harmonica.filters.upward_continuation_kernel

harmonica.filters.upward_continuation_kernel(fft_grid, height_displacement)

Filter for upward continuation in frequency domain

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

\[g(\mathbf{k}) = e^{-|\mathbf{k}| \Delta h}\]

where \(\mathbf{k}\) is the wavenumber vector (\(\mathbf{k} = 2\pi \mathbf{f}\) where \(\mathbf{f}\) is the frequency vector) and \(\Delta h\) is the height displacement of the upward continuation.

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.

height_displacementfloat

The height displacement of upward continuation. For upward continuation, the height displacement should be positive. It has the same units as the input xarray data coordinates.

Returns:

da_filterxarray.DataArray

Array with the kernel for the upward continuation filter in frequency domain.

See also

harmonica.upward_continuation

References

[Blakely1995]