Service: Decorrugation rectifies poor line-to-line leveling

Data decorrugation service post image

SOMETIMES important geological features can be partly or totally wiped from a geophysical dataset as an unintended result of standard decorrugation methods. We have an alternative method on hand that minimizes this problem. It removes undesired artificial corrugations efficiently but at the same time maximizes the amount of geological signal left intact.

Corrugations arise in geophysical data when earlier data-cleanup steps, such as base-station subtraction and tie-line leveling, fail to completely remove the various unwanted influences on measured data values.

Corrugations in data make an area's geophysical signal look as though it's been draped over corrugated cardboard or an old-fashioned washboard. They present themselves in geophysical images as low-amplitude, high-frequency ripples.

"The effect is that the long-wavelength component of any one [survey flight-line] is often slightly out of register with that of its neighboring [flight-lines]," Australian national geological survey researcher Colin Reeves remarked back in 1993. [1]

"Individual lines of data, therefore, tend to stand out, particularly when shaded relief effects in directions near-normal to the flight-line direction are calculated."

Even though survey contractors try to do their best to level the data they acquire, a myriad of factors can contribute to producing corrugations [2], so it's fairly common for them to show up in data (see Figure 1). The list of contributing factors varies too, depending on the data type. [3]

Data decorrugation service figure 1FIGURE 1: Image showing corrugations arising in an airborne electromagnetic dataset covering the Bancroft area of Ontario, Canada. The corrugations appear as fine straight lines trending from west-northwest to east-southeast. Data source: AeroTEM III survey (time domain) from the Ontario Geophysical Atlas, dataset identification number GDS 1234.

Decorrugation

Decorrugation, also known as micro-leveling, is carried out on affected datasets to remove these line-to-line leveling errors.

The general aim is to identify long, narrow, artificial anomalies that are parallel with the flight-line direction and subtract them from the data.

The consequences of failing to remove corrugations as completely as possible include:

  • It looks a bit untidy. According to Reeves: "Good images demand good technical-data quality. Some quite minor data-processing errors become clearly visible after image [construction] and can easily make an aeromagnetic image appear unattractive and cast suspicions on the quality of the survey."
  • Other signals may remain obscured: "Not only does [corrugation] make the image unattractive, but [also] subtle features may be masked." [4]
  • Knock-on effects may be severe: "This systematic error [i.e., corrugation] must be reduced since it could be amplified substantially in the subsequent enhancement steps of data processing and interpretation." [5]

Historically, decorrugation has been tricky to accomplish well. In 1997, geophysics researcher Tony Luyendyk noted: "Though conceptually simple, the implementation is difficult, owing to the mathematical limitations of digital filters and the subtle nature of errors compared with the large dynamic range of the data." [4]

"[T]he object of the exercise is to extract residual errors with the longest possible wavelength along the line, the shortest possible wavelength perpendicular to the lines, and the smallest dynamic range such that the procedure still produces a visually well-leveled grid," he said.

More recently, Italian scientists Maurizio Fedi and Giovanni Florio warned: "[D]ecorrugation, must be very carefully applied, since it could also affect anomalies originating from geological features." [5]

A standard decorrugation approach is typically done in the frequency domain using a Butterworth filter combined with a directional cosine filter (see Figure 2).

Data decorrugation service figure 2FIGURE 2: Results of standard decorrugation of the original data, using a Butterworth filter combined with a directional cosine filter. Note that the very fine corrugations are now gone, but longer-wavelength corrugations remain in the form of blotchy-looking stripes trending WNW to ESE. In addition, some features that stem from the area's geology (namely the wide pink blobby lines and arcs) have been markedly distorted.

Problems with standard decorrugation

Typically, standard decorrugation works best on potential-field data, and can produce less-than-satisfactory results when other data types are involved.

But even when it's used on potential-field data, standard decorrugation can introduce complications in certain circumstances, because the procedure is relatively undiscriminating.

For instance, a long, geologically-induced, high-amplitude magnetic anomaly is in danger of being treated as a corrugation if it runs in the same direction as survey flight-lines. An example of this situation would be when an east-west-striking mafic dike exists in an area covered by an east-west-flown magnetic survey. In cases such as this, sometimes all of the dike-related signal is removed erroneously.

