Located An-Eul Solutions

Use the Euler 3D > Located An-Eul Solutions menu option (E3ANEULER GX) to apply the An-Eul method to determine the source depths and structural indexes of a list of anomaly locations in the current database.

Located An-Eul Solutions dialog options

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
Line containing grid peak locations	The "group" line in the database in which the grid peak locations had been saved. Script Parameter: EULER3D.XYSOLGRP
Line for An-Eul solutions	The "group" line in the database to which the solutions (depths and indexes) are to be written. If the selected group already exists, it will be overwritten. If it left blank (the default), the solutions are to be written to the existent grid peak locations line. Script Parameter: EULER3D.SOLGRP
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. By default the flying height will be used, unless a survey elevation is entered. Script Parameter: EULER3D.OBSELEV

Application Notes

Located An-Euler Method

The An-Eul method (E3ANEULER GX) determines the depth and structural index of a list of anomalies. The anomaly list is generally produced using an automatic peak-finding routine which locates peaks (E3PEAKS GX). The depth and index are then calculated at these locations using the An-Eul method.

Theory

Based on substituting derivatives of Euler’s equation into the analytic signal equation, An-Euler method is able to estimate simultaneously the source parameters, depth and index:

Depth = (AS1*AS0) / (AS2*AS0 - AS1*AS1) at the peak location x=x0, y=y0 

Index = (2*AS1*AS1 – AS2*AS0) / (AS2*AS0 - AS1*AS1) at the peak location x=x0, y=y0 

Where  

AS0(x,y) = sqrt ( (dT/dx)^2 + (dT/dy)^2 + (dT/dz)^2 ) 

AS1(x,y) = sqrt ( (dT/dxdz)^2 + (dT/dydz)^2 + (dT/dzdz)^2 ) 

AS2(x,y) = sqrt ( (dT/dxdzdz)^2 + (dT/dydzdz)^2 + (dT/dzdzdz)^2 ) 

Input and Output Channels

Input Channels	(Created using the E3PEAKS GX)
X	= x coordinate of the center of the search window.
Y	= y coordinate of the center of the search window
Output Channels
Depth (or Elevation)	= solution depth (z coordinate). If a survey elevation is entered, the channel name becomes "Elevation"
Index	= solution index (structure index)
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.

The following table provides an appropriate model for the 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

References