Norwegian seiches from the giant 2011 Tohoku earthquake



[1] Seismic waves of the giant 2011 Tohoku earthquake triggered seiches in western Norwegian fjords. The seiching began a half hour after the earthquake origin time. The oscillations were noted by eyewitnesses and recorded by surveillance and cell phone cameras. The observations show maximum trough-to-peak amplitudes of 1.0–1.5 m and periods of 67–100 s. The water waves were not triggered from the arrival of the surface waves, the timing inferred for other seiches. Instead, the seiching began during the passage of horizontal S waves. We reproduced the S wave trigger by means of a shallow-water wave model calibrated previously to Norwegian tides and storm surges. The simulations, which used the observed earthquake motion as forcing, show water waves with periods and amplitudes similar to those in the film clips. However, the strongest horizontal ground oscillations with shorter periods (20–30 s) did not contribute much to the formation of the seiches.

1 Introduction

[2] Seismic waves from large earthquakes can trigger water bodies to oscillate thousands of kilometers away from the fault-rupture area, and the Tohoku earthquake (Mw 9.0) on 11 March 2011 set Norwegian fjords into oscillations (Figure 1). Eyewitnesses were amazed, and some frightened, by the wave activity on the calm fjord surface that morning. Several of them contacted the local newspaper and the national radio station to tell their story. To explain the phenomenon, they used words as “It was like a maelstrom”; “the sea was boiling”; “the fjord changed between high and low tide continuously.” Such oscillations, called seismic seiches, are standing waves that occur in closed or semiclosed basins, initiated from the movements of the ground during the earthquake [e.g., Kvale, 1955; Rabinovich, 2009]

[3] Seiches occur when the eigen-period of the basin coincides closely with the periods of the earthquake [Kvale, 1955; McGarr, 1965]. But exactly what part of the earthquake motion and what kind of earthquakes can trigger far-field seiching are not clear for two reasons: (1) The largest movements of the ground due to earthquakes usually fluctuate with much shorter periods than the resulting oscillations of water in the natural basins [Rabinovich, 2009]. Predicted fundamental periods of seiches in basins like rivers, lakes, and fjords—where the oscillations have a node at the center of the basin and highest displacement occurs along the sides of the basin—are normally much longer than the periods of the seismic waves. Barberopoulou et al. [2004] and McGarr and Vorhis [1968] suggested that seiches oscillate with higher modes, although higher modes with their shorter wavelengths are less likely to occur because they are damped out much faster [McGarr, 1965]. The oscillations in Norway lasted more than 2.5 h. (2) Some of the largest earthquakes failed to generate seiches in Norway. Norwegian fjords are sensitive to seiching because of their great depths [McGarr, 1965] and oscillated from distant earthquakes in 1755, 1920, and 1950—but to our knowledge, seiches have not been reported here between 1950 and 2011. The Assam earthquake in 1950 (Mw 8.6) triggered waves in 29 fjords in Norway and in English reservoirs [Kvale, 1955].

[4] To explore the causes of far-field seiching, we analyzed film clips from cell phone- and surveillance cameras that show the movement of the fjord surface in the morning of 11 March 2011 and compared them with numerical simulations. From these images we determined when the oscillations in the fjords started relative to the arrival of the earthquake, the periods, and amplitudes of the waves. We use the observed seismic ground motion from the nearest broadband seismic station (Figure 1b) as input to numerical simulations of the seiches and compare the simulations with the observations from film clips (stars in Figure 1b) and eyewitness reports (see supporting information).

Figure 1.

(a) Epicenter of the Tohoku Earthquake (Mw 9.0) in Japan and the oscillating fjords in western Norway. The distance along a great circle between these locations is about 8300 km. (b) Locations of reported seiches on 11 March 2011 in fjords in western Norway. Red stars indicate film clip recordings of the waves, red circles eyewitness accounts. The nearest seismic broadband station is SUE at the mouth of Sognefjorden.

2 Seismic Waves

[5] The Tohoku earthquake was well recorded by the Norwegian National Seismic Network. The nearest broadband station (120 s sensor) to the observation points is SUE located at the island Sula near the mouth of Sognefjorden, 80–130 km west of the fjords that oscillated (Figure 1b). All times quoted in this paper are in universal time (UTC), 1 h later than Norwegian standard time.

[6] The first P phase arrived at SUE at 05:58 (Figure 2a), and the ground was moving for more than 1.5 h after that. The S phase arrived at 06:08 with duration of approximately 4.5 min (Figure 2a). Most energy arrived with the surface waves that began about 12 min after the S waves (Figure 2a). The largest horizontal displacement at SUE exceeded 1.1 cm in the E-W direction.

