harmonica.tilt_angle

harmonica.tilt_angle(grid, *, pad=True, pad_kwargs=None)

Calculate the tilt angle of a potential field grid.

Compute the tilt of a regular gridded potential field \(M\). The horizontal derivatives are calculated through finite-differences while the upward derivative is calculated using FFT.

Parameters:

gridxarray.DataArray

A two dimensional xarray.DataArray whose coordinates are evenly spaced (regular grid). Its dimensions should be in the following order: northing, easting. Its coordinates should be defined in the same units.

padbool, optional

If True, will add padding to the grid before taking the Fourier Transform and applying the filter and remove it after the inverse Fourier Transform. Adding padding usually helps reduce edge effects from signal truncation. Default is True.

pad_kwargsdict or None, optional

Any additional keyword arguments that should be passed to the xarray.DataArray.pad function in the form of a dictionary. If none are given, the default padding of 25% the dimensions of the grid will be added using the “edge” method.

Returns:

tilt_gridxarray.DataArray

A xarray.DataArray with the calculated tilt in radians.

Notes

The tilt is calculated as:

\[\text{tilt}(f) = \tan^{-1} \left( \frac{ \frac{\partial M}{\partial z} }{ \sqrt{ \left( \frac{\partial M}{\partial x} \right)^2 + \left( \frac{\partial M}{\partial y} \right)^2 } } \right)\]

where \(M\) is the regularly gridded potential field.

References

[Blakely1995] [MillerSingh1994]

Examples using harmonica.tilt_angle

Tilt of a regular grid

Tilt of a regular grid