Crustal movements in the tohoku district, Japan, during the period 1900–1975, and their tectonic implications

Tectonophysics, 60 (1979) 141-167 o Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

CRUSTAL MOVEMENTS THE PERIOD 1909-1975,

TERUYUKI Earthquake

141

IN THE TOHOKU DISTRICT, JAPAN, DURING AND THEIR TECTONIC IMPLICATIONS

KATO Research Institute,

University

of Tokyo,

Tokyo

(Japan)

(Received March 15, 1978; revised version accepted October 27, 1978)

ABSTRACT Kato, T., 1979. Crustal movements in the Tohoku district, 1900-1975, and their tectonic implications. Tectonophysics,

Japan, during the period 60: 141-167.

Vertical crustal movements in the Tohoku district in the past 75 years are discussed with reference to their tectonic implications. For this purpose, the author first compiled a map of accumulated vertical movement in the past 75 years, by making proper correction for closure. In addition, a new presentation technique utilizing a time-space domain representation of elevation changes is applied to the data. These contour maps provide an informative summary of the vertical crustal movement history in this district. From them, we see that the northeastern part of the district has subsided continuously and aseismically, with an area of significant subsidence inland at a distance about 300 km or more from the trench axis. In order to explain the mechanism of the remarkable extension of the subsiding area, the finite element method is applied to model the elastic strain field in the district. It is shown that a simple model of uniform dragging at the interface of a sinking slab does not provide a good interpretation of the inland distribution of subsidence. A modification of the conventional model is proposed which hypothesizes vertical movement of the subducting lithospheric slab under the Tohoku district.

INTRODUCTION

The Tohoku district, Japan, has been of interest to many earth scientists because of its tectonic importance as a typical island arc region (e.g., Utsu, 1971; Nagumo, 1976; Yoshii, 1977; Seno, 1978). Recent intensive geophysical research has revealed various important aspects of this district. Explosion seismic experiments, for example, have provided the detailed structure of the crust and the upper mantle (Yoshii and Asano, 1972), and micro-earthquake observations that have been carried out by Tohoku University revealed the double layered structure of deep-focus earthquakes (e.g., Hasegawa et al., 1978). These observations, as well as other kinds of data such as gravity and topography, are summarized and integrated by Yoshii (1977). Although these results are not described in the present paper, some

Fig. 1. Map of disastrous earthquakes in and near Japan {taken from the map compiled by J.M.A.). Open and closed circles represent earthquakes which occurred before and after 1900, respectively. Legend: = the trench axis, - - - - - - = the aseismic front, - - - = the volcanic front.

143

of the fundamental information is shown in Fig. 1. This is a part of the map of “Disastrous Earthquakes in and near Japan” recently compiled by the Japan Meteorological Agency (JMA). The axis of the Japan trench, the aseismic front which was proposed by Yoshii (1975) and the volcanic front are also inserted in the same figure. These extensive studies also make it possible to understand and interpret the crustal movements deduced from geodetic data. Geodetic work by the Geographical Survey Institute (previously the Land Survey Department) which began around the turn of the century in Japan provides important information on secular crustal movements of the past 70 years. A second triangulation survey was completed by 1968. In this district, this survey shows generally east-west contraction having a maximum shear (tensor) strain velocity of about 1.2 - lo-‘/yr (Nakane, 1973). Leveling surveys have been repeated three or four times in this district up until 1968 and their results show general subsidence along the Pacific coast (Dambara, 1970). These geodetic results have been understood as the effect of relative motion between the Pacific and Eurasian plates, A new revision survey of leveling which was completed in 1975, however, has shed new light on the tectonics in the district. The wealth of data accumulated allows a detailed analysis of vertical movements to be made. In particular, the present paper discusses the temporal change of the vertical movements in detail as well as the accumulated movements of Tohoku. Secondly, the vertical movements are quantitatively modelled. Dambara (1970) expressed his doubt about the interpretation of vertical movement using simple tectonic models. One of the purposes of this paper is to respond to his comments. Numerical tests are conducted for this purpose. Two possible models to interpret the leveling results based on recent seismological results and plate tectonics are proposed and discussed.

ACCUMULATED PAST 75 YEARS

VERTICAL

MOVEMENT

IN THE TOHOKU

DISTRINCT

IN THE

Vertical movements in Japan have been studied by several authors (e.g., Miyabe et al., 1965; Hayashi, 1969). Dambara (1970) recently compiled a map of vertical movement rate in Japan using the leveling data obtained up until 1968. His map provides us with a nation-wide view of movements; but it does not necessarily represent the details of local patterns. For the Tohoku district, for example, it refers to only about 35 bench marks out of more than 1000. More recently, the G.S.I. conducted new releveling all over the district for the period 1973-1975. The author referred to these latest data and compiled a new map, after network adjustment for closure errors. All of the bench marks which are located on the routes shown in Fig, 2 are considered in this study. Original data used are taken from the Annual Report of the First Order Leveling Measurement in Japan (~01s. l-19, and four suppl.

