The 2021 South Sandwich Island Mw 8.2 Earthquake: A Slow Event Sandwiched Between Regular Ruptures

We determined the rupture sequence of the 12 August 2021 Mw 8.2 South Sandwich Island earthquake which appears to be a complex sequence in both time and space. Notable tsunamis were recorded by tide gauges at global distances. Given the complexity of this event, we conducted a multiple subevent inversion on broadband seismograms, to resolve its complex variations of fault geometry, location, depth, and temporal characteristics. We found that the rupture initiated as a regular deep thrust earthquake; it then ruptured shallower and triggered a silent and dominantly slow subevent extending ∼200 km to the south, and ended with two other regular subevents. The total duration is ∼260 s, unusually long for an Mw 8.2 event. Our result is qualitatively consistent with other moment tensor solutions and the deviant mB–Mw and MS–Mw relations, and provides a more quantitative space‐temporal pattern of this unusual sequence.

• The South Sandwich Island M w 8.2 earthquake appears to have extended deep depth, yet displayed tsunami earthquake-like features • Inversions including long-period data revealed a M w 8.16 slow subevent at shallow depth, connecting regular deep ruptures at the ends • The hybrid of deep and shallow ruptures represents an extreme example of the broad spectral behaviors of subduction zone earthquakes

Supporting Information:
Supporting Information may be found in the online version of this article.  Table S1 in Supporting Information S1). Given the variability of these solutions, we attempted W-phase inversion (Kanamori and Rivera, 2008). Because of the complex interference of the waveforms of several events, only with a very narrow long-period pass band (0.00125-0.002 Hz, i.e., 500-800 s), we could obtain a solution that can fit long-period waveforms satisfactorily for 40 stations (more details in Text S1, Figures S2 and S3 in Supporting Information S1).
The depths reported by different catalogs range from 10 to 50 km, and the hypocenters scatter around the Slab 2.0 (Hayes et al., 2018) interface ( Figure 1b). This is probably caused by difficulty in locating the events accurately, due to the complex interference of seismic waves from the foreshock and mainshock. Nevertheless, the deeper depths of the South Sandwich Island earthquake appear to contradict the shallow slip inferred from the global-spreading tsunami. While detailed rupture analyses would be needed to understand this disparity, it is difficult to define a physical fault plane for slip inversions due to the diverse locations and focal mechanisms from different sources (Figure 1). In addition, the aftershocks extend ∼400 km along the curved subduction zone, making a planar fault unphysical. Thus, we need to analyze the rupture properties of this earthquake with flexibility in fault geometries, while maintaining the depth-dependent complexities.
In this study, we first investigate the overall spectral characteristics of the event. Then, we determine the kinematic rupture process with a multiple subevent inversion of broad-band seismic waveforms, and evaluate the contributions of subevents and discuss their relationships.

General Spectral Characteristics
Given the complex rupture characteristics of the 2021 South Sandwich Island earthquake, we first investigate this event using three magnitude scales, m B , M S , and M w . Although m B and M S are old somewhat qualitative parameters, they are available for global earthquakes and useful for understanding the spectral characteristics of the South Sandwich Island sequence in global context. To the first order, m B , M S , and M w represent the spectral amplitudes of the sequence at about 4, 20, and 200 s or even longer period.

m B Versus M w Relationship
For the measurement of m B , we used the method described in Kanamori and Ross (2019) which follows the method developed by Gutenberg and Richter (1956). We used the vertical component P-waves recorded at 54 global network stations (epicentral distance of 30°-80°, Figure S4 in Supporting Information S1), which include peak amplitudes for the mainshock. The medians of station m B are 6.87 and 7.10 for the foreshock and the mainshock, respectively. Figure 2a compares the m B -M w relationship for these events with the m B values of about 3,000 events with M w ≥ 6 for a period from 1988 to 2018 taken from Kanamori and Ross (2019). The m B data for the global events shown by small dots represent the range for ensemble of global events. The m B for the mainshock is probably the upper bound because the time window for the m B measurements contains some energy from the foreshock, only 145 s earlier. The m B values for the foreshock and the mainshock are 0.4 and 0.6 m B unit, respectively, smaller than the average global m B -M w trend; this indicates that these events, especially the mainshock, are deficient in short-period energy.

