三陸海岸は典型的なリアス式海岸であり、大地の長年にわたる沈降によって形成 されたといわれています。東北日本弧の前弧（太平洋側）のGPSデータは、地震間 地震時の両方で沈降を示し、この地域の上下動が地震サイクルでの和がゼロでなく 負になっていることを物語っており、沈降海岸の地形とも調和的です。一方西南 日本弧では地震サイクル毎に室戸岬などの突端は隆起してゆくことが知られています。 この違いを理解するために、島弧に直交する方向の速度断面をとり、鉛直および 水平速度を海溝からの距離の関数として表し、沈み込み帯の速度場の説明に従来 用いられているすべり欠損モデルの予測との比較を行いました。 その結果西南日本では上下、鉛直ともほぼ観測された速度はモデ ルに一致、一方東北日本では水平速度はモデルと良く一致するものの、鉛直速度 に関してはモデルは太平洋岸では隆起を予測するのに現実は沈降しており、鉛直 速度が有意に負にずれることが見いだされました。その原因として本論文では造 構性侵食(subduction erosion 又はtectonic erosion)との関連を論じています。 これは1973年に小松左京の「日本沈没」で日本を沈没させた過程がゆっくりでは あるが現実に進行していることを示唆しています。

Observation of tectonic erosion in a subduction zone has been difficult as it leaves little geological and geophysical evidence. Three-dimensional velocity profiles of crustal movement obtained by Global Positioning System (GPS) across the northeastern Japan (NEJ) and southwestern Japan (SWJ) agree well with those predicted by the elastic loading of the subducting slabs. However, vertical velocities in the NEJ forearc show significant negative deviation (relative subsidence). This may indicate loss of material at the plate interface that can be attributed to the erosion of the upper plate by the underthrusting slab (basal subduction erosion). The estimated rate (15 mm/yr down to a slab depth of 90 km) is somewhat faster than the geological average; the erosion speed may be variable being controlled by the surface roughness of subducting slabs.

日本で発生する地震の頻度に季節変化があることは百年前の大森房吉の時代から 現在に至るまで多くの研究者が指摘してきました。中でも顕著な南海・相模・ 駿河トラフ沿いのプレート境界地震の発生時期の秋冬への集中に関しては Ohtake and Nakahara (1999) がその統計的有意性を確認し、大気圧の冬季の上昇 が海溝のプレート境界断層のクーロン破壊応力(CFS)に及ぼす影響を見積もりまし た。しかし計算されたCFSの変化の値はあまりにも小さく、大気圧が地震発生へ及 ぼす影響はほとんど無いと結論しています。本研究では東北日本のGPS点に季節変 化をもたらす積雪荷重が日本列島の直下型地震の発生に及ぼす影響をCFSを用いて 評価し、宇佐美(1996)にまとめられている過去の被害地震の発生時期の季節性と 比較検討しました。脊梁山脈の西北側を中心に日本列島に沿って分布する積雪帯は その直下の地震断層の法線応力を数kPa増加させ、CFSを下げることにより地震の発 生を妨げます。その結果雪どけ時期の春夏により多くの地震が発生することが期待 されます。過去のM7以上の直下型地震から積雪地域で発生したものを抽出して発生 月の分布を見ると、６月頃を極大期として発生頻度に数倍の変動が見られます。こ れは積雪荷重の消長に伴うCFS変化から予測される変動量と調和的で、地表の荷重 の季節変化が地震発生をコントロールするという興味深い現象の観測例と考えられます。

Snow load along the western flank of the backbone range of the Japanese Islands causes seasonal crustal deformation. It perturbs the interseismic strain buildup, and may seasonally influence the seismicity in Japan. Intraplate earthquakes in northeastern Japan occur on reverse faults striking parallel with the snow-covered zone. In central and southwestern Japan, they occur on strike-slip faults striking either parallel with, or perpendicular to the snow cover. The snow load enhances compression at these faults, reducing the Coulomb failure stress by a few kPa. This is large enough to modulate the secular stress buildup of a few tens of kPa/yr. Past inland earthquakes with magnitudes >7.0 that occurred in regions covered with snow in winter, tend to occur more in spring and summer than in autumn and winter, while those in the snow-free regions do not show such variation. Although its statistical significance is not strong due to limited number of past earthquakes, it suggests that the spring thaw enhances seismicity beneath the snow cover.

国土地理院の村上亮氏のグループによって発見されたGPSデータ中に見られる年周 変動は、国内外の多くの研究者の関心を引きました。私の論文では年周変動の主な 原因は海溝ではなく陸上に分布する積雪の荷重であると断定しています。東北日本 を日本海側と太平洋側に分けると、日本海側の基線には冬季に基線長が短縮する顕 著な季節変動が見えますが、太平洋側には明瞭な季節変動が見えない、あるいは見 えても冬季に基線長がわずかに伸張するという逆センスを示します。一方東北日本 全体に冬季の沈降が顕著に見えます。これらのことから年周変動の原因が積雪にあ ることが示唆されます。論文では、GPS点の季節変動成分から冬季と夏季の位置の差 を求め、それを積雪による変位と考え、グリーン関数を用いて荷重分布を推定し、 さらに平均積雪密度を仮定して荷重を積雪深度に換算し、アメダス積雪計のデータ と矛盾がないことを示しています。積雪荷重は定性的に日本海溝での逆断層のすべ りを促進しますが、その大きさはせいぜい数hPa程度で地震発生の季節性をもたらす にはいささか小さすぎるようです。

