Deformations of Land, Sea and Gravity Levels by the 2009 Samoa Earthquake

The Samoa Islands were struck by the September 2009 earthquake of M w 8.1. We study the effect on the land level by means of GPS monitoring and on ocean level by tide-gauge records. This allows us to present a new picture of the interaction of crustal movements, gravitational adjustment and sea level changes. The land level exhibits a co-seismic uplift followed by a post-seismic crustal subsidence. The ocean level records a fall, significantly larger than the uplift and delayed by several months, followed by a significant rise, by far ex-ceeding the crustal subsidence and delayed by several months. This indicates a significant contribution from changes in gravity (geoidal eustasy), besides relative sea level changes due to crustal movements. High amplitude, and high frequency changes in tidal range provide evidence of changes in gravity and geoidal eustasy.


Introduction
The Samoa Islands are located in the Southwest Pacific just to the NE of the active plate boundary marked by the Kermadec-Tonga subduction zone ( Figure   1). The area has been struck by a number of high-magnitude earthquakes. We

Geological Setting
The Kermadec-Tonga subduction zone ( Figure 1) is a part of the notorious "Pacific Ring of Fire" named for its high seismic and volcanic activity in association with plate collision and subduction at a rate of about 24 cm/yr [1] [2] [3] [4].
Therefore, it is no surprise that the Tonga-Samoa region has experienced numerous high magnitude earthquakes in recent times [5] [6]. The Samoa and American Samoa Islands constitute a chain of islands continuing to the west in a number of submerged seamounts [3] [7]. The age of the islands grows younger to the east with an active submarine volcano located 30 km the east of Ta'u Island ( Figure 3). This is consistent with a plate moving westwards over a fixed hot spot. The Samoan hot spot seems to have existed for at least 23 million years [3]. Volcanic rocks of the Savai'i Island, the Upolu Isl-    ison with our studies in Fiji [11], this would, in the first case, imply stability and, in the second case, a subsidence of about 0.6 mm/yr.
They record a habitation layer at a level between present mean and low tide level

The Mw 8.1 Earthquake and Tsunami in 2009
On September 29, 2009, the Samoa region was struck by a magnitude M w 8.  International Journal of Geosciences was 11.9 m, which implies that it reached a maximum level in the relation between earthquake magnitude and tsunami wave height [16].

The tsunami had disastrous effects along the coasts of the Samoa and Tonga
Islands [5]. In total, 183 people were killed in the Samoa Islands.
Because it was a normal fault seismic event, we can a priori assume that the seafloor was affected by vertical crustal movements. The a posteriori proof of subsidence comes both from GPS records and from tide-gauge records to be explored below.

The GPS Records at Samoa and American Samoa
Continual measurements of changes in the land level by means of GPS are available from Upolu Island in Samoa and from Tutuila Island in American Samoa ( Figure 3). The records are accessible from the SONEL [17] and JPL [18] databases. The SONEL records are more detailed but end in 2014. The JPL records end in 2018, and hence provide a longer record.

Tutuila Island in American Samoa
The  September 29, 2009, deformation at the ASPA station on Tutuila Island; a co-seismic jump of +3.58 cm followed by a post-earthquake subsidence [19]. International Journal of Geosciences to 2008 [19] gives a continual mean subsidence of −0.60 ± 0.20 mm/yr. This is important, because it suggests that Tutuila Island may be experiencing a weak long-term subsidence.
The JPL record [20] covers the period 2002-2018 ( Figure 6). It shows a pre-seismic period of weak subsidence (0.07 mm/yr). There is no record of the co-seismic vertical uplift so well documented in Figure 5. There is a clear post-seismic subsidence; a rapid fall of −3.87 cm followed by a subsidence, which for the last 6 years had a mean rate of 10.0 mm/yr. Consequently, the subsidence has continued for more than 8 years.
The horizontal components (latitude and longitude) record a co-seismic slip of 11.1 mm to the SW in 134˚ (Figure 2; [20]).

