is the imaginary unit and \(n\) is the order of the derivative.

Parameters:

fft_gridxarray.DataArray

Array with the Fourier transform of the original grid. Its dimensions should be in the following order: freq_northing, freq_easting. Use xrft.xrft.fft and xrft.xrft.ifft functions to compute the Fourier Transform and its inverse, respectively.

orderint

The order of the derivative. Default to 1.

Returns:

da_filterxarray.DataArray

Array with the kernel for the northing derivative filter in frequency domain.

See also

harmonica.derivative_northing

References

[Blakely1995]