Distinct periodic variation with annual frequencies are often found in the time series of continuous GLobal Positioning System (GPS) site coordinates in northeastern Japan. They show maximum arc-normal contraction of a few millimeters as well as maximum subsidence of 1 to 2 centimeters, both in March. In northeastern Japan, it shows heavily on the western flank of the backbone range, attaining a maximum depth of several meters in March. When observed snow depths were compared with the load distribution estimated from the GPS data, the surface loads caused by the snow were found to be largely responsible for the annual displacement of GPS sites. The snow load modulates secular strain buildup in northeastern Japan due to the Pacific Plate subduction, but its relevance to the seasonal change of earthquake occurrences remains uncertain

Distinct periodic variations with annual frequencies are often found in the ti me series of continuous Global Positioning System (GPS) site coordinates in northea stern Japan. They show maximum arc-normal contraction of a few millimeters as well as maximum subsidence of 1 to 2 centimeters, both in March. In northeastern Japan, it snows heavily on the western flank of the backbone range, attaining a maximum depth of several meters in March. When observed snow depths were compared with the load distribution estimated from the GPS data, the surface loads caused by t he snow were found to be largely responsible for the annual displacement of GPS sit es. The snow load modulates secular strain build-up in northeastern Japan due to the Pacific Plate subduction, but its relevance to the seasonal change of earthquake occurrences remains uncertain.

The GPS Earth Observation Network (GEONET), the nationwide continuous GPS arra y run by the Geographical Survey Institute (GSI), Japan, has been useful as a sens or for secular (1) and earthquake-specific (2,3) crustal deformation. These GPS site coordinat es often show conspicuous seasonal variations in addition to interseismic secular movemen ts. Recently, Murakami & Miyazaki (4) found that the seasonal signals are coherent i n phase to a large extent and their amplitudes are systematic in space. They fixed a station in central Japan (Komatsu, Fig. 1) and showed that the directions of the annual signals rel ative to Komatsu coincide with the plate convergence at the Japan Trench and that their a mplitudes are larger where secular velocities are faster. These features suggest an unfor eseen possibility that the plate velocity or the coupling strength at depth changes an nually, i.e. faster subduction or stronger coupling occurs in winter.

Murakami & Miyazaki (4) confirmed that the annual signals are consistent for d ifferent receiver and antenna types, and for the solutions with different software packag es with and without the estimation of atmospheric delay gradients (5). They further confirm ed that similar annual signals exist in the data from the Japanese domestic very long ba seline interferometry (VLBI) observations (6). Thus, despite the lack of physical expl anation for the seasonal variations, they suggested that the signals are real. Here I inves tigated whether snow accumulation in northeastern Japan can provide a sufficient surface load to reproduce the necessary elastic deformation of the solid Earth to account for the GPS vari ations. Such a finding would thus serve as an independent confirmation of the reality of the signal.

Daily solutions of the GEONET GPS site coordinates relative to the central sta tion at Tsukuba, Ibaraki (Fig. 1), were taken from the GSI website (www.gsi.go.jp) for n ortheastern Japan covering the period 1998.9 to 2001.0. The data are based on a routine ana lysis strategy (7) of GSI and are essentially of the same quality as the 1996 to 1999 data used by Murakami & Miyazaki (4). They fixed the Komatsu station (Fig. 1) because its secular vel ocity represents that of the Eurasian Plate. Here, however, I considered pairs of GPS points that represent the western and eastern sides of the island arc, and compared their ba seline length time series.

The baselines on the Japan Sea side have large annual components: they shorten by a few millimeters in winter (Fig. 2B,E), a result consistent with (4). On the other h and, seasonal signatures are smaller on the Pacific side of the arc (Figure 2A,D) and have the opposite sense (shortening in summer). Such a contrast across the backbone range is seen for most pairs of baselines. If the annual signal reflects changes in the convergence ra te or the coupling strength at the Japan Trench, its amplitude would be proportional to th e secular shortening rate irrespective of which side of the arc the baseline lies. Anothe r feature not mentioned in (4) is the annual signals in vertical components (Fig. 2C,F). Most of the sites subside relative to Tsukuba in the winter, and the amplitudes, up to ~2 cm peak- to-peak, are larger along the backbone range than along the coasts. Neither faster subductio n nor stronger coupling predicts such a subsidence pattern for the arc. These feature s make the trench-origin mechanisms untenable.

Four seasons characterize the environment in Japan. In winter, cold and dry a ir over Siberia becomes humid as it travels across the Japan Sea, leaving heavy snowfall s as it collides with the backbone range of the northeastern Japan. Snow mainly falls o n the western side of the arc but the amounts vary from place to place. The deepest s now, seen along the western flank of the backbone range, starts to accumulate in late autu mn reaching a few meters deep in March; it then disappears in May (Fig. 1) except at the highe st peaks. Loads on Earth’s surface cause subsidence beneath and around the load, along wi th horizontal deformation such that the land shortens beneath the load and extends outside of it. Snow loads distributed along the western half of the arc would cause crustal deformat ion qualitatively consistent with the GPS baseline data (Fig. 2), arc-normal crustal shortening beneath the snow cover (Fig. 2B,E), and smaller extension outside the cover (Fig . 2A,D). It would also cause the subsidence whose maximum lies below the snow load center (F ig. 2C,F).