Upolu Island in Samoa
The GPS station (at Fagali'i airport) is     earthquake, indicating that this earthquake followed other mechanisms and spatial distributions.

Tide Gauge Records at Apia and Pago Pago
There are two tide gauges; one at Pago Pago on Tutuila Island in American Samoa (station 539; [23]) and one at Apia on Upolu Island in Samoa (station 1840; [24]) and. The location of the stations is marked in Figure 3.

The Tide-Gauge at Pago Pago
The tide-gauge of Pago Pago, American Samoa, is managed by NOAA/NOS [25]. The source of data is PSMSL [23], station 539. It covers the period 1948-2016 with a completeness of 93% (Figure 9). Spanning 68 years, this record qualifies for analysis of sea level changes. At a superficial view, Figure 9 may look like recording a sea level acceleration (of +0.152 mm/yr 2 ). A more correct analysis reveals that it records a pre-seismic relative sea level rise (partly due to subsidence) of −2.21 ± 0.81 mm/y [25], a somewhat unclear co-seismic sea level fall (due to uplift) of 5 -8 cm, and post-seismic sea level rise of 19 -22 cm within a year (due to subsidence and gravitational effects) followed by variations around a seemingly stable level during the last 6 years.

Tide-Gauge at Apia
The

Discussion
The earthquake magnitude (M w 8.1) and geographical extension reaching far beyond the Samoa Islands (Figure 3) imply that direct effects are likely to have affected both land and sea levels in the Samoan Islands.
The GPS stations on Upolu and Tutuila Islands (Figure 3) both record an instantaneous co-seismic uplift followed by an exponentially decaying subsidence ( Figures 5-8).
The tide-gauge station close-by on the same islands both record a sea level fall followed by a sea level rise (Figure 9 and Figure   In Figure 13, we plot the changes in land level (red) and ocean level (blue recorded at the stations on Tutuila (a) and Upolu (b) Islands.
Right at the earthquake, the land levels jumps up by a few cm. This uplift is followed by a subsidence from a slowly relaxing crust, recorded by an exponentially decaying subsidence (continuing for, at least, a decade). This post-seismic subsidence is interpreted in terms of a viscoelastic response of the upper mantle [28] [29].
The ocean level shows a fall taking a few months to culminate. The falls in sea level by far exceed the amount of uplift. Together with the delay in culmination, this enhanced fall in sea level (with respect to amount of uplift) is indicative of simultaneous gravitational changes deforming the gravitational potential surface (or geoid). The same applies for the subsequent rise in sea level, which, by far, exceeds the post-seismic crustal subsidence. Besides, it is significantly delayed with respect to the crustal subsidence phase.
In conclusion, Figure 13 records a combination of crustal movements, gravitational change due to tectonics and geoidal eustatic changes in sea level [30].
The apparent sea level acceleration at Pago Pago ( Figure 9) is revealed as illusive due to the co-and post-seismic changes in land and sea levels. The real mean rate of sea level changes seems to be in the order of 0.88 mm/yr with an acceleration of only +0.0252 mm/yr 2 [31].
Besides the co-seismic vertical changes in crustal level, there was also a co-seismic slip in horizontal direction [20] [22] of about 11 mm (as shown by  Figure 2). This is indicative of sudden horizontal slip in the under-thrusting of the Pacific Plate of the Australia Plate.

Conclusions
We have demonstrated that an earthquake in September, 2009, affected the land level of Upolu Island in the Samoan Islands and Tutuila Island in American Samoa by initiating a co-seismic uplift followed by crustal subsidence, and the ocean level at the same islands by sea level fall followed by sea level rise. Even the tidal amplitude was significantly deformed due to short-term changes in gravity and geoidal eustasy [30].
The effects of the 2009 earthquake observed imply the interaction of crustal deformation, gravitational compensation and changes in sea level as summarized below.