M S Versus M w Relationship
We made a similar comparison of M S versus M w relationship. We computed M S using 20 s surface waves from 483 global seismic stations (distance range of 30°-120°), and measured the peak ground motion amplitudes. Since the surface waves of the foreshock and mainshock overlap, we could not measure M S for each event separately, and obtained just one M S = 7.68 ( Figure S5 in Supporting Information S1). Compared with the empirical global  Giacomo et al., 2015) from the ISC M S data set (ISC, 2021), the observed M S is 0.5 smaller than the average trend ( Figure 2b).
The smaller m B and M S than the global average trends indicate depleted seismic energy release at short periods and slow rupturing characteristics (Kanamori, 1972;Kanamori & Ross, 2019). As shown in Figures 2a and 2b, the South Sandwich Island earthquake is among the biggest outliers from the general trend. Other anomalous events similar to the South Sandwich Island earthquake includes the 1992 Nicaragua M w 7.6, the 1994 Java M w 7.8, the1996 Peru M w 7.5, the 2006 M w 7.7 Java, and the 2010 M w 7.8 Mentawai Island earthquakes, all of which are well-known shallow slow tsunami earthquakes. This similarity suggests that the South Sandwich Island earthquake probably involved a substantial slow rupture component at the shallow subduction interface.

Multiple Subevent Inversion
To image the detailed rupture process of the earthquake, we applied the multiple subevent inversion method. Our subevent inversion algorithm represents a complex rupture with multiple simpler sources, each of which can have different timings, locations, source durations and focal mechanisms (Jia, Shen, et al., 2020;Jia, Wang, & Zhan, 2020;Ross et al., 2019;Zhan et al., 2014). This simple parameterization allows flexible representation of time history and fault geometries, thereby capturing the first-order spatiotemporal rupture complexities. Our subevent method is particularly suitable for describing the South Sandwich Island earthquake which contains at least two major events in 3 min and involves potential fault geometry variations along the curved South Sandwich trench. As the possible slow rupture may propagate long distance with strong directivity effects, we introduce a finite subevent with a unilateral Haskell rupture model with a constant rupture velocity (Haskell, 1964). In this study, we use the Haskell model only for the long duration (>100 s) subevent with potentially significant rupture directivity. We applied a Markov Chain Monte Carlo inversion in a Bayesian framework, and increased the number of subevents iteratively until the waveforms fit well (Text S2 in Supporting Information S1 for more details).
We collected 58 teleseismic (distance of 30°-90°) P velocity and displacement records, 43 teleseismic SH displacement records, and 12 three-component regional (distance within 40°) full waveforms in displacement (Figure S6 in Supporting Information S1) for the subevent inversion. We removed their instrumental responses, and filtered the P and SH waves between 0.005 and 0.05 Hz for modeling short period features. For the regional full waves, we used them in two datasets with different filter bands. One of them with a 0.002-0.02 Hz passband represents intermediate period waves, and the other with 0.002-0.0033 Hz, long period motions. This combination of short, intermediate and long period bands allows mapping the ruptures of different length scales simultaneously. The teleseismic Green's functions are calculated combining the propagator matrix method and plane wave approximation (Kikuchi & Kanamori, 1991;Qian et al., 2017), using the CRUST 2.0 (Laske et al., 2001) model at the source region and the IASPEI91 model (Kennet, 1991) at other places. The regional full-wave synthetics are computed with a frequency-wavenumber integration algorithm (Zhu & Rivera, 2002), using the PREM model (Dziewonski & Anderson, 1981).