Next, I fixed an arbitrary station, and modeled each component of the relative position time series of 88 GPS points in northeastern Japan with the linear, annual and biannu al terms (8). I discarded 13 sites (9) whose root-mean-squares of the post-fit residuals excee ded 4 mm (horizontal) or 15 mm (vertical). Then, I obtained instantaneous values of the periodic components on 15 March (relative to 15 August) for all the sites (Fig. 3) and es timated the load (heights of the water columns above ground) on each of the rectangular area s as large as 0.5 o in latitude and 0.75 o in longitude covering the land area in Fig. 3 that best explained the observed winter-summer site displacements in a least-squares sense (10). I simu ltaneously estimated the translation of the whole network to ensure that the obtained loads were free from the fixed-point problem. To calculate site displacements due to a unit loa d on an elastic half space, I used the formulation by Farrel (11), 30 GPa for rigidity a nd 0.25 for Poisson’s ratio. Typical formal errors of the estimated load were around 20 to 25 cm, and the post-fit residuals of the input data were 1.3 mm, 0.9 mm, and 2.9 mm for the north, east, and up components, respectively.

In Fig. 3, some stations have anomalously large residuals, a part of which mig ht be explained by localized high snow masses often found over the high mountains. No ntheless, the observations agree with the calculated displacements. To convert the load i nto snow depth, I needed data for average snow density, which can be obtained only by fie ld observations of snow cross sections. Such observations have been carried out at Mount Zao (Fig. 1D), and Yamaya et al. (12) report that the average snow densities there d uring the 1999 to 2000 winter increased with time, i.e. 0.30 to 0.32 g/cm3 from January to February, 0.42 g/cm3 in late March, and 0.50 to 0.53 g/cm3 from the end o f April to May.

REFERENCES

• S. Miyazaki, K. Heki, J. Geophys. Res. 106, 4305 (2001).
• H. Tsuji, Y. Hatanaka, T. Sagiya, M. Hashimoto, Geophys. Res. Lett. 22, 1669 (1995).
• K. Heki, S. Miyazaki, H.Tsuji, Nature 386, 595 (1997).
• M. Murakami, M. S. Miyazaki, Geophys. Res. Lett. in press.
• D.S. MacMillan, Geophys. Res. Lett. 22, 1041 (1995).
• R. Ichikawa et al., Proceedings of the Third Joint Meeting of U.S.-Japan Natu ral Resources Panel on Earthquake Research (2001).
• S. Miyazaki, T. Saito, M. Sasaki, Y. Hatanaka, Y. Iimura, Bull. Geog. Survey Inst. 43, 23 (1997).
• The annual variation curve is asymmetric about the peak. For example, the sub sidence in winter is somewhat slower than the uplift in spring (Fig.2C, F), which can be mo deled by combining annually and biannually changing terms. It was also confirmed that th e results are not dependent on the particular station chosen as the fixed point.
• The discarded stations mostly belong to the first generation GPS points (esta blished in 1994) of GEONET and are not concentrated in a particular area. They had larger post-fit residuals than the newer points.
• A weak continuity constraint was imposed to stabilize the solution so that t he difference of the loads of the adjacent rectangles is 0 +/- 20 cm (or +/- 50 cm for the dep th of snow as dense as 0.4 g/cm3).
• W.E. Farrel, Rev. Geophys. Space Phys. 10, 761 (1972).
• M. Yamaya et al., Tohoku J. Natural Disaster Sci. 36, 171 (2000).
• Japan Meteorological Agency, Monthly report of Japan Meteorological Agency, vol. 3, No. 5 (2000).
• Because AMeDAS stations need public electricity and communication lines, the y are generally located in inhabited lowlands. This may have negatively biased observ ed snow depths, and would partly explain the apparent absence of snow on the Pacifi c side in Fig. 4A.
• National Astronomical Observatory (ed.), Chronological Scientific Tables 74 (Maruzen, Tokyo, 2000).
• T. van Dam et al., Geophys. Res. Lett. 28, 651 (2001)
• P. Sillard, Z. Altamimi, C. Boucher, Geophys. Res. Lett. 25, 3223 (1998).
• F. Omori, Pub. Earthquake Investigation Comm. 8, 1 (1902).
• K. Mogi, Bull. Earthq. Res. Inst. 47, 419 (1969).
• M. Ohtake, H. Nakahara, PAGEOPH 155, 689 (1999).
• R.S. Stein, Nature 402, 605 (1999).
• S.S. Gao, P.G. Silver, A.T. Linde, I.S. Sacks, Nature 406, 500 (2000).
• K. Heki et al., J. Geophys. Res. 104, 29147 (1999).
• I thank Makoto Murakami, who first reminded me of the geophysical importance of the annual signals. I also thank Tetsuya Iwabuchi for providing AMeDAS snow depth d ata, and Shin’ichi Miyazaki for reviewing the earlier version of the manuscript.

