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Observation of the long-period monotonic seismic waves of the November 11, 2018, Mayotte event by Iranian broadband seismic stations

On November 11, 2018, an event generating long-lasting, monotonic long-period surface waves was observed by seismographs around the world. This event occurred at around 09:28 UTC east of the Mayotte Island, in the Indian Ocean off the coast of East Africa. This event is unusual due to the absence of body waves in the seismograms and no feeling of earth shaking by people locally. The purpose of this study is to investigate this unusual event using the waveforms recorded by 26 stations of the Iranian National Broadband Seismic Network. The stations are located at epicentral distances ranging from 4542 to 5772 km north-northeast of the event’s epicenter. The arrival of monochromatic long-period signals is visible around 10 UTC in the recordings of all the stations and the signals lasted for more than 30 min. Frequency analysis of the seismograms shows a clear peak at 0.064 Hz (15.6 s/cycle). The maximum amplitude of the transverse components is less than a half of the radial components. This is in agreement with the theoretical radiation pattern of Rayleigh and Love waves at a frequency of 0.06 Hz for a vertical compensated linear vector dipole source mechanism. The average apparent phase velocities were calculated as 3.31 and 2.97 km/s, in the transverse and radial directions, corresponding, respectively, to Love and Rayleigh waves in the frequency range of 0.05–0.07 Hz. A surface wave magnitude of Ms 5.07 ± 0.22 was estimated. Just before the monochromatic signal arrives, there is some dispersion in the surface waves. This observation may suggest a regular earthquake of Ms 4.3 ± 0.11 that triggered the November 11, 2018, event. The difference between the arrival times of the recorded surface waves of the two events is estimated to be less than 31 s, and most likely of ~ 7 s only.


Introduction
The November 11, 2018, Mayotte event was first introduced in the media by Wei-Haas (2018) in National Geographic as a strange earthquake in which seismic waves were recorded by instruments around the world, but, unusually, nobody felt shaking. The event occurred offshore around 9:28 UTC near Mayotte Island in the Mozambique Channel between the northern tip of Madagascar and the eastern coast of Africa. Mayotte Island is one of the four main islands in the volcanic Comoros archipelago. The November 11 Mayotte event, in the absence of body waves, caused large, long-lasting, monotonic long-period surface waves that traveled around the globe. Before May 2018, the seismic activity in this archipelago was dispersed and moderate, with only a few earthquakes having a magnitude greater than 4. But in the year following the Mayotte volcanoseismic sequence on May 10, 2018, 32 earthquakes with a magnitude greater than 5 were recorded . The biggest earthquake ever recorded in the area was a Mw 5.9 event that happened on May 15, 2018 (USGS). Figure 1 shows the recorded waveforms for the May 15, 2018, earthquake, and the Mayotte event at a regional station, ABPO, Ambohimpanompo, Madagascar (part of the global IRIS/IDA seismic network), and at a teleseismically distant station, ASAO, Ashtian, Iran (part of the Iranian National Broadband Seismic Network). The epicenters of these two events were located very close to each other, and the epicentral distances were 713 and 5261 km from the ABPO and ASAO stations, respectively. The waveforms show clear differences in the nature of the propagated waves between the regular earthquake and the Mayotte event.
The most obvious feature of the Mayotte event is that while large long-period monotonic surface waves are visible, body waves are absent. The long-period waves appeared for more than 30 min at both the regional and teleseismic distances. Moreover, several smaller tremors with similar characteristics were recorded during the 2018-2019 Mayotte seismo-volcanic crisis . Thus, there is still much to learn about these very-long-period (VLP) signals occurring during the Mayotte event. We call the November 11 event the "monotonic very-long-period" signal and abbreviate it as MVLP. The event has been described in the framework of underwater volcanic activity, as the result of the resonance of a deep magma reservoir, in response to the sagging of the reservoir roof . In this study, we investigate this event using the waveforms recorded by the Iranian National Broadband Seismic Network. The objective of our study is to characterize the seismic signal and its source by analyzing seismic data recorded by the Iranian National Broadband Seismic Network: in particular, we aim at (1) evaluating its spectral properties, (2) estimating the magnitude, and (3) assessing the occurrence of an earthquake just before the event for possible interaction that may have triggered the event.