1449

,-.v

Fig. 2. Leveling routes in the Tohoku district. Arrows indicate loops for calculation closure errors. Underlined values are closure errors divided by the length of the loop.

of

~01s.) published by the G.S.I. Data compiled in these volumes are raw and unadjusted. Figure 3 compiles leveling survey epochs for each route. As Fig. 3 shows, the first (1897-1902) and the latest (1971-1975) levelings were completed in a relatively short time, so that the adjustment can be made without introducing significant errors due to crustal movements occurring during the leveling. Reference

point

Proper selection of the reference point is critical for obtaining successful results. Unfortunately, no reliable tidal station having a long history of

145

1910

1900

1920

1930

1940

1950

1960

1970

I..

I

(W - E) JI - J4 J4 xl5496 J 9 -J5466 J5466J 3 J6547- J2179 J4398-J4201 IN - S) J6960-J6006 J6006-J5496 JI -J9 J5496-J5466 J6960J3 J9 -J6547 J 8 -J3817 J5466-J2179 J 3 - 5689 5689 -J2179 J6547- 6517 6517 - J4410 J4410- J4398 J3797- J4264 J2169- 2142 2142-J2114 . J2179-J2169 . J2169- J4201

Fig. 3. Survey surveys.

* . . .

* . . .

l

.

a

v-

.

. . . .

m

.

. . *

. .

. .-

l

* .

. l

. .

HZ

l

. . . . . .

. .

.

epochs

* . I....

of each route

shown

in Fig. 2. Closed circles

are the time of leveling

recording is available in the Tohoku district. The general tendency of tidal records around Japan, however, is that the land along the Japan Sea coast seems generally stable in comparison with the Pacific coast (see Coastal Movements Data Center (1976) for reference). This suggests that a bench mark on the Japan Sea side may be used as a provisional reference. Among the bench marks along the Japan Sea coast, the southern ones were disturbed by the Niigata earthquake (1964, M = 7.5), so we should choose one in the northern part. Bench mark Jl, Noshiro or J9, Akita, may be suitable for this purpose. The tidal record at Fukaura about 50 km north of Jl shows no recognizable secular change since 1897, although the data are missing from 1939 to 1951. The leveling results between Fukaura and Jl show a negligible uplift of 0.3 mm/yr or less of Jl relative to Fukaura. Taking these facts into consideration, Jl, Noshiro, is selected as the reference point and this point is assumed to have been stationary since around the turn of the century. It should be noted that the Oga earthquake (1939, M = 7.0), which occurred 30 km away from Jl, did not affect Jl much as the post-seismic resurvey found a level change at Jl of only a few centimeters at most. Judging from this, the assumption that, Jl has been stationary for the past 75 years seems reasonable.

146 Origin time

The origin time is set at January, 1900, and all original data are adjusted linearly to this starting point. That is, the original data of the first epoch are multiplied by a certain factor so as to reduce them to the period beginning in January, 1900, assuming uniform movement in time for the first epoch. This kind of fundamental operation seems especially important as a preliminary step prior to correction for closure errors. Correction

for closure

error

Leveling data from the routes in Fig. 2 were corrected for network closure errors. Correction must be carried out with great care, as a small area that shows unusual land movement may seriously affect the entire loop after correction. The natural consolidation of alluvial plains, the static deformation accompanying large earthquakes and subsidence caused by artificial means are examples of such local effects. Taking care to exclude such unusual areas, a primary loop is made, which starts at Jl, and closes at 55496, passing through J9, 58 and 55466 on the southern route and 54 on the northern route. Displacements along the southern and northern routes are summed for the past 75 years and are compared at 55496. Their difference is attributed to uniform error along the route, for which the respective bench mark reading is corrected. In practice, the calculated error rate is 0.16 mm/km along this loop. Starting from the corrected primary loop, this procedure of adjustment is repeated from loop to loop until all the loops are corrected for the respective error rate. Figure 2 illustrates the selected loops (thin arrow lines) together with the correction values. Notice that the correction increases as we go southward. This is naturally attributed to error accumulation. The Niigata earthquake and Zyoban mining region along the Pacific coast may have contributed to the error, as well as systematic survey error. Results

