Rotation in a ShapeArray (SAA) can drastically affect the apparent deformation of the instrument. Even small rotations of the ShapeArray can cause the data to show hundreds of millimeters of deformation. ShapeArray™ Viewer (formerly known as SAAView) can be used to determine whether the ShapeArray has been subjected to rotation and can enable a data adjustment for rotation in SAACR_raw2data. 

NOTE: The rotation diagnostics and the guidelines outline in this article were designed for Measurand's SAAF model ShapeArray™ instrument. Due to differences in construction and installation, these guideline for diagnosing rotation are not immediately applicable to newer model ShapeArray™ instruments such as the SAAV.

To diagnose rotation of a ShapeArray it is important to understand the effect rotation will have on the data. Each segment in a ShapeArray has a MEMS accelerometer for the X-, Y-, and Z-axes to measure tilt relative to gravity. As a segment rotates, the output of each sensor will be sinusoidal, as shown in the figure below.

Figure 1: Sinusoidal output from a MEMS accelerometer as the segment rotates 

This behaviour means that a segment with a constant tilt that is rotating about its long axis will output incremental displacement data in a circle in the horizontal plane. This incremental displacement describes the shape of an inverted virtual cone with the segment's vertex travelling around the top. The apparent movement of the vertex will always be orthogonal to the tilt of the segment.

Figure 2: A rotating segment with a constant tilt describes a inverted virtual cone

It is also important to realize that rotation in ShapeArray data occurs to large groupings of segments over a significant portion of the ShapeArray. Since segments are physically connected to each other, it would be impossible for a single segment to rotate on its own. This means that when the incremental displacement around the base of cone is modeled for each segment in the ShapeArray, multiple adjacent segments must be moving around the cone in the same direction to indicate rotation. Incremental displacement in opposite directions by adjacent, or groups of adjacent, segments is an indicator that the displacement being observed is not produced by rotation.

Given the behavior described above, the following conditions must exist for rotation to be occurring.

  • Apparent deformation must be orthogonal to the tilt of the borehole.
  • Apparent incremental displacement must be in one large group of adjacent segments over a significant extent of the ShapeArray length.
  • The apparent incremental displacement for a group of segments must be predominantly all positive or all negative. Groups of segments with opposing signs in their apparent incremental displacements do not indicate rotation.
  • The ShapeArray data must show increased cumulative displacement at the top of the borehole.

A deeper discussion of the effects of rotation on vertical ShapeArrays can be found in the following article from our online manuals.

Measurand's ShapeArray™ Viewer provides Antirotation Diagnostic graphs to help you diagnose rotation in ShapeArray data. These graphs display the tilt magnitude of each segment in the ShapeArray and the modeled cumulative or incremental rotation effect (the distance traveled around the virtual cone due to rotation). Examining these diagnostic graphs for the conditions described above will help you to identify rotation in your ShapeArray data that can be adjusted with the Anti-rotation software adjustment.

The following steps can be followed to identify rotation in your ShapeArray using ShapeArray™ Viewer.

Step 1 - Review Raw Data and Convert to Cartesian Data

Before you can diagnose rotation in ShapeArray™ Viewer, you must first acquire all of the project files from the data logger. You should have the following project files from your logger.

  • _SAA#_DATA.dat

These files are required for converting the raw ShapeArray data to Cartesian data and for diagnosing issues with the ShapeArray and logger’s connections. You can find more information about the content of these files in the following article from our online documentation:

Once you have these files together in a folder on your computer, it is a good idea to do a sanity check on the data recorded. In situations where not enough voltage has been supplied to the ShapeArray, the ShapeArray can return erroneous raw data and temperature values. You should check the recorded voltages and temperatures in your _SAA_DIAGNOSTICS.dat file to ensure they are within acceptable limits. Acceptable voltages will vary based on the length of the ShapeArray. For more information on an acceptable voltage reading for your ShapeArray, please contact Measurand Support. For temperatures, you should check that the value recorded is reasonable for the environment in which the ShapeArray is installed.

The key thing you are looking for in the voltage and temperature data (found in the _SAA_DIAGNOSTIC.dat file) is unusual spikes and dips in the values. A good way of reviewing this data is with View Pro in Campbell Scientific’s LoggerNet or PC200W software. This application will allow you to graph the data values to easily identify unusual readings or trends. If you find that unusual readings exist for voltage and temperatures, then the ShapeArray data recorded at those times might need to be removed from the data files using a text editor like Notepad before the conversion process.