Other problems that can arise when using standard decorrugation include the undesirable phenomenon of 'ringing', also known as the Gibbs effect. Steps taken to avoid ringing limit how precisely Butterworth-cosine decorrugation can be applied. According to Fedi and Florio: "The above filters are designed to suppress the corrugations along only the desired directions and with respect to a selected frequency band, but their effect is no longer so sharp, since the rejection band must be tapered off to [avoid] the Gibbs effect. Therefore, great care must be taken in order to assess whether the performance of the decorrugation algorithm allows a good separation of the corrugations from the [geological] anomalies, with low distortion of the physically-based signal." [5]

We can largely overcome these problems by doing the decorrugation processing in the space domain.

Alternative approach

Our alternative technique is performed in the space domain and makes use of a Naudy filter, which acts as a high-pass filter, followed by a Gaussian smoothing filter, which is a low-pass filter acting perpendicular to the Naudy filter (see Figure 3).

Data decorrugation service figure 3FIGURE 3: Results of alternative method of decorrugation of the original data, using a Naudy filter followed by a Gaussian smoothing filter. The very fine corrugations are now gone, and so are most of the longer-wavelength corrugations. Features that stem from the area's geology (the wide pink blobby lines and arcs in particular) have largely been left intact.

We implement the technique on grids as follows:

  1. Take a sampling interval of 5 adjacent cells that are perpendicular to the flight-line direction.
  2. Look at the sampling interval's central cell and see if its value is greater than the average value of its neighbors in the interval.
  3. If this is the case, determine whether this peak is a simple peak, or has troughs flanking it.
  4. Optional step: Employ any user-defined limits that will allow a peak to be categorized as either a corrugation (whose value will be adjusted) or a geological anomaly (that will be left intact).
  5. If the above optional step is not used, then all peaks detected will be adjusted according to the next step.
  6. Adjust downward the central cell's value according to one of two different interpolation formulas (i.e., one formula to adjust a simple peak, the other formula to adjust a peak flanked by troughs). [^]
  7. Repeat the above steps for every other 5-adjacent-cells combination in the dataset. (To look at longer-wavelengths: The procedure is carried out in the same manner as above, but instead of looking at intervals of 5 consecutive cells, the 5-cell sampling interval involves every other cell. Intervals involving every third cell will also be analyzed. And so on. Datasets that are badly affected by corrugations will have these longer-wavelength sampling intervals examined.)
  8. Obtain a grid of the corrugation values only (see Figure 4). Note that anomalies arising from geological bodies show up as "ghosted" forms — that is, remain relative untouched and appear as flattish areas.
  9. Smooth the corrugation grid values. [*]
  10. Subtract the smoothed corrugation grid from the original grid data-values.

Data decorrugation service figure 4FIGURE 4: Grid showing the corrugations identified using the alternative Naudy-Gaussian method.

This procedure allows us to precisely define and remove the offending corrugations. [**]

This Naudy-Gaussian method minimizes the removal of geologically-related signal from the data. This is because Naudy filters by their nature are relatively selective. By construction, they "leave some categories of anomalies unaltered while they remove the others completely". [6]

When introducing their non-linear filter in a 1968 paper, Henri Naudy and Henri Dreyer outlined their dissatisfaction with existing methods, namely linear filtering.

"[T]he main drawback of such filtering [methods] is that a given anomaly has a very broad spectrum. The results [of filtering] are retained anomalies that have suffered more-or-less noticeable deformation, and removed anomalies that [in fact] weren't removed completely." [6]

The standard decorrugation method involving Butterworth and directional cosine filters is an example of linear filtering. A grid of corrugation values obtained via this method will show that anomalies arising from geological bodies are clearly being adjusted too (see Figure 5).

Data decorrugation service figure 5FIGURE 5: Grid showing the corrugations identified using the standard method (Butterworth and directional cosine filters). Note that some of the largest adjustments made to the original data using this method of decorrugation (they appear as marked blue and pink areas) are in areas containing geologically-induced signal.

Judging results

To see how well a particular decorrugation method worked, we can look at the first-vertical-derivative image or the tilt-angle image of the decorrugated data (see Figure 6). A lack of a striated fabric typically indicates a good decorrugation result.

Data decorrugation service figure 6aFIGURE 6a: The first vertical derivative of the original data prior to any decorrugation (which shows a strong linear fabric throughout).