This work extends previous results Lemoine et al. 2020), which partially addressed these objectives, by investigating the largest VLP signal in the light of teleseismic recordings at a dense regional seismic network. The red triangles show the stations that were selected for array analysis. The inset enlarges the view of the locations of the biggest regular earthquake (black star behind red star), Mw 5.9 event of May 15, 2018 (USGS), and the MVLP (red star) . The blue lines indicate great circles connecting the epicenter and ABPO station, which is located SSE about 6.4° from the events, and ASAO station, which is located NNE about 47.5° from the events. (Right) Seismic waves for the two events recorded by ABPO (IRIS/IDA seismic network) on the left and by ASAO (Iranian National Broadband Seismic Network) on the right. The duration of the seismograms is 4000 s, and their start time, which is given at the lower left of each plot, corresponds to the origin time of the May 15 event at 15:48:09 UTC and for the MVLP at 09:28:00 UTC. The waveforms are vertical components and have been filtered in the range of 0.01 to 0.1 Hz

Observations
The broadband seismic network of the Iran International Institute of Earthquake Engineering and Seismology (IIEES) started operating with 4 stations in 1998 and currently has 31 stations (IIEES 2020). The stations are equipped with Güralp CMG-3 T sensors with a flat velocity response from 120 s (0.0083 Hz) to 50 Hz. Twenty-six of the stations (triangles in Fig. 1) were in operation on November 11, 2018, and recorded the MVLP. The stations are located from 4542 to 5772 km north-northeast of the MVLP's epicenter, which was assumed from the study of Lemoine et al. (2020). A 1.5-h trace view of the vertical component of the broadband records filtered between 0.01 and 0.1 Hz, and the frequency spectra of their unfiltered waveforms, are displayed in Fig. 2. All the stations show clear long-period seismic waves arriving around 10:00 UTC on November 11, 2018, and a frequency analysis of the seismograms shows a clear peak in the spectral amplitudes. The peak is in a narrow frequency band of 0.05-0.07 Hz. Among the stations, no significant changes are observed in the monochromatic wave trains and the narrow-band spectral peak.

Seismic waves and focal mechanisms
We compared the seismic waves for the MVLP and the largest regular earthquake (called "May 15" in Fig. 1 and hereafter). Figure 3 shows the seismic waves for the three components observed at the ASAO station. The ground noise level for the ASAO station is low. It is clear that the observed waveforms for the two earthquakes differ greatly even though the epicenters are close. The MVLP waveforms are dominated by long-lasting monochromatic surface waves, and body waves are lacking altogether. The maximum amplitude of the transverse component is less than a half of the radial component. Clear P-and S-phase arrivals are observed on the May 15 seismograms, and dispersion of the surface waves clearly appears in all three components on the seismograms. The maximum amplitude of the transverse component is 1.2 times that of the radial component. Figure 4a displays the focal mechanisms for the MVLP and May 15 events as beach-ball representations of their moment tensors (MTs). The MT components of the MVLP are proposed by averaging the MTs of 21 events with monochromatic long-duration and VLP signals that are provided in the seismic catalogs of the 2018-2019 crises that occurred east of Mayotte Island (Cesca et al. 2019). To eliminate the seismic moment (event size) effect, the components of each moment tensor were first normalized to 1 by dividing by the maximum absolute value of its elements, and then the normalized components were averaged (Eq. 1).
