The

The western segment of the Eurasia–Nubia plate boundary extends from the
Mid-Atlantic Ridge in the Azores towards the Strait of Gibraltar. Between

General overview of the Northeast Atlantic at the latitude of Iberia and focal mechanism of the earthquake. The yellow star represents the epicentre of the earthquake. Black dots show the location of the tide stations.

In this study, we present a reanalysis of the seismic data of the 25 November 1941 event and the first comprehensive analysis of the associated tsunami. We use a newly acquired set of historic seismograms to re-evaluate the position of the epicentre and the computation of the seismic moment. We digitized, de-tided and filtered all tide records available in the Northeast Atlantic basin. The use of seismic and tsunami data provides a better understanding of this earthquake and tsunami.

The 25 November 1941 earthquake occurred at 18:03:54 UTC. Madeira, Azores and western Portugal recorded the strongest shaking – VI (MSK). The earthquake impacted the neighbouring countries, Spain and Morocco. The studies by Debrach (1946), Di Filippo (1949) and Moreira (1968) present macroseismic data analyses.

Antunes (1944) presented the first epicentre location, using only data from
the Portuguese seismic network, at

In this study, we present a relocation of the earthquake source using the
phases published by the ISC bulletin complemented with readings from nearby
stations AVE in Morocco (

Additionally, we tested two velocity models to compute the epicentre. The
IASPEI91 velocity model (Kennett and Engdahl, 1991) locates the epicentre at

Top panel: digitized seismograms corresponding to the N–S and E–W components of the 1941 Atlantic earthquake as recorded by the Wiechert seismograph at Uppsala (UPP). Bottom left panel: ground motion spectra of the P waves, as marked at the top figure (blue and red, respectively), recorded at UPP, and the corresponding fit to the Brune model. Bottom right panel: ground motion spectra of the S waves, as marked at the top figure (blue and red, respectively), recorded at UPP, and the corresponding fit to the Brune model.

We computed the scalar seismic moment using the Dineva et al. (2002)
approach. Original analogue seismograms were digitized, and the seismic
moment is computed independently from the spectra of body waves' ground motion for each component. Twenty-six seismograms from
14 seismic stations were digitized. Using P waves from 13 stations, we
obtain a seismic moment of 3.96 1021 Nm, while using S waves from seven
stations, the seismic moment gives 2.96

After the earthquake, the tide stations in Portugal mainland, Morocco,
Madeira and Azores islands (see Fig. 1 for locations) recorded a small
tsunami. In the United Kingdom, Newlyn (

POIs (points of interest) of the 1941 tsunami used in this study. Longitude, latitude and depth refer to the POI. POIs are named after the closest tide station.

In this study, we selected the records of seven tide stations presented in Table 1. We digitized the original paper records except those of Casablanca and Essaouira (Morocco). Debrach (1946) presents drawings of these tide records: Casablanca-Petite Darse, Casablanca-Jetee Transversale and Essaouira. We could not find the original records of these stations. Instead, we had to rely on the drawings reproduced in Debrach (1946). We discarded the station Casablanca-Petite-Darse because the position of the tide gauge is uncertain. In this study, we use Casablanca-Jetee Transversale, here named Casablanca. We did not use the record of Newlyn because of the quality of the record.

All digitized records were linearly interpolated into a 1 min time
step. For de-tiding, we used a least squares algorithm to fit the
interpolated data into polynomials whose degrees guaranteed an adjusted

For each station: tsunami signals (de-tided and filtered record) (left panels), wavelet amplitude spectrum (middle panels) and global wavelet spectrum (GWS) (right panels). The initial time, 18:04 UTC, is the time of the earthquake.

Tsunami source location given by BRT. The red star represents the
minimum of the backward ray tracing misfit (

Figure 3 depicts the tsunami signals and the results of wavelet analysis. Madeira station presents the smallest dominant period close to 6 min. Ponta Delgada, Cascais and Lagos present a dominant period close to 12 min. Leixões presents a dominant period close to 20 min but this period is present in the spectrum well before the arrival of the tsunami – in this station the signal-to-noise ratio is low, when compared with the other records. Casablanca presents a 22.5 min dominant period. In the case of Essaouira, the dominant period is 45 min.

We used the travel time of the first wave arrival at each station to compute
a preliminary location of the tsunami source. To do this, we used the
backward ray tracing (BRT) technique (Gjevik et al., 1997). We defined a set
of points of interest (POIs), one per tide station. The position of each POI
is the grid node closest to the actual location of the tide station, at a
depth not less than 10 m to avoid strong non-linear effects. Table 1
shows the location and depth of POIs used in this study. We back-propagated
the wave fronts from each POI using the algorithm implemented in the Mirone
suite (Luis, 2007). The location of the tsunami source is the minimum of the
averaged travel time square errors (in the least squares sense). The spatial
distribution of the misfit is given by

To compute the BRT solution, we used the tsunami travel times shown in Table 1
and a bathymetric grid with a horizontal resolution of
0.1

The BRT method has limitations inherent to the linear shallow water approximation, implying an overestimation of the speed in shallow waters. Nevertheless, in the case of the 1941 tsunami, the good azimuthal coverage ensures that these limitations are partially averaged out.

To estimate the initial sea surface displacement (tsunami source) we need to invert the tsunami waveforms. Moreover, for tsunamis generated by earthquakes, we assume that the initial sea surface displacement mimics the elastic deformation of the seafloor, thus providing information on the earthquake focal mechanism.