A contour chart of recent vertical crustal movement is drawn after these corrections have been made (Fig. 4). This is the most recent and reliable result obtained so far. Its features may be characterized as follows: (1) The most fundamental trend is extensive subsidence along the Pacific coast. Notice that the 30 cm contour line lies on the Sanriku coast, north of Sendai. As we go southward from Sendai, however, the subsidence is not as great. This may be due to the post-seismic recovery following the ShioyaOki earthquakes (1938, see the next section) (Abe, 1977). (2) There is a large local subsidence around the Yokote basin (about 80 km in diameter). Its details will be discussed later. (3) The only significant uplift is seen near Shinjo, with a rate of about 1.3

147

-

40”

-

380

Fig. 4. Accumulated vertical crustal movement in the Tohoku district for the period 1900-1975. Contours are drawn for every 10 cm. Dashed lines of +5 and -25 cm are drawn, in addition. The dashed line near 53797 is hypothetical since there is no leveling route in that area.

mm/yr. A dashed contour line in its southern part is only hypothetical, as no leveling route is available there. This uplift zone extends southward forming a wide uplift zone along the Japan’s “backbone” mountain range (Dambara, 1970). This trend of uplift might reflect an up-warping movement of the island arc as suggested by Miyamura and Mizoue (1964), although the local subsidence around the Yokote basen diminishes the plausibility of this suggestion. (4) A considerable subsidence of 10 cm or more is observed in the southern part of the Japan Sea coast. This is assumed to be the coseismic land movement during the Niigata earthquake. In fact, its geographical distribution and amplitude fit fairly well with the surface displacement calculated using a dislocation source model (Abe, 1975; see also Fig. 10).

JSlAkitd-

J5466(Kitakamt)

(a)

J5466lKitakami)

-J 3lKamaishi)

(b) Fig. 5. a. Leveling data from J9 to 55466. Abscissa is taken along the route (this coordinate system is also used in Figs. 5b--d). Survey epochs are: (I) 1934-1897, 1900; (2) 19X1934; (3) 1966-1956 and (4) 1974-1966. b. Leveling data from 55466 to 53. (1) 19331900, (2) 1966-1933, and (3) 1974-1966. c. Leveling data from 56547 to 52179. (I) 1942-1894,1899; (2) 1956-1942; (3) 1966-1956 and (4) 1973-1966. d. Leveling data from 54398 to 54201. (I) 1939-1897, 1898; (2) 1954, 1955-1939; (3) 1967-1954, 1955 and (4) 1973-1967.

J6547(Sakata)-J2179lSendai)

-100

,

-150

I J4398(Yasudal-

J4201(lwakl)

. -50

-100

-150 -

-200

_

20 km

20, km ,

150 VERTICAL TIME-SPACE

MOVEMENT DOMAIN

IN THE TOHOKU

DISTRICT

AS SEEN ON THE

CHART

In order to understand the causes and mechanisms of vertical land movements, it is important to study their temporal variation. Kato and Kasahara (1977) introduced a suitable technique for this purpose; namely the presentation of leveling data along a route on a time-space domain chart so that crustal dynamic ch~acte~stics are shown as a twodimensiona1 pattern. From the viewpoint of plate tectonics, we should choose routes that run nearly perpendicular to the strike of the Japan trench, because they are expected to illustrate well the effect of plate interaction at the subduction zone. The following three routes are chosen on this basis: (1) JS(Akita)-J3(Kamaishi) - 242 km (the northern route). (2) J6547( Sakata)-J2179( Sendai) - 148 km (the central route). (3) J4398( Yasuda)-J4201(Iwaki) - 227 km (the southern route).

19701274~ (a)

i 340

Fig. 6. a. Vertical land displacement on the northern route (relative to J9), cumulative from January, 1900. The route is divided into two parts; J9--55466 and J5466--53. Arrows indicate the times of leveling surveys. Abscissa is taken along the route. Uplift (shaded area) is taken as positive. Unit: mm. b. Annual rate of vertical land displacement on the northern route. Uplifting sense (shaded area) is taken as positive. Unit: mm/yr.

