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Background and aim of the study To reveal a technical feasibility and safety of valve-sparing partial aortic root repair for spontaneous aortic dissection limited to the right coronary sinus of Valsalva. Methods A 68-year-old woman presented with chest pain. Twelve-lead electrocardiogram revealed atrioventricular dissociation and ST-segment elevation on II, III, and aVF. Enhanced computed tomography images showed aortic dissection limited to the right-coronary sinus and the other non-dilated sinuses of Valsalva. Localized aortic dissection was repaired by valve-sparing partial aortic root repair using a trimmed U-shaped Dacron graft and a felt strip, and the right coronary artery was revascularized by coronary artery bypass grafting using saphenous vein graft. Results The patient was discharged on postoperative day 12 with no complications. Conclusion Valve-sparing partial aortic root repair with the patch and coronary artery bypass grafting for aortic dissection limited to the right coronary sinus of Valsalva were technically feasible and safe.

The appropriate timing of aortic repair in patients with bicuspid aortic valve-related aortopathy remains controversial. We describe the changes in diameter of the non-aneurysmal ascending aorta after aortic valve replacement for bicuspid or tricuspid aortic valve stenosis. This retrospective review included 189 patients who had undergone aortic valve replacement for severe stenotic aortic valve with a non-aneurysmal ascending aorta diameter of 45 mm or less between January 2008 and December 2018. A linear mixed-effect model was used to analyze and compare the enlargement rates of the non-aneurysmal ascending aorta at the tubular portion after aortic valve replacement in bicuspid and tricuspid aortic valve patients. The enlargement rate of the non-aneurysmal ascending aorta after aortic valve replacement was significantly greater in the bicuspid aortic valve group than in the tricuspid aortic valve group (0.36 mm/year vs. 0.09 mm/year, p

This report highlights the usefulness and applicability of various gravimetric methods for studying earthquakes and volcanic activities. A high-resolution gravity anomaly map of Japan reveals areas with very steep horizontal gradients, where potential seismic faults are likely to be buried. Such traditional geoprospecting is coupled with novel cosmic-ray radiography to produce a fine-resolution (

The water in Earth’s mantle is closely related with plate subduction and volcanism. Recent studies revealed that the mantle wedge corner at approximately 30 km depth holds high-pressure water, where many slow earthquakes occur. To quantify how such water behaves during slow earthquakes helps us understand the mechanisms of these earthquakes and (eventually) a part of the long-term water cycle between the interior and surface of the Earth. However, little evidence has thus far been reported on the transient flows of such deep water. Here, we report anomalous, negative mass anomalies during two recent long-term slow slip events in the Tokai area in Japan, which were detected by absolute gravity measurements over 20 years. We present a poroelastic fluid flow model assuming a localized deformation within the fault fracture zone. The model can reproduce the gravity change with a permeability range between those suggested by laboratory experiments and numerical simulations of slow earthquakes.

We describe a simple and reproducible technique to achieve complete and immediate hemostasis of the distal anastomosis in total arch replacement with the frozen elephant trunk technique. The adventitia was left seamlessly 1.0 cm longer than the level of the suture line. The adventitial remnant covered most of the distal anastomosis line tightly while the distal anastomosis was completed with continuous sutures. The adventitia was thin and tough, making it suitable to cover the suture line. This technique can contribute to eliminating bleeding from the distal anastomosis independent of unreliable blood coagulability during aortic surgery for acute aortic dissection.

We performed three-dimensional density modeling of Showa-Shinzan lava dome, Usu, Japan, by joint inversion of the gravity anomaly and recently obtained muon radiography data. Our multilayer emulsion muon detector significantly reduces the background noise in our measurements of the muon flux through the dome. The high-quality muon data enables us to more accurately reconstruct the density structure of the lava dome compared with our own previous work. We find that the lava dome consists of a cylindrical column of massive lava with a diameter of 300 m, and that there is no evidence of magma intrusion in the shallow part of the plateau, located east of the dome.

