Bull. Volcanol. Soc. Japan
Vol. 58 (2013) No. 1, pp. 77-90

ArticleAn Interpretation on Secular Changes in Deformation Caused by
the 1914 Eruption of Sakurajima Volcano
Izumi YOKOYAMA＊(Received January 4, 2011 ; Accepted April 16, 2012)
The 1914 eruption of Sakurajima volcano was one of the largest ones in its history and first observed with
scientific methods of those days. The eruption flowed out a large volume of lavas, and was accompanied withremarkable deformations on and around Aira caldera. The deformations consist of three stages: pre-eruptive, coeruptive and post-eruptive ones: The first one is determined by temporal tide-gauge observations at Kagoshima Port but,its origin is still unsettled. The second one is a quasi instant and elastic deformation, and therefore interpretable by asimple model. However, the location of center of depression is ambiguous due to the insufficient number ofobservations. Prior to the interpretation, it is re-examined considering the results of triangulations in the wider area, andthe location changed about 5 km S, on Sakurajima Island. The revised location of depression center can well interpretthe observed depression and compromises with seismological and petrological knowledge. The last one is a secular
recovery stage, and it has remained highly problematic whether its origin is endogenous or exogenous. The present
author interprets that the recovery changes are composed of two factors: In the period before around 1940,
viscoelasticity of the crust acted predominantly (endogenous) and later magma pressure accumulated in the reservoir
gradually joined to act (exogenous) and its contribution had become noticeable after 1955. The recovery of thedepression is interpreted as viscoelastic with retardation time of 16.6 years. Hence, viscosity of the earth crust around19
Aira caldera is determined at about 3 × 10 Pa· s on the assumption that the crust is Kelvin-type. The value iscomparable to those obtained with Miyake volcano and by laboratory measurement of a granite piece.
The other cases of viscoelastic deformations accompanied with volcanic eruptions are searched: the 1779 eruptionof Sakurajima volcano and the 1983 eruption of Miyake volcano are exemplified.
Key words : Sakurajima volcano, volcanogenetic deformation, recovery of deformation, viscoelasticity of the crust

1．Introduction
Sakurajima volcano stands on the S rim of Aira caldera
measuring about 20 km in diameter. The historical records
of eruptions on Sakurajima date back to 708 A.D. In its
eruption history, the 1471〜76, the 1779〜80 and the 1914
eruptions are the largest threes, all discharging considerable amounts of lavas from parasitic craters. At present,
the volcano is one of the most active volcanoes in theworld.
The 1914 eruption was fully described and studied
geophysically by Omori (1914-1922) and geologically by
Kotô (1916). The present discussion owes very much totheir works though it is limited to a study on deformations
caused by the eruption. The significant subsidence around
Aira caldera caused by the 1914 eruption were confirmedby repeated precise levelings and triangulations by the
Military Survey as shown in Figs. 1 and 4 where the location of center of the subsidence is inevitably ambiguous
because the observations were limited on land and their
number was not enough. The secular recovery of the 1914＊

Higashi 1-17-7-1304, Kunitachi, Tokyo 186-0002, Japan.

subsidence has been pursued for about one century after
the eruption. During the period, the 1946 eruption issued
lava flows and the recovery was partly reversed. After
that, the recovery has proceeded further and attained theoriginal level around 1970.
Such remarkable crustal deformations and their secularchanges have held the earth-scientistʼs interest and roused
many arguments. Firstly Sassa (1956) mentioned possible
relationship between the secular recovery of the 1914
subsidence and the activities of Sakurajima volcano. And
Mogi (1958) discussed the deformation and achieved tointerpret it by a source of dilatational type. Later
Yokoyama (1986) studied the secular changes on the dataof those days, and further, extended his idea to a discussionof caldera structure in general (Yokoyama, 2005).
2．Deformation Related to the 1914 Eruption of Sakurajima Volcano
Networks of precise levels along the route circulating
Aira caldera were first established in 1892 by the Military
Corresponding author: Izumi Yokoyama
e-mail: yokoizu@aol.jp

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Izumi YOKOYAMA

Fig. 1. Vertical deformations around Aira caldera caused by the 1914 eruption of Sakurajima volcano obtained by theprecise leveling (after the Military Survey). Hatched areas are the 1914 lavas. “Ai” indicates the islets produced by the1799 eruptions. Encircled “E” is the epicenter of the earthquake M 7.1 (after Abe, 1981). B.M. 2469 (double circle) is
the reference point in the discussion of the secular changes. Star-mark “A”: The center of the subsidence determined inthis figure, and “B”: Ditto determined by the results of the triangulations in Fig. 4.

Survey, referred to the tide-gauge station of Hosojima at
about 140 km distant NE. After the 1914 eruption of
Sakurajima volcano, the leveling routes were extended
toward the south and around Sakurajima Island. Since
then, however, several benchmarks in the networks havesuffered from re-settings due to changes of circumstances
during roughly one century. It is a perplexing problem tokeep the reasonable reference point for deformation studies.
Six months after the 1914 eruption, a precise leveling
was repeated around Aira caldera: It was the second survey
after 1892. This survey could reveal a subsidence of wide
area: The subsidence-contour of 5 cm encircled an area ofroughly 60 km in diameter, centering at Aira caldera (Fig.
1). Such deformation area is comparable to that of aseismic deformation caused by a large earthquake.
Dambara (1966) obtained an empirical formula relating
mean diameter L (km) of the deformed area to magnitude
Ms of the earthquake as:log L=0.51 Ms−1.96,(1)where L corresponds to earthquake volume. For L =60
km, Ms is estimated at 7.3. The 1914 eruption of Sakurajima volcano caused crustal deformation of the same orderas an earthquake of magnitude 7.3. This suggests that theeruption of Sakurajima volcano was a large catastrophe in
the crust. Matuzawa (1976) compared the Sakurajima
eruption to a great earthquake and suggested his hypothesis that if a large tectonic earthquake is compared to a
subterranean volcanism, a fault should correspond to an
eruption.
It is necessary to study the pre-eruptive and co-eruptive
deformations to bring the whole aspect of the eruption tolight.
2-1 Pre-eruptive deformation of the 1914 eruption
As shown in Fig. 1, B.M. 2474 may be supposed to be
the nearest to the center of the subsidence. Hereafter wewill treat with B.M. 2474 as the main object. It subsided
75 cm referred to B.M. 2469 located in Kagoshima City,
about 10 km SW of B.M. 2474 and to the year of 1892.
We had no surveys between 1892 and the eruption in 1914.
The pre-eruptive deformation was not observed intentionally. Hence, we canʼt know the exact height of B.M. 2474
just before the eruption and even tendency of its changes,
and also its behaviors just after the eruption.
In the present paper, B.M. 2469 (a double circle in Fig.
1) is adopted as the reference point to examine the secularAn Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano

79

Fig. 2. Secular changes in vertical deformation at B.M. 2474 referred to B.M. 2469 and the year of 1892 (double circle):
The base line is “Reference level”. Volcanic activities are indicated by arrows in arbitrary scale. The deformation of B.
M. 2474 after 1960 has been observed by the Sakurajima Volcanological Observatory, Kyoto University. The right top
shows annual numbers of summit explosions since 1967 after Iguchi et al. (2008). Striped parts are probablecontributions of magmatic pressure and broken curves are viscoelastic recoveries. Hollow circles denote assumed
values. A question mark means doubt on the origin of the uplift between 1892 and 1914, volcanic or tectonic origin.

changes uniformly for long periods as far as possible, andthe reference time is assigned at the year of 1892 when thebench marks for precise leveling were first established.
The problem is the difference of the height of B.M. 2469
between 1892 and early 1914. Fortunately temporary tide
observations at Kagoshima Harbor were repeated for
1903〜1905 and 1909. In the following, we refer to thereport of Omori (1916, No. 2). B.M. 2469 is located at a
distance of about 0.6 km from the harbor, and we assume
that both the points deformed equally. Kagoshima Harbor
uplifted 6 cm for 5 years (1904〜1909), or 1.2 cm/yr inannual rate according to the results of the above tide
observations. Then, we may assume the uplift of B.M.
2469 during the period 1892 to early 1914 to be 1.2 cm/yr
×22 yr=26.4 cm, as shown in the left part of Fig. 2 where
the reference point is marked by a double circle aside theordinate. The value may have some errors, probably±10
cm because it is obtained by an extrapolation of the 6
yearsʼ observation to 22 yearsʼ one. Here, we take anassumed premise that this reference point was free fromstrain in the year of 1892. The true “no-strain level”
cannot be defined exactly at present, and should be
definitely determined in future after repetitions of thesimilar observation. Now “reference level” is adopted for“no-strain level”, as an auxiliary.
Furthermore, we cannot determine the origin of the
uplift observed between 1892 and 1914, magmatic or
tectonic forces: We suspect Sakurajima volcano may havebeen activated without noticeable surface manifestations.
During the period, a smoking at the summit was solely
recorded in 1899. Seismic activities were not detected: It
was the early stage of seismic observations in Japan. A
seismic observation using a Grey-Milne seismograph was
temporarily made in Kagoshima City on Jan. 11 and 12,1914 (top of Fig. 3).
2-2 Co-eruptive deformation of the 1914 eruption
Strictly speaking, co-eruptive deformation canʼ t be
defined clearly: The 1914 eruption was so violent that noexact reports on the sequence of the deformation wereavailable. After the large eruption in January 1914, heightchanges of B.M.s 2469 and 2474 were determined as −40.7
cm and −89.4 cm, respectively, referred to the Hosojima
tide-gauge station, by the second survey in July 1914.
Hence, B.M. 2474 subsided 48.7 cm referred to B.M. 2469
and the year of 1892. As mentioned above, B.M. 2469
uplifted 26.4 cm, and hence we may conclude that B.M.
2474 subsided 48.7+26.4=75.1 cm referred to B.M. 2469
and the year of 1892. Its error may be probably±10 cm as80

Izumi YOKOYAMA

Fig. 3. The 1914 eruption activities of Sakurajima volcano.
Top: Volcanic and seismic activities during the period Jan. 09 to 14, 1914.
Bottom: Vertical deformation of B.M. 2474 referred to B.M. 2469 and the year of 1892
from Jan. 1914 to Dec. 1918. Lava-flow activity is shown in an arbitrary scale.

mentioned above. Thereafter the survey was repeated in
February 1915 and December 1918 as shown in the lower
part of Fig. 3.
How and when the subsidence of 75 cm did proceed?
To discuss this problem, we can refer to only the resultsof the precise leveling in July 1914 and February 1915 (Qand R in Fig. 3). It is still not clear whether the subsidence
was elastic or viscoelastic or combined together. Linkingof the three points is not unique. Yokoyama (1997) discussed some possible patterns of the subsidence: partly
elastic and partly viscoelastic. In the present paper, wetreat with the simplest pattern, totally viscoelastic, for thesake of convenience. In Fig. 3, the curve between P, Q
and R can be fitted approximately by an exponential curve.
Motive forces of the subsidence are important and shall be
discussed in the next section.
The upper part of Fig. 3 shows the seismic and volcanic
activities related to the 1914 eruption. The first explosion
issued white smoke at the crater of South-Peak at 8 a.m.,Jan. 12. The violent explosions began at the vents on the E

and W flanks at 10 a.m. and continued for Jan. 12 and 13.
The explosion cloud reached at a height of 8 km at thehighest. The lavas began to flow out from both the craterlines at 20 h, Jan. 13 and continued for about 20 days.
This is the 1st stage of the lava flows, and the 2nd stage
continued for about one year at the E vents (Yamaguchi,1975). The majority of the 1914 lava flows issued in the
1st stage: According to Kotô (1916) and Omori(1914-1922), volume of the lava flows from the W vents
amounted to 0.35 km3 and that from the E vents to 1.2 km3,
and that of the 2nd stage was not estimative. It isnoticeable that depression process was not parallel to lavaeffusing activity in Fig. 3.
A large earthquake with a small tsunami took place on
Jan. 12. It is exceptionally large as of volcanic origin.
Abe (1981) studied this earthquake examining theJapanese and world seismograms and determined its
magnitude as 7.1 and its epicenter as indicated in Fig. 1.
At that time, the nearest seismic station was in Nagasaki,
about 150 km distant. Seismogenetic deformation of thisAn Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano

earthquake, if any, could not be distinguished because thegeodetic and seismometric networks were not sufficient inthis area at that time.
B.M. 2474 may have been triggered to subside 75 cm (Qin Fig. 3) by this earthquake, totally or partly. The present
author suspects that some parts of the subsidence werecompleted while the lavas were still issuing.
2-3 A model of the co-eruptive subsidence
The Aira deformation occurred in the upper crust, andthe maximum subsidence may be about 1 m (Fig. 1), andthe depth of source 10 km. Then, its strain is estimated atan order of 10−4. Because elastic limits of the crust isreported as (5 ± 4) × 10−5 from the data of tectonic
earthquakes (Rikitake, 1975), one may barely treat withthe 1914 deformation around Aira caldera as an elastic
deformation.
The subsidence around Aira caldera was caused by
implosive source related to strong explosions and extrusion of a large amount of magmas. Deformations of theground surface caused by volcanic eruptions were first
analyzed by Sezawa (1931) who applied simple source
models such as expressed in spherical harmonics P 00 (cosθ) in semi-infinite elastic medium. For instance, verticaldisplacements Δ h at the surface are given against radial
distance r from the source as follows:Δh=−D
3a 3 P,
4μ (D 2+r 2)32(2)

where P denotes the pressure amplitude, μ rigidity of
the crust, D depth of the pressure source, and a radius of
the sphere. Actually a is assumed to be small comparedwith depth D.
Mogi (1958) first applied this model to the deformationof the 1914 Sakurajima eruption, and succeeded to obtainthe source depth D at 10 km on the assumption that thecenter of subsidence is located around “A” in Fig. 1. Later
Yokoyama (1986) applied the model of P 01 (cos θ) type to
express upward magmatic pressure at the source, andobtained D as 8 km.
An alternative configuration of the depression
As shown in Fig. 1, as of 1914, benchmarks for precise
levels were not sufficient in number, especially on theisland and the S part of this area. The contours of Fig. 1
were drawn by the Military Survey and rather ambiguous:
It is true that B.M. 2474 sank the most among the benchmarks surrounding the caldera, but we cannot determine
exactly the location of the center of the subsidence because
of insufficient number of benchmarks. Provisionally it
was assumed to be at “A” in consideration of the results ofthe precise levels only, mainly at the N of the volcano (Fig.
1). A supplementary method is height determinations by
triangulations though the accuracy is a little lower than
precise levels. The results are shown in Fig. 4 that was
originally prepared by the Military Survey and was once
discussed preliminarily by Yokoyama (1986). In the81

figure, double circles denote triangulation points of 2ndorder, open circles those of 3rd order, and solid circles
optical observations. There are several triangulation points
on the S part of the island and the S off the island while noleveling points were on the island. On the island, thecentral part of the volcano locally uplifted probably due toparasitic effusions of lavas at the flanks. Comparing thetwo distributions of subsidence obtained by leveling andtriangulation, and neglecting the very local uplifts on theisland and the optical observations, we may assume thecenter of depression of Aira caldera at “B” on the island,
toward the S of “A”. Assuming the center of depression at“B” in Fig. 4, we obtain the relation between Δ h versus r(radial distance from the center of subsidence) is obtained
as shown by dots in Fig. 5 where similar relation obtainedby the precise levels (the subsidence center “A”) is reproduced by a broken line (Mogi, 1958, Fig. 5). B-centerdistribution has nearly the same tendency as that of Acenter-distribution, and satisfies Eq. (2) as well. And
therefore, we obtain the same results on the depths ofpressure source by the two distributions. In fact, the Acenter-distribution covers only Aira caldera while the Bcenter-distribution does wider area including the island.
Here, it deserves our attention that these subsidence
centers are possibly different from the center of theactivities in formation of Aira caldera.
If the “B” location holds good, we may figure a simple
model of magma reservoirs, and interpret both the deformation of Aira caldera and the activities of Sakurajima
volcano: The source of the latter model (“B”) located at a
depth of 8〜10 km, approximately coincides with the main
magma reservoir of Sakurajima volcano suggested by
Iguchi (2007) using seismological data. On the other hand,from viewpoint of magmatology, Tsukui and Aramaki(1990) concluded that the andesite magma of Sakurajima
volcano should be basically independent of rhyolite magmaof Aira caldera. Thus we may assume that the Sakurajima
activity is independent of the past Aira activity. Such
relationship between a caldera and its post-caldera volcano
poses an interesting problem common to all calderas.
In the following discussion, we assume the center of the
Aira depression is located at “B” if we deal with the large
subsidence, independently of the local uplift on Sakurajima Island. The location of the center of subsidence does
not effect the discussion of the secular changes in the Aira
deformation because we are concerned with solely the
secular movements of B.M. 2474.
3．Secular Changes in the Deformation after the 1914
Eruption
3-1 A typical pattern of secular changes in the
deformation
B.M. 2474 along the W rim of Aira caldera subsided
about 90 cm by the 1914 eruption, the largest on land(Figs. 1 and 4). The secular changes in deformation of B.

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Izumi YOKOYAMA

Fig. 4. Vertical deformations around Aira caldera obtained by the triangulations (after the Military Survey). In the northernpart, the contours are drawn with the help of the leveling results. Star-mark “B” indicates an assumed center ofsubsidence. The three asterisks correspond to the same in Fig. 5.

Fig. 5. Relation between subsidence (∆ h) and distance (r)from the subsidence center. Hollow circles: triangulation results on Sakurajima Island; asterisks: the values
in the southern area in Fig. 4. A broken line isreproduced from the same relation of “A” distribution
in Fig. 1 (after Mogi, 1958, Fig. 5).

M. 2474 referred to B.M. 2469 and the year of 1892, as a
typical pattern, is shown in Fig. 2. The data before 1970
were obtained by the Military Survey and theGeographical Survey Institute, and later by the Sakurajima
Volcanological Observatory, Kyoto University. After the1946 eruption, a precise leveling was repeated in the area,
but both the benchmarks had been lost before 1946. A
probable value in 1946 (a hollow circle) is determined byinterpolation among the subsidence contours obtained by
the surrounding benchmarks.
B.M. 2474 subsided about 90 cm quasi simultaneouslywith the explosions in 1914, and began to recover after ayear. Miyabe (1934) already doubted what did the gradualcounter deformation mean admitting that the remarkable
and rapid subsidence was caused by the volcanic eruptions.
If the 90 cm subsidence was crustal strain caused by the
explosions, the following reverse movements were arecovery towards equilibrium. However, if the subsidence
was the result of releases of stresses accumulated preceding the eruption, the recovery means accumulation ofstresses deviating from equilibrium. Miyabe (1934) correctly concluded that he had no observational data at thattime to solve the problem whether the recovery is
endogenous or exogenous.
Later, Sassa (1956) took notice of that Sakurajima
volcano issued a large amount of energy such as 1018 J in
the 1914 eruption and caused subsidence of the ground,and hence there was a deficit of 1.6 km3 at the magma
reservoir after the 1914 eruption. He interpreted that thecaldera began to uplift next year (Fig. 3) according as theactivity regained, and suspected that a small eruption
would occur when the activity power reached an ultimate
value. In short, Sassa (1956) assumed that the ground
uplift was caused totally exogenously.
It is high time that the problem should be answered one
step more. The present author suspects the upward recovery
should be composed of two factors: One is viscoelastic
recovery movement of the crust, and the other is upheavalof the ground due to injection of magmas into theAn Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano

reservoir. The former would begin to appear immediately
after the eruption while the latter would join with theformer after some periods because a speedy reactivation ina few years is not always probable. Another evidences
shall be discussed in 3-2.
The volcano manifested small activities several times
after the 1914 eruption, in 1935, 1939 (1938〜42), 1946,
1948, 1950, and 1955 as shown at the top of Fig. 3 where
volcanic activities are expressed in an arbitrary scale
mainly depending on volume of the ejecta. It is suggestivethat we had no surface activities for about 20 years until
1935: The present author assumes that, during that period,
magma gradually had been accumulated to contribute theupward deformation of B.M. 2474.
In September 1935, the crater of South-Peak erupted
ejecting ashes after a small group of volcanic earthquakes,
and the activity continued for a month. In October 1939,
an eruption took place at the E flank of South-Peak, around
750 m a.s.l. forming a small crater that is called “Showa
Crater”.
The 1946 eruption burst at Showa Crater issuing lavasof 0.15 km3 (DRE) that is about one tenth of the 1914 lava.
Such activities mean that Sakurajima volcano was
gradually activated since 1935. After 1955, the volcano
has been continuously active at the summit crater of SouthPeak, usually in Vulcanian type. On June 4, 2006, Showa
Crater was reactivated and thereafter solely it has been
active as of 2011.
An accidental observation: In December 1958 (Fig. 2), alava pool was formed in the summit crater of South-Peakafter tremors continued for about 21 hours, and a cooledlava field was accidentally photographed from the air: Its
diameter was about 100 m, its depth about 30 m, the radiusof its vent about 9 m, and the total volume of the lava 7.9×104 m3. Within the following week, all lava blocks were
exploded off. Yokoyama (1961) estimated a probabledepth of the vent at about 3 km by applying the HagenPoiseuileʼ s law to the ascent of magmas. Yoshikawa(1961) also assumed a magma pocket at a depth of about 5
km right below Sakurajima volcano from analyses of thedeformation of Sakurajima Island.
This phenomenon means that magmas had ascended to ashallow depth beneath Sakurajima volcano at that period.
Since 1955, some magma may have appeared at the crater,and some may have exploded before they reached thecrater. Such magma movements at the depths probably
contributed to the uplift of the caldera area as shown in
Fig. 2 where the solid lines indicate the observed deformation connecting the observations (dots) and the brokenlines beneath the hatches do assumptive viscoelastic
recovery: the hatched parts indicate the contributions ofmagmas to the deformations. In the figure, the broken line
after 1946 has the same viscoelastic characteristics (retardation time) as the curve before 1946 and may
asymptotically approaches the reference level.

83

In short, the present author interprets the secular
deformations of Aira caldera by dividing into two periods:
one is a viscoelastic recovery of the crust since 1915 andthe other is the contributions of magma activity that
became effective after 1935 or thereabouts according asmagmas accumulate at the source (8〜10 km deep).
In Fig. 2, around 1935, magma pressure beneath thevolcano may have begun to contribute to the uplifts of thecaldera area as qualitatively indicated by hatches. It is apity that we had no measurement for about 10 years
preceding the 1946 eruption.
In the same figure, the recovery stagnated around 1962
for a few years. Kamo (1976, 1978) interpreted it as theeffect of significant explosive activities centering at 1960.
He also remarked that increased recovery during the period
1962 to 1972 was related to the low explosive activities ofthe same period.
On the other hand, it was already reported that the
volcano body expands in advance of summit eruptions due
to increase in magmatic pressure at the source at a depth
deeper than 4 km right beneath Sakurajima volcano, by
Kamo and Ishihara (1986) and Ishihara (1990).
3-2 Secular changes in regional deformation around
Aira caldera
The recovery rates of 9 benchmarks around Aira caldera
were already mentioned by Yokoyama (1986) and are
reproduced in Fig. 6 where the rates of the two recovery
stages, 1918〜1943 and 1946〜1960, are plotted against
the initial displacements. They show roughly linear
relationship: the larger the initial displacement the higher
the recovery rate. This is characteristic of elastic or viscoelastic deformations of a medium, the crust in the present
case. In Fig. 6, open circles (1946〜1960) a little diverge
from linearity due to effect of magmatic pressure during
the period (Fig. 2). Hence, the recovery is mainly spontaneous or endogenous, and partly effected by magmaticFig. 6. Recovery rates vs. initial deformations at several
benchmarks for precise levels.

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Izumi YOKOYAMA

force during the period 1946〜1960.
The other model may be possible. As discussed above,
point source models can interpret subsidence or uplift
caused by volcanic eruptions. Here we check their possibility in interpretation of temporal changes in the deformations. As shown in Eq. (2), vertical displacement isdirectly proportional to P. If P changes exponentially withtime, Δh changes in the same way. This model may
interpret exponential changes of the Aira deformation, butneeds to explain reality of such origin, and furthermore has
difficulty in explaining the above characteristics; namely,
the larger the initial displacement the higher the recovery
rate (Fig. 6). Anyway, this is an exogenous origin model.
Equation (2) can model the surface deformations caused
by magmatic pressure successfully but not the secularchanges in deformations.
3-3 Viscoelastic behavior of the ground around
Aira caldera
From the standpoint that the recovery of the deformation
around Aira caldera is endogenous, we interpret theprocess as illustrated in Fig. 7:
Assuming the crust to be viscoelastic body of Kelvintype, we get the following relation:p=γe+η

de
,
dt

(3)

where p denotes force, e strain, γ Youngʼs modulus andη viscosity. The second term is viscous resistance. Eq.
(3) is solved under the condition that the initial stress iszero and a constant stress p0 is applied to the system:e=p01−e   ･t .
γ





(4)

When t tends to ∞, e tends to e∞ =p0 /γ. The term(η/γ) has dimension of time:
τK=η/γ ,(5)And τK is the time necessary for the strain to decrease
from the initial value e0 to 1/ e, and named retardation
time. A body is assumed to be strained initially e0 byforce p. When p is removed instantly, strain e of the bodychanges as follows:

Fig. 7.

