# Tensor and gradient grid notes (R35)

These notes are about samples of gradients of potential fields and some unique methodology of INTREPID’s handling of Tensor and Gradient grids.

## Location of sample data and task files

#### Location of sample data for Cookbooks

Where `install_path` is the path of your INTREPID installation, the project directory for the Cookbooks sample data is `install_path``/sample_data/cookbooks`

.

For example, if INTREPID is installed in `C:/Intrepid/Intrepid 6.1.0f3e954b6ca6_x64`

,

then you can find the sample data at `C:/Intrepid/Intrepid 6.1.0f3e954b6ca6_x64/sample_data/cookbooks`

For information about installing or reinstalling the sample data, see the relevant section in “About the sample data for the INTREPID Cookbooks” in Using INTREPID Cookbooks (C12).

For a description of INTREPID datasets, see Introduction to the INTREPID database (G20). For more detail, see INTREPID database, file and data structures (R05).

These notes refer to the example tensor grids in `examples/datasets/TensorGradients`

.

## Creating a tensor grid

You can create a tensor grid for line data using the gridding tool, see the Aurizonia example set. Example files and task files can be found under `sample_data/cookbooks/tensors/Aurizonia/`

For more information using Aurizonia see “Aurizonia example” in Full tensor gravity gradient cookbook (C18)

To create a tensor grid from component grids see the example task `gridop_create_tensor.task`

, in `examples/Tasks/Gridding/Grid_Operations`

Or create a tensor grid using the Grid Operations tool interactively, see “Constructing a tensor grid” in Grid Operations (T25)

` `

`# create a tensor grid from 6 component grids!`

`# unfortunately, you must run dbedit in the directory where all the grids are stored`

`# this test when the trace condition is not exactly met, still allows the creation of a tensor grid`

` `

`IntrepidTask {`

` GridOp {`

` XX: “${examples}/datasets/TensorGradients/single_txx.ers”;`

` XY: “${examples}/datasets/TensorGradients/single_tyx.ers”;`

` ZX: “${examples}/datasets/TensorGradients/single_txz.ers”;`

` YY: “${examples}/datasets/TensorGradients/single_tyy.ers”;`

` YZ: “${examples}/datasets/TensorGradients/single_tyz.ers”;`

` ZZ: “${examples}/datasets/TensorGradients/single_tzz.ers”;`

` Output: “Traw.ers”;`

` Method: ManipulateTensor;`

` TensorOperation: TENSOR_Complete;`

` OutputDataType: TensorGrid;`

` }`

`}`

## Tensor Grids – Example Files

Example files can be found under {install_path}`/sample_data/examples/datasets/TensorGradients`

The grids such, as `single_txx.ers`

are individually gridded components.

The second two grids that are magnetic gradients, long base line, from a marine situation are:`NorthSouthHorizontalMagneticGradient_25.ers EastWestHorizontalMagneticGradient_25.ers`

You can recover a magnetic anomaly, using the Transform gradient grids to TMI tool (in other words, FFT additions) See Transform horizontal gradient to grid (T41). This is done in the Fourier domain by exploiting the LaPlace equation.

Montezuma FTG grid (`zuma_tensor.ers`

), DTM (`mv_dem.grd`

), and the analysis for 2D geological causative bodies, by solving the eigenvalue problem (`zuma_2DBodies..DIR`

).

Small Falcon AGG samples 2 Falcon tensor grids with filename `aggT_Sub6`

_*.* and a terrain corrected Falcon survey dataset created from Broken Hill (`BH_TC..DIR`

). These files are produced incorporating SLERP.

## Proprietary tensor processing algorithms (SLERP, MITRE, FTNR and FTGD)

### SLERP

The INTREPID gridding methods that use spherical linear interpolation (SLERP), produce results that are consistent with the physics when compared to standard interpolation of components between observations. This is because the tensors/matrices created from standard interpolation methods do not follow the rotational properties of curvature gradients of a potential field.

A process of Linear interpolation by component generates the image on the left, on the right is the result from Tensor SLERP.

### MITRE

The MITRE process, Minimise Tensor Residual Errors, is a noise removal method for tensor grids.

The above equation shows that there exists a local linear relationship between the 3rd order components. These approximations are used for the least squares by the MITRE process.

MITRE uses the 3D gradient physics of tensors to minimize those parts of the observed tensor gradients that are not consistent. MITRE is performed by producing and minimising a least squares best fit for all Tensor components, simultaneously. The least squares is performed on the 3rd order difference of the tensor components.

The MITRE process removes localised "speckle" or noise from gridded datasets, this is seen above where the left image is before MITRE and right, after.

The noise in tensor data for a field *U* is defined as:

### FTNR

The Full Tensor Noise Reduction (FTNR) filter can be used for both line and gridded datasets.The filter achieves the Noise Reduction through the use of a Truncated 3D Fourier Series approximation of potential field components to solve 48 coefficients for the third order equation. Once this best fit 3rd order equation is available, the tensor signal can be estimated anywhere in 3D space provided it is in the local domain of the observation of the discontinuities. This method is an effective de-noising technique.

### FTGD

FTGD Full Tensor Gradiometery Dip Determination method was first developed at the annual SEG meeting. The method:

- Begins with a Tensor grid of gravity gradients observations.
- Applies a terrain correction
- Creates a points database of all the Principal Components of the tensor observation, when the mid PC is approximately zero. This implies the curvature geology body is a 2D structure.
- Uses anisotropic clustering tool to group these solutions and map regions of influence of these 2D structures
- Checks that at the centre of each cluster the strike population is homogeneous
- Determines dip, by inverting for best fit tensor ellipsoid.