Methodology

This section provides technical details regarding the algorithm used for the detection of 1D anomalies.

Anomalies are identified from the detection of maximum, minimum and inflection points calculated from the first and second order derivatives of individual data channels. The algorithm relies on the Numpy.fft routine for the calculation of derivatives in the Fourier domain.

Detection parameters are available for filtering and grouping co-located anomalies. The selection process is done in the following order:

Primary detection

Loop over the selected data channels:

1. Apply the Minimum Data Value threshold.

2. For every maximum (peak) found on a profile, look on either side for inflection and minimum points. This forms an anomaly.

3. Keep all anomalies larger than the Minimum Amplitude

Grouping

Anomalies found along individual data channels are grouped based on spatial proximity:

1. Find all peaks within the Maximum Peak Migration distance. The nearest peak is used if multiple peaks are found on a single channel.

2. Create an anomaly group that satisfies the following criteria:

   • The data channels must be part of a continuous series (maximum of one channel skip is allowed)

   • A group must satisfy the Minimum number of channels

Minimum Amplitude

property PeakFinderParams.min_amplitude: int

Threshold on the minimum amplitude of the anomaly, expressed as a percent of the height scaled by the minimum value.

Threshold value (\(\delta A\)) for filtering small anomalies based on the anomaly minimum (\(d_{min}\)) and maximum (\(d_{max}\)).

\[\delta A = \left|\left|\frac{d_{max} - d_{min}}{d_{min}}\right|\right| \cdot 100\]

See figure for a visual example of the anomaly amplitude.

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Add figure showing the effect on anomaly identification

Minimum Data Value

property PeakFinderParams.min_value: float

Minimum absolute data value to be considered for anomaly detection.

The minimum data threshold (\(\delta_d\)) (see Figure) can be defined by:

\[\begin{split}\begin{equation} d_i = \begin{cases} d_i & \;\text{for } d_i > \delta_d \\ nan & \;\text{for } d_i \leq \delta_d\\ \end{cases} \end{equation}\end{split}\]

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Minimum Width

property PeakFinderParams.min_width: float

Minimum anomaly width (m) measured between start and end of bounding minima.

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See figure for a visual example of the anomaly width.

Maximum Peak Migration

property PeakFinderParams.max_migration: float

Threshold on the lateral shift (m) of peaks within a grouping of anomalies.

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See figure for a visual example of migration within a group of anomalies.

Minimum number of channels

property PeakFinderParams.min_channels: int

Minimum number of data channels required to form a group.

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See figure for a visual example of channels making up a group of anomalies.

Merge N Peaks

property PeakFinderParams.n_groups: int

Number of consecutive peaks to merge into a single anomaly.

Todo

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Max Group Separation

property PeakFinderParams.max_separation: float

Maximum separation between peaks to merge into single anomaly.

Todo

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Smoothing

property PeakFinderParams.smoothing: int

Number of neighbors used in running mean smoothing.

The running mean replaces each data by the average of it’s N neighbours:

\[d_i = \frac{1}{N}\sum_{j=-\frac{N}{2}}^{\frac{N}{2}}d_{i+j}\]

where averaging becomes one sided at both ends of the profile. The result is a smoothed data set where the degree of smoothing scales with the number of neighbours used in the mean.

Todo

Add reference figure shown for plot residuals.

Show residual

Option to show the positive (blue) and negative (red) residual between the original and smoothed profile. Useful to highlight smaller anomalies within larger trends.

Masking Data

property PeakFinderParams.masking_data: geoh5py.data.data.Data | None

Mask object to focus peak finding within an area of interest.