Vertical Derivative Convolution

Use the Grid and Image > Filters > Vertical Derivative Convolution menu option (GRIDVD GX) to apply a vertical derivative convolution filter to a grid.

Vertical Derivative Convolution dialog options

Input grid file

Name of the input grid.

Script Parameter: GRIDVD.GRD

New resultant grid

Name of the vertical derivative grid.

Script Parameter: GRIDVD.NEW

Application Notes

The vertical derivative convolution filter (VDCF hereafter) method will benefit a very large grid for both memory storage economy and speed improvement.

The VDCF is a 5th order radially symmetrical filter, formulated by Henderson1 as expressed below:

Where:

a is the filter increment

f(a) is the field value at point a

m is the order of the convolution filter

Herderson further evaluated the VDCF for 10 numeric coefficient. Simplifying the above equation to the form below:

The coefficients D(ai) are:

Index a Coefficient
0 0 1.87282
1 1 -1.13625
2 √2 -0.05949
3 √5 -0.30210
4 2√2 -0.05857
5 √13 -0.07597
6 5 -0.07072
7 5√2 -0.05758
8 √136 -0.03905
9 √274 -0.02286
10 25 -0.05020

VDCF Radial Graph:

These coefficients are interpolated and normalized on a 51x51 convolution window and applied to the input grid.

Reference

  • R. G. Henderson, "A Comprehensive System of Automatic Computation in Magnetic and Gravity Interpretation", Geophysics, vol. 25 (1960), pp. 569 - 585.