26 March 2001; accepted 31 May 2001

Fig. 1. (A to C) Time series of snow depth during the 1999 to 2000 winter season at three points shown in (D) by squares drawn with bolder lines (tick marks in the horizo ntal axes show months). Other squares in (D) show the maximum snow depths in the 1999 to 2000 winter obtained at the AMeDAS sites (13). Only sites with maximum depths of >30 cm are plotted. In (D), tectonic plates and their boundaries are shown [na, North American Plate; am, Amurian Plate (23); pa, Pacific Plate; ph, Philippine Sea Plate]; lin es connecting the white circles are the baselines whose changes in lengths are plotted in Fig. 2.

Fig. 2. Time series, covering the period 1998.9 to 2001, of the baseline lengths on the eastern (A and D) and the western (B and E) sides of northeastern Japan. (C and F) Vert ical position of the Naruko and Shizukuishi stations, respectively, relative to Tsuku ba, Ibaraki, far to the south (Fig. 1D). Gray dots show daily solutions; solid curves are be st-fit lines assuming periodic (annual and biannual) and linear changes.

Fig. 3. Values of the periodic terms of the vertical (A to C) and horizontal (D to F) coordinates on 15 March relative to 15 August [(B) and (E)], those calculated fr om the estimated loads distribution [(A) and (D)] and their differences [(C) and (F)]. Error ellipses attached to the residual vectors show 1 sigma uncertainties of the obse rved vectors. Translation of the whole network, estimated together with loads, is added to the observed vectors to make them absolute.

Fig. 4. (A) Snow depth data at the AMeDAS (13) sites on the middle day of March 2000. (B) Snow depths converted from the loads estimated by the GPS data. The average snow density was assumed to be 0.4 g/cm3.

Miyazaki & Heki (2001)の続編、同様の議論を西南日本から中部日本に 広げたもの。すべり欠損による陸側プレートの弾性変形は、やはりプレート 運動モデルと熱モデルからくるカップリング強度を仮定してアプリオリに求 めていますが、陸側プレートが西日本のアムールプレートから東日本の北米 プレートにこの地域で遷移するため、陸側のプレート内変形を考慮しつつすべ り欠損による弾性変形が正確に求められるように計算に工夫しています。中部 日本の沖合のプレート収束帯では海側プレートがフィリピン海プレートから伊 豆マイクロプレート（駿河トラフと銭州海嶺に囲まれた地域）に変わり、さら に陸側プレートがアムールから北米に変わる影響で、東にゆくほどプレート収 束速度が遅くなります。たとえば東海地震の想定震源域では、四国や紀伊半島 沖の年間6cmと比べておよそ三分の一の約2cm/年となっており、東海地域で地震 の繰り返し周期が長いことがこれで説明できます。また日本列島をアムール プレート側と北米プレート側に色分けしてみると、ちょうど1600年に天下分け 目の戦いが東軍と西軍の間で行われた関が原のあたりが境界になるところが 興味を引きます。この論文でのべられている東海地域での沈み込みベクトル、 N72W、1.88cm/yrは、中央防災会議の東海地震に関する専門調査会で正式に採用 されました。

Surveys by continuous Global Positioning System in and around Japan revealed that the Amurian Plate collides with the North American Plate in central Japan by about 2 cm/yr. Long-term crustal deformation seems to be influenced mainly by this collision although subduction of oceanic plates governs short-term elastic deformation over the arc. Here we study the long-term deformation field by carefully removing the short-term signals inferred from a-priori plate convergence vectors and coupling strengths predicted by a thermal model. The obtained field shows that the change in velocities occurs along the longitude 135°-137°E, and there exist a relatively rigid block and zones accommodating strains. Characteristic compressional deformation is found northwest of Izu due possibly to the collision of the Izu-Bonin arc with Honshu. Plate convergence rate along the Nankai-Suruga Trough is considerably smaller in eastern parts, due partly to the transition from the Amurian to the North American Plate of the landward side, and partly to the motion of the Izu Microplate relative to the Philippine Sea Plate. This accounts for longer recurrence intervals of interplate earthquakes in the Suruga Trough where the Tokai earthquake is anticipated to occur.

図の説明

図１ GEONETによる中部日本の速度場から海洋プレートの沈み込みに伴う弾性 変形成分を取り除いたもの。(a)はそれらをアムールプレート(AM)固定で、(b) は北米プレート(NA)固定でそれぞれ描いたもの。それぞれのフレームでのフィ リピン海(PH)、伊豆マイクロ(IMP)、北米、アムールの各プレートの運動ベク トルを太い矢印で示す。

図2沈み込みに伴う弾性変形分を取り除いた速度場からGEONET各局をアムール、 北米のいずれのプレートの運動に近いかで二種類に分類し（伊豆マイクロプレ ート内の局は除く）、(a)ではアムールプレートの動きに近い局についてそれ らのアムールプレートから見た速度の大きさを、(b)では同様に北米プレート から見た速度の大きさを色の濃さで描いたもの。白に近いほどそれぞれのプレ ートの動きに近いことを示す。灰色の太線はSagiya et al. (2000)による新潟 ―神戸変動帯。