Creep and its recovery of Kelvin-body.

e=e 0 e t K ,(6)This is creep recovery.
Here it is a priori assumed that magma gradually
accumulated in the reservoir and gradually exerted pressure to the earth crust. In Fig. 2, a probable height of B.
M. 2474 in 1946 (a hollow circle) is determined byinterpolation among the subsidence contours obtained by
the surrounding benchmarks because it was lost at thattime. We do not know its exact movements, and assume
that B. M. 2474 suffered from a small subsidence and kept
the same recovery rate because the volume of the 1946
lava was about 10 % of the 1914 lava. In the figure, thestriped parts indicate probable contributions of magmaticpressure and the broken curves do viscoelastic recoveries.
Hence the retardation time is estimated as 16.6±1 yr forthe recovery curve (solid and broken line) between 1918
and 1946. The viscoelastic recovery between 1946 and2000 (broken line) is drawn on the assumption that thebenchmark continued to recover with the same retardation
time. As a result, Fig. 2 may support acceptability of theabove assumptions.
The accuracy of determination of the viscosity depends
equally on Youngʼs modulus and retardation time. Mogi
(2006) measured Youngʼ s moduli of rocks (andesite,
marble and tuff) as a range of 1〜10×1010 Pa. Here we
adopt the averaged value 5×1010 Pa, and then, we getviscosity of the ground as:
η=τK×γ=3×10 19 Pa･s
The deformation analyzed in the above discussion originated in the upper crust of about 10 km deep because they
can be interpreted by a point dilatation located at the same
depth.
To interpret the meaning of Fig. 2, it is schematically
redrawn in Fig. 8 where we assume “no-strain level”
independent of volcanic activity. In the figure, the hatchedpart indicates the contribution of the magma pressure andthe broken curve approaches asymptotically to the nostrain level due to elastic recovery. Actually, in Fig. 2,“no-strain level” cannot be defined exactly at present
though it must be roughly near “reference level”.
In the present discussion, we assume the crust of
volcanic regions to behave with viscoelasticity of Kelvintype. Just before an eruption, the volcano and its surroundings may uplift somewhat due to a partial release ofincreasing magmatic pressure. In advance of a gigantic
eruption of the volcano, the crust around the volcano
suffers from magmatic pressure expressed by a pointsource pressure P at depth D (about 8〜10 km in the event
of Sakurajima volcano). The pressure P may reach highvalues, especially at andesitic volcanoes, at the climactic
moment. When accumulated pressure is almost instantly
released through the vents by an explosion, and simultaneously implosive force acts at the point source P,

An Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano

85

critical condition for the next eruption.

Fig. 8. A schematic secular deformation curve of B.M.
2474, corresponding to Fig. 2. Actually “No-strainlevel” cannot be determined and “Reference level” isused in Fig. 2.

causing the crust to subside beyond the equilibrium level.
The subsidence proceeds viscoelastically as exemplified in
the 1914 Sakurajima eruption (Fig. 2). Shortly after the
rapid subsidence is completed, the crust begins to recover
towards the no-strain level (equilibrium level) due toviscoelasticity of the crust itself, and the crustal strain
attains equilibrium in due time. Simultaneously with therecovery, magma pressure gradually accumulates at thesource as the volcano is reactivated, and beyond theequilibrium that cannot be determined exactly at present.
After 1980, as shown in Fig. 2, the recovery approaches
the reference level, and the surface deformations areapparently governed by magma pressure (hatched parts).
According to Iguchi (2007), the explosion activity ormagma activity was highest around 1985 as shown in Fig.
2 (top) and thereafter decreased in number of explosions:
Magma activity again tended to lift the ground after 1993.
Anyway, in such a way, the volcano may approach the

4．Deformation Caused by the 1779〜80 Eruption of
Sakurajima Volcano
The 1779〜80 eruption of Sakurajima volcano wascomparable to or larger than the 1914 eruption: Explosion
cloud reached a height of 12 km and ashes reached toTokyo. According to Kobayashi (1988), pumices andlavas were issued from parasitic craters on the NE and S
flanks, and almost simultaneously several small islands(“Ai” in Fig. 1) off the NE coast were formed by submarine eruptions and by upheaval of the sea bottom. The
area covered with lavas of the 1779 eruption is nearly 9
km2 while that of the 1914 eruption is about 20 km2.
These values do not always exactly correspond to theirmagnitudes because their thicknesses are variable fromplace to place. As a volcanic activity before the 1779〜80
eruption, a summit eruption in 1766 is reported. After the
1779〜80 eruption, the volcano showed after-activities at“Ai” area in 1781〜82. We can refer old documents
reporting that the N coast of Kagoshima Bay including thetownships of Kagoshima, Kajiki and Kokubu (Fig. 1),
were flooded to a depth of 1.5〜3 m by high tides for 4 or 5
years after the 1779 eruption. The subsidence was significant even without instruments at that time. Consideringthat B.M. 2474 subsided about 0.8 m in 1914, we provisionally assume that the site of B. M. 2474 subsided in
1779 within a range of 0.8〜1.5 m, or 1.2 m on the average,
referred to the same height as the 1914 subsidence, i.e. 26.
4 cm above the reference level. Furthermore, the recovery
after a subsidence in 1779 is assumed to have begun
instantly.
Now we may extrapolate the time-axis in Fig. 2 back to
the 1779 eruption as shown in Fig. 9. There occurred small
5 activities after 1779. However, the recovery should havenot been influenced by these volcanic activities because
they were not so much energetic. In Fig. 9, it is noticeable

Fig. 9. Deformation curve of B. M. 2474; The time-axis in Fig. 2 is hypotheticallyextrapolated back to the 1779 eruption. The notations are the same as Fig. 2.