Data decorrugation service figure 6bFIGURE 6b: Image showing the first vertical derivative of the Butterworth-directional-cosine decorrugated data. Throughout most of the image area, the background to the geology shows a noticeable linear fabric.

Data decorrugation service figure 6cFIGURE 6c: Image showing the first vertical derivative of the Naudy-Gaussian decorrugated data. The background to the geology shows at most only minor linear fabric here and there.

Aside from generally superior decorrugation results, additional advantages of using a Naudy-Gaussian decorrugation include:

  • Unlike frequency-domain decorrugation, there'd be no need to do any coordinate transformations if survey flight-lines are curved. All we need to know is the direction the plane is flying at any given location.
  • Possible use: Sometimes it's desirable to remove geological features that are as much of a nuisance as corrugations. For instance, a regionally-extensive dike swarm may obscure the signal of underlying and nearby geology. [7] Removing the signature of large dike swarms is straightforward with our alternative decorrugation method, even if dikes assume a radiating pattern: there is no need for any coordinate transformations if dike-trend directions are known.
  • The method works on decorrugating EM data, including helicopter-borne EM surveys, as well as other data types (e.g., radiometric data).

While there are tradeoffs and sacrifices with any decorrugation method, Naudy-Gaussian decorrugation may help in cases where other methods prove unsuitable.

As Henri Naudy and Henri Dreyer concluded in their seminal paper on the Naudy method: "Our method of non-linear filtering certainly does not solve all of the problems posed by the filtering of airborne magnetic surveys. It is primarily an attempt at numerical processing without the defects of linear filtering, and gives, in favorable cases, filtered values and residual values that are interpretable quantitatively." [6]

References and notes

[1] C.V. Reeves (1993) "Limitations imposed by geomagnetic variations on high-quality aeromagnetic surveys", Exploration Geophysics, 24, 115-116.

[2] See, for example, mention of some of these factors in: S. Mogren and D. Fairhead (2007) "Advantages of decorrugation of aeromagnetic data using the Naudy-Fuller space domain filter", workshop presentation slides, Exploration 07 Conference Workshop 6: Geophysical Contributions to New Discoveries.

[3] M. Beiki (2009) "Leveling of aerogeophysical data using differential polynomial fitting", 71st EAGE Conference, 8-11 June 2009, Amsterdam.

[4] A.P.J. Luyendyk (1997) "Processing of airborne magnetic data", AGSO Journal of Australian Geology and Geophysics, 17, 2, 31-38.

[5] M. Fedi and G. Florio (2003) "Decorrugation and removal of directional trends of magnetic fields by the wavelet transform: Application to archeological areas", Geophysical Prospecting, 51, 261-272.

[6] H. Naudy and H. Dreyer (1968) "Essai de filtrage non-lineaire applique aux profils aeromagnetiques", Geophysical Prospecting, 16, 2, 171-178.

[7] M. Pilkington and W.R. Roest (1997) "Suppressing varying directional trends in aeromagnetic data", Applications of Regional and Geophysics and Geochemistry, Paper 117, Proceedings of Exploration 97, 877-880.

[^] Note: While we currently treat both peak types at once, Naudy and Dreyer (1968) did say: "[I]t is preferable to first treat all the single-arch anomalies with the sought width, and in a second round the several-arch anomalies, because intense single-arch anomalies constitute for filtering purposes a disruptive element that should be removed first."

[*] Note: Naudy and Dreyer (1968) do mention that they ensure continuity in their data following peak downward-adjustments by carrying out interpolations on both sides of each former peak. Our technique replaces this step with an essentially equivalent procedure: Gaussian smoothing.

[**] Note: Other methods are out there. For instance, Huang 2008 (reference details are given below) selects a reference/datum flight-line and then levels all other flight lines with respect to it — a process needing no survey tie-lines. (Another method not needing tie-lines is the one described in Beiki 2009, using polynomial line- and surface-fitting.) However, Huang said the method is unable to "distinguish a linear geologic feature in the direction of flight lines from leveling errors. If such a feature is removed by the leveling process [described in the paper], the geologic feature can be retrieved by applying a high-pass filter to the removed leveling errors and adding them back to the leveled data." [H. Huang (2008) "Airborne geophysical data leveling based on line-to-line correlations", Geophysics, 73, 3, F83-F89.]