Figure 3: The _SAATOP_VOLTAGE from an _SAA_DIAGNOSTIC.dat file graphed in LoggerNet's View Pro

After you have confirmed that your data is valid, use SAACR_raw2data to process the raw data into Cartesian data using a Reset conversion. You can find step-by-step instructions for this in our online SAACR_raw2data How-To Guide.

After processing the raw data with SAACR_raw2data, you will have generated a multi_saa_allcart.mat file in the same folder as the project files.

Step 2 - Open the Cartesian Data in ShapeArray™ Viewer and View the Unfiltered Data

Start ShapeArray™ Viewer from SAASuite and click the Open Project button to select the multi_saa_allcart.mat file created in step 1. This will open the Cartesian data and display an unfiltered and filtered preview of the data.

Figure 4: Sample data opened in ShapeArray™ Viewer

For troubleshooting and applying adjustments, you must always use the unfiltered view. To view the unfiltered data in more detail, you need to click on the View Unfiltered button near the graphs on the left side of the window.

Figure 5: The Unfiltered Data View Window appears after you click the View Unfiltered button in the main ShapeArray™ Viewer window

By default, the unfiltered data view window will show you graphs for cumulative displacement in the X and Y directions. Rotation often exhibits itself as a large deformation in one or both axes that progressively increases along the length of the ShapeArray. In the example shown in Figure 3 above, you can see cumulative displacement starting approximately at the 4 m elevation and increasing to the top of the ShapeArray. It This is typically the first sign that rotation could be an issue.

Step 3 - Determine Whether Apparent Deformation is Orthogonal to the Angle of the ShapeArray Installation

Rotation presents itself itself as large apparent deformations in an axis orthogonal to the angle at which the ShapeArray is installed. You should first examine the absolute shape of the ShapeArray to determine the axis in which the instrument is predominantly angled. You can display this by opening the View menu and selecting the Absolute Shape (CumDeviation) x,y option.

Figure 6: Absolute Shape (left) compared with Deformation (right) - ShapeArray mostly angled in Y-axis but deformation primarily in X-axis

Once you know the axis in which the instrument is primarily angled, compare it with the deformation data by opening the View menu and selecting the Deformation (CumDisplacement) dx,dy option. If the deformation is primarily in an axis orthogonal to the angle of the ShapeArray's installation, it may be the result of rotation of the ShapeArray rather than actual movement in the ground. This would be cause to continue the investigation with the Anti-Rotation Diagnostic graphs.

Step 4 - Enable the AntiRotation Diagnostics

Once you suspect rotation in your data, you should enable the AntiRotation Diagnostics. This is done by clicking the ADJUSTMENTS tab in the top right corner of the window and selecting the AntiRotation Diagnostics checkbox.

Figure 7: The AntiRotation Diagnostic is accessed through the ADJUSTMENTS tab

This will present you with the TiltMagnitude perSegment, incrRotation perSegment, incrRotation, mm, and Variables vs. T. graphs. These graphs will ultimately allow you to determine whether or not your ShapeArray is rotating.

Figure 8: The TiltMagnitude perSegment, incrRotation perSegment, incrRotation, mm, and Variables vs. T. graphs

The TiltMagnitude perSegment graph displays the magnitude of tilt for each segment at each elevation of the ShapeArray. This is how far from vertical the segment is tilted in relation to gravity. A dotted black line indicates the point at which rotation modeling is the least accurate (0.34 degrees). Elevations where a segment's is near this limit should not be relied upon when trying to identify rotation.

The incrRotation perSegment graph displays a model of how far around the segment's virtual cone each vertex has moved due to rotation. This model is less accurate when the segments are very close to vertical.

Figure 9: The TiltMagnitude perSegment graph (left) and the incrRotation perSegment graph (right) - Elevations at the top and bottom are selected with the dotted yellow lines

The incrRotation, mm graph also shows far around the segment's virtual cone each vertex has moved due to rotation over time.

Figure 10: The PureRotation, degrees graph

The Variables vs. T. graph shows the rotation in millimeters over time for the selected elevations in the TiltMagnitude perSegment and incrRotation perSegment graphs. Elevations are selected by left-clicking and dragging the dotted yellow lines near the top and bottom of these graphs, as shown in Figure 9 above.