86

Izumi YOKOYAMA

Fig. 10. The 1983 eruption of Miyake volcano: Distributions of vents (black) and lava flows (dotted) after
Aramaki and Hayakawa (1984), and the benchmarks ofprecise levels. “TS” denote the tide-gauge station.

that the volcano was rather calm from 1799 until 1914
except phreatic activities at the summit in 1860 and 1899.
The recovery curve of the 1779 subsidence is governed by
the retardation time 16.6 years deduced from the recovery
curve of the 1914 subsidence. As for “no-strain level”, thereference level in Fig. 2 is extrapolated to the year of 1779.
In Fig. 9, we may imagine that the 1779 depression may
have taken roughly the similar recovery process as the1914 depression. This figure may offer us some suggestions regarding long-term prediction of the future activities
of Sakurajima volcano.
5．Another Examples of Secular Changes in Volcanogenetic Deformation
Viscoelastic recovery of vertical deformation caused byvolcanic eruptions is not particular to Aira caldera, but wehave another example at Miyake volcano.
5-1 Deformation caused by the 1983 eruption of
Miyake volcano
Miyake volcano is on a volcano island of basaltic rocks
and has erupted repeatedly in historical times, such as
1811, 1835, 1874, 1940, 1962, 1983 and 2000 after the
19th century. In this paper, we refer the deformation
caused by the 1983 eruption.
In October 1983, linear fissures of about 4 km long on
the SW flank (Fig. 10) ejected lava flows of 8×10 6 m3
DRE. In June 2000, a small submarine eruption occurredFig. 11. Vertical deformations along the leveling route on
Miyake Island caused by the 1983 and the 2000 eruptions. TS: Tide-gauge station. The 1983 eruption curveshows the changes between Dec. 1982 and Dec. 1983,
and the 2000 eruption curve does between June 1999
and Feb. 2002. Hollow circles indicate assumed
values. (original data after the Geographical Survey
Institute).

1 km west off the island, and phreatic explosions occurredat the summit crater issuing ashes and bombs, no lavas andcaused collapses of the crater bottom.
The Geographycal Survey Institute established theleveling routes circulating Miyake Island in 1979. Thereis a tide-gauge station at the SW shore of the island. In thepresent discussion, the tide-gauge station is adopted as thereference point because the height of the station wascalibrated with a benchmark at the Izu Peninsula bycontinuous GPS observations of the Geographycal Survey
Institute. Height changes at the benchmarks around theisland caused by the 1983 and the 2000 eruptions weresurveyed by the Geographycal Survey Institute (1984,2005) referred to November 1981 and the tide-gauge
station, as shown in Fig. 11. The distance between the
successive benchmarks is about 1. 5 km on the average.
Yokoyama and Maekawa (1984) studied the deformationin 1983 and showed that the island tilted as a whole about
4×10−5 (rad.) and in a direction N 30° E up. The heightchanges of bench marks caused by the 2000 eruption are
also given in Fig. 11 where both the changes are similar inpattern: The latter shows a tilt movement with a similar tilt
axis but with a larger angle, 1.5×10−4 (rad.). The tilts
caused by the 1983 eruption had recovered roughly half asof 1993 (Yokoyama, unpublished), and therefore the tilt of
the 2000 eruption may have been smaller than the above
value. We may say that Miyake Island would tilt a certain
amount in roughly the same direction by an eruption of the
volcano and the tilt would recover at a certain rate after the
eruption. In the present paper, the author does not discuss
the tilt movements because the data are not sufficient.

An Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano

87Fig. 12. Secular changes in height of B.M. 10250 referred to the tide-gauge station and the year of 1979.
Hollow circles denote assumed values. (original data after the Geographical Survey Institute).

BM. 10250 is the benchmark nearest to the eruption site,
about 230 m distant and was bombarded with rock ejecta
from the new vents around P point in Fig. 10. The S partof the island centering at B.M. 10250 locally uplifted by
the eruption as shown by a hatched part in Fig. 11. B.M.
10250 was found to have uplifted about 18 cm referred tothe tide-gauge station and the year of 1979. This uplift
was clearly caused by a magmatic intrusion during the1983 eruption. This is confirmed by gravity changes
observed along the route of precise leveling (Yokoyama
and Maekawa, 1984): In a diagram of gravity changes vs.
height changes, B. M. 10250 deviates plus 65 μ gal fromthe line of Free-air gradient line. This means that magmas
of high density had intruded below the benchmark. An
upheaval of 18 cm per a span of about 6 km is within
elastic limits. B.M. 10250 was lifted by an increase ofmagmatic pressure, and began to recover viscoelasticallyafter release of the magmatic pressure by explosions at thenear vents.
5-2 Secular changes of deformations caused by the
1983 and 2000 eruptions of Miyake volcano
The secular changes in the height of B.M. 10250 since
1979 are shown in Fig. 12. After the 1983 eruption, thebenchmark has subsided with time exponentially though
the process was reset by the 2000 eruption. B.M. 10250
subsided about 17 cm by the 2000 eruption. This is a
result of a tilt movement as a whole island. The present
author assumes that BM. 10250 was instantly uplifted bymagma intrusion near the benchmark, and after magma
activities finished, the benchmark began to recoverviscoelastically.

In the case of Miyake volcano (Fig. 12), the retardation
time is roughly 5.8 years. Assuming Youngʼs modulus γ=5×1010 Pa, the same to the case of Aira caldera, we getviscosity of the upper crust surrounding B.M. 10250 as:
η=τK×γ=0.92×10 19 Pa･s
This is about 1/3 of that of Aira caldera (η=3×1019
Pa·s) and the difference may be due to the shallower originof the Miyake deformation.
In the 2000 eruption, the activities were confined to thesummit area, and B. M. 10250 subsided about 17 cm asshown in Fig. 11. This subsidence was resulted from a tiltof the island as a whole, not local deformation.
For reference to non-volcanic regions, Artyushkov(1971) gave the viscosity of asthenosphere beneath theCanadian shield as the order of 1019 Pa·s by analyses ofrheological properties of the crust according to data on
isostatic movements.
5-3 Secular changes in volcanogenetic deformation
due to self-loading compaction: Serapeo andShowa-Shinzan
On the other hand, we know another examples of secularsubsidence of volcanic structures:a) Serapeo close by the port of Pozzuoli near Naples:
Secular changes in height of Serapeo, one of the Romanruins, have been well documented since 200 B. C. The
spot is located at the center of Campi Flegrei caldera, andusually would tend to subside monotonously and change toinstant upheaval when major local earthquakes and major
eruptions of nearby volcanoes. Oliveri del Castillo andQuagliariello (1969) attributed the linear subsidence (1.4