The gravity signal originating from magma mass movement in a volcanic conduit is retrieved from the hydrologically disturbed absolute gravity data obtained at Asama Volcano (Central Japan) in 2004, using a three-dimensional hydrological model. We improve the hydrological model of the previous study using realistic soil parameters and boundary conditions, to better estimate the spatiotemporal land-water distributions and the consequent hydrological gravity disturbances. The newly estimated gravity disturbances agree with the absolute gravity values observed by FG5 gravimeters in 2004–2009 within about 2.6 μGal, by additionally accounting for the excess discharge of groundwater mass associated with a sloping impermeable surface below the discharge area. After the gravity disturbance of 20 μGal amplitude is subtracted from the absolute gravity data observed during the 2004 eruptive event, the gravity residual of 5 μGal amplitude shows a significant decrease in synchronization with eruptions, because the ascending magma mass in the conduit affects the upward attraction force to the gravimeters installed on the flank of Asama Volcano. The magma head altitude, to which the residual gravity is converted assuming a homogeneous linear density in the conduit, shows a comprehensive agreement of the time variation in the magma head with those in other volcanic observations, such as gas emission rate and earthquake frequency. By correcting the hydrological gravity disturbances using this hydrological model and simultaneously obtained meteorological data in real time, spatiotemporal variations in the magma mass can be instantaneously monitored at Asama Volcano, even before eruptions during future volcanic events.

We have developed an integrated processing method for muon radiography and gravity anomaly data for determining the 3-D density structures of volcanoes with a higher spatial resolution than is possible by conventional gravity inversion. In the present paper, we demonstrate the performance of the proposed method by performing numerical tests using synthesized data, and we present the results obtained by applying the proposed method to a volcano, Showa-Shinzan lava dome, Hokkaido, Japan. We obtained the detailed shape of a vent beneath the dome and detected the presence of solidified dense lava near the top of the dome. The results demonstrate the advantage of a hybrid measurement based on both gravity and muon radiography for imaging small structures with sizes of a few hundreds of meters near the surface of a volcano.

A 63-year-old man with ruptured acute type A aortic dissection was referred to our hospital. Computed tomography showed a false aneurysm arising from the false lumen located beside the ascending aorta. His hemodynamic status was stable inspite of the ruptured acute aortic dissection. We consider that the containment of the false aneurysm by thin mediastinal structures prevented worsening of his hemodynamic status, and this is extremely rare.

This study investigates data-processing methods and examines the precipitation effect on gravity measurements at the Dali gravity network, established in 2005. High-quality gravity data were collected during four measurement campaigns. To use the gravity data validly, some geophysical corrections must be considered carefully. We first discuss data-processing methods using weighted least-squares adjustment with the constraint of the absolute gravity datum. Results indicate that the gravity precision can be improved if all absolute gravity data are used as constraints and if calibration functions of relative gravimeters are modeled within the observation function. Using this data-processing scheme, the mean point gravity precision is better than 12 μgal. After determining the best data-processing scheme, we then process the gravity data obtained in the four measurement campaigns, and obtain gravity changes in three time periods. Results show that the gravity has a remarkable change of more than 50 μgal in the first time period from Apr–May of 2005 to Aug–Sept of 2007. To interpret the large gravity change, a mean water mass change (0.6 m in height) is assumed in the ETOPO1 topographic model. Calculations of the precipitation effect on gravity show that it can reach the same order of the observed gravity change. It is regarded as a main source of the remarkable gravity change in the Dali gravity network, suggesting that the precipitation effect on gravity measurements must be considered carefully.

We report here on continuous absolute gravity measurements made between February 2011 and March 2012 and repeated relative gravity measurements in the vicinity of Shinmoe-dake volcano, which commenced erupting in late January 2011. We find that 20 of 24 eruptive events are associated with precursory short-term gravity decreases occurring over 5–6 hours followed by quick recoveries lasting 1–2 hours. Also evident are significant long-term gravity changes arising principally from hydrological processes around the volcano, where annual precipitation exceeds 5,000 mm. To isolate the gravity signal associated with volcanic processes, we compared gravity measurements made at 15 sites in March 2011 and again in March 2012. The gravity changes and crustal deformation observed during the one year period are well explained by 6×106 m3 inflation of a magma reservoir at a depth of 9 km and intrusion at shallower depths of a dike with dimensions of 10 km × 0.5 km × 0.5 m.