where M i is the MT of the ith event and |M i | max is the maximum absolute value of its elements, and n is the number of MTs. The focal mechanism for May 15, from the (GCMT) catalog, indicates a dominant strike-slip with NW-SE-directed compression.  suggested a vertical compensated linear vector dipole (CLVD) for the Mayotte VLP events, which are not always exactly vertical. In a vertically symmetric CLVD, no Love waves or azimuthal variations in Rayleigh waves are expected, but the proposed focal mechanism for the MVLP shows no vertical symmetry axes. Previous studies discussed the relation between active volcanism and the occurrence of rarely observed non-double-couple earthquakes (e.g., Shuler et al. 2013a, b). Their study used a standard source time function as in a GCMT solution, while  modeled the VLP events with a damped resonator source time function. Although the present study cannot draw definitive conclusions, to compare the MVLP with a regular earthquake, we have to make a model for the radiation pattern of surface waves considering the MTs. Figure 4b shows the theoretical seismic energy radiation patterns for Rayleigh and Love waves at a frequency of 0.06 Hz. The spectral amplitudes based on the considered source mechanism were calculated with an azimuthal spacing of 1° using the data product (Rösler and van der Lee 2020) of the IRIS DMC's Surface-Wave Radiation Pattern. Seismic radiation for the MVLP is dominated by Rayleigh waves displaying a nearly oval form with larger elongation in the northeastsouthwest direction. Love waves are clearly less energetic than Rayleigh waves and show more azimuthal variation in the maximum amplitude. Seismic radiation for May 15 shows larger spectral amplitudes for Love waves than for Rayleigh waves. The spatial variation of the maximum amplitude shows a clear four-lobe pattern for Love waves; while for Rayleigh waves, the radiation pattern has a twolobe shape. The broadband station in Iran is located in  Figure 5 presents spectrograms of the power spectral density (PSD) in (m/s) 2 /Hz, Fourier spectra, and dominant periods for the MVLP and May 15 vertical and transverse components at the ASAO station (the seismograms are shown in Fig. 3). As we expected from the model of the radiation pattern for the MVLP, the surface waves in the vertical components (dominated by Rayleigh waves) have larger amplitudes than the transverse components (Love waves). In addition, the MVLP shows four clear differences from regular earthquakes. The first obvious difference is the very long duration of its surface waves. The second difference can be seen through the spectrograms, where a dominant monochromatic surface wave (around 0.06 Hz) extends throughout the signal duration. The Fourier spectra show a clear large peak at 0.064 Hz. The third and fourth differences can be observed in the graph of the dominant period over time; the dominant period for the transverse component is lower than that for the vertical component, and the signals in both components propagate with nearly the same velocity. A convergence of surface wave velocities can also be seen in the graph of the dominant period for May 15 around a period of 16.5 s (0.06 Hz), which corresponds to the Airy phase with a The dominant periods are plotted by dots, and the lines are piecewise linear interpolations through the data points. Note that periods with a power less than the mean values for the spectrogram are removed from the graph. The gray circle on the Fourier spectra for May 15 indicates a peak of around 0.06 Hz related to the Airy phase of surface waves. This peak is also clearly displayed by the maximum values of PSD on the spectrograms of transverse components minimum in the group velocity dispersion curves (Bullen and Bolt 1985). The Airy phases in the transverse component can be observed by large amplitudes after an abrupt termination in the wave trains (see Fig. 3, bottom). The gap between the red lines around 1600 s in the dominant period graph (right-bottom in Fig. 5b) for the transverse component are due to this termination, and also our criterion to select power values greater than the mean value of the PSD.

Phase and group velocities of the surface waves
We used two analysis methods, frequency-wavenumber (f-k) analysis and regression analysis, to estimate the group velocity of the MVLP surface waves. We applied f-k analysis to a group of nine relatively closely spaced stations as an array using the python library Obspy (Beyreuther et al. 2010). The selected stations are marked by red triangles in the map in Fig. 1. The array response function for the directional sensitivity and its resolution power are shown in Fig. 6. This function was computed for a frequency band of 0.05-0.07 Hz. There are no distinct side lobes in the array response.