Leveling surveys have been carried out four or five times in the past 75 years for these routes (Fig. 3). With so many data, it may be possible to determine the secular change of crustal movement in this district. All of the original data for the above three routes are shown in Figs. 5a--5d. No correction for closure to the original data is made in this part of our study. Since the observational error expected for a route of S km is 2.5 d/s mm, the maximum errors expected are 38.9, 30.4 and 37.7 mm for the northern, central and southern routes, respectively. However, for simplicity, we will disregard the possibility of errors (Kato and Kasahara, 1977). In order to make it easy to compare the contour charts, the original

152

leveling data of these routes are modified according to the following criteria. First, the reference points for each route are taken at the bench mark of the Japan Sea side, for simplicity, assuming that these points have been stationary in the past 75 years. That is, the reference points are J9 for the northern route and 54398 for the southern route. As for the central route, B.M. 6552, which is located a little inland, is taken as the reference point, since there might be natural consolidation of the Sakata alluvial plain (Dambara, 1974). Second, the origin time is again reduced to January, 1900, as in the previous section. After removing abnormal data values and editing the original data, timespace domain contour charts are made for each route. These results are shown in Figs. 6a, b for the northern route, Figs. 7a, b for the central route, and Figs. 8a, b for the southern route. Brief interpretations for each route are described in the following.

153

(b)

Fig. 7. a. Vertical land displacement on the central route (relative to J6552), cumulative from January, 1900. Unit: mm. b. Annual rate of vertical displacement on the central route. Unit: mmjyr.

The northern route Figures 6a, b show that the main feature of this route is the smooth subsidence over almost all of the route. The rate of subsidence is about 4 mm/yr at the eastern end of the route. Intensive study of Fig. 6, however, reveals that there is a relatively stable area in the western part, though it is narrow. Its movement rate is less than +l mm/yr till 1967. We can also notice that there is an area gradually inclining between this stable area and the broad subsiding area, as stated previously. As for the route from 58 to 53, Fig. 4 shows that the amount of accumulated subsidence is relatively large and un~orm, but its subsidence modes are different between J8--55466 and J5466--53. As Fig. 6b shows, the sub-

154

sidence rate from 58 to 55466 was large in the older epochs, but became smaller and there has been uplift in the latest epoch (see also Fig. 5a). On the other hand, the subsidence of J5466--53 has continued smoothly over the whole period in contrast to the former route. Recently, however, its subsidence rate has decreased. The southeastern Akita earthquake (1970, M = 6.4) which occurred just south of B.M. 5551 affected the route very locally as seen in Fig. 5a, (4) and Fig. 6b (Mikumo, 1974). The effect of larger earthquakes which occurred during 1900-1975 will be discussed later. The ten tral route Time-space domain pictures of the vertical movements along this route are shown in Figs. 7a, b. Differing from the previous route, the generally subsiding area is concentrated in the eastern part of the route. Movements west (or northwest) of 53797 are predominated by short wavelength components

1960

1300

1910

1320

1930

1350

1960

1970 1374

Fig. 8. a. Vertical land displacement in the southern route (relative to J4398), cumulative from January, 1900. Unit: mm. b. Annual rate of vertical land displacement on the southern route. Unit: mm/yr.

and recent uplift. This uplift Fig. 4), and it seems that this This uplift might be explained B.M. 6552. Data are insufficient The southern

movement has its center near 53817 (see uplifting area has been expanding eastward. by local subsidence of the reference point to choose between these two possibilities.

route

The general trend of movement of Fig. 8a is represented by subsidence in the eastern part and relative stability or slight uplift in the inner part. This is similar to that observed on the central route. The most marked feature in this route is that the subsidence seen on the first survey epoch was compensated in the second epoch. This might be due to the after effect of the large Shioya-Oki earthquakes (1938, M = 7.1-7.8) which occurred just before

156 Land

Subsidence

I

Along

I

The

Pacific

Coast

I

0 c

1 -10

-20

-30

2 1900

1910

I920

1930

1940

IE

Fig. 9. Vertical displacement at the eastern end of the three routes relative to the western end. Folded lines are the tide gauge records at the Pacific coast.

the first revision survey of 1939, as pointed out by Abe (1977). Figures 5d and 8b show, however, that this recovery ends around 1968 and subsidence predominates over almost the entire route at the latest survey epoch, though observational errors and the movement of the provisional reference point make it difficult for us to conclude whether it is real or not. Rapid but very local subsidence is recognized at the eastern end, which seems to be due to the Zyoban mining region and the hot spring area. Although further features might be discovered and interpreted by the intensive study of these figures, we will leave this for future work and focus our attention on the large scale tectonics dominating this district. From the viewpoint of plate tectonics, one might be inclined to attribute the subsidence extending along the Pacific coast to the dragging effect of an oceanic plate. Dambara (1970), however, doubted this simple interpretation, as the coast is located far (200 km or more) from the axis of the Japan trench. One possible explanation for this subsidence is the effect of decoupling as proposed by Kanamori (1972). Numerical tests of this idea using the finite element method will be made in the following section. Before ending this section, benchmarks at the eastern end of the routes are compared with tidal records along the Pacific coast (Fig. 9). Solid lines are the tide gauge records at Kamaishi and Onahama, located along the Pacific coast. Although oceanographic and meteorological conditions will strongly affect short-period sea-level changes, long term variations of tidal records may faithfully represent land movement. The record at Kamaishi, which is

