C4 · Publication Volume 14

Filtering, Enhancement and Artefacts

edge effects, noise amplification and processing assumptions

Learning goals

The learner should be able to express a filter as a reproducible operation; connect spatial and temporal filters to bandwidth and support; distinguish interpolation from observation; predict derivative, continuation and edge artefacts; and audit whether enhancement preserves the evidence needed to test a geological hypothesis.

Enhancement changes representation, not information content. It can separate scales, suppress known noise or expose subtle continuity, but it can also spread spikes, ring around edges, amplify line noise and create apparent boundaries. Every enhanced product must remain linked to original data and its transfer function.

Filters, bandwidth and phase

A linear filter combines neighbouring values through a kernel or multiplies spectral components by a transfer function. Low-pass filters suppress short wavelengths; high-pass filters suppress long wavelengths; band-pass filters retain a selected range. The cutoff is not a geological boundary. It is a processing choice with transition width and edge behaviour.

Filter phase controls feature location. A symmetric zero-phase operation can preserve central position offline but may be non-causal and use future samples. A causal field filter can shift peaks. Forward–reverse processing changes effective amplitude response. Record kernel coefficients, sample interval, direction, padding and number of passes.

Nonlinear filters such as median or clipping operations may suppress spikes but do not have a simple linear transfer function. Preserve an edit or replacement mask. Never filter each line independently without checking whether line ends and direction create stripes in the map.

Gridding and interpolation artefacts

An interpolated grid is a model conditioned on observed locations. Search radius, anisotropy, trend model, barriers and blanking determine what appears between lines. Small cells increase display resolution, not survey resolution. Contours crossing large gaps should be styled or masked as unsupported.

Minimum-curvature-type surfaces can overshoot; nearest-neighbour surfaces create blocks; local weighted averages smooth extrema; directional kernels can manufacture continuity along the preferred direction. Cross-validation at withheld observations tests predictive behaviour but does not validate unsampled geology where coverage geometry differs.

Mosaicking surveys requires compatible datum, calibration, height, bandwidth and processing. Matching means or colours at overlaps can erase real regional differences. Reconcile line data and uncertainty before blending, and retain survey boundaries and adjustment surfaces.

Derivatives, continuation and normalisation

Differentiation multiplies high-frequency components and amplifies short-wavelength noise. Horizontal gradients can emphasise lateral change; vertical derivatives can emphasise shallow structure. Compute them only after checking sampling and noise, report units and show edge masks. Normalising by local amplitude can inflate noise in quiet areas.

Upward continuation predicts the field farther from sources under potential-field assumptions and suppresses short wavelengths. Downward continuation attempts the reverse and is unstable because noise grows rapidly. Stabilisation, maximum wavenumber and continuation distance must be declared. Continuing through topography with a flat-plane assumption can distort shallow sources.

Analytic-signal, tilt-type and other combined derivatives can reduce some directional dependence or display edges, but their maxima are not unique contact positions under arbitrary remanence, interference and depth. Treat them as hypothesis generators and validate with original profiles and forward models.

Filtering can suppress, shift, spread or amplify features; audit plots compare raw data, transfer function and residual
Filtering can suppress, shift, spread or amplify features; audit plots compare raw data, transfer function and residual

Artefact recognition and sensitivity panels

Common artefacts include ringing beside sharp steps, halos around isolated spikes, edge roll-off, line-direction striping, bullseyes around sparse stations, seam lines between surveys, amplified grid noise and false continuation structure. Diagnose them by acquisition-order profiles, data-location residuals, alternate grids and parameter sweeps.

Build a sensitivity panel with the original data, minimally corrected data, preferred product, correction or removed component, residual and two reasonable parameter alternatives. If the interpreted feature changes sign, location or continuity across reasonable choices, classify it as processing-sensitive.

Use synthetic injection: add a known feature to actual background data, process it through the full chain and measure recovery and distortion. Also inject a spike or line offset to learn its artefact signature. This tests the pipeline without claiming the synthetic feature is real.

Worked synthetic example

Consider five equally spaced synthetic profile values [2,2,12,2,2]. A three-point moving average produces interior values

$[(2+2+12)/3,(2+12+2)/3,(12+2+2)/3]=[5.33,5.33,5.33].$

The isolated peak has been reduced from 12 to 5.33 but spread across three positions. If the peak was a real narrow source, its location and amplitude are blurred. If it was a spike, contamination now looks spatially coherent. A filter cannot decide which explanation is correct.

For a derivative example, two adjacent values 10.0 and 10.6 units separated by 20 m give a finite difference of 0.03 unit/m. If each value has independent standard uncertainty 0.4 unit, derivative uncertainty is \sqrt{0.4^2+0.4^2}/20\approx0.0283 unit/m. The apparent gradient is barely larger than its uncertainty.

Processing-artefact audit workflow

  1. preserve raw and minimally corrected data at native support.
  2. state the physical or noise component each operation targets.
  3. record kernel, bandwidth, phase, padding, direction and order.
  4. inspect profiles before and after every material operation.
  5. map grid support and residuals at observation locations.
  6. compare reasonable interpolation and filter alternatives.
  7. display removed components and edge or low-support masks.
  8. inject synthetic signal and defect signatures through the pipeline.
  9. classify interpretations as robust or processing-sensitive.

Practice and review

  1. Apply a three-point moving average to [1,1,7,1,1] and describe spreading.
  2. Explain why small grid cells do not create resolution.
  3. List signatures of line levelling error in profile and map views.
  4. Design a parameter panel for downward continuation.
  5. Write a release checklist for an edge-enhanced map.

Review questions: What bandwidth was altered? Did feature position shift? Where is the grid unsupported? Is a gradient greater than propagated uncertainty? Can the feature be reproduced from raw profiles? Does it survive reasonable processing alternatives?

Sources