The saphenous vein graft (SVG) is widely used in coronary artery bypass grafting because of its availability and ease of use. However, the patency rate of the SVG grafted to the right coronary artery (RCA) is poor. Diameter mismatch between the coronary artery and SVG is an important cause of graft occlusion. In this study, we assessed how the degree of diameter mismatch affects SVG patency. We reviewed the records of 123 patients who underwent aorto-right coronary artery bypass grafting with an SVG. The patency rate of the SVG, SVG diameter, RCA diameter and SVG-RCA diameter ratio (SR ratio) was assessed based on angiography and CT. The mean SVG diameter was 3.61 ± 0.72 mm, the mean RCA diameter was 1.57 ± 0.32 mm and the mean SR ratio was 2.37 ± 0.57. Cumulative patency rate of the SVG was 95.5 % at the early phase, 85.2 % at 1 year, and 70.2 % at 5 years. Multivariate analysis showed that the SR ratio was an independent predictor of SVG occlusion. The cutoff value of the SR ratio was 2.8, calculated from the point of maximal specificity (81.2 %) and sensitivity (64.7 %), and the area under the ROC curve was 0.734. When the SR ratio was ≤2.8, the 3-year patency rate was 86.1 %. A mismatch between SVG diameter and RCA diameter has an impact on the patency rate of the SVG. Evaluation of the saphenous vein before surgery and selection of a graft to minimize mismatch should improve SVG patency.

Coseismic gravity changes are interesting signals to be studied with precise gravity observations by means of the superconducting gravimeter (SG). Using the data from two SG stations in Japan, Matsushiro and Kamioka, an attempt is made to detect permanent gravity changes caused by the two recent earthquakes, the 2007 Noto Hantou earthquake ( M w = 6.9) and the 2007 Niigataken Chuetsu-oki earthquake ( M w = 6.8). Although these earthquakes are much smaller in magnitude than the 2003 Tokachi-oki earthquake studied by Imanishi et al. (2004) , the expected magnitude of the coseismic signals reaches the observable level of the order of 0.1 μGal (=1 × 10 −9 m s −2 ), owing to the fact that the epicentral distances are relatively short (120–170 km). A total of four possible combinations of source and receiver are investigated. In two cases in which the epicentral distances are shorter, there are instrumental offsets in the gravimeter records inhibiting estimation of gravity changes of natural origin. In the remaining two cases, the observed gravity changes are in agreement with theoretical predictions at least in their sign, but the differences between them are unexplained. Our result indicates the difficulty in identification of the coseismic signals caused by typical inland earthquakes.

Coseismic gravity change, correlated with the 2004 off the Kii peninsula earthquakes (∼M7), was detected with a superconducting gravimeter installed at the Inuyama station of Nagoya University, central Japan, where distances from epicenters were ∼250 km. The influence of precipitation in the vicinity of the site just before the earthquakes was included in the observed temporal gravity variation. Therefore the precipitation effect was removed using a simple tank model with the Radar-AMeDAS precipitation data. As a result, the magnitude of the coseismic gravity decrease was ∼10 nm s −2 (1 μGal). The gravity changes were calculated using a dislocation model with two fault models those defined by GPS estimates. These theoretical values corresponded to the observed value in the order of 1 μGal.

SUMMARY Post-seismic deformation caused by the 2004 Sumatra-Andaman Earthquake (M= 9.3) has been observed by space geodetic techniques such as the Global Positioning System (GPS) and the Gravity Recovery and Climate Experiment (GRACE). To estimate such deformation with a spatial scale exceeding 100 km, we can use theories of global post-seismic deformation in which the Earth is treated as a self-gravitating viscoelastic sphere. Previous theories have imposed limitations on employed earth models, such as neglecting compressibility and time variation of self-gravitation or simplifying the radial profile of the viscosity. This is because the normal mode method on which these theories are based cannot evaluate a denumerably infinite set of eigenmodes that will appear when those limitations are removed in the practical computation. To bypass this difficulty, in our previous paper, we showed that the numerical inverse Laplace integration with a rectangular path enabled us to obtain the vertical deformation without using those approximations. In this paper, we apply the same method to the horizontal deformation for a complete set of the fault mechanisms (strike-slip, dip-slip and vertical and horizontal tensile). Next, we reveal error sources in our approach. The largest error arises in different selections of the integration path. This error is less than 1 per cent in the lower-degree deformations (n∼ 10) and 0.1–0.5 per cent in the higher-degree ones (100 < n < 1000), relative to the result obtained with an independent method. Finally, we elucidate differences in far-field deformations obtained for the earth model employed in this study and those used in the previous studies for a large dip-slip event (Mw= 8.3). The result shows that (1) differences of 6–50 per cent are seen in the coseismic offset and (2) horizontal rate differences of 1–5 mm yr−1 (5–25 per cent of the rates) are observed at the epicentral distance of 100 km during the first thirty years after the event. These differences are detectable with GPS. Therefore, for theory to meet observational accuracy, effects of compressibility and stratification on global post-seismic deformation should be considered.