88

Izumi YOKOYAMA

cm/year) during the period, the 1820ʼs to 1968, to selfloading compaction of the caldera fills.
b) Showa-Shinzan (the 1944 lava dome) of Usu volcano,
Hokkaido: This dacitic lava dome was formed by aparasitic eruption for the period, January 1944 to October
1945. After its completion, it has gradually subsided, andsecular changes of its height have been observed, andproved to be roughly linear at 5 cm/year (Yokoyama andSeino, 2000, Fig. 13). The subsidence may be caused also
by self-loading compaction of the basements of the dome.
These two examples are contrasts to viscoelastic behaviorsof Aira caldera and Miyake volcano.
5-4 Laboratory measurements of viscoelastic behavior of granite specimens
Kumagai (1991) and Itô (1979) carried out laboratory
measurements of viscoelastic behavior of granite specimens for long years. Since 1957, they measured creeps oftwo large beams of granite, 215×12.3×6.8 cm in size.
One of these specimens was bended under its own weightplus a center-load (22. 06 kg). The maximum bending
stress in the unloaded beam is 1.3 MPa. After more than
30 year experiment, they analyzed deflection curves of the
granite beam and obtained its Youngʼs modulus at 2.6×1010 Pa and its viscosity at 6.5×10 19 Pa·s assuming the
flowage of the granite beam to be Maxwell type. The
value of viscosity is a little larger than the above estimatesof the field data.
Deformations at Aira caldera and Miyake volcano are
related to the upper crust of 10 km and a few km deep,
respectively. Considering that the viscosity, in general,
increases rapidly with the hardness of the material and thepressure, the above three values of viscosity, 6.5×1019 Pa·
s for a granite specimen, 3×1019 Pa·s for Aira caldera, and
0.9×1019 Pa·s for Miyake volcano, are of a reasonable
order of magnitude though their Youngʼ s moduli are
assumed to be identical.
6．Concluding Remarks
Co-eruptive deformation of the 1914 eruption of Sakurajima volcano is reexamined: If we use the results of triangulations in the area, we can interpret the deformation
by assuming the center of subsidence on Sakurajima
volcano. Secular changes in the deformation caused by
the 1914 eruption can be interpretable into that they arecomposed of two factors: One is viscoelastic recovery of
the ground and the other is uplifts due to accumulation ofmagmatic pressure at the source. These two affected withtime lags: In the early period, the viscoelastic factor solely
acted, and after 20〜30 years, magmatic pressure began tojoin in uplifting the ground.
Recovery of the upheaval caused by the 1983 eruptionof Miyake volcano is also interpreted by viscoelastic
behavior of the volcano ground, of which viscosity proves
to be a little smaller than that of the Aira deformation
though these values have some ambiguity of the Youngʼs

moduli.
At the beginning of the 21st century, from the secularchanges in the Aira deformation caused by the 1914
eruption of Sakurajima, we may suppose that theviscoelastic recovery is approaching to no-strain level andthe pressure effect of the magma reservoir is predominantthough the no-strain level canʼt be exactly defined. Now,
for a century, the results of various geophysical andgeological observations on and around Sakurajima volcano
have been fairly accumulated. It is high time that one
should synthesize and interpret the observational results,
and build, if possible, long-range prospects for future
volcanic activities of Sakurajima volcano.
Acknowledgements
The author thanks the late Profs. F. Omori and B. Kotô
who left their valuable reports on the observations of the1914 eruption of Sakurajima volcano. The author isdeeply appreciates the published data of seismological andgeodetic observations by the Sakurajima Volcano Observatory, Kyoto University since 1960. This paper benefited
greatly from discussion with K. Ishihara for many years.
The author wishes to thank heartily K. Kamo, T.
Kobayashi and M. Iguchi for their willing supply of new
findings in the course of the present study. The author isindebted to H. Y. Mori for helpful discussion with him.
Infalliable reviews by K. Ishihara and an anonym are
greatly appreciated.
References
Abe, K. (1981) Seismometrical re-evaluation of the Sakurajima
earthquake of January 12, 1914. Geophys. Bull., Hokkaido
Univ., 39, 57-62 (in Japanese with English abstract).
Aramaki, S. and Hayakawa, Y. (1984) Sequence and modes of
eruption of the October 3-4, 1983 eruption of Miyakejima.
Bull. Volcanol. Soc. Japan,29, 524-535 (in Japanese withEnglish abstract).
Artyushkov, E. V. (1971) Rheological properties of the crustand upper mantle according to data on isostatic movements.
J. Geophys. Res., 76, 1376-1390.
Dambara, T. (1966) Vertical movements of the earthʼs crust in
relation to the Matsushiro earthquake. J. Geod. Soc. Japan,
12, 18-45 (in Japanese with English abstract).
Geographical Survey Institute (1984) Vertical deformation at
Miyake island. Bull. Comm. Predic. Volca. Erup., 30, 32-34(in Japanese).
Geographical Survey Institute (2005) Crustal deformations in
Miyake island. Bull. Comm. Predic. Volca. Erup., 90, 92103 (in Japanese).
Iguchi, M. (2007) Structure of Sakurajima volcano revealed
by geophysical observation and significance of its survey.
BUTSURI-TANSA, 60, 145-154 (in Japanese with English
abstract).
Iguchi, M., Tameguri, K. and Yokoo, A. (2008) Sequence ofactivities of Sakurajima volcano -1997〜2007-. In Reportof the 10th Concentrated Observation of Sakurajima

