# harmonica.filters.upward_continuation_kernel¶

harmonica.filters.upward_continuation_kernel(fft_grid, height_displacement)[source]

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_grid (xarray.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_displacement (float) – 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_filter (xarray.DataArray) – Array with the kernel for the upward continuation filter in frequency domain.

References

[Blakely1995]