Figure 2.

Seiche movement deduced from film clip analysis of a boat that oscillated due to the waves in Flåm, compared to ground movements and numerical simulation of the seiches. (a) Input to the numerical simulations is ground acceleration filtered between 0.01 and 0.05 Hz (20–100 s). Here the E-W component is shown. (b) Movement of the masthead of the boat Lady Elisabeth; maximum horizontal movement is about 120 cm, vertical is about 25 cm. (c) Output from the numerical simulation, current velocity, and wave height, close to the location where the boat was anchored.

[7] The frequency content of the seismic waves changes with time. The S waves are dominated by rather long-period shaking with an average period of about 60 s. The surface waves are clearly dispersed, starting with dominating periods of 50–60 s in the first part of the surface wave train, which reduce to approximately 20–30 s or even less later in the surface wave train (Figures 2a and S1 in the supporting information).

3 Seiche Observations and Film Clip Analysis

[8] That morning of 11 March 2011, the fjord surface was completely calm before the seiches started, a fact stressed by many of the observers and also evident from the film clips. Luckily, the tide was close to low when the seiches started, and that probably saved boat houses and docks from damage. No damage to infrastructure was reported. For eyewitness accounts, film clip analysis, and weather conditions, see supporting information. The film clips are also available as video files in the supporting information.

[9] Maximum observed trough-to-peak amplitude is 1.0–1.5 m (Table 1). Best documented is this in the film clip from Leikanger (Figure 1b) where we measured the rise and fall of the water surface along a ladder that goes into the water from a pier (Figure S15). From this, trough-to-peak amplitude is more than 1.2 m, probably as much as 1.5 m. Many of the eyewitnesses reported a range equivalent to that of spring tides or about 1 m.

Table 1. Amplitude (Peak to Trough) and Period Deduced From Film Clipsa
LocationLatitude (N)Longitude (E)Time (UTC)Duration of Film ClipAmplitude (Peak to Trough)PeriodComment
  1. a

    See supporting information for film clips, more details about the film clip analysis, and eyewitness accounts.

  2. b

    See supporting information.

Framfjordenb61° 0′ 25″6° 24′ 50″ca 08:15–08:302 min 30 sAbout 1 m100–105 sWe observe the water level rising to the high tide level and then falling, exposing the delta surface, rising again, and returning. In total, a little more than one period is recorded (Figure S17). Flow resembles a river. Low resolution (320 × 240 pixels)
Leikangerb61° 11′ 01″6° 47′ 57″06:27–06:292 min 28 s1.2–1.5 m64–66 sSurges of water run up against a pier. We estimate amplitude and period from the elevation of the water surface relative to ladder steps that go from pier to sea floor (Figure S15). Waves arrive perpendicular to beach. High resolution (1280 × 760 pixels)
Flåm harborb60° 51′ 44″7° 07′ 03″05:57–08:432 h 39 min0.2–0.3 m79–82 sSurveillance camera shows two anchored boats that oscillate in the waves. We traced the masthead of Lady Elisabeth—a 200-passenger sightseeing boat—in horizontal and vertical direction from 05:57–06:57—in all through 30 cycles (Figure 2a). Resolution is 640 × 480 pixels, but only one image every 3–9 s.

[10] The seiching started about 30 min after the origin time of the earthquake offshore Japan (05:46 UTC). The earliest observation of distinct and regular wave motion is at 06:16 from a surveillance camera at the Flåm harbor (Figure 1b). However, the camera reveals a few earlier cycles with smaller amplitudes beginning at 06:11 that probably mark initial seiching (see below and Figure 2b). The film clip from Leikanger (supporting information; Figure 1b) was recorded at 06:27, and according to the person recording the film, they became aware of the waves about 5–10 min before that. Another eyewitness (Framfjorden; Figure 1b and supporting information) noticed the waves shortly before 06:30. Thus, the waves probably began more or less at the same time in the different fjords, with initial movements at about 06:11 (Figure 2b) and regular oscillations at 06:16.

[11] The strongest wave activity was observed between 06:25 and 06:40. At Flåm harbor, the most distinct and pronounced movements were recorded between 06:27 and 06:41 (Figure 2b). The person recording the film in Leikanger (Figure 1b) reported that the waves were the strongest around 06:25–06:30. Most of the eyewitnesses reported the wave activity to between 06:30 and 07:30 (supporting information).

