Question: very low RMS?

[Cthuulhaa]

Hello Anthony,

I have a question which might have an evident answer: for a high-quality location with several tens of picks I have seen that the RMS can be about 0.1 s. For a location with a poor station network and, say <10 phase picks I have seen anomalously low RMS with values about 0.06 s. Why is that?

Cheers!

[alomax]

I think the main issue is likely due to RMS not being a measure of location quality, but instead a measure of fit to the data (arrival time location procedures directly or indirectly minimize residuals and RMS). With ≤ 4 observations the RMS can be zero, since there are 4 parameters to fit (x, y, z, t). So, in general, with fewer observations the RMS should decrease. See also: http://www.corssa.org/export/sites/corssa/.galleries/articles-pdf/Husen-Hardebeck-2010-CORSSA-Eqk-location.pdf

With NLL-EDT there is a second issue that the RMS is weighted by the posterior weight of the contribution of each pick to the maximum likelihood solution. So, since EDT is very effective at down-weighting outlier readings, the NLL-EDT RMS indicates the fit to the data mainly for the readings that best fit the optimal solution. Yes, I think this is a bit circular, but is informative for the majority of cases where EDT correctly removes outliers. To calculate the RMS for all picks would require reading their residuals the NLL output phase file and calculating the corresponding RMS without weights, or using only prior weights.

Anthony

[alomax]

My preferred simple, single measure of location quality is the ellipsoid major half-axis length. See https://pubs.usgs.gov/of/1999/ofr-99-0023/ Chapter 3 for a discussion of the error ellipsoid as used in NLL.