157

near B.M. 53, shows rapid subsidence of the Sanriku coast at the rate of about 1 cm/yr, a considerably larger value than that of the leveling data, i.e. about 4 mm/yr. Unfortunately, we do not have sufficient data to identify the real reason for such a large difference. However, the sense of the tidal record seems to show good consistency with that of leveling. Movement at Onahama which is located near B.M. 4208, shows fairly good agreement with leveling data. DISCUSSION

Let us first estimate the seismic displacement fields of major earthquakes in and around this district as a possible contribution to the recent crustal movement. The vertical surface displacements caused by major earthquakes (M > 7.5) which occurred in the past 75 years are calculated using the program written by Matsu’ura and Sato (1975) based on an elastic half space model (Mansinha and Smylie, 1971). Table I lists source parameters used for the calculations. The pattern of surface displacements shown in Fig. 10 depends critically on the source geometry; if we change the strike or dip angle, for example, the displacement field changes considerably. Nevertheless, it is evident that the accumulated surface displacement cannot be as large as the movement observed by leveling. In particular, an area of superficial local subsidence in the northern part is not affected by these big earthquakes (see also Fig. 4). Further information from seismicity data shown in Fig. 1 reveals that the spatial patterns of historical earthquake generation along the Japan trench is different between 38-40”N and other places. This is justified by Ichikawa (1976) using the recent shallow seismicity data. Although there could be considerable uncertainty in the epicenter determination of earlier earthquakes, this difference seems real judging from other evidence; for example, the sea-bottom topography abruptly changes at 38”N (Honza, 1974), so that it may reflect a difference in tectonics. The above stated seismicity features, together with other kinds of data such as leveling, demonstrate the interesting nature of the tectonics of the northern Tohoku district. It is clearly worthwhile to investigate various possible causes of land movement in this area, especially from the standpoint of plate tectonics. Fortunately, the leveling route from J9 to 53 (the northern route) extends across this area, so that it is useful to discuss and analyse the data of this route. Figure 11 shows the vertical displacement along this route for the respective periods 1900-1975 and 1934-1975, which is practically a projection of a reference line perpendicular to the trench axis. In order to eliminate unnecessary local movement, the data from every fifth bench mark is used in the figure. As shown in Fig. 4, local but marked subsidence amounting to 10 cm or more occurred around the Yokote basin during the first period only (19001934). There are two suspicious earthquakes that might have contributed to

1933, 1936, 1938, 1938, 1938, 1938, 1960. 1964, 1968,

Sanriku-Oki Kinkasan-Oki Shioya-0 ki 1 Shioya-Oki 2 Shioya-Oki 3 Shioya-Oki 4 Sanriku-Oki Niigata Tokachi-Oki

Mar. Nov. May Nov. Nov. Nov. Mar. Jun. May

M, = surface wave magnitude. from: (1) Kanamori (1971b); (1971a).

Date

Source

Earthquake

I

parameters

TABLE

8.3 7.7 7.4 7.7 7.8 7.7 7.5 7.5 8.0 39.2 38.2 36.58 36.97 37.24 37.33 39.8 38.40 40.84

?N)

Location

144.5 142.2 141.34 141.71 141.75 142.18 143.5 139.26 143.22

(‘=E)

h

90 80 70 70 70 80 110 81 24

(‘NW)

Dip direction

Depths are taken from the earth’s surface (2) Yamashina (personal communication,

3 3 23 5 5 6 21 16 16

M,

normal thrust thrust thrust thrust normal thrust thrust thrust

Fault motion

185 70 75 100 100 85 60 80 150

(km’)

Fault area

X 100 X 48 X 40 x 60 x 60 x 45 x 40 x 30 x 100

0 44.4 20 20 20 20 0 0 0

(km)

3.3 1.6 2.7 2.3 1.6 2.0 1.1 3.3 4.1

Depth

Dislocation (m)

(2) (3) (3) (3) (3) (2) (4) (5)

(1)

to the top of the fault plane. These fault parameters are taken 1977); (3) Abe (1977); (4) Abe (1975) and (5) Kanamori

45 19 10 10 10 80 66 56 20

(“)

Dip angle

159

,

IOOkm

Fig. 10. Static surface displacements due to large earthquakes which occurred within the past 75 years. Unit: cm.