The problem of tsunami waveform inversion without assuming a fault model was firstly addressed by Aida (1972 in Satake, 1987). Since then, many studies have focused on the use of waveform inversion methods to estimate the tsunami source. These studies can be broadly divided into two categories: with a priori assumptions on the fault model (e.g. Satake, 1987, 1993; Hirata et al., 2003; Titov et al., 2005), and without a priori assumptions on the source, namely Baba et al. (2005), Satake et al. (2005), Tsushima et al. (2009), Wu and Ho (2011) and Yasuda and Mase (2012).

Here, we use the method proposed by Tsushima et al. (2009), Koike (2011)
and Miranda et al. (2014) based on the use of empirical Green's
functions to efficiently perform the linear shallow water forward problem,
where the synthesis of the tsunami waveform

Chessboard test of the inversion approach. The source has
alternating

Comparison between observed and synthetic waveforms. The solution
shown corresponds to

In this work, the study area is shown in Figs. 1 and 3, of which the limits are

Experience shows that giving the same weight to all data points is misleading as waves that arrive later carry information resulting from reflections and interference, which are very hard to simulate with the inversion procedure. Here, we used a simple strategy of attributing a larger weight to the first incoming wave. We used only two different weights (Eq. 8) for the data set. Data between the origin time of the earthquake and the first tsunami wave weighted 100 times more than the remaining data values, except for the Essaouira data.

Using the results of the BRT, we selected the area within the 10 min
contour (corresponding to an average travel time error of less than 10 min)
as the influence area (see Fig. 4). We performed several tests to
assess the best choice of the parameters (

In Fig. 5, we show a “chessboard” synthetic source, with alternating

Figure 6 shows the solutions for the same set of parameters used in the chessboard test. In all cases the maxima of the initial displacement field correspond to segment BC (see Fig. 4), matching the 10 min error contour of the BRT and the earthquake epicentre. The lateral extent of the source is roughly 160 km. If we look at the solutions presented in Fig. 5 more closely, there is an apparent rotation when compared with the strike of segment BC. This is not a result of the azimuthal distribution of the tide gauge stations as the chessboard test shows (Fig. 4). It can be the result of the apparent contradiction between the records from Cascais (see lines 230–231) and Lagos tide stations, but we have no independent assessment of this problem to weight the station data differently.

Figure 7 depicts the comparison between the forward computation using the
initial displacement field depicted in Fig. 6 for the preferred solution
(

The seismological data of the 25 November 1941 earthquake lead to an
epicentre location at

The analysis of the tsunami data shows a clear signal of small amplitude in most of the stations, with an apparent change in the frequency content except for Leixões. The spectral analysis of the tsunami records shows different frequency contents. These differences are mainly caused by differences in local morphological conditions and to the relative position of the station and the seismic source. Madeira station located approximately across-strike shows the smallest dominant period of 6 min. Leixões, located along-strike, shows the largest dominant period of 20 min. Ponta Delgada, Cascais and Lagos show dominant periods close to 11 min (see Figs. 1 and 3). These results are consistent with a tsunami source located along the Nubia–Eurasia plate boundary.

The BRT simulation locates the minimum of the averaged travel time (7.2 min),
at

Because of the limitations inherent to the use of the linear shallow water
approximation and the location of the tide gauges inside the harbours, we
opted to give different weight to the data points corresponding to up the
first incoming wave. The set of solutions shown in Fig. 6, corresponding
to different values of

The results presented in Fig. 7 show that the inversion technique used here can fairly reproduce the first incoming wave for most of the observations presented in Table 1. In Cascais, the synthetic wave arrives 8 min earlier than the observed wave. The location of the tide station inside the old harbour in a very shallow area (less than 4 m) might be responsible for this discrepancy. In addition, the smoothness coefficient used to compute the inverse solution may contribute to a “spreading” of the lateral extent of the source, thus producing earlier arrivals at some points on the coast. The observation in Essaouira is incompatible with all solutions presented in Fig. 6. The lack of the original tide records of Morocco and the poor quality of their reproduction in Debrach (1946) does not allow for further investigation. However, we cannot exclude the hypothesis of a local second tsunami source close to the coast of Morocco. Debrach (1946) and Rothé (1951) report damage to the submarine cables Brest–Casablanca and Brest–Dakar after the earthquake. This fact may suggest the occurrence of a submarine landslide close to the coast of Morocco.

In spite of the limitations inherent to the use of old instrumental records, some of them with a low-amplitude signal-to-noise ratio, the inversion of the tsunami waveforms provides an independent estimate of the extension of the tsunami source and indirectly, the extent of the seismic source.

The seismic source solution (strike 76

We cannot discard the fact that a local landslide occurred because the break of the submarine cables is documented. We do not have information either on the location of the submarine cable nor where it broke. This lack of information makes the modelling of the landslide very difficult. We think that the occurrence of a landslide close to the coast of Africa (Morocco and Senegal) might influence the signal of the Morocco tide records. However, our strongest tsunami observation is in the Azores (Ponta Delgada); this station is too far away from the submarine cable (and to the possible landslide location), therefore we conclude that the tsunami observed there is mostly due to the earthquake's co-seismic deformation.

Due to the small Eurasia–Nubia relative motion in this segment of the plate
boundary (5 mm yr

Copies of the paper tide records can be obtained from the authors.

This work received funding from ASTARTE project Assessment Strategy and Risk Reduction for Tsunamis in Europe – grant 603839 FP7. The authors wish to thank the fruitful discussions with Nuno Lourenço about the geology of the Gloria Fault and the reviewers for their suggestions to improve this paper. The authors also thank Direção Geral do Território for making data of Cascais and Lagos, Portugal, available. Edited by: I. Didenkulova Reviewed by: two anonymous referees