図3 　Miyazaki and Heki (2001)で用いられた南海―駿河トラフの断層セグメ ントのそれぞれについて上盤と下盤の相対速度を示したもの。東海地域におけ る小さな収束速度が顕著である。

Heki et al. (1999)でのべたように、西南日本がアムールプレートに属する と仮定し、西南日本の速度場をアムールプレート準拠でプロットすると、東進が 消えてフィリピン海プレートによる弾性変形が浮かび上がってきます。普通はそ れらの速度データを用いて南海トラフ深部でのすべり欠損(backslip)の分布を 最小自乗推定するのが定石ですが、西南日本ではもう一つ東日本（北米プレート） との衝突に伴う未知の地殻変動が重なっており簡単には行きません。そこで本論 文ではAM-PHのEuler vectorをきちんと求め直し、海溝における相対速度ベクトル と熱的モデルから類推されるカップリング強度を掛け合わせて得られたすべり 欠損を既知として与えます。それによって予測される速度場と、観測された速度 場の差がとりもなおさずAM-NAの衝突に伴う long-termな変形場ということになり ます。

We investigate crustal deformation in southwest Japan over a three year period revealed by a permanent dense Global Positioning System (GPS) array. Southwest Japan is a part of the Amurian Plate, a microplate moving about 10 mm/yr toward the east with respect to the Eurasian Plate. It overrides the Philippine Sea plate at the Nankai Trough, and collides with the northeast Japan arc in the central part of Japan. In this paper we first derive GPS site velocities relative to the stable part of the Amurian plate in order to isolate signals of crustal deformation caused by the subduction and/or the collision. The velocity field has a conspicuous feature indicating the interseismic elastic loading by the Philippine Sea Plate slab at the Nankai Trough, characterized by the northwestward movements of points throughout the studied area. Their amplitudes are the largest at the Pacific coast and decay toward the Japan Sea coast with a subtle systematic shift of azimuths. A model assuming an elastic half space, the convergence rate at the Nankai Trough based on a refined Euler vector, and the strength of the coupling inferred from a thermal model, could explain the velocity field in the western part of the studied area to a large extent. Those in the eastern part systematically deviate from them, and the residual components there show east-west shortening and north-south extension. This suggests that the collision between southwest and northeast Japan gives rise to not only crustal thickening but also trenchward extrusion of crustal block. A velocity contrast was found across the Median Tectonic Line, the largest inland active fault in Japan, but the current permanent GPS network is not dense enough for us to discuss its coupling depth.

国土地理院の全国GPS網により、西南日本のGPS点がユーラシアプレートに対して東向きに動いている ことがわかってきました。この論文では大陸側のGPS点のデータを用いてこれがアムールプレートの運動に 起因することを明らかにしました。ロシア沿海州、中国東北部、韓半島等の点は互いに静止しており、それ らは全体としてユーラシアプレートに対して年間1cm程度の速さで東進しています。またその範囲はサハリ ン南部のユジノサハリンスクや中国中央部の西安までおよんでおり、従来考えられていたよりアムールプレ ートの範囲が広いことを物語っています。またアムールプレートを仮定することによって、東日本を北米プ レートと別のオホーツクプレートと考えなくても日本海東縁の地震のすべり方向が説明できます。プレート テクトニクスが標準的な理論となって30年を経てようやく東日本＝北米プレート、西日本＝アムールプレー トという日本列島の帰属が解明されたことになります。西南日本の速度場をアムールプレートに対してプロ ットすると、最初に述べたような東進が消えてフィリピン海プレートによる弾性変形が浮かび上がってきま す。これについては続編である Miyazaki and Heki (2001) でより詳しく議論されています。

We use Global Positioning System (GPS) velocity data to model eastern Asian plate kinematics. Out of 15 stations in Korea, Russia, China, and Japan studied here, three sites considered to be on the stable interior of the hypothetical Amurian Plate showed eastward velocities as fast as ~9-10 mm/yr with respect to the Eurasian Plate. They were stationary relative to each other to within 1 mm/yr, and these velocity vectors together with those of a few additional sites were used to accurately determine the instantaneous angular velocity (Euler) vector of the Amurian Plate. The predicted movement between the Amurian and the North American Plates is consistent with slip vectors along the eastern margin of the Japan Sea and Sakhalin, which reduces the necessity to postulate the existence of the Okhotsk Plate. The Euler vector of the Amurian Plate predicts left-lateral movement along its boundary with the south China block, consistent with neotectonic estimates of the displacement at the Qinling fault, possibly the southern boundary of the Amurian Plate. The Amurian Plate offers a platform for models of interseismic strain buildup in southwest Japan by the Philippine Sea Plate subduction at the Nankai Trough. Slip vectors along the Baikal rift, the boundary between the Amurian and the Eurasian Plates, are largely inconsistent with the GPS-based Euler vector, suggesting an intrinsic difficulty in using earthquake slip vectors in continental rift zones for such studies.