The semblance technique (Neidell and Taner 1971) was used to measure the slowness and back-azimuths of the coherent wave phases that crossed the array. The analysis was applied to 1-h sections from 2018-11-11, 09:45:00, to 2018-11-11, 10:45:00. After the waveform data were filtered using a bandpass filter with a bandwidth of 0.05-0.07 Hz, the semblance coefficient was calculated for a sliding window length of 20 s in steps of 1 s. The range of slowness was searched from 0.1 to 1.5 s/km in steps of 0.05 s/km. The quality of the stacked signal was measured by the semblance coefficient, which is a dimensionless quantity between 0 and 1, representing no coherency and perfect coherency, respectively. The semblance values show a coherency peak at about 75% for the radial (Rayleigh waves) components (Fig. 7a). According to Lemoine et al. (2020), the latitude and longitude of the MVLP were 12.777° S and 45.590° E, respectively, corresponding to a back-azimuth of ~ 185° from the center of the array. From Fig. 7a, the back-azimuth was determined to be ~ 200°, but its error was large. In contrast, for the transverse (Love waves) components, the semblance values did not show a unique peak and the coherency was higher than 55% (Fig. 7b). For the regression analysis, we manually picked the wave group arrivals for bandpass-filtered radial and transverse components for all 26 stations. One station was taken as a reference, and the relative delays, positive or negative, in arrival times for the other stations were calculated. Assuming a planar wavefront propagating horizontally with a constant apparent velocity across the array, the tau-p method (Havskov and Ottemöller 2010) was used. The apparent velocity and back-azimuth were estimated by fitting a plane wave, that is, a leastsquares regression line, to the time delays. The procedure was repeated using another station as a reference. The averages of the apparent velocities in the transverse and radial directions were calculated as 3.31 and 2.97 km/s, respectively. These correspond to the phase velocities of Love and Rayleigh waves, respectively, in the frequency band of 0.05-0.07 Hz. Figure 8 shows the average backazimuth (black arrows). They are generally in good agreement with the back-azimuth to the MVLP epicenter (red arrows) according to Lemoine et al. (2020). In this figure, a clear pattern of back-azimuth errors from positive to negative moving from west to east in Iran is found. Such systematic errors can be due to velocity variations in the crust and upper mantle, while we assumed a homogenous structure.

Estimation of magnitudes
Using seismic data from the 26 Iranian seismic stations, we estimated the surface wave magnitudes (Ms) of the MVLP and the regular earthquakes occurring around Mayotte Island. We used Eq. (2), named the Prague formula Vanek et al. 1962): where A is the peak amplitude of the surface waves in micrometers, T is the period in seconds, and Δ is the epicentral distance in degrees. First, the surface wave magnitude for the MVLP was calculated to be Ms = 5.07 ± 0.22.  estimated a similar value of Ms = 5.1. Second, we calculated the surface wave magnitudes for the 24 regular earthquakes with body wave magnitudes (2) Ms = log (A/T ) + 1.66 log� + 3.30, Fig. 6 Array response function at 0.05 to 0.07 Hz. The color scheme corresponds to the normalized amplitude of the relative power, as shown by color bar on the right (mb presented by USGS) > 4.5 occurring from May 13 to June 1, 2018. The surface wave magnitudes for the selected events were calculated using averages of at least 10 amplitude readings. These Ms values and body wave magnitudes (mb) are listed in the Table in the Appendix. It is important to note that the biggest earthquake is mb = 5.8 and a lower limit of mb = 4.5 was defined based on the signal strength and quality for reliable amplitude measurements. Then, we compared the relationship between Ms and mb, as shown in Fig. 9. Assuming that the best regression equation between Ms and mb has the form mb = a + bMs, we obtained Eq. (3): shows that the average Ms in the range of 4.5-5.8 is lower by 0.5-0 than mb on average. Scordilis (2006) studied empirical global relations for magnitude scale conversions and found nearly the same result for Ms < 6.2. We defined the converted body wave magnitude, mb(conv), using the following Eq. (4): The obtained mb(conv) values are listed in Table 1 for the three largest earthquakes and the MVLP. The (4) mb(conv) ≡ 2.54 + 0.56Ms. Fig. 7 Semblance values, back-azimuth in degrees, and apparent slowness in s/km for radial components (a) and