An Interpretation on Secular Changes in Deformation Caused by the 1914 Eruption of Sakurajima Volcano
Volcano, Research Center of Volcanology, Disas. Prev.
Res. Inst., Kyoto Univ., 1-18 (in Japanese).
Ishihara, K. (1990) Pressure sources and induced grounddeformation associated with explosive eruptions at anandesitic volcano: Sakurajima volcano, Japan. In Magma
Transport and Storage (Ryan, M. P. ed.) John & Sons Ltd,335-356.
Itô, H. (1979) Rheology of the crust based on long-term creep
tests of rocks. Tectonophysics, 52, 629-641.
Kamo, K. (1976) Some problems on the prediction of volcanic
eruptions -In case of the Volcano Sakura-jima-. Bull.
Disas. Prev. Res. Inst., No. 19, A, 31-39 (in Japanese withEnglish abstract).
Kamo, K. (1978) Some phenomena before the summit eruptions at Sakura-zima volcano. Bull. Volcanol. Soc. Japan,
23, 53-64 (in Japanese with English abstract).
Kamo, K. and Ishihara, K. (1986) Precursor of summit eruption observed by water-tube tiltmeters and extensometers.
Ann. Disas. Prev. Res. Inst., Kyoto Univ., 29B-1, 1-12 (inJapanese with English abstract).
Kotô, B. (1916) The great eruption of Sakurajima in 1914. J.
Col. Sci., Imp. Univ. Tokyo, 38, 1-237.
Kobayashi, T. (1988) Geological map of Sakurajima volcano.
In: A guidebook for Sakurajima volcano (Aramaki, S.,
Kamo, K., Kamada, M., and Kagoshima Prefectural Government (eds)), Kagoshima Internat. Conf. on Volcanoes,
88 p.
Kumagai, N. (1991) Collected Papers on the Ongoing Laboratory Experiments on the Creep of Granite to Commemorate Thirty Years of Continued Research. Yoshioka
Shoten Co., Kyoto, 289p. (in Japanese).
Matuzawa, T. (1976) Theory of Earthquakes and Its Applications. Univ. Tokyo Press, Tokyo, 223p. (in Japanese).
Miyabe, N. (1934) Deformation of the earthʼ s crust in theneighborhood of Sakurazima. Bull. Earthq. Res. Inst., 12,471-481.
Mogi, K. (1958) Relations between the eruptions of various
volcanoes and the deformations of the ground surface
around them. Bull. Earthq. Res. Inst., 36, 99-134.
Mogi, K. (2006) Experimental Rock Mechanics. Taylor &Francis, London, 361p.
Oliveri del Castillo, A. and Quagliariello, M. T. (1969) Sulla
genesi del bradisismo Flegreo. Atti Ass. Geofis. Ital., 18°
Convegno, 557-594.

89

Omori, F. (1914-1922) The Sakura-jima eruptions and earthquakes. Bull. Imp. Earthq. Inv. Comm., 8, 1-525.
Rikitake, T. (1975) Statistics of ultimate strain of the earthʼs
crust and probability of earthquake occurrence. Tectonophysics, 26, 1-21.
Sassa, K. (1956) Some problems on the forecasting of theearthquake (II) (On the observation of the crustal strain
accompanied by the earthquake). Collected Papers for the 5
Year Anniversary of Disas. Prev. Res. Inst., Kyoto Univ.,
1-5 (in Japanese with English abstract).
Sezawa, K. (1931) The plastico-elastic deformation of a semiinfinite solid body due to an internal force. Bull. Earthq.
Res. Inst., 9, 398-406.
Tsukui, M. and Aramaki, S. (1990) The magma reservoir of
the Aira pyroclastic eruption -A remarkably homogeneous
high-silica rhyolite magma reservoir. Bull. Volcanol. Soc.
Japan, 35, 231-248 (in Japanese with English abstract).
Yamaguchi, K. (1975) Research on Sakurajima Volcano- Geological and Petrological Researches of the Surrounding Area of Kagoshima Bay and Sakurajima
Volcano -. Educ. Soc. Earth Sci. Japan, 128p. (in Japanese).
Yokoyama, I. (1961) The flow and upwelling of lava (Parts I
and II), Bull. Volcanol. Soc. Japan, 6, 51-59 (in Japanesewith English abstract).
Yokoyama, I. (1986) Crustal deformation caused by the 1914
eruption of Sakurajima volcano, Japan and its secularchanges. J. Volcanol. Geotherm. Res., 30, 283-302.
Yokoyama, I. (1997) An interpretation of the 1914 eruption of
Sakurajima volcano. Proc. Japan Acad., 73, Ser. B, 53-58.
Yokoyama, I. (2005) A side view of geophysical research of
caldera structure for the recent 50 years. Bull. Volcanol.
Soc. Japan, 50, Spec. Issue, S59-S76 (in Japanese withEnglish abstract).
Yokoyama, I. and Maekawa, T. (1984) Ground deformationand gravity change associated with the 1983 eruption of
Miyakejima volcano. Bull. Volcanol. Soc. Japan, 29, Spec.
Issue, S130-S140 (in Japanese with English abstract).
Yokoyama, I. and Seino, M. (2000) Geophysical comparisonof the three eruptions in the 20th century of Usu volcano,Japan. Earth Planets Space, 52, 73-89.
Yoshikawa, K. (1961) On the crustal movement accompanying with the recent activity of the volcano Sakurajima(Part 1). Bull. Disas. Prev. Res. Inst., Kyoto Univ., 48, 2-15.

(Editorial handling Masato Iguchi)

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Izumi YOKOYAMA

桜島火山の 1914 年噴火によって生じた地殻変動の永年変化に関する一解釈
横山泉

桜島火山は歴史時代において，数度にわたり大噴火が起こり，溶岩流出と地盤の変動が記録されている．
それらの中で，
1914 年噴火は当時の水準で種々の定量的観測がなされている．ここでは特にこの噴火によって生じた沈降の回復を詳論した．水準測量の結果は 1916 年の発表以来，しばしば議論されているが，姶良
カルデラ周辺の沈降の中心は，海域のためもあり，その位置の決定には任意性がある．今回，噴火直後の三角測量の結果をも参考にして，従来より広範囲の沈降について，その中心の位置を桜島の北岸辺に決めた．
そして，1914 年噴火に伴った大規模の沈降の回復を B.M. 2474 を例にとり解析した．その際，活動的なこの地域で変動の基準を決めることは極めて難しい．本来は歪みなしの状態(No-strain level)を基準とすべきであるが，ここでは全く便宜上，1914 年噴火に先立つ 1892 年（水準測量の開始）を基準 (Reference level) にした．将来，観測を重ねることにより，漸近的に，歪みなしの状態を決められるであろう．結論として，その永年変化は地盤の粘弾性的回復と桜島直下の圧力源の増強との 2 要素で説明される．1914 年噴火直後から粘弾性的回復が進行した（遅延時間は約 16.6 年）．平行して，次第に圧力源へマグマが蓄積するに従って，
約 20 年を経て，その効果が沈降回復へ寄与している．2000 年現在は，沈降歪みは既に 1892 年の基準まで回復して，それにマグマ圧の効果が蓄積している状態である．この議論に付随して，姶良カルデラ地域の地殻
上部の粘性を求めた．
このような火山地域における粘弾性的地殻変動の他の例として，1983 年三宅火山噴火後の沈降を論じ，上記と同じ桁の粘性値を得た．