Figure 11: The Variables vs. T graph

After you have selected the Antirotation Diagnostics checkbox, you can deselect the Incremental Rotation checkbox to display the cumulativeRotation Effect graph. This graph will take the place the of the incrRotation perSegment graph. The cumulativeRotation Effect graph displays how far around the segment's virtual cone each vertex has moved due to rotation cumulatively from the bottom of the ShapeArray. This graph will help to determine whether rotation of the instrument has a cumulative effect at the top of the ShapeArray.

Figure 12: The cumulativeRotation Effect graph is displayed when the Incremental Rotation checkbox is deselected

Step 4 - Identify Rotation

With the AntiRotation Diagnostics and Incremental Rotation checkboxes selected, examine the incrRotation perSegment graph. In a ShapeArray suffering from rotation, you should see multiple adjacent segments with significant incremental movement around their virtual cones in the same direction. 

For example, in Figure 9 above, the segments between the 0 m and 25 m elevation are showing incremental movement in the positive direction. In Figure 13 below, the segments between the 1 m and 21 m elevation are also showing incremental movement in the positive direction. Both of these Figures show classic examples of rotation.

Figure 13: Antirotation Diagnostics graphs - segments between the 1 m and 21 m  from the bottom elevations clearly show rotation

When reviewing the incrRotation perSegment graph, play close attention to the tilt of the segments in the TiltMagnitude perSegment graph. As the tilts of the segments approach vertical, as indicated by the dotted black limit line at 0.34 degrees, the software model for rotation becomes less accurate. In Figure 13 above, make note that the model shows no incremental rotation for segments that are at or beyond the 0.34 degree limit between the 22 m and 25 m elevations.

The color and thickness of the lines in the TiltMagnitude perSegment graph should also be observed. Thicker lines showing multiple gradations of colour indicate changes in tilt which is indicative of real movement rather than rotation. Elevations with thinner, single colour (red), lines on the graph indicate little or no change in tilt in the segments which is a requirement for rotation effects.

When diagnosing rotation with the diagnostic graphs, be wary of the following contra-indicators of rotation.

1. Apparent incremental displacement that occurs in just a few segments, or in opposite directions in isolated pairs of segments.

2. Apparent incremental displacement that occurs in two or more significant groups of adjacent segments with opposite signs.

3. Little cumulative displacement at the top of the borehole

Step 5 - Apply AntiRotation Trial and Preview Results

Once you have identified that rotation is indeed occurring, you can apply the AntiRotation Trial to preview how the data adjustment will affect the existing data. This done by deselecting the AntiRotation Diagnostic checkbox and selecting the AntiRotation Trial checkbox on the ADJUSTMENTS tab. 

Figure 17: The AntiRotation Trial enabled on the ADJUSTMENTS tab

The anti-rotation adjustment is then applied to all segments. and the results displayed in the Data View window as a preview of how the adjustment affects the data. Make note of the data displayed in the Cumulative Displacement graphs before and after selecting the AntiRotation Trial checkbox. Most noticeably, you should see a change in the scale of the graphs.

NOTE: The scales presented on all graphs in ShapeArray™ Viewer are dynamic by default. As the range of the data displayed changes, so will the scales presented on the graphs. This scale can be manually set from the Settings menu by selecting the Manual Scale option.

Figure 12: Sample data before enabling the AntiRotation Trial (left) and after enabling the AntiRotation Trial (right) - Note the change in scale for the graphs

NOTE: It is important to note that the antirotation adjustment will only apply to segments whose tilts have not changed. Changes in a segment’s tilt is how the ShapeArray measures deformation. If rotation occurs when there is also a change in tilt, then the rotation will not be corrected.

Step 6 - Optional, Enable AntiRotation Adjustment in SAACR_raw2data

If you are happy with the results of the AntiRotation Trial, you can enable the adjustment for SAACR_raw2data so that it is automatically applied on the raw data on subsequent conversions. To do this, you must perform a Reset conversion on the data set with SAACR_raw2data and in the settings page, click on the On/Off button in the Adjustments column. In the Adjustment dialog, select the checkbox next to the Anti-rotation option and click the Save button.

Figure 13: Set adjustments in the Settings page of SAACR_raw2data

Attached is another presentation on diagnosing rotation which covers many of the same principles described above.