Our subevent model consists of five subevents that span ∼300 km along the trench (Figure 3, Table S2 in Supporting Information S1). We fixed the first subevent at the NEIC M w 7.5 event hypocenter. Data fittings (Figure 3c, Figure S7 in Supporting Information S1) and model uncertainties (Figure 3b, Figure S8 in Supporting Information S1) suggest that the source parameters are well constrained. The rupture begins with two short-duration subevents E1 (centroid time τ C = 13s after the origin time, duration d C = 23s, M w 7.2) and E2 (τ C = 36s, d C = 19s, M w 7.2), which in total (M w 7.4) generally represents the NEIC M w 7.5 foreshock. They have close locations and similar shallow dipping thrust focal mechanisms (average strike/dip/rake = 157°/18°/82°), but the centroid depth of E1 is deep (39 km) while E2 is shallow (7 km), suggesting an updip rupture propagation along the plate interface. They are located near a patch of dense aftershock seismicity (Figure 3a).
Concurrent with the rupture initiation represented by E1-E2 in the first 50 s, the subevent E3 (τ C = 90s, M w 8.16) emerged and continued for ∼180 s. E3 contributes the most seismic moment of the South Sandwich Island earthquake, and its moment rate function (Figure 3d) has a remarkably smaller aspect ratio (peak moment rate over duration, 1.2 × 10 17 N-m/s 2 ) than regular subevents E1-E2 (average of 3.3 × 10 17 N-m/s 2 ). As a Haskell source, E3 initiates close to the locations of E1-E2, and unilaterally propagates toward the south with a slow velocity (∼1 km/s) and a long fault length (∼180 km). E3 is located at 14 km depth with an uncertainty of ±5 km (Figure 3b), and it has a very shallow-dipping thrust mechanism (strike/dip/rake = 134°/4°/22°), although the strike and rake angles are not well constrained due to the shallow dip angle ( Figure S9 in Supporting Information S1). The shallow slow slip of E3 presumably transfers the stress along the slab, which explains the downdip dense aftershock seismicity as well as the triggered outer-rise earthquakes (Figure 3).
The rupture terminated with the final two subevents E4 (τ C = 195s, d C = 26s, M w 7.6) and E5 (τ C = 226s, d C = 50s, M w 7.7) at 250-300 km south of the epicenter. They occurred about 3 min after the rupture initiation. E4 and E5 are also shallow dipping thrust subevents (average strike/dip/rake = 206°/23°/106°), but their strike angles are ∼50° rotated clockwise from E1-E2. This rotation is consistent with the geometry of the curved South Sandwich Island trench. Their locations are close to the downdip high-density aftershock patch (Figure 3). This spatial pattern is similar to that for the other two major slip asperities (E1-E2 and E3). The depth of E4 (25 km) is significantly deeper than E5 (9 km), indicating coexisting megathrust slip at different depth domains. Moment rate functions of E4-E5 display similar aspect ratios (average of 5.3 × 10 17 N-m/s 2 ) to E1-E2, indicating that E4 and E5 are, unlike E3, more like regular ruptures.
The low aspect ratio, slow rupture velocity, overall shallow depth, and shallow-dipping mechanism of E3 suggest that it is a "slow earthquake" at the shallow subduction interface. This feature can be most prominently demonstrated in Figure 4. The regular subevents E1, E2, E4, and E5 contributed almost all of the short and intermediate period waveforms, while E3 barely excited short and intermediate period signals (Figures 4a-4c and S10 in Supporting Information S1). In contrast, E3 generated large long-period waves, comparable to the sum of all other subevents (Figure 4d, Figure S10 in Supporting Information S1). The diminished short period excitation explains the smaller-than-average m B and M S of E3 (Figure 2).  Figure 3d compares the overall rupture sequence determined by our multiple subevent inversion with the events determined by other methods. The sequence starts with E1 which is the foreshock (NEIC1). The long duration subevent E3 connects the short duration subevents E1-E2 at the beginning and E4-E5 at the end, forming a continuous megathrust rupture process. This approximately corresponds to the unusually long-duration GCMT1 (M w 8.3) in the middle of the rupture extent ( Figure 1). The GCMT2 (M w 7.9, half duration = 24 s), with the centroid time 48 s later than GCMT1 probably overlaps with GCMT1 in time, and roughly corresponds to E4-E5 at the southern tip with rotated strike angles (Figure 1). The W-phase solution, which is similar to the NEIC M ww , probably represents a very long-period component of the latter half of the sequence (Figure 1, Figure S2 in Supporting Information S1).

