Tilt Derivative

Use the Tilt Derivative option (TILTDRV GX) from the 2D Filtering menu to calculate the tilt derivative of a grid and optionally the total horizontal derivative of the tilt derivative grid.

Tilt Derivative dialog options

Input grid

Select the name of the input grid.

Script Parameter: TILTDRV.IN

Output tilt derivative grid

Specify the name of the output tilt derivative grid.

  • If the grid file exists, an overwrite confirmation prompt is displayed.

    • Script Parameter: TILTDRV.OUT

    Horizontal derivative of output grid

    Specify the name of the output total horizontal derivative of the tilt derivative grid.

    If left blank, the grid is not created unless an output tilt depth database is specified. In this case, the name of the grid is set to the name of the output tilt derivative grid appended by _HD_TDR.

  • If the grid file exists, an overwrite confirmation prompt is displayed.

    • Script Parameter: TILTDRV.OUT2

    Vertical derivative method

    Select the filter method for calculating the vertical derivative. The options are:

    • FFT (Fast Fourier Transform) - [default]
    • Convolution

    Script Parameter: TILTDRV.METHOD [0: FFT, 1: Convolution]

    Output tilt depth database

    Specify the name of the database in which to save the tilt depths. If left blank, the tilt depths are not calculated.

  • If the database file exists, an overwrite confirmation prompt is displayed.

    • Script Parameter: TILTDRV.GDB

    Application Notes

    The tilt derivative and its total horizontal derivative are useful for mapping shallow basement structures and mineral exploration targets.

    The tilt derivative is defined as:

    Where VDR and THDR are first vertical and total horizontal derivatives, respectively, of the total magnetic intensity T.

    range

    The total horizontal derivative of the tilt derivative is defined as:

    HD_TDR is in units of radians/distance.

    Tilt Depth Estimate

    The tilt depth estimate is based on a technique published by Salem et al (2008). This is a simple and fast method to locate vertical contacts from Reduced to the Pole (RTP) magnetic data. The tilt-depth method only depends on mapping specific contours of the magnetic tilt angles. The zero contours delineate the spatial location of the magnetic source edges, while the depth to the source is the distance between the zero and either the -45° or the +45° contour or their average. The method in its simplest form assumes the source structures have vertical contacts, there is no remanent magnetisation, and the magnetisation is vertical.

    The tilt depth is calculated only at inflection points (zero values) in the tilt-derivative grid, by the following expression:

    1 / HD_TDR

    The calculated depth is relative to the survey elevation and in the same units as the projected coordinate system of the input magnetic grid.

    The two principal advantages of the method: its simplicity both in its theoretical derivation and in its practical application. It provides both a qualitative and quantitative approach to interpretation by allowing the interpreter to visually inspect the tilt-depth map to identify locations where depth estimates may be compromised by interfering magnetic anomalies and locations where more reliable depth estimates can be made. These reliable locations can then be re-evaluated using different magnetic depth estimation methods.

    Other advantages: by virtue of using first order derivatives, the method is potentially less sensitive to noise in the data compared to methods relying on higher order derivatives, and unlike Euler deconvolution there is no need to choose window size, nor is there a problem of solution clusters to contend with.

    References

    • [1] H.G. Miller and V.J. Singh, "Potential Field Tilt - a New Concept for Location of Potential Field Sources", Journal of Applied Geophysics, vol. 32 (1994), no. 2-3, pp. 213-217.
    • [2] B. Verduzco et al., "New Insights into Magnetic Derivatives for Structural Mapping", The Leading Edge, vol. 23 (2004), pp. 116-119.
    • [3] A. Salem, S. Williams, J. D. Fairhead, R. Smith, and D. Ravat, "Interpretation of magnetic data using tilt-angle derivatives", Geophysics, vol. 73 (2008), no. 1, pp. L1-L10.