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{{OR/17/062}}
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Ground motions from the earthquake were recorded across the UK by seismometers operated by BGS at distances of more than 700 km. Figure 2 shows these ground motions as a function of time and distance from the epicentre. P-wave and S-wave arrivals are well-recorded. The first aftershock is clearly visible approximately two minutes after the mainshock.

[[Image:OR17062fig2.jpg|thumb|center|350px| '''Figure 2'''    Ground motions for the Moidart earthquake of 4 August 2017. Recordings are shown as a function of increasing distance. ]]

P-wave phase arrival times were measured at 27 recording stations and S-wave arrivals measured at 6 recording stations giving 33 phases to determine the earthquake hypocentre. In addition, amplitudes to determine magnitude were measured on the horizontal components at 24 stations. The stations used for each are shown in Figure 3.

[[Image:OR17062fig3.jpg|thumb|center|500px| '''Figure 3'''    Stations with phase arrivals used to determine the location and magnitude for the earthquake. (a) Stations with P-wave arrivals. (b) Stations with S-wave arrivals. (c) Stations with a measured amplitude. ]]

The closest seismometer to the epicentre is KPL at Plockton, 61 km to the north. The most distant station used was Monmouth almost 600 km to the south.

<center>
{| class="wikitable"
|+ Table 1    Crustal velocity model used in earthquake location<br>(Bamford et al., 1978<ref name="Bamford 1978">BAMFORD, D, NUNN, K, PRODEHL, C, JACOB, B. 1978. LISPB-IV. Crustal structure of Northern Britain. ''Geophys''. J R Astron. Soc. 54, 43–60.</ref>; Assumpcão and Bamford, 1978<ref name="Assumpcão 1978">ASSUMPCÃO, M, and BAMFORD, D. 1978. LISPB V. Studies of crustal shear waves. ''Geophys''. J R Astron. Soc. 54, 61–73.</ref>).
|- style="vertical-align:top;"
| ! scope="col" style="width: 175px;" | '''Depth to top of layer (km)'''
| ! scope="col" style="width: 160px;" | '''P-wave velocity (km/s)'''
| ! scope="col" style="width: 150px;" | '''Vp/Vs'''
|- style="vertical-align:top;"
| 0.00
| 4.00
| 1.73
|- style="vertical-align:top;"
| 2.52
| 5.90
| 1.73
|- style="vertical-align:top;"
| 7.55
| 6.45
| 1.73
|- style="vertical-align:top;"
| 18.87
| 7.00
| 1.73
|- style="vertical-align:top;"
| 34.15
| 8.00
| 1.73
|}
</center>

The arrival time data were input to the HYPOCENTER location algorithm (Lienert et al., 1986<ref name="Lienert 1986">LIENERT, B R E, BERG, E, and FRAZER, L N. 1986. HYPOCENTER: An earthquake location method using centered, scaled, and adaptively least squares. ''Bulletin of the Seismological Society of America'', 76:771–783.</ref>) to determine the earthquake hypocentre. In the absence of any definitive crustal velocity model for this area, from refraction or other sources, we used the 1-D velocity model shown in Table 1, determined from the LISPB refraction experiment (Bamford et al., 1978<ref name="Bamford 1978"></ref>; Assumpcão and Bamford, 1978<ref name="Assumpcão 1978"></ref>), over northern Britain. Strictly speaking, this model is valid only for the Midland Valley region of Scotland and contains a near-surface low velocity zone; however, the model has been widely used to locate earthquakes throughout Scotland, so this is model used for consistency. and has given reasonable results. An additional weighting factor based on the distance parameters ''XNEAR ''and ''XFAR'', where the weight is linearly decreased from 1 to 0 between ''XNEAR ''and ''XFAR'', was used to systematically reduce weighting with distance and is typically applied to reduce the effect of lateral heterogeneity in the velocity model. In this case, an ''XNEAR ''of value 300 km and an ''XFAR ''value of 600 km were applied.

<center>
{| class="wikitable"
|+ Table 2    Earthquake hypocentre determined using the<br>HYPOCENTER location algorithm.
|- style="vertical-align:top;"
| ! scope="col" style="width: 75px;" | '''Date'''
| ! scope="col" style="width: 75px;" | '''Time'''
| ! scope="col" style="width: 75px;" | '''Latitude'''
| ! scope="col" style="width: 75px;" | '''Longitude'''
| ! scope="col" style="width: 50px;" | '''Depth'''
| ! scope="col" style="width: 50px;" | '''ML'''
| ! scope="col" style="width: 50px;" | '''Npha'''
| ! scope="col" style="width: 50px;" | '''GAP'''
| ! scope="col" style="width: 50px;" | '''RMS'''
| ! scope="col" style="width: 50px;" | '''ERX'''
| ! scope="col" style="width: 50px;" | '''ERY'''
| ! scope="col" style="width: 50px;" | '''ERZ'''
|- style="vertical-align:top;"
| 04/08/2017
| 14:43:38.71
| 56.805
| -5.888
| 12.2
| 4.0
| 33
| 153
| 0.41
| 7.0
| 1.7
| 4.9
|}
</center>

Details of the best-fitting hypocentre are given in Table 2, together with the azimuthal gap, the root-mean-square (RMS) travel time residual and the horizontal and vertical errors in the hypocentre. The azimuthal gap is the largest azimuthal gap between azimuthally adjacent stations, and a value of 153° is relatively large and may lead to higher than desirable location errors. The RMS residual, measured in in seconds, provides a measure of the fit of the observed arrival times to the predicted arrival times for the given location and chosen velocity model. The horizontal and depth errors are determined from projections of the 95% confidence ellipsoid, assuming that the measurement errors are normally distributed. The size of the confidence regions depends on the variance and is computed using the χ2 statistic (Evernden, 1969<ref name="Evernden 1969">EVERNDEN, J F. 1969. Precision of epicenters obtained by small numbers of world-wide stations. ''Bulletin of the Seismological Society of America'', 59, 1365–1398.</ref>). The orientation of the error ellipsoid depends on both the number and geometry of the recording stations. The hypocentre and the 95% confidence ellipsoid are shown in Figure 4.

[[Image:OR17062fig4.jpg|thumb|center|400px| '''Figure 4'''    Projections of 95% confidence ellipsoid for the calculated hypocentre in: (a) the horizontal (XY) plane; (b) the YZ plane; and (c) the XZ plane. Each plane shows an area of 20 km by 20 km. (d) Shows the location of (a). ]]

The horizontal errors in X (EW) and Y (NS) are ± 7.0 km and ± 1.7 km. The error is much larger in the EW direction primarily as a result of the distribution of stations and the large azimuthal gap.

It is important to note that the modelling errors of calculated travel times depend strongly on the choice of velocity model.

The source depth was determined at 12.2 km with a corresponding error of ± 4.9 km. However, the nearest station to the epicentre is 61 km to the north, where both P- and S-wave arrivals were recorded. Considering the uncertainties associated with the 1-D velocity model, we conclude that the earthquake depth is likely to be poorly constrained. To further examine the depth resolution, we determined RMS error as a function of depth in the 0 to 30 km range with a spacing of 1 km. The results are shown in Figure 5 and display a well-defined minimum at 12 km, supporting the conclusion that the earthquake occurred in the mid-crust.

[[Image:OR17062fig5.jpg|thumb|center|300px| '''Figure 5'''    RMS error in earthquake location as a function of depth. ]]
==References==
{{reflist}}
[[Category: OR/17/062 The Moidart earthquakes of 4 August 2017 | 03]]

OR/17/062 Earthquake location - Revision history

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Ajhil at 13:32, 21 March 2018