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Transform horizontal gradient to grid (T41)

Overview

Airborne magnetic surveys measure variations in the magnetic field caused by flying over magnetic geological structures and by time variations in the earth’s field. The most common method of estimating and removing the effects of time variations in the earth’s field is called levelling. This requires flying additional ‘tie-lines’ that may comprise a significant fraction of the total survey time and cost.

Some aeromagnetic survey aircraft are capable of measuring not only the total-field, but both horizontal gradients of the magnetic field as well. Temporal changes in the earth’s magnetic field have coherency lengths that are much larger than the dimensions of the aircraft, so horizontal gradients measured with two magnetometers should contain virtually no time variation noise. It follows from this that a total field grid constructed from its gradient components should be free from time variations, and thus the need for tie-line levelling should be reduced or eliminated.

The measured compensated horizontal gradients can be resolved into orthogonal gradients and gridded. Hansen (1984) showed that the gridded total field can be calculated from the gridded, levelled horizontal gradients using the generalised 3-D Hilbert transform relations. This is the basis of the Transform Gradient Grids to TMI tool.

The process exploits Laplace’s equation in the Fourier domain to obtain the TMI from the missing vertical component, it follows from:

The following diagram shows a typical horizontal gradient installation, using three magnetometers.

G_longitudinal vector #1 = mag_1 – mag_2 G_transverse = mag_2 – mag_3 G_longitudinal vector #2 = mag_3 – mag_1

The across-track gradient (G_transverse) is measured by subtracting the output of two wing-tip mounted magnetometers while the along-track gradient (G_longitudinal) may be calculated with either one or two magnetometers. Determining G_longitudinal from one magnetometer is done by dividing the time derivative of the total field by the ground speed. Determining G_longitudinal from two magnetometers is done by using vector addition of the two longitudinal gradients, including an appropriate correction factor for aircraft geometry.

Local sign conventions for plane gradients

This is relevant not only for this tool but also in gridding.

Currently the convention is that the forward direction of a plane should be treated as positive Y, left to right as positive X as far as defining a local co-ordinate system for the plane. The current bearing of the plane is then used to convert to real East, North as appropriate. The difficulty is that a gradient is + or – depending on the sign convention from above.

References

J. Bradley Nelson (1994). ‘Leveling total-field aeromagnetic data with measured horizontal gradients’ Geophysics, Vol. 59, No. 8, pp. 1166-1170.

Using the Horizontal Gradient to Grids tool

Steps in operating the tool

Follow these steps to use the Horizontal Gradients to Grid tool interactively. For batch mode, see Running the tool in batch mode.

To use Horizontal Gradient to Grids interactively:
  1. In Project Manager, from the Gridding menu, choose Horiz Grad to Grid or use the command hzcomp2grid.exe. INTREPID displays the Horizontal Gradients to Grid window.
  2. If you have previously prepared file specifications and parameter settings for Horizontal Gradient to Grids, load the corresponding task specification file – see Specifying input manually for detailed instructions. If all of the specifications are correct in this file, go to step 6. If you want to modify any settings, carry out the following steps as required.
  3. hggpage1.png
  4. Specify the input and output datasets using the corresponding options from the Horizontal Gradient to Grids window. (See Specifying input and output files for detailed instructions.)
  5. (If you want INTREPID to calculate the vertical derivative) Specify the vertical derivative options in the Levelling Parameters area. See Levelling parameters.
  6. If you want to record your settings so that you can re-use them, save a .task file. See Saving settings for later use for detailed instructions.
  7. Run the process by pressing Run in the lower right, or by selecting Run in the File menu.
  8. If you want to repeat the process, repeat steps 2–6, varying the parameters and data files as required.
  9. To exit from Horizontal Gradient to Grids, select exit from the File Menu, or by pressing the exit button in the upper right.

After using this tool, you can inspect the output using 3D Explore visualisation tool (See 3D Explore (T61).