Discussion and Conclusions
The 2021 South Sandwich Island (M w 8.2) earthquake is a complex multiple event, including a slow subevent E3 connecting other regular thrust subevents at the beginning and the end. The slow subevent E3 contributes over 70% of the total seismic moment of the sequence. The large moment and the relatively shallow depth of E3, with weak short-period seismic radiation, make this sequence as a whole look like a tsunami earthquake. The total duration of the whole sequence (E1 to E5) is about 260 s; thus, the centroid time shift, 130 s, estimated from the half duration is anomalously long on the centroid time delay versus M w scaling relation obtained by Duputel et al. (2013), as shown by Figure 5. The 2002 Guerrero earthquake (Kostoglodov et al., 2003) and the 2006 Java earthquake (Ammon et al., 2006), both of which are slow tsunami earthquakes, share a similar trend on Figure 5. Thus, the South Sandwich Island earthquake appears to be a hybrid of deep rupture and slow tsunamigenic slip; this explains the somewhat unusual combination of the relatively large depth and the globally observed tsunami.
Although the shallowest subduction interface is often considered seismically inactive due to the velocity-strengthening frictional properties (Scholz, 1998), some large tsunami earthquakes were found to host major slip at near-trench depths (Kanamori & Kikuchi, 1993;Lay et al., 2011). Lower upper plate rock rigidity at shallow depths has been illustrated to produce tsunami earthquake-like properties, including depleted short period seismic energy and slow rupture (Bilek & Lay, 1999;Sallarès & Ranero, 2019;Sallares et al., 2021), which well explains our observations for E3, suggesting the subduction zone geologic conditions could largely impact the tsunami potential. However, the slow component of the South Sandwich Island earthquake may have a broader depth extent than the traditional tsunami earthquakes. The slow subevent E3 has an overall shallow centroid depth of 14 km, which explains its global-spreading tsunamis and the two large (∼M w 7) outer-rise aftershocks ( Figure 1) due to the possible stress transfer at shallow subduction interface (Sladen & Trevisan, 2018). However, it is probably not confined in the near-trench depths like other tsunami earthquakes, but could have extended to deeper domains, which is consistent with absence of observation of devastating tsunami. The deeper slip could trigger slow rupture by dynamic weakening (Ma, 2012;Noda & Lapusta, 2013), making the slip span over a broad depth range. However, the detailed depth-dependent slip distribution of the slow subevent remains unclear and difficult to resolve, because of the tradeoff between seismic moment, dip angle and depth (Tsai et al., 2011). This requires further investigations.
In summary, the 2021 South Sandwich Island M w 8.2 earthquake involves a complex depth-varying rupture process. The complex interaction of deep regular slip and shallow slow subevent explains the somewhat contradicting combination of the deep subevents, the tsunami earthquake-like features with diminished short-period seismic radiation and the global-spreading tsunamis. This highlights the importance of accurately mapping the slow components of megathrust earthquakes over a broad frequency band for reliable tsunami warning.

Acknowledgments
We thank the IRIS for providing public access (http://ds.iris.edu/wilber3/find_ event) to all the seismic data. We thank the IOC of UNESCO for providing public access (http://www.ioc-sealevelmonitoring.org/) to the tide gauge data. We thank Luis Rivera and Gregory Beroza for constructive discussions, and thank two anonymous reviewers for their comments. This work is supported by USGS grant G19AP00030.