リストの下にAdv. Space Res.の２論文 Heki et al.(1999)と Matsumoto et al. (1999) がありますが、それの解説版です。日本の月探査周回衛星（SELENE)計画では初めて月の重力 計測に相対VLBIによる三次元的な重力加速度の計測(VRAD)とリレー衛星を用いた月の裏側の重力の直 接計測(RSAT)が行われます。それらに関してGEODYNIIというソフトウェアを用いて月重力場の ストークス係数の推定精度を共分散解析で評価したもの。従来の方法ではセレノイド高の推定誤 差が月の裏側で大きいのがRSAT観測によって表側と同程度に下がるのが劇的です。

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Abstract of Heki, K., K. Matsumoto and R. Floberghagen, Three-dimensional tracking of a lunar satellite with differential very-long-baseline-interferometry, Adv. Space Res., 23, 1821-1824, 1999.
Lunar gravimetry mission in the Japanese lunar exploration project SELENE (Selenological and Engineering Explorer) is characterized by inter-satellite tracking by means of a relay satellite in a high eccentric orbit, combined with differential Very-Long-Baseline-Interferometry (DVLBI) and conventional 2-way Doppler tracking. DVLBI provides information on the satellite position and velocity complementary to conventional range and range rate measurement, and allows us to measure lunar gravitational accelerations in all the three components. In this article, DVLBI and 2-way Doppler numerical simulation results are compared to those obtained from 2-way Doppler observations only, so that we can evaluate the contribution of DVLBI to the SELENE lunar gravimetry mission.

リストで少し上にあるNatureの論文では一日毎の測位データから1年間の地震後の地殻の動き を求めましたが、この論文では国立天文台江刺地球潮汐観測施設の石英管伸縮計の１時間毎のデータを用 いて地震直後から数日にわたる地殻変動の様子を明らかにしました。その結果地震直後の一日の間に地震 時の瞬間的な断層ずれのおよそ三分の一の量のゆっくりしたすべりが発生していたことがわかりました。 Kawasaki et al. (1995)は1992年に三陸はるか沖で発生した地震の直後に一日程度の時定数の断層すべ りが発生したことを報告していますが、1994年の地震でも同様の時定数のすべりが存在したことになりま す。またGPSのデータを通常より高時間分解能で解析し、伸縮計と調和的な１日以内の地面の動きを捉えた ことも報告しています。

The Sanriku-Haruka-Oki earthquake, that occurred on December 28, 1994 at the Japan Trench as a typical interplate thrust event, was followed by year-long afterslip as large as the slip in the high-speed rupture [Heki et al., 1997]. Here we report on the transition between these, inferred from crustal movements during the five days interval before and after the earthquake. Since this timescale is too long for seismometers but not suitably long for Global Positioning System (GPS), we rely primarily on strainmeter data taken ~200 km southwest of the epicenter. To confirm that the recorded strain changes are not local disturbances, we compare them with crustal movements derived by high time resolution analyses of GPS data in the same period. The transition to the long term afterslip was gradually achieved by slow fault slip with a time constant of a few hours. The cumulative slow slip in 24 hours amounts to ~1/3 of the coseismic slip, i.e. we may overestimate the coseismic displacement if we look at GPS data time series composed of daily solutions. The result presented here indicates that a single earthquake could have multiple aspects in its slowness, visible with different seismological and geodetic tools, and we need to use all such data to understand fully such a hybrid earthquake.

1994年の御用納めの夜に三陸はるか沖で発生したプレート間地震につづいて非地震性の断層すべり が一年以上続いたことを全国GPS網のデータから明らかにした論文。粘性が異様に低くないと地殻深部 の流動では説明ができないため、afterslipに対する半無限弾性体の応答として論文にしました。その後 類似のafterslipや完全なsilent earthquakeが同様なGPS観測によって次々に発見されましたが、その嚆矢 となるものです。この論文に関しては同じNatureの号で C. DeMetsがNews & Viewsの欄で "Afterslip no longer an afterthought"という題名で紹介記事を書いてます。

A permanent Global Positioning System network recorded distinct postseismic crustal movements following an earthquake 28 December 1994 (moment magnitude Mw=7.6) at the convergent plate boundary, off the northeastern coast of Honshu, Japan. Cumulative aseismic fault slips were estimated from postseismic displacements of the GPS points assuming an elastic half space. Seismic moment released by the afterslip over the first year was comparable to those released in the high-speed rupture. Such seismically ・ 'invisible’ slips in deep sea trenches, which may be accelerated creeps in a field of the plate interface with velocity-strengthening friction behaviour, possibly account for the shortage of seismic slips relative to the requirement from time averaged plate velocities.

NASA/GSFCの研究者が過去のすべてのVLBIデータをコンパイルして各観測局の位置と速度を推定 したものを、nnr-NUVEL1モデルに合うように平行移動と回転を施し、三次元速度基準系として 発表したもの。新規な点は（１）プレート境界から十分離れた複数の点を世界中にとり、それらとモデルの 「水平」速度の差の自乗和を最小にしたこと、（２）地磁気逆転年代の改定に伴うNUVEL1モデルの スケール誤差を吸収するために平行移動と回転に加えて速度のスケールを推定したこと、（３）得られた 鉛直速度を氷床後退に伴うリバウンドモデルと比較したこと等です。論文のscopeは広いのですが、実際 には筑波VLBI局のユーラシアプレートの安定部分に対する速度が国内のGPS点の速度をユーラシア固定に 変換する目的で便利に使われることとなりました。速度のスケールの議論は、その後太平洋プレートの速度 が現在一時的に速いのだという話などが出てややこしくなったまま未解決です。測地学的な支持のないまま に標準モデルとして従来の速度を約5%遅くしたNUVEL1Aが使われているのが現状です。

