Differential Reduction to Magnetic Pole (DRTP)

Use the Differential Reduction to Magnetic Pole option to apply a differential reduction-to-pole filter to magnetic data.

Differential Reduction to Magnetic Pole dialog options

Input grid	This field appears only if an input grid has not been previously defined. The input grid must include projection information. Using the grid projection and survey date, inclination and declination grids aligned with the input data are automatically calculated.
Date (YYYY/MM/DD)	Enter the date of the original survey so that the corresponding inclination and declination grids can be calculated. This field is optional if these grids already exist (see Application Notes).
Amplitude correction inclination	The amplitude correction inclination Ia is a factor that prevents discontinuities near low magnetic latitudes. The default is 20.0º in the Northern Hemisphere and –20.0º in the Southern Hemisphere (see Application Notes).

Application Notes

For a georeferenced magnetic input grid and a defined survey date, the DRTP filter calculates inclination and declination grids that match the input grid. These are named:

• _Inc_inp.grd

• _Dec_inp.grd

(where inp is the input grid name)

These grids are saved in the working directory. If they exist, the DRTP filter uses them directly and does not recalculate them. To force recalculation, delete both grid files and re-enter the survey date when setting up the filter.

If the input grid has no assigned coordinate system, you will be prompted to define one. The IGRF date and parameters, once entered, are stored in the grid.

Special considerations near the magnetic equator (inclination = 0°)

If the grid approaches or crosses the magnetic equator, pay close attention to the following factors:

1. Potential instability
   Instability may appear as strong regional highs in the output grid. Increase the Amplitude correction inclination value to mitigate this. This parameter helps control the discontinuity, though it reduces the anomaly amplitudes. The resulting grid is well‑behaved, but anomalies with inclinations below this angle will appear attenuated.
2. Amplification of edge anomalies
   Strong anomalies along the grid edges—especially near the magnetic equator—may be exaggerated. If this occurs:
   • Run the grid preparation step separately.
   • Ensure that edge anomalies are rapidly attenuated within the filled grid area.
3. Default correction may be insufficient
   The default amplitude correction of 20.0º may not provide a stable result. In some cases, increasing the amplitude correction inclination to as much as 45.0° is necessary. While this produces a stable output, the signal magnitude will be significantly attenuated. Such grids should not be used for numerical modeling, as the results will be unreliable.

Formulation

The Fourier-domain Reduction to Magnetic Pole (RTP) assumes a constant inclination and declination, and is denoted by the equation below:

Where:

The RTP operator makes two assumptions:

1. M=B

2. The geomagnetic field is constant across the grid

Differential Reduction to Magnetic Pole

DRTP assumes that B and by extension M vary across the survey area. We can thus formulate that the geomagnetic field B can be the sum of a mean value B₀ at the centre of the grid and a deviation from the mean δB.

B = B₀ + δB

M = M₀ + δM

Where δB and δM vary spatially.

The equation then can be expanded (see references) as:

The first term is equivalent to the pole reduction for a constant inclination and declination. The two additional terms account for the perturbation for deviations from the mean field.

Where:

The DRTP equation is solved iteratively in the wavenumber domain using a perturbation method (Arkani-Hamed, 1988; 2007)^[1,2].

Low Magnetic Latitudes

To stabilize the pole-reduction term (RTP operator), the denominator components B₀ & M₀ are replaced by modified components B'₀, M'₀, calculated using an amplitude correction inclination I_a > I:

Wavenumber Domain Variable Definitions

The following variables are used in the wavenumber domain:
k	Wavenumber increment, used to depict a radially symmetrical variable.	Where: np: number of points cs: cell size
μ	X-component of the wavenumber.
v	Y-component of the wavenumber.
r	Radial component of the wavenumber.
θ	Angular (polar) component of the wavenumber.

References