Calculate Depths and Weights using Euler Deconvolution

Use the Calculate Depths and Weights using Euler Deconvolution option (geosoft.uxo.gxnet.dll(Geosoft.GX.UXO.UxoCalculateDepthsWeightsEuler;Run)*) to calculate the apparent depths and magnetic weights of selected magnetic targets.

Calculate Depths and Weights using Euler Deconvolution dialog options

Target database	Select the target database. Script Parameter: UXDETECT.TARGET_GDB
Group	Select the name of the target group in which to save the target data. This value is the same as the most recently specified target group from any of the other dialogs that require a Target Group.The target data is stored separately from the regular line data, in its own target line/group. Script Parameter: UXDETECT.TARGET_GROUP
Mask channel	Select the target database mask Channel of class type "MASK" that is used for selecting a subset of solutions from the target group.  channel to filter out specific targets. Only the targets with a mask (channel value) of 1 will be processed. If the value is set to 0 or dummy (*), the corresponding target will be ignored. If the field is left blank, no mask will be applied. Script Parameter: UXDETECT.TARGET_MASK
Target type	Select the target type. See the Application Notes section below for more information. Script Parameter: UXYEULER.STRUCT
Target size channel	Select the channel containing target sizes. Script Parameter: UXYEULER.WNDCH
Instrument height (m)	Enter the instrument sensor height above the ground, in the same units as the X-Y coordinate system. Apparent depths will be reported as depth below ground (in the same units) by subtracting this height from the calculated distance of the sensor to the magnetic sources. If no instrument height value is entered the depth below instrument height is reported. Script Parameter: UXYEULER.HEIGHT
Data Grids
Analytic signal	Specify/browse to select the analytic signal grid. Script Parameter: UXYEULER.AS
Total magnetic field	Specify/browse to select the total field magnetic grid. Script Parameter: UXYEULER.TF
X-derivative magnetic field	Specify/browse to select the X-derivative grid. Script Parameter: UXYEULER.DX
Y-derivative magnetic field	Specify/browse to select the Y-derivative grid. Script Parameter: UXYEULER.DY
Z-derivative magnetic field	Specify/browse to select the Z-derivative grid. Script Parameter: UXYEULER.DZ

Application Notes

Calculation of Apparent Source Depth

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".

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 / background magnetic field.

N is the measure of the fall-off rate of the magnetic field. N is directly related to the source shape and is referred to as the structural index (SI) or target type.

The Target type or "structural index" is a measure of the rate of change of the magnetic anomaly strength with distance from that target. For UXO applications, generally a structural index of 3 or 2.7 is used.

The following is a list of magnetic bodies with the structural indices:

magnetic ordnance	3
magnetic sphere	3
magnetic barrel	3
magnetic ordnance	2.7
magnetic projectile	2.5
Magnetic cylinder	2
magnetic pipe	2
Magnetic sheet	1
Magnetic sill	1
Magnetic step	0.5
Magnetic contact	0

At each target location, a square window of data is extracted centred on the target. The size of the window is determined by the target size channel. The window should be large enough to include each target anomaly of interest in the total field magnetic grid, but ideally not large enough to include any adjacent anomalies.

The Euler deconvolution method involves selecting an appropriate SI value and using least-squares inversion to solve the equation for an optimum x₀,y₀,z₀ and B. All points in the window are used to solve Euler’s equation for target depth, inversely weighted by distance from the centre of the window. This is a statistical process, resulting in depth solutions with an associated uncertainty. The depth uncertainty is normalized and reported as a percentage of the depth below the sensor.

Arriving at acceptable solutions for features of interest may involve some trial and error by adjusting the target type/structural index, (and possibly the target/window size, and the uncertainty tolerances). If results from a number of different target types are desired, one can process the data using the mask channel for each type.

Calculation of Apparent Magnetic Weight

Apparent weight calculations are obtained from the magnetic data using a table lookup. Given the analytic signal data calculated, which is directly related to magnetic moment, and the calculated apparent depth of the magnetic source, the apparent magnetic weight can be found. The table of weight information included in the lookup table is based on theoretical and empirical evidence (Pennella, 1982). The magnetic moment response of a given target depends on a number of variables such as inclination, dip, shape, size, demagnetisation and anisotropy, etc. While the analytic signal tends to somewhat standardize the response, there is still some variability in the outcome. As a result, the lookup weight is referred to as the apparent weight and should be considered as such. Also, see the Knowledge Base article, Information relating to target weight using the UX-Detect module, on MySeequent Support.

Output Channels

These channels will be created in the specified target group:

X	= x coordinates
Y	= y coordinates
Mag_Depth	= apparent depth
App_Weight	= apparent weight in kg
Bkgrd_fld	= background field
Depth_Err	= depth uncertainty (%)
Target_ID	= Target ID with the first target being 1.

References