An 80-year-old woman was admitted to our hospital because of congestive heart failure. Transthoracic echocardiography revealed severe aortic valve stenosis, and a mobile calcified mass was attached to the interatrial septum in the right atrium. We suspected that the mass was cardiac myxoma. We urgently performed aortic valve replacement and resection of the mass. The histological diagnosis of the mass was thrombus, and her post-operative course was uneventful. Although the mechanism of right atrial thrombus formation in our case was unclear, it is important to continue anticoagulation therapy after surgery to avoid recurrence. Furthermore, strict follow-up in this patient is needed.

SUMMARY A set of Green's functions is presented for calculating the coseismic strain caused by four independent seismic sources in a spherically symmetric, non-rotating, perfectly elastic, and isotropic (SNREI) earth model. Corresponding expressions are derived assuming that the seismic sources are located at the polar axis. The proper combination of these expressions allows calculation of the coseismic strain components resulting from an arbitrary seismic source at any Earth position. Calculations of strain components are made for the near field resulting from the four independent sources at a depth of 32 km inside the 1066A earth model. Results agree well with those calculated for a half-space earth model, thus confirming the validity of the theory presented in this research. A case study is performed and earth model effects are investigated. Furthermore, this paper investigates effects of spherical curvature and the stratified structure of the Earth in computing coseismic strain changes. Curvature effects are small for three types of seismic sources, but extremely large for the horizontal tensile opening on the vertical fault plane. Because a general coseismic deformation comprises four independent solutions, the large curvature effect on the horizontal tensile opening source contributes to the general result. Effects of Earth's stratified structure are large for all depths and epicentral distances. They reach a discrepancy greater than 30 per cent almost everywhere, and 100 per cent in a very far field. Results show that effects of crustal structure mainly exist in the near field; they do not affect results for a far field.

SUMMARY We present a numerical formulation for computing elastic deformations caused by a dislocation on a ¢nite plane in a spherically symmetric earth. It is based on our previous work for a point dislocation (Sun & Okubo 1993). The formulation enables us to compute the displacement, potential and gravity changes due to an earthquake modelled as spatially distributed dislocations. As an application of the ¢nite-fault dislocation theory, we make a case study of the theoretical and observed gravity changes. The computed results are in excellent agreement with the observed gravity changes during the earthquake. The gravity changes in the near ¢eld can reach some 100 ]gal, which can be easily detected by any modern gravimeter. In the far ¢eld they are still signi¢cantly large:jdgj > 10 ]gal within the epicentral distance h 1 ]gal within h 0:1 ]gal within h 0:01 ]gal globally. We also calculate the geoid height changes caused by the 1964 Alaska earthquake and by the same earthquake with revised parameters and an assumed barrier. We ¢nd that the earthquake should have caused geoid height changes as large as 1.5 cm.

We present a case of subepicardial aneurysm that developed as a complication of acute myocardial infarction. Although the patient had stable hemodynamics, the diameter of the aneurysm tended to increase over time; thus, an operation was performed. We thought that approaching the aneurysm from outside the heart would injure the papillary muscle or distort the left ventricle and exacerbate mitral regurgitation. Therefore, we performed patch repair using bovine pericardium and approached the aneurysm from inside the heart. This is the first case report of a subepicardial aneurysm that was approached and repaired from inside the heart.