[12] The periods of the waves vary among the different fjords (Table 1). The longest record is from the Flåm harbor where we measured 30 cycles over 41 min (Figure 2b); that corresponds to an average period of 82 s. However, the periods through the Flåm sequence vary between 79 and 94 s (Figure 2b). The two short film clips (<3 min) show the period in Leikanger to be about 67 s (Figure S15) and in Framfjorden to be around 100 s (Figure S17). One eyewitness (Finden) counted 10–12 s from when his boat would start to be lifted until it reached the top. That would indicate a shorter period of 25–30 s (supporting information).

[13] The fjords oscillated for almost 3 h. The latest film clip that shows wave motion was recorded sometime between 08:15 and 08:30 (Framfjorden). Eyewitnesses mention that the waves faded very gradually but were still noticeable at 08:30. One eyewitness claims they lasted until 09:00. The fjord is still moving at Flåm harbor at the end of the film clip at 08:43, though with much smaller amplitude than earlier.

4 Numerical Simulations

[14] We simulated the seiches in a 16 km long section of the fjord Aurland-Flåm (Figure 1b) that includes the harbor where the longest film clip was recorded and a shallow area north of Aurland (Figures 3 and S9), where an eyewitness observed oscillations. As input to the model, we used the observed time series of the ground acceleration at the station SUE (Figure 1b)—both the E-W (Figure 2a) and N-S components filtered at 20–100 s were implemented in the model. The depth matrix has a horizontal resolution of 25 m.

Figure 3.

Simulated water surface displacement of the fjord Aurland-Flåm (Figure 1b) at 06:35. Location of boat in Figure 2b and eyewitness (supporting information) is indicated. The depth matrix has a horizontal grid resolution of ∆x = ∆y = 25 m and was constructed in ArcGis from depths soundings.

[15] The numerical model is a shallow-water model previously used for high-resolution modeling of tides and storm surges along the Norwegian coast. This model is well documented, tested, and validated by comparison with observational data both for sea level and currents [Hjelmervik et al., 2005; Lynge, 2011]. We used a linearized version of the shallow-water equations since amplitudes of the waves are relatively small compared to the water depth (except near shore), and the wave length is large compared to water depth. More details about the numerical model are presented in the supporting information.

[16] The numerical simulation at the site of the swaying boat is in good agreement with the film clip observations. The simulated period is 84–86 s, close to the period from the film clip images (Figure 2). Maximum vertical movement of the boat is estimated from the film clip to be about 25 cm—peak to trough in the simulated waves is about 15–20 cm (Figure 2c). A simulated current speed of approximately 10 cm/s and period of approximately 80 s corresponds to a horizontal excursion of approximately 250 cm. The observed excursion of the boat is about half of that. The reduction is most likely due to the response characteristics of the anchoring system, which is not known.

[17] Only the first two wave groups of the horizontal earthquake motion generated most of the observed seiching. We ran the simulations and cut the earthquake forcing off after 06:27—the forcing thus contains the S wave group and the first wave group of the surface waves (Love waves)—excluding the rest of the earthquake motion (Figure 2a). Results were nearly identical to those of the simulations with a full earthquake forcing from 06:05 to 07:05. This means that the strongest ground oscillations, which occur after 06:27 and with shorter periods (20–30 s) (Figure 2a), did not contribute much to the formation of the seiches. Film clip of the boat supports this: The initial movement of the boat is 2.5 min after the arrival of the S waves, and the boat begins with strong and distinct oscillations 4 min before the arrival of the surface waves.

[18] The numerical simulations show a tendency to group formation of the waves, which, somewhat surprisingly, corresponds to the movements of the boat (Figure 2). Wave group period of the simulated waves is about 10 min and consists of five to eight oscillations in one group. This pattern of regular waves that come in packages is also present in the film clip images of the boat (Figure 2b). Such grouping of waves of similar periods is caused by interference of waves with slightly different periods.

[19] Along the sides of the Aurland-Flåm fjord, the numerical model reveals a complex interference pattern with large variation in amplitudes (Figure 3). Localized areas along the shore show oscillations up to 25 cm, whereas at other places, the simulations show minor oscillations, less than a few centimeters. This is in agreement with eyewitnesses; some did not observe anything being near the fjord while others at a different location witnessed large oscillations. The model predicts 40 cm waves at Grønnene near Aurland (Figure 3)—a shallow sandy beach area—where an eyewitness observed waves (supporting information). This complex pattern along the fjord is partly related to interference of different waves, but most important is bathymetry: shallow water amplified the waves and produced edge waves that ran along the shores of the fjord's upper reaches (Figure S5).

5 Discussion

[20] People noticed the fjord oscillations only at places where the shores slope very gradually. Fjords usually have steep slopes, but the waves were observed in shallow areas with accumulations of sand and gravel at delta and beach deposits. At these sites, the sea floor is shallow and has a convex bottom topography that favored amplification of the long water waves [Didenkulova et al., 2009; Sælevik et al., 2013].