the subsidence: the Riku-u earthquake (1896, M = 7.5) which activated the Senya fault near the center of the subsidence area (Kochibe, 1896), and the Ugo-Senboku earthquake (1914, M = 6.4) which occurred just west of the route near B.M. 5766-5757. However, the former earthquake occurred four years before the first survey, suggesting that any post-seismic subsidence would have been very small after the first survey. For example, the postseismic subsidence of the Kanto earthquake (1923, M = 7.9) increased by no more than a few centimeters after the first four years following the earthquake (Scholz and Kato, 1978). Also, the Ugo-Senboku earthquake is

160

350

250

300

220 km

DISTANCE

FROM

TRENCH

AXIS

Fig. 11. Vertical displacement of the period 1900-1975 and 1934-1975 in the northern route, projected onto a line perpendicular to the trench axis. Dashed line corresponds to the place where the Senya fault cuts this route.

obviously too local to explain such wide subsidence, but may possibly have caused a local subsidence as pointed out by Hayashi (1969). Alternatively, one might attribute this subsidence to plate motion. However, the size of this region and its remoteness (300-350 km) from the trench axis seem contrary to this suggestion. If this inland subsidence was produced by plate motion (such as interseismic subduction or seismic slip during the 1933 earthquake), it would appear on a more regional scale. From these considerations, the author suspects this subsidence to be tectonic movement of local origin, with a small contribution from the post-seismic movement of the 1896 earthquake. It’s origin may be shallow, lying perhaps in the crust. More extensive studies of the crustal structure and local tectonics are needed to substantiate this hypothesis. We now turn to an examination of the larger scale, regional features of the tectonics of the Tohoku district. In order to filter out the local subsidence discussed above, we shall take the most recent period 1934-1974, which seems to represent predominantly secular tectonic movement. Using the finite element technique, we now attempt to find a model that will fit the observations well. Applications of the finite element technique

161

1‘ V. F.

Fig. 12. The finite-element ratio and Young’s modulus,

grid used in this study. respectively.

T AS. F.

u and E are assumed

values of Poisson’s

to this kind of problem have been discussed by many authors (e.g., Jungels and Frazier, 1973; Shimazaki, 1974). The present author will follow the procedures used by Shimazaki (1974). The problem is a static, purely elastic, two-dimensional one in plane strain. Figure 12 shows the finite element network designed for the continental side of the upper surface of a sinking slab. The elements are divided into three parts, each of which is assigned and appropriate elasticity, considering recent geophysical results. The Tohoku district is characterized by a highly attenuating low velocity zone in the upper mantle (e.g., Utsu, 1971; Yoshii and Asano, 1972). Therefore, an elasticity contrast of about 36% relative to the adjacent area is assumed for this zone, considering the velocity contrast determined from observations (Yoshii and Asano, 1972). This parameter is provisional, of course, so that the calculation in the following is only to a first order of approximation. On these assumptions, we calculate the surface displacement by taking plausible boundary conditions at the plate boundary. The upper surface of the medium in Fig. 12, which corresponds to the earth’s surface, is assumed free, and the other boundary surfaces are fixed except the portion having a prescribed displacement. The boundary representing the plate interface is divided into thirteen unit segments as shown in Fig. 12. The lowest segment corresponds to a depth-range 115.2-120.7 km, whereas the uppermost one to 41.0-47.3 km. Surface displacements are calculated by giving a unit displacement of arbitrary direction to each of these segments.

162

Tangential displacement model The first case represents the simplest plate model, where purely tangential displacements are assigned to each division. Surface displacements due to a prescribed unit displacement on each segment are superposed with suitable weights. If we need a solution for a non-uniform distribution of displacement at the interface, we may weigh the respective contributions to that the summed displacements fit the observations well. This can be solved by an inverse method (Shimazaki, 1974). Figure 13, A illustrates the non-uniform model obtained by this method, which shows fairly good agreement with the observations even in regard to their details. However, the amphtude distribution at the interface is physically unrealistic as seen in the same figure. On the other hand, B and C in the same figure are uniform tangential displacement models. Model B assumes a 0.7 m displacement at the interface to a depth of 120 km, whereas model C assumes 1.5 m to 70 km. Model B is similar to that obtained by Shimazaki (1974) in eastern Hokkaido, and shows fairly good agreement with the observations except for the area between 300-350 km from the trench axis. This model suggests 2 cm/ TANGENTIAL

350

DISPLACEMENT

300

MODEL

250

220 km

Fig. 13. Tangential displacement models. Circles connected by lines are the observed displacements for the period 1934-1974, the same as shown in Fig. 11. Model A is the solution by inversion. Model I3 and C are uniform tangential displacement models. Prescribed displacements at the interface are 0.7 m to a depth of 120 km for model B, and 1.5 m to 70 km for model C.