Three-dimensional kinematic reference frame of geodetic Very Long Baseline Interferometry (VLBI) stations, tied to a geologic plate motion model, was established using the GLB907 solution, by first selecting globally distributed stable plate interior stations, and then applying a small translation and a rotation for the entire network in a three-dimensional space so that the differences in the ``horizontal" velocities between the VLBI observations and the model predictions are minimized. Since the VLBI network is global, we only assume that the horizontal movements of tectonically stable stations obey a plate motion model; we need not to introduce any unwarranted constraints to the vertical velocities of specific stations to realize the frame. A suggestive correlation was found between the estimated vertical velocities of North American stations and those predicted by a post-glacial rebound model. The revision of the magnetic polarity time scale (MPTS) causes a uniform increase or decrease of the predicted velocities, which could be detected as the small difference between the measured and the predicted relative plate velocities. Direct estimation of the correction suggests that the VLBI data fit best to the model when the NUVEL1 model is corrected by +3.4 % (+/- 1.2 %), which differs significantly from the -4.5 % deduced from the astronomical MPTS calibration. This was further confirmed by estimating the rotation rates for individual plate pairs.

1980年代から行われてきた鹿島ー上海VLBI実験のまとめ。当初鹿島からVLBI用バックエンド 一式を持ち込んでXバンド単周波で始めたVLBI実験ですが、2周波化され実験期間が長くなるに したがって上海の速度の推定精度も上がってきました。年間3cmの基線長短縮は予測より有意に 速く、太平洋プレートに押された鹿島の西進だけでは説明がつきません。Molnar & Tapponnier (1975)が主張するインドーユーラシア衝突に伴うブロックの東への押し出しが測地学的に観測 された嚆矢になります。リストのすぐ下にあるJGRのHeki (1996)にもこのデータが紹介さ れているので、引用される機会はそちらの方が多いのですが、この論文の方が出版時期は早い です。21人の共著者を持つ論文を書いたのも初めて。

Very Long Baseline Interferometry (VLBI) data between the Shanghai station, China and other stations in the world suggest that Shanghai is moving east-southeastward by about 1 cm/yr with respect to the stable interior of the Eurasian plate. This agrees with a kinematic model of crustal blocks in Central and Eastern Asia inferred from geologic and neotectonic obserations and the results of geophysical numerical studies of the continental collision. The present result gives the first space geodetic evidence supporting the hypothesis that the northward movement of the Indian subcontinent after its collision with Eurasia is partly accomodated by eastward displacements of crustal blocks in Central and Eastern Asia.

1989年に行われたトルコ南西部のGPS測量の解析結果。トルコ西部に発達するエーゲ 海から続く東西走向の地溝をはさむ南北基線の伸長を検出しようと試みたGPSキャンペー ン。英国のDurham大学とトルコ共和国Izmir市のDokuz Eylul 大学の共同研究。トルコ では測量データは軍が一切取り仕切っており、このデータもトルコ軍の測地担当Alp 将校と共同で解析し座標値の「変化」のみを公表するという条件でデータの持ち出しが許可 された。このGPSキャンペーンの第２回の予算は認められなかったが、米国MITを中心とした 大規模なトルコ国内のGPS測量が行われ、我々のデータもそこで活用されている。今ではトル コ国内の速度場は日本なみに詳細に研究されています。かつての座標値持ち出しに関する厳 しい規制の現状は不明。

リスト上部のNatureのLetter to the editorをJGRでfull paper化したもの。 Natureの時点では一次元モデルで解析モデルにデータを当てはめていたが、JGR論文で はplane-stressの仮定のもとに二次元化、差分法で数値的に応力の拡散係数を求めて いる。当時使用していたUNIRASと呼ばれる描画プログラムを駆使した三次元プロットが 随所に登場。なおこの論文で仮定した薄いニュートン流体と弾性体の成層構造は後に後 継者のM.Hoftonによって薄い弾性体と半無限マックスウェル粘弾性体の成層構造モデル に進化し、同じくJGR誌上で近年発表された。

The bulk of a tectonic plate is thought to move continuously at a rate consistent with the geologic average. On the other hand, movements are highly episodic at plate boundaries. We study the plate dynamics that relate to these two different modes by modeling the displacements observed using the Global Positioning System (GPS) in Northeast Iceland 1997-1990. These observations were made about ten years after an episodic divergent movement between the North American and Eurasian plates 1975-1981. The horizontal displacement field fits well a two-dimensional model of post-rupture stress relaxation assuming a thin elastic layer overlying a layer of Newtonian viscosity. This analysis indicates values of about 10 m2/s for the stress diffusivity and 0.3-2 x 1918 Pa s for the Newtonian viscosity of the lower layer. However, no significant correlation exists between the observed and modeled vertical displacements probably because of the relative inaccuracy of the vertical component observations. Assuming that contemporary plate motion is the sum of many displacements that have diffused from boundaries where episodic displacements occur periodically, we simulate the spatial transition from episodic to continuous plate movements. The plate "boundary zone" where movements are episodic or quasi-episodic is of the order of 100 km wide, depending on the stress diffusivity (which may be fairly uniform throughout the world) and the frequency of episodic movements.