[21] Seismic seiches are believed to be triggered from the arrival of the larger amplitudes of the seismic surface waves [Barberopoulou et al., 2004; McGarr and Vorhis, 1968], but the surveillance camera data from Flåm and the numerical simulation show that the seiches were actually triggered from the arrival of the earlier S waves. Images from Flåm show regular and strong oscillations of the boat about 5 min before the arrival of the seismic surface waves (Figure 2). The filtered seismic signal shows five cycles of maximum ground acceleration of about 8∙10−3 cm/s2 for the S waves. This ground motion was enough to start the oscillation of the fjord water, but the numerical simulations show a somewhat later start for oscillations than the video images. A test simulation, where the first S wave group were given an idealized form as in Figure S4, shows wave motion that fits better to the observed initial movement of the boat.

[22] The oscillations are further enhanced when the seismic surface waves arrive. The largest arrival of seismic energy occurs between 06:20 and 06:35 (Figure 2a), but according to the simulations, it is mainly the first wave group of the seismic surface waves, between 06:20 and 06:27, that contributes to the seiche formation because of the longer periods. Strongest and steadiest seiches occur in the 15 min time interval between 06:27 and 06:42 (Figure 2b). Only earthquakes that contain sufficient energy in the horizontal direction at long periods around 60–120 s, which is near the fundamental mode of the transverse eigen-oscillation of the fjords, would generate seiches.

[23] We tested whether other big earthquakes also would generate seiches by simulating the Chile (Maule) earthquake (27 February 2010, Mw = 8.8) as it was recorded at SUE (Figure 1b), but the model returned insignificant water oscillations in the Aurland-Flåm fjord. That earthquake also happened in the morning (06:34 UTC) of a cold winter day in western Norway (below freezing, without precipitation) so most likely it would have been noticed had it been triggered. The main difference between the Maule and Tohoku seismograms at SUE is that Maule has less energy distributed in the horizontal directions and in the longer period band (50–60 s period). The propagation path (a great circle) from Chile to this part of Norway trends almost W-E; thus, most of the horizontal ground motion would be parallel to the long axis of the Aurland-Flåm fjord (Figure 1b) and not across the fjord as is the case with the Tohoku earthquake.

[24] Earthquake oscillations responsible for the seiches were probably not amplified due to soft sediments in the fjord basins. Seiches triggered from Alaska 1964 and Denali 2002 earthquakes [Cassidy and Rogers, 2004] were partly explained by soil amplification of the earthquake [Barberopoulou et al., 2004; McGarr and Vorhis, 1968; Rabinovich, 2009]. Fjords in Western Norway contain up to 150–200 m of unconsolidated deposits [Aarseth, 1997], but the good fit between observations and simulations without soil amplification indicates that the earthquake shaking at periods >50 s was not amplified much by the sediments in the fjords.

[25] The oscillating fjords (all but one) are oriented NE-SW (Figure 1b), in the same direction that the seismic waves traveled from Japan (Figure 1). According to numerical simulations (supporting information; [Barberopoulou, 2008]), the seiches are generated only if the ground movement is across the fjord. Forcing directed along the fjord gave only a very weak response in the model. Orientation of the oscillating fjords and simulations shows that it is the transverse horizontal components of the ground motion that are the main contributors to the generation of seiches. The largest horizontal amplitudes from the earthquake shaking would thus come at 90° to this direction, at right angles to the sides of the fjords that oscillated.

6 Conclusions

  1. [26] Seiches were triggered from horizontal S waves. This was confirmed from video evidence and numerical simulations.

  2. [27] In addition to the S waves, the first wave group of the surface waves (Love waves), which preceded larger surface waves, was responsible for generating the seiches.

  3. [28] Earthquakes usually have their largest amplitudes at much shorter periods than the fundamental mode of natural basins. However, it is the seismic waves with the longer periods but usually smaller amplitudes that excite natural basins like fjords.

  4. [29] Earthquakes that contain sufficient energy in the long-period band (60–120 s) in the horizontal direction would generate seiches if the large-amplitude earthquake shaking includes horizontal components that are near perpendicular to the long axis of the fjords.


[30] We thank John Erik Johnsen, Leif Hus, and Endre Nese for providing their film clips to us; journalist Terje Eggum who wrote about the observations in the local newspaper SognAvis and connecting us with eyewitnesses; eyewitnesses for sharing their observations; Morten Slinde for helping to make the depth matrix from Flåm-Aurland; and Brian Atwater, Aggeliki Barberopoulou, and Art McGarr for reviews and helpful comments.