Producing complex grids

Note:

  • We recommend that you produce a complex output grid and examine both the real and imaginary grids carefully. Ideally, the imaginary part of the grid should not contain much coherence.
  • At present, running the tool interactively only produces a real output grid, and it is only by using the batch processing options that you can produce a complex grid, consisting of a real and an imaginary component.

Specifying input and output files

To use Merge Datasets, you need to specify the dataset to be processed and the dataset for saving the results.

Specifying input, settings and output using a .task file

An example .task file can be found in {install_path}/sample_data/examples/Tasks/Gridding/Horiz_Grad_TMI_Enhance/hzcomp2grid.task

You can choose to either Open with Task or Run Task File

Specifying input manually

Specify the X and Y input components Input Information area.

Type in or paste the path and filenames or use the Browse button (ico-java-folder.png). If you use a Browse button, INTREPID displays an Open or Save As dialog box for you locate or specify the file you require. (See “Specifying input and output files” in Introduction to INTREPID (R02) for information about specifying files).

hgg-input.png

X component – This grid corresponds to the across-track gradient (G_transverse).

Y component – This grid corresponds to the along-track gradient (G_longitudinal).

Specifying output manually

Specify the output dataset Output area. Type in or paste the path and filenames or use the Browse button (ico-java-folder.png). If you use a Browse button, INTREPID displays an Open or Save As dialog box for you locate or specify the file you require. (See “Specifying input and output files” in Introduction to INTREPID (R02) for information about specifying files).

hgg-out.png

Levelling parameters

If you want INTREPID to calculate the vertical derivative, use the settings in the Levelling Parameters area

hgg-diff.png

Do vertical differentiation –

Degree of differentiation –

Displaying options and using task specification files

This section has information about .task file operations with this tool.

Displaying current tool settings

You can, of course, examine the settings in the Transform Gradient Grids to TMI window.

Alternatively, for a complete, convenient list of all settings, save a .task file. You can then examine the current tool settings in the .task file using a text editor. See Saving settings for later use.

Saving settings for later use

You can save the current settings to a .task file. This enables you to repeat the operation later with the same settings. You can also change the settings by editing the file. For more information about .task files, see INTREPID task, HISTORY, report and log files (R06). To save the .task file, use options in the File menu:

jmenu-savetask.png

Save Task File— If you want to save the current file specifications and parameter settings in the current task specification (.task) file, use this option. If there is no current file then INTREPID prompts you to specify a name for the new file. Shortcut keystroke: ctrl+s

Save Task File As— If you want to save the current file specifications and parameter settings as a new task specification (.task) file or to replace an existing one, use this option. INTREPID prompts you to specify a name for the new file. Shortcut keystroke: ctrl+shift+s

Running the tool in batch mode

You can run this tool in batch mode.

To use a task specification file for a batch mode Transform Gradient Grids to TMI task

Type the command hzcomp2grid.exe with the switch -batch followed by the name of the task specification file.

For example, if you had a task specification file called surv329.task in the current directory, you would use the command:

hzcomp2grid.exe –batch surv329.task

Task specification file example

Here is an example of a Transform Gradient Grids to TMI task specification file. This task produces a complex grid.

# use a FFT method to add the two horizontal gradient grids # in complex Fourier domain space, and estimate the Vertical gradient of magnetics, using the LaPlace constraint # then go on to estimate the scalar TMI gradient, as the magnitude of the vector of the mag gradients # n.b. the output is a complex or two band grid, with an estimate of the errors in the second band. MagneticTask { hzcomp2grid { InputXComponent: "${cookbook}/magnetics/Trend_Gridding/TG_2_GRIDS/EastWestHorizontalMagneticGradient_25.ers"; InputYComponent: "${cookbook}/magnetics/Trend_Gridding/TG_2_GRIDS/NorthSouthHorizontalMagneticGradient_25.ers"; OutputGrid: "tmi_from_hzgrid"; OutputDataType: IEEE8ByteComplex; } }