163

yr as the dragging rate. This value seems reasonable judging from the speed of the subducting oceanic plate. Recent seismological studies, however, point to some difficulty with this model. Yoshii (1977) concluded that there would be no interaction on the interface below 70 km. If this is the case, we must only prescribe the displacement above 70 km such as is done in model C. However, such models cannot explain the subsidence extending 300 km or farther from the trench axis as seen in model C. Consequently, each of these models has some defects, to the extent that we consider the leveling data to reflect pure tangential displacement at the interface. Two alternatives are proposed to overcome this difficulty: (1) The inland subsidence is not explained by the boundary conditions at the interface. Some shallower sources or special material properties of the shallow part could be hypothesized to account for the inland subsidence. For example, some unknown geological effects of crustal and upper mantle layers, or some special response of the crust due to its distribution of elastic properties are possible explanations. These possibilities, however, are not studied further here. (2) The boundary condition might not involve purely tangential displacement, but may also have some vertical component. This possibility is easily tested by applying the finite element technique again. Let us examine this possibility in detail in the next section. Decoupling model Yoshii (1977) recently compiled various kinds of geophysical information for the Tohoku district. He proposed that the undersurface of the continental plate beyond the aseismic front is decoupled from the sinking slab. In his model, therefore, it is only the shallower part of the interface which is subject to dragging. If this is the case, movement of the continental side beyond a certain distance from the trench axis would not have a tangential component. If we suppose, however, that the slab does not continue to move parallel to the shallow interface dip direction, but tends to sink, we can also expect a vertical component of movement of the continental plate. This mechanism is more or less in harmony with the decoupling hypothesis of Kanamori (1972), which seems to suggest a downward component of the continental side. This case is modeled by introducing a downward displacement of appropriate amplitude to each grid element deeper than the aseismic front as a boundary condition, in addition to a tangential displacement for shallower divisions; that is the 12-th segment and the shallower half of ll-th segment. A method similar to that described in the previous section is used in this calculation. Surface displacements resulting from the prescribed unit displacement (vertical for deeper segments and tangential for shallower ones) are superposed with proper weighting. Two models are presented in Fig. 14,

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DECOUPLING

350

MODEL

300

250

220 km

Fig. 14. Decoupling models. Model A is the solution by inversion, whereas model B is obtained by trial and error. Values with arrows indicate the prescribed vertical displacements at the interface. Other values are tangential displacements.

A being obtained by the inversion technique, and B by trial and error on the basis of A. Model A does not fit the observations very well. Yet, qualitatively, both of these models explain the inland subsidence. In particular, model B shows a remarkable fit with the observations and is schematically given in Fig. 15. It suggests that the observed subsidence can be explained by a downward displacement of 60 cm (2 cm/yr) just beneath and a little west of the volcanic front, and a tangential displacement of 1.3 m (4 cm/yr) at the shallower part of aseismic front. The rate of the tangential displacement seems reasonable judging from the plate tectonics estimate of the relative plate motion (8-9 cm/yr, e.g., Le Pichon, 1968; Minster et al., 1974).

100 km

Fig. 15. Schematic diagram of decoupling model B in Fig. 14. Arrows are the assumed displacements at the interface.

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As stated previously, the models given above are, of course, provisional, so that the real mechanism is still uncertain. However, the decoupling model hypothesized by Kanamori (1972) may be the most attractive mechanism as far as the leveling data are concerned. Honza (1974) indicated that the depth of the wave-cut base at the shelf edge in this district is 400 m between 38”N and 40”N, 200 m deeper than in other places. This suggests that this area is sinking, on a geological time scale, relative to the other places. This is also in accord with geodetic data. If we assume the constant subsidence rate of 4 mm/yr deduced from leveling, the subsidence started about 50,000 yrs ago.