1990年夏に北東アイスランドで７台の受信器を用いたGPS測量が行われ、1987年に行われた 同様の測量の結果との比較で３年間の地殻変動が求められた。GPS受信機は巨大なTI4100、受信 機と発動発電機を始めとする膨大な機材を車に積んでの大規模な測量プロジェクト。データ解析 はBernese Softwareによる英国Durham大学チームとGeonap Softwareを用いる独Hannover大学 チームで並行して行われた。両者の解析結果を1991年のウィーンにおけるIUGGで持ち寄って比較 し、プレート運動モデルの予測速度の数倍のプレート運動が北東アイスランドのプレート境界を またぐ基線でみられたことを確認し、論文執筆のはこびとなった。Einarssonは地元アイスラン ドの地球物理学者、Julianは米国の火山物理学者。北東アイスランドでは1975年からクラブラ火 山を中心としたrifting episodeがあり、本研究で見出された速いプレート運動は1975年以来の イベントがElsasserの応力拡散モデルによってプレート内部に伝搬してゆく過程が観測されたもの。

Interaction of the elastic lithosphere with the underlying anelastic asthenosphere causes strain to propagate along the Earth's surface in a diffusion-like manner following tectonism at plate boundaries. This process transfers stress between adjacent tectonic segments and influences the temporal tectonic pattern along a plate boundary. Observations of such strain transients have been rare, and have hitherto been confined to strike-slip and underthrusting plate boundaries. Here we report the observation of a strain transient at the divergent (spreading) plate boundary in Iceland. A Global Positioning System survey undertaken a decade after an episode of dyke intrusion accompanying several metres of crustal spreading rate. A simple one-dimensional model with a thin elastic layer overlying a viscous layer fits the data well and yields a stress diffusivity of 1.1 +/- 0.3 m2/s. Combined with structural information from magnetotelluric measurements, this implies a viscosity of 0.3-2 x 1019 Pa s, a value comparable to that derived for Iceland from post-glacial rebound, but low compared with estimates for mantle viscosity obtained elsewhere.

1988年暮れに東京工業大学で行われたDELP国際シンポジウムの集録中の論文。過去数年に わたる鹿島VLBI局と他局との距離変化からグローバルな枠組みの中で鹿島の動きを求めたもの。 東日本をユーラシアプレート、北米プレートのいずれを仮定しても、鹿島の動きは予測より西 向き成分が大きくなる。今日では日本海溝における太平洋プレートの沈みこみによるelastic loadingとして簡単に片付けられますが、当時その発想はすぐ出ませんでした。茨城沖の日本 海溝では大きなプレート間地震が発生しないことから、列島の東西短縮は間違いないとしても、 弾性変形ではなく活断層や活褶曲を伴う塑性変形なのだろうと考えました。現在では全国GPS 連続観測網により日本全土にわたって詳細な速度場が求められており、地震の発生の有無にか かわらず海溝でのカップリングはかなり一様であることがわかっています。地震が「発生して いない」のではなく「見えない」だけだということが、90年代後半の三陸はるか沖地震の発生と 全国GPS網に記録されたafterslipからわかってきました。

Kashima very long baseline interferometry (VLBI) station is situated on the outer arc of the northeast Honshu Arc and its position has been monitored in international geodetic VLBI networks since 1984. Kashima station is found to be moving with respect to the stations on the stable North American craton by about 1.4 cm/yr, which is inconsistent with the general concepts that the Japanese eastern half belongs to the North American plate and that plates are rigid. The direction of the movement (N60W) is almost the same as the subducting Pacific plate which creates the compressional stress field in the island arc. This suggests that the east-west intraplate contraction of the arc under this stress field is responsible for the movement of Kashima.

通信総合(旧電波)研究所の所内談話会で行った、「間違いだらけのスケジュール選び」、 「究極のパラメータ推定」、「大気マッピング関数について」という三題噺を論文化した もの。大気マッピング関数の改良で上下位置の系統誤差を減らし、低仰角観測で大気と上下位 置の分離性を向上させ、連続性の拘束を入れて安定化を図った天頂遅延の高時間分解能推定に よって残差を減らす、という上下位置の推定精度の向上の三指針を示した内容。その後のGPS 気象学のコンセプトのひとつ「測地精度の向上」を先取りしていたかもしれない。

It has been pointed out that very long baseline interferometry (VLBI) is less accurate in determining the station positions in a vertical axis than in a horizontal plane. However, possible applications of VLBI for sea level monitoring, terrestrial reference frame for astrometry and earth rotation studies, etc., require accurate determination of the station position in the vertical axis as well as in the other axes. I propose three different approaches to improve the accuracies of the estimated vertical site positions, that is, to control the vertical elongation of the positional error ellipsoids by low elevation observations, to reduce the size of the ellipsoids by decreasing the residuals, and to select a "right" atmospheric mapping function to avoid systematic errors in vertical positions.