Cross Correlation Coefficient (CCC)

[mmesim]

What if instead of CCC we use |CCC|*CCC.

See -> https://academic.oup.com/gji/article/228/1/355/6356567?login=true

Figure 2. https://academic.oup.com/view-large/figure/303129936/ggab344fig2.jpg

[damb]

Thanks @mmesim for pointing me to this paper.

Some notes from my side regarding the referenced paper (please correct me if I got some of the details not correctly):

• scdetect implements https://en.wikipedia.org/wiki/Pearson_correlation_coefficient for computing the CCC. The current implementation does not normalize the template waveform, though it caches parameters if possible. You can find the implementation in https://github.com/damb/scdetect/blob/4e549b72505ad42fb53a7ca857de3dd9fa74a8fb/src/apps/scdetect/filter/crosscorrelation.ipp#L114-L214.
• Cross-correlation is performed in frequency-domain. In contrast, scdetect performs the cross-correlation in time-domain. This is mainly due to the real-time requirement.
• Cross-correlation is performed station based (i.e. more precisely sensor location-based). That is, the resulting CCC for a sensor location is stacked. However, scdetect does not enforce the cross-correlation to be performed sensor location based. Though, I can imagine a configuration option which allows stacking in case of correlating multiple streams from a sensor location (given that the corresponding template waveforms cover one and the same time window).
• Apparently, the |CCC|*CCC detection statistics were originally introduced in order to avoid computing the square root of the denominator:

As stated by Gibbons & Ringdal (2012), the change to this detection statistic was motivated by efficiency; without the need to compute the square root terms in the denominator, this term consists only as a product and a quotient of two convolutions.

• P waves and S waves were considered separately. The template waveform duration is 2s (which is comparably short). Note that currently, scdetect does not implement matching multiple templates with regard to a single stream and a single detector. See Multiple templates per stream #21.
• I think, this statement concludes the paper's work quiet nicely:

What we have done is ultimately to demonstrate that the C|C| trace has a greater contrast between values at times of interest and values at other times.

Questions:

• Does this approach generalize if stacking the streams w.r.t. a sensor location is not applied? (I assume, yes.)
• Does this approach generalize for other filter configurations?

[mmesim]

Does this approach generalize if stacking the streams w.r.t. a sensor location is not applied? (I assume, yes.)

I don't see a reason why not to be applied to a single channel. My understanding is that CC * |CC| will help to suppress the noise. Of course that will work better on a network/stacking approach.

Does this approach generalize for other filter configurations?

What do you mean?

[damb]

I was referring to the fact that the study uses a specific filter configuration. However, I assume that the characteristics of the CCC*|CCC| approach (i.e. suppressing the noise) are independent from this particular filter configuration.