Standard Euler Deconvolution

Use the Euler 3D > Standard Euler Decon menu option (E3DECON GX) to apply Euler depth deconvolution as a tool for potential field interpretation.

Euler Deconvolution dialog options

Magnetic/Gravity grid (.grd)	Input Grid file name. Script Parameter: E3DECON.GRID
X derivative grid (.grd)	Input X-Derivative Grid file name. Script Parameter: EULER3D.DX
Y derivative grid (.grd)	Input Y-Derivative Grid file name. Script Parameter: EULER3D.DY
Z derivative grid (.grd)	Input Z-Derivative Grid file name. Script Parameter: EULER3D.DZ
Output solution database (.gdb)	Output database (Solution) file name. The solution database is no longer deleted and re-created each time, since it is now possible to store multiple solution sets to the same database. Script Parameter: EULER3D.SOLDB
Solution list	The "group" line in the output database to which the solutions are to be written. Up to 20 different sets of solutions can be written to a solution database. If the selected group already exists, it is overwritten. Script Parameter: EULER3D.SOLGRP
Structural index	Structural index, from 0.0 to 3.0 (default=1.0) See application notes below for details. Script Parameter: EULER3D.GI
Max. depth tolerance to allow (%)	Maximum depth tolerance to allow (percentage) (default=15.0) All depth solutions with error estimate smaller than this tolerance will be accepted. The default is 15 percent. A smaller tolerance will result in fewer but more reliable solutions. Script Parameter: EULER3D.TOLRNC
Window size (at least 3)	Window size (at least 3) (default=10) A square window with this edge dimension in grid cells is used to calculate the Euler solutions. All points in the window are used to solve Euler's equation for a source position. Script Parameter: EULER3D.WNDSIZ
Max dist. to accept	Maximum distance (from window center) acceptable (0 for infinite) (default=0.0). Solutions at a distance (from window center) greater than this maximum will not be accepted. Enter 0.0 for the default of infinity. This is the total distance in X, Y and Z, not just the horizontal distance. Script Parameter: EULER3D.MAXDIS
Flying height	Flying height of observation plane (default=0.0) For drape airborne surveys, enter the flying height. Depths will be reported as depth below ground by subtracting the flying height. By default, depth below plane of observation is reported. Script Parameter: EULER3D.OBSHGHT
Survey elevation	Elevation of observation plane For barometric airborne surveys, enter the survey elevation. Depths will be reported as elevations by subtracting the model depth from the survey elevation. Results are output to the "Elevation" channel, not the "Depth" channel. Note: By default the flying height will be used, unless a survey elevation is entered. Script Parameter: EULER3D.OBSELEV

Application Notes

The apparent depth to the magnetic source is derived from Euler’s homogeneity equation (Euler deconvolution). This process relates the magnetic field and its gradient components to the location of the source of an anomaly, with the degree of homogeneity expressed as a "structural index". The structural index (SI) is a measure of the fall-off rate of the field with distance from the source.

Euler’s homogeneity relationship for magnetic data can be written in the form:

Where:

is the position of the magnetic source whose total field (T) is detected at (x, y, z,).

B is the regional magnetic field.

N is the measure of the fall-off rate of the magnetic field and may be interpreted as the structural index (SI).

The Euler deconvolution process is applied at each solution. The method involves setting an appropriate SI value and using least-squares inversion to solve the equation for an optimum xo,yo,zo and B. As well, a square window size must be specified which consists of the number of cells in the gridded dataset to use in the inversion at each selected solution location. The window is centred on each of the solution locations. All points in the window are used to solve Euler’s equation for solution depth, inversely weighted by distance from the centre of the window. The window should be large enough to include each solution anomaly of interest in the total field magnetic grid, but ideally not large enough to include any adjacent anomalies.

Output Solution Database (*.gdb):

E3DECON GX writes out a twelve channels in the following format:

X_Euler	= solution x coordinate
Y_Euler	= solution y coordinate
Depth (or Elevation)	= solution depth (z coordinate). If a survey elevation is entered, the channel name becomes "Elevation"
Backgrnd	= solution base level
WndSize	= window size. This is coverted to ground units by multiplying the number of cells in the window size by the grid cell size. In the E3DECON GX, all these values are the same.
dZ	= percentage depth uncertainty
dXY	= location uncertainty as percentage of solution depth Z
X	= x coordinate of the center of the search window
Y	= y coordinate of the center of the search window
X_offset	= X_Euler – X
Y_offset	= Y_Euler – Y
Mask	= a flag indicating whether this solution is to be plotted or not (1 for plot, * for don't plot). Initially all Mask values are 1. The E3WINDOW GX edits the Mask channel to select only significant solutions for plotting.

Structural Index (SI):

A structural index is an exponential factor corresponding to the rate at which the field falls off with distance, for a source of a given geometry.

From the following table choose an appropriate model for your structural index value:

SI	Magnetic Field	Gravity Field
0	Contact / Step	Sill / Dyke / Ribbon / Step
1	Sill / Dyke	Cylinder / Pipe
2	Cylinder / Pipe	Sphere
3	Sphere / Barrel / Ordnance	N /A

Another way to determine an appropriate structural index is to determine how many infinite, or reasonably large dimensions are present in a given model. The model SI is this number subtracted from the maximum SI for a given field, which is 3 for magnetic data and 2 for gravity data.

Note that a zero index implies that the field (magnetic or gravity) is constant regardless of distance from the source model. These solutions are physically impossible for real data, and a zero index represents a physical limit which can only be approached as the so-called ‘infinite’ dimensions of the real source increases. In practice, an index of 0.5 can often be used to obtain reasonable results when an index of zero would otherwise be indicated.

Geological Model	Number of Infinite dimensions	Magnetic SI	Gravity SI
Sphere	0	3	2
Pipe	1 (Z)	2	1
Horizontal cylinder	1 (X or Y)	2	1
Dyke	2 (Z and X or Y)	1	0
Sill	2 (X and Y)	1	0
Contact	3 (X, Y and Z)	0	NA

Window Size

The "WndSize" channel is created and filled with the actual size of the window used in the Euler deconvolution. This is equal to the user input window size, multiplied by the actual size of a single grid cell. This is directly comparable to window size calculated using the located Euler deconvolution (E3XYEULER GX).