transverse components (b) of MVLP. Data from nine array stations (red triangles in Fig. 1) were used. The pair of vertical gray lines in a indicates the solution with the maximum semblance value of 0.75% hypocenters of the three regular earthquakes were obtained from USGS, while the location of the MVLP was assumed from the source location that best fit the ground deformation after the early July 2018 event reviewed by Lemoine et al. (2020). Lemoine et al. (2020) stated that no strong earthquakes preceded the MVLP event, but some earthquakes are embedded in its seismic record, especially at the beginning of the monochromatic MVLP signal. Here, we want to take a closer look at the beginning of the signal to investigate the possibility of an earthquake occurring before and triggering the MVLP. Figure 10 shows the waveform and time variation of the dominant period at the ASAO station for the vertical component of the MVLP. It is clear from the figure that immediately before the arrival of the long-lasting monochromatic signal of the MVLP, the surface waves (Rayleigh waves) are dispersed. The period decreases from 17.5 to 16 s during the time period from 09:56:56 to 09:58:38 UTC, for about 100 s, as shown in Fig. 10b. This could be the result of the occurrence of a regular earthquake just before the MVLP event. We call this event the "just before the monochromatic event" (JBE) in this paper. Compared with the arrival time of the equivalent dominant periods of the regular earthquakes (listed in Table 1) that occurred in the vicinity of the MVLP, the origin time of the JBE was estimated to be 09:27:56 UTC ± 13 s. The surface wave magnitude of Ms = 4.3 ± 0.11 was calculated for JBE. Cesca et al. (2019) detected a volcano-tectonic earthquake at 09:27:59.575 on November 11, 2018, at a latitude of 12.8058° S and a longitude of 45.4736° E. They determined its magnitude based on a regional moment tensor inversion following the record of Mw 3.8 at a single strong-motion station on Mayotte Island. This earthquake must be the JBE. Now, the question is, how long before the MVLP did it occur? An answer can be obtained by comparing the frequency of these two events. Figure 10b shows that the dominant period curve for the JBE is bent at around the 16-s period at 09:58:38 UTC (red arrow). This may suggest that the surface wave of the JBE lasted until at least 09:58:38 UTC. For a more accurate determination, we applied a notch (a band-stop with narrow stopband) filter to separate the two merged events. In the spectrum of the MVLP, the largest peak is at 15.6 s. Therefore, we filtered out the 15.6-s signal from the waveform using the notch filter to remove the main component of the MVLP signal. The results are shown in Fig. 10c. This figure shows that the filter removed the main content of the waveform corresponding to the long-duration monochromatic signal of the MVLP after 09:59:09 UTC (black arrow). This suggests that the MVLP surface wave arrived at 09:59:09 UTC at the latest. When we assume that the difference in surface wave velocities between the periods of 15.6 and 16 s are nearly the same, the time difference between 09:58:38 UTC and 09:59:09 UTC may suggest that the JBE occurred less than 31 s before the start of the MVLP. Because the interpretation of the MVLP triggering mechanism may differ depending on the accuracy of the delay time between the JBE and MVLP, we examined the record of the ABPO broadband station in Madagascar (Fig. 1). Figure 11 shows the recorded waveforms filtered at different frequency bands. The presence of several volcano-tectonic earthquakes accompanying the MVLP is seen in Fig. 11a. The first is the JBE, which makes the arrival of the P and S waves more clearly visible when enlarged (Fig. 11b). The first arrival time for the JBE Rayleigh wave and the time interval for the MVLP arrival are marked in Fig. 11c. Regardless of the difference in group velocity due to the Rayleigh wave period, the MVLP surface wave appears to start ~ 7 s after the JBE arrival, as shown in Fig. 11c. However, it is difficult to mark the MVLP onset accurately.

Trigger earthquake just before MVLP
Globally observed long-lasting monochromatic surface waves with dominant periods of about 230 and 270 s, generated by the 1991 Mt. Pinatubo eruption (Philippines), were reported by Watada and Kanamori (2010). They demonstrated that the mechanism of these harmonic ground motions can be explained by the resonant oscillation between the atmosphere acoustic waves and the Rayleigh waves in the solid Earth. Both MVLP and Pinatubo Rayleigh waves are monochromatic but their