Theoretical Background

Earthquake detection

scdetect-cc allows to configure multiple detectors by means of the template configuration. Detectors are handled completely independently. The most important properties of the detector configuration are the (template) earthquake "originId" and a set of template waveforms. Again, these template waveforms may be configured individually with so-called stream configuration parameters.

Once scdetect-cc has successfully initialized the configured detectors it is ready for processing. The waveform data to be processed is dispatched record-wise to the individual detectors, optionally pre-processed (e.g. resampled, filtered, etc.) and cross-correlated. The cross-correlation algorithm itself is based on computing the Pearson Correlation Coefficient . The results of the cross-correlation are time series of Pearson correlation coefficients, i.e. one time series per previously configured template waveform. During the next processing step the local maxima are extracted. By now, the processing for each template waveform was completely independent. That changes during the linkage phase. The local maxima are fed to the detector’s linker whose main task is to associate these tuples (time, correlation coefficient). In fact, these tuples already correspond to potential picks. During the association process the linker maintains a set of detection candidates. For each detection candidate a score is computed that is the arithmetic mean of the correlation coefficients from the associated picks. Once the score of a detection candidate exceeds the configured "triggerOnThreshold" the linker emits the detection candidate. In case a "triggerDuration" was configured the detection candidate still is put on hold i.e. it might be overridden by a detection candidate with both a higher score and at least the same number of associated picks. This approach guarantees that within the "triggerDuration" configured only the best candidate is emitted until either the time from the "triggerDuration" is passed by or the score of subsequently emitted detection candidates falls below the configured "triggerOffThreshold". Without a "triggerDuration" enabled every detection candidate immediately qualifies to a detection.

Further processing of the detection involves to optionally compute so-called template arrivals i.e. arrivals which are part of the origin identified by the template earthquake "originId", but not used for detection. The detection’s coordinates and depth are those of the template earthquake.

Depending on the configuration scdetect-cc subsequently computes amplitudes and magnitudes.

Finally, the detection (in terms of SeisComP this corresponds to a new origin), picks, amplitudes and magnitudes are send to scmaster and may be used for further processing with other SeisComP modules.

Phase association

Note

Phase association is only relevant if a detector is configured with at least two template waveforms.

Each detector comes with its dedicated linker which is responsible for phase association. The linker continuously consumes local maxima and performs the association based on template arrival times and a configurable "arrivalOffsetThreshold".

Given a detector is configured with $n$ template waveforms $T_k, k \in \mathbb{N}, 1 \leq k \leq n$ . Then, the original template arrival times form a reference matrix $\mathbf{A}$ :

where the entry of the $i-th$ row and $j-th$ column correspond to the absolute value of the difference between the original template arrivals referring to $T_i$ and the original template arrival referring to $T_j$ . Therefore, the matrix $\mathbf{A}$ has the following properties:

$\mathbf{A}$ is symmetric, i.e. $a_{ij} = a_{ji}$
the diagonal elements $a_{ii}$ are all zero.

Based on this information the linker maintains a list of detection candidates where each candiate $c$ has its own association matrix $\mathbf{B}^c$ . During operation the linker constantly tries to insert new local maxima into the association matrices. A local maxima referring to the template waveform $T_k$ is merged if the absolute values of all the differences in either the $k-th$ row or the $k-th$ column between the entries of the reference matrix and the association matrix are smaller than or equal to the configured "arrivalOffsetThreshold" $\epsilon$ , i.e.

$\left|a_{ij} - b_{ij}\right| \leq \epsilon$

Once a association matrix $\mathbf{B}^c$ is complete the candidat’s score is computed that is the arithmetic mean from the correlation coefficients of the associated local maxima. If the score is greater than or equal to the configured "triggerOnThreshold" the detection candidate is emitted.

scdetect-cc linking — The linker maintains a list of detection candidates where each candidate has its own association matrix $\mathbf{B}^c$ . Missing elements are indicated with a $-$ .

Changing the number of "minimumArrivals" to a value smaller than $n$ allows the user to influence the completeness of an association matrix. I.e. in fact a detection candidate is emitted once both the candidate’s score exceeds the "triggerOnThreshold" and the number of associated local maxima is at least equal to the value specified by the "minimumArrivals" configuration parameter.

Amplitude calculation

Computing amplitudes is a prerequisite in order to perform a magnitude estimation later on. Since multiple magnitude estimation methods are provided, each magnitude estimation method requires to compute a corresponding amplitude type. In accordance with the magnitudes methods described in the magnitude estimation section scdetect-cc implements the following amplitude types to be computed:

MRelative: Amplitude computed as the ratio between the template waveform and the detection. The approach is outlined by e.g. Peng and Zhao [2] and Ross et al. [3] and uses the same instrument components as specified by the detector configuration.
MLx: Amplitudes required for the amplitude-magnitude regression approach. The implementation follows the approach outlined in Herrmann et al. [1] (section 3.3.3 Magnitude Estimation) . Amplitudes used for the amplitude-magnitude regression are so called sensor location RMS (root-mean-square) amplitudes (i.e. the maximum sample-wise RMS regarding the horizontal components for a certain sensor location w.r.t. velocity seismograms).

Amplitudes are calculated once an origin has been declared.

In general, the computation of amplitudes is sensor location dependent. In order to provide dedicated configuration for different sensor locations scdetect-cc makes use of SeisComP’s bindings configuration concept. Note that amplitudes are calculated only:

for those sensor locations with bindings configuration available,
if the internal waveform buffer still contains the required time window.

The waveform buffer size may be configured using the processing.waveformBufferSize module configuration parameter.

Magnitude estimation

scdetect-cc estimates magnitudes as so called SeisComP station magnitudes ( for further details, please refer to the scmag documentation) . Magnitudes may be estimated for only those sensor locations, the corresponding magnitude types were computed, previously. In accordance with the amplitude types described in the amplitude calculation section, the following magnitude types are available:

MRelative: Template-detection ratio based magnitude estimation. Besides, of the corresponding amplitudes to be computed, this particular type requires station magnitudes to be available through EventParameters. For further details please refer to either Peng and Zhao [2] or Ross et al. [3].
MLx: Amplitude-magnitude regression based magnitude type. Besides, of the corresponding amplitudes to be computed, this particular type requires both amplitudes and station magnitudes to be available by means of EventParameters. Moreover, the approach is based on so-called template families which in fact are groups of related templates. The corresponding template family configuration must be provided by scdetect-cc‘ s --templates-family-json path/to/templates-family.json CLI flag. For further information please refer to Herrmann et al. [1] (section 3.3.3 Magnitude Estimation).

All magnitude estimation methods listed above are based on the following types of template station magnitudes:

MLh: please refer to the SeisComP documentation
MLhc: based on MLh, but uses a slightly adjusted relationship (i.e. corrected for near-field observations) and allows for station specific corrections.

Note

Magnitudes of type MLhc are preferred over magnitudes of type MLh.

Recall, that template station magnitudes must be available through EventParameters (for further details, please refer to the related section on providing these data products).