Computing earthquake magnitudes for El Hierro

Introduction

Since the onset of many earthquakes on El Hierro, questions are posed in the media (and by some blog authors) on the quality of information provided by various official bodies. It is understandable that the authorities seek to avoid panic or rumors, but this implies a good communication policy leaving no room for improvisation.

Given the diversity of knowledge of the general public, the relevance of disclosing raw data is not obvious. However, for individual researchers or even curious amateurs, access to these data is crucial. The scientific method is based on the disclosure of the work done and the data used (to communicate new theories and results, but also to allow independent verification).

El Hierro

Seismograms and spectrograms are available on the IGN website, but can only be used qualitatively. In fact,

• There is no mention of procedure used to obtain them and, in particular, filters (e.g. frequency) applied

• For seismograms, there is no mention of measurement unit, it is not possible to know if the graph is displaying a raw recording (in general, the speed of the ground) or the actual displacement (calculated by integrating the speed).

• Regarding the spectrograms, the same problem exists.

By comparison, the USGS indicates that information. If we consult http://earthquake.usgs.gov/monitoring/helicorders/nca/51/latest/ for instance, we can see the unit indication

We clearly recognize a speed (in centimeters per second).

Fortunately, IGN provides bulletins in IMS format. These bulletins are caused by the need for monitoring seismic waves related to detection of nuclear tests, under the "Comprehensive Nuclear-Test-Ban Treaty" and their use in scientific research is an indirect consequence, but it is very important.

One of the entities set up by the treaty is the International Monitoring System (IMS), and this organization has defined the content of the bulletins that are used to report the detection of seismic events and waves.

In the case of earthquakes on El Hierro, the only source of information for serious analysis in this context is the availability of the IMS bulletins.

Using IMS bulletins

It is beyond the scope of this article to describe the format of a IMS bulletin, and it suffices to note that the following information is available:

• The depth of the epicenter (km)
• The distance between a station and the epicenter (in degrees)
• The amplitude of the waves reported (in nanometers)
• The wave period (in seconds)
• The local magnitude calculated by IGN

The local magnitude is calculated by IGN based on a formula of its own:

mbLg(L) = log (A/T) + 1.17 log R + 0.0012R + 0.67

With:

• A: amplitude (micrometers)
• T: period (second)
• R: hypocentre distance (kilometers)

Important point: in everything that follows the assumption is that the information found in these reports are correct.

Can we recalculate these magnitudes? The answer is yes. As an example, for event 1165013:

Station	Distance (degree)	Amplitude (nm)	Period (s)	MbLg(IGN)	MbLg Computed.	Difference (IGN-Calc.)
CTAN	0.06	15.4	0.06	-	1.3
CTAB	0.07	85.8	0.08	2.0	2.0	0.0
CCUM	0.08	14.0	0.22	-	0.8
CJUL	0.09	132.6	0.18	-	1.9
CMCL	0.11	21.9	0.16	-	1.2
CHIE	0.14	3.1	0.16	0.4	0.4	0.0
CTIG	0.14	3.2	0.28	0.2	0.2	0.0

Table 1: Data and results for event 1165013

Surprisingly, IGN does not calculate the magnitude for all stations, even if the data are available. In the table above, only three values are calculated (for stations CTAB, CTIG and CHIE). We can immediately make other comments:

• We can see that the recalculated magnitudes correspond to those calculated by IGN. The procedure seems to be in good agreement with that of IGN.
• The period is always a multiple of two. It is therefore likely that the period is the result of a calculation.
• The dispersion of the values calculated for the magnitude is large (0.2 to 2).

Now we visualize the magnitude (depending on the distance from the hypocentre).

Fig 1. Magnitude vs distance.

We note that:

• The more the distance grows, the less the magnitude calculated is high
• The correlation coefficient R ² is intermediary (it can vary between 0 and 1, and here it is about 0.5), which indicates a misalignment with a straight line (if the points are perfectly aligned, the value is 1). Warning: this coefficient is not the "R" value used in the calculation of the magnitude, it is just the same symbol.

The first point is surprising: although it is known that the effect of earthquakes fades with distance (attenuation), the formula used by IGN has two terms (1.17 log R + 0.0012 R) dependent on the distance and it might therefore be expected that the damping effect is taken into account. This point will be discussed further in a future article.

We can still do other analyses. So ...

to be continued ...