CONCLUSIONS

Geodetic surveys in the past 75 years have revealed the general trend of crustal movements in the Tohoku district, as well as various local movements such as earthquake related movements. The general pattern of vertical movement has been interpreted in the tectonic framework of an island arc. Its fundamental feature is that the Pacific coast subsides steadily as subduction proceeds along the trench system off the Pacific coast. Land subsidence along the Pacific coast, especially the Sanriku coast, is very pronounced in this district. Its rate amounts to 4 mm/yr and is consistent with the rate of movement of the sinking slab. We have not been able to explain the observations quantitatively in terms of a purely subducting slab model. In the northern part of this district, a remarkable subsiding area reaches 350 km or more from the trench axis even if localized subsidence of the Yokote basin is eliminated. To overcome this difficulty, we introduced a decoupling model that entails 2 cm/yr of downward displacements of the oceanic slab under the island. This model not only shows fairly good agreement with leveling data but also is in accord with seismological and geomorphological evidence, although the actual cause of inland subsidence is still uncertain. Further geodetic work including not only leveling but also trilateration, gravity measurements and so on would reveal the mechanism in more detail. ACKNOWLEDGEMENTS

The author wishes to express his sincere thanks to Professor Keiichi Kasahara of the Earthquake Research Institute, University of Tokyo, for suggesting this problem, stimulating discussion and critical reading of the manuscript. Thanks are also due to Dr. W. Thatcher and Dr. P. Somerville for critical reading of the manuscript. Mr. T. Arai of the Geographical Survey Institute kindly furnished valuable leveling data at the author’s frequent requests. Dr. K. Shimazaki of the Earthquake Research Institute, and Dr. M. Matsu’ura of Geophysical Institute of

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the University of Tokyo provided the computer programs for the finite element calculation and the calculation of surface displacement due to multiple faulting, respectively. The author would like to express his great gratitude for their help. Thanks are also due to Dr. T. Yoshii of E.R.I. for his helpful discussions. The computations involved were done at the computer centers of the University of Tokyo and the Earthquake Research Institute. REFERENCES Abe, K., 1975. Reexamination of the fault model for the Niigata earthquake of 1964. J. Phys. Earth, 23: 349-366. Abe, K., 1977. Tectonic implication of the large Shioya-Oki earthquakes of 1938. Tectonophysics, 41: 26Q-289. Coastal Movements Data Center, 1976. Tables and graphs of annual mean sea level along the Japanese coast 1894-1975.37 pp. Dambara, T., 1970. Synthetic vertical crustal movements in Japan during the recent 70 years. J. Geod. Sot. Jpn., 17: 100-108 (in Japanese). Dambara, T., 1974. Vertical movement near Sakata and Shinjo. Rep. Cood. Corn. Earthq. Pred., 11: 62-63 (in Japanese). Hasegawa, A., Umino, N. and Takagi, A., 1978. Double-planed structure of the deep seismic zone in the northeastern Japan arc. Tectonophysics, 47: 43-58. Hayashi, T., 1969. A study on the vertical movements of the earth’s crust by means of the precise leveling. Bull. Geogr. Surv. Inst., 15: l-67. Honza, E., 1974. On crustal units - crustal movement of the Pacific coast of northeast Japan --. Mem. Geol. Sot. Jpn., 10: 55-61 (in Japanese). Ichikawa, M., 1976. Seismicity gaps in and near Japan. Proc. Symp. Earthquake Prediction Res., pp. 91-96 (in Japanese with English abstract). Jungels, P.H. and Frazier, G.A., 1973. Finite element analysis of the residual displacements for an earthquake rupture: source parameters for the San Fernando earthquake. J. Geophys. Res., 78: 5062-5083. Kanamori, H., 197Ia. Focal mechanism of the Tokachi-Oki earthquake of May 16, 1968: Contortion of the lithosphere at a junction of two trenches. Tectonophysics, 12: l-13. Kanamori, H., 1971b. Seismological evidence for a lithospheric normal faulting - the Sanriku earthquake of 1933. Phys. Earth Planet. Inter., 4: 289-300. Kanamori, H., 1972. Mechanism of tsunami earthquakes. Phys. Earth Planet. Inter. 6: 346-359. Kato, T., and Kasahara, K., 1977. The time-space domain presentation of leveling data. J. Phys. Earth, 25: 303-320. Kochibe, T., 1896. General report on the disaster caused by the large Akita earthquake. Rep. Imp, Earthquake Invest. Comm., 11: 75-83 (in Japanese}. Le Pichon, X, 1968. Sea-floor spreading and continental drift. J. Geophys. Res., 73: 3661-3697. Mansinha, L. and Smylie, D-E., 1971. The displacement fields of inclined faults. Bull. Seismol. Sot. Am., 61: 1433-1440. Matsu’ura, M. and Sato, R., 1975. Displacement fields due to the fault. Zisin, 28: 429434. Mikumo, T., 1974. Some considerations on the faulting mechanism of the southeastern Akita earthquake of October 16, 1970. J. Phys. Earth, 22: 87-108. Minster, J.B., Jordan, T,H., Molnar, P. and Haines, E., 1974. Numerical modeling of instantaneous tectonics. Geophys. J.R. Astron. Sot., 36: 541-576.

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