Intraplate Earthquakes in Europe—Source Parameters from Regional Moment Tensor Analysis

Abstract

Plate tectonics provides a highly successful framework to describe a wide range of geological observations invoking the motion of lithospheric plates. In its simplest form the plates are rigid and earthquakes are confined to boundaries where plates move relative to each other.

Appendix

Of the earthquake shown in Fig. 2, including the sub-crustal events with depth z > 40 km, 87 have a RMT and a Global CMT solution. This appendix compares results from the two methods to illustrate overall robustness and reliability of waveform modeling derived source parameter estimates.

Figure 8 shows the double couple (DC) fault plane solutions for the common events. With few exceptions, the agreement between the RMT (black and white) and GCMT (gray) solutions is high. Most events with large focal mechanism differences occurred before 2004 when GCMT analysis started to include intermediate-period surface waves (Ekström et al. 2012), which lowered GCMT analysis threshold and stabilized results for M ≈ 5 and smaller events common in the European intraplate dataset. Expansion of broadband seismic networks in the European-Mediterranean region also improved RMT solution quality.

Fig. 8

Fault plane solutions for 87 common RMT (black and white) and GCMT (gray lines) earthquakes in Europe. Numbers on top are year, month, and day of occurrence; events are in chronological order. Additional labels are “D”: 20 sub-crustal events (z > 40 km); “a”: 13 events with |ΔAx| ≥ 30°; “e”: 20 events with η_p ≤ 0.8; and “s”: 12 events with S_Hmax difference ΔS_Hmax ≥ 15° (see text for explanation of |ΔAx| and η_p). Four events labeled “aes” indicate large mechanism differences, they are: A. Event 000421 in western Anatolia, which is characterized by N-S extension; nearby events (970121, 030723, 030726) are consistent with the RMT solution. B. Event 010720 is one of the common intermediate-depth Vrancea, Romania events; the closest other events (050618, 051213) show high similarity. C. Event 030222 in eastern France is tightly constrained by regional waveforms (Deichmann et al. 2004); the event predates inclusion of intermediate-period surface waves and with M_w = 4.8 is small for traditional GCMT analysis. D. The GCMT solution for event 040918 in the Pyrenees has a 6% double-couple contribution and its orientation differs significantly from other nearby and internally consistent events in the RMTs database

The overall agreement is further illustrated in Fig. 9, which shows different measures of moment tensor similarity plotted against each other. The Kagan angle (Kagan 2007) is the minimum 3-D angle required to rotate the principal axes of one moment tensor onto another (‘angular difference’ between two double couples), |ΔAx| is the mean angular difference between principal axes (Bernardi et al. 2004), which is a similar quantity as the Kagan angle and simple to calculate, and η_p is the radiation pattern coefficient (Kuge and Kawakatsu 1993), which describes the P-wave radiation pattern similarity between two moment tensors. Small values of |ΔAx| and the Kagan angle, and large values of η_p indicate similar solutions. The roughly linear relation between |ΔAx| and the Kagan angle is expected since both describe principal axes rotations. A strong correlation exists only for events with small Kagan angle and large η_p. About 74% of the events (64 of 87) satisfy high similarity criteria |ΔAx|≤30° and η_p ≥ 0.8 while the rest shows moderate similarity. Low DC percentages in moment tensors, shown as dark circles, account for a disproportional number of events with moderate similarity (23%) compared to their frequency of occurrence (14%). In contrast, all 22 events with high DC source contributions, shown as open circles, have low rotation angles and 86% of them satisfy high similarity criteria. Low DC percentages in RMT and GCMT solutions might thus, in many cases, indicate limited source parameter resolution rather than actual deviations from a simple faulting source.

Fig. 9

Comparison between RMT and GCMT solutions. Kagan angle and |ΔAx| measure angular difference between principal axes systems while η_p measures P-wave radiation pattern similarity (normalized to [−1, 1]). An interchange of two axes results in |ΔAx| = 60°. Left: Kagan angle versus |ΔAx|. Dark circles indicate solutions with double-couple percentage of DC ≤ 35% in either RMT or GCMT; these solutions on average show larger differences. Open circles are events with DC ≥ 85% in both RMT and GCMT; all have |ΔAx| ≤ 30°, which Bernardi et al. (2004) considered to indicate high similarity. Gray circles are all other events. Kagan angle and |ΔAx| roughly show a 4/3 scaling (solid line) Right: Kagan angle versus η_p. Symbols are as on left. High correlation exists only for low Kagan angle and high η_p events (upper left of diagram); the larger scatter at lower similarities reflects that the two indicators measure separate aspects of radiation differences

The RMT and GCMT moment magnitudes agree very well with each other (Fig. 10 left). The average difference is 0.00 ± 0.11. The data indicate a slight tendency of M_w(GCMT) > M_w(RMT) for small events and vice versa for large events with linear regression resulting in a slope of 1.08. Figure 10 (right) shows centroid depths of all events in light gray. For shallow events, GCMT depth is often fixed while for deep events, depth is sometimes not well resolved by long-period regional data. The subset of dark gray circles consists of events with free (GCMT) and resolved (RMT) depth. For these 35 events, the average depth difference GCMT-RMT is 2.8 ± 10.1 km, and, for 19 crustal events (z ≤ 40 km) is 1.3 ± 3.4 km indicating excellent agreement considering that RMT depth analysis is performed as grid search with 3 km steps.

Fig. 10

Left: Comparison of M_w(GCMT) and M_w(RMT). Solid black line is a 1:1 relation and gray dashed line shows the average difference (0.00 ± 0.11). Right: Comparison of GCMT and RMT centroid depth. Light gray shows all 87 events. Dark gray shows 35 events with free (GCMT) and resolved (RMT) depth; their average difference, shown as gray dashed line, is 2.8 ± 10.1 km and for crustal events (z ≤ 40 km) is 1.3 ± 3.4 km

A histogram of the differences in the maximum horizontal stress orientation S_Hmax is shown in Fig. 11. Excluding low DC events (≤20% for either GCMT or RMT) and events with “unknown” stress regime (using Zoback (1992) assignments) results in 70 events. The average difference between RMT and GCMT is −0.7° ± 10.2°, while the median is −1° with 75% of all observations between −7° and 9° indicating S_Hmax orientations are stable and well resolved. The three outliers in Fig. 11 correspond to the suspicious 000421 (−48°), 030222 (24°), and 010720 (28°) events discussed in the context of Fig. 8 and should be disregarded. This leaves a remarkably small largest difference of −22° (normal faulting event 041003 at northwestern edge of Black Sea).

Fig. 11

Histogram of S_Hmax differences between RMT and GCMT solutions. Events with low DC (≤20%) or of “unknown” stress regime are excluded resulting in 70 common events. Red lines show average and standard deviation (−0.7° ± 10.2°) and blue lines median (−1°) and range containing 75% of observations (−7°–9°) indicating a tight distribution