Corner reflectors are suitable as ground control points when they are placed in spaces that are very large, flat, and empty. Since their reflection points are known, they can be detected and identified with relative ease in SAR images through comparisons of images before and after their installation. However, in practical applications, large flat empty spaces are not often availble near the locations necessary for a particular application. Even when these corner reflectors are placed in a flat empty lot closest to the desired location, they are not always easily identifiable in SAR images due to insufficient size or influences from surrounding areas. Using existing singular corner reflectors which were installed as ground control points for JERS-1 SAR images, we examined the minimal conditions required for empty lots to be used as installation sites, considering factors such as the number of observations, identifiability of the area surrounding the installation site, identifiability of the installation site in the images, and existence of any confounding point targets surrounding the corner reflector. We also investigated whether the same corner reflectors could be used as ground control points for the C-band ERS-2 SAR, which has an incident angle relatively similar to that of the JERS-1 SAR. We found that the most crucial condition necessary for easy detection and identification of corner reflectors in both JERS-1 SAR images and ERS-2 SAR images was that the installation site be located with adequate accuracy in the JERS-1 SAR image by visually locating the site or estimating the location from nearby distinct features. It was not necessary for the site to be very large. As long as they were larger than 10 x 10 pixels (roughly 150 m in the range direction and 50-60 m in the Azimuth direction), we could detect these sites, including any adjacent areas that appeared very dark, such as agricultural fields, rice paddies, tea plantations, water bodies, grassland and athletic fields, from single look JERS-1 SAR images.

Employing both absolute and relative gravimeters, we carried out a hybrid microgravity survey at Miyakejima volcano, Japan. We detected significant gravity changes, e.g., exceeding 1000 At gal, during the course of our measurements since June 1998. The spatio-temporal gravity changes provide us with strong evidence of preexisting vacant space beneath the island before the summit collapse of the volcano. Also, our data are totally in conflict with the so-called magma drainback model, suggesting that the magma flowed out laterally.

Basalt magma sometimes moves through volcanic conduits causing only minor deformation. In that case, we may detect magma movements directly by microgravity observations. After the 1986 eruption of Izu-Oshima volcano, we observed anomalous gravity variations localized at the summit. Based on a vertical cylindrical conduit model, we estimate the time variations of the head of magma in the summit conduit and clarify the magma drain-back process after the 1986 eruption.

We carried out a several day experiment at two sites to verify the precision of the FG5 absolute gravimeter through collocation with superconducting gravimeters. We found 2 to 4 microgal diurnal/semi-diurnal signals in the time series of absolute gravity measurements. These signals agreed well with theoretical ocean tide both in amplitude and in phase, demonstrating that the FG5's precision is better than 2 microgal. Furthermore, we found that the discrepancy between the FG5 measurements and the SG measurements is 1.3 to 1.5 microgal. These results verify that the FG5 is precise to 1 to 2 microgal.

We define dislocation Love numbers [h nm ij , l nm ij , k nm ij , l nm t , ij ] and Green's functions to describe the elastic deformation of the Earth caused by a point dislocation and study the coseismic displacements caused in a radially heterogeneous spherical Earth model. We derive spherical harmonic expressions for the shear and tensile dislocations, which can be expressed by four independent solutions : a vertical strike slip, a vertical dip slip, a tensile opening in a horizontal plane, and a tensile opening in a vertical plane. We carry out calculations with a radially heterogeneous Earth model (1066A). The results indicate that the dominating deformations appear in the near field and attenuate rapidly as the epicentral distance increases. The shallower the point source, the larger the displacements. Both the Earth's curvature and vertical layering have considerable effects on the deformation fields. Especially the vertical layering can cause a 10% difference at the epicentral distance of 0.1°. As an illustration, we calculate the theoretical displacements caused by the 1964 Alaska earthquake (m w = 9.2) and compare the results with the observed vertical displacements at 10 stations. The results of the near field show that the vertical displacement can reach some meters. The far-field displacements are also significant. For example, the horizontal displacements (u ψ ) can be as large as 1 cm at the epicentral distance of 30°, 0.5 cm at about 40°, magnitudes detectable by modern instrument, such as satellite laser ranging (SLR), very long baseline interferometry (VLBI) or Global Positioning System (GPS). Globally, the displacement (u r ) caused by the earthquake is larger than 0.25 mm.

We carried out dense gravity measurements with the Fast Static GPS positioning along five survey lines across the Rokko fault system. We calculated the Bouguer anomaly to estimate the underground structure relevant to the 1995 Hyogo-ken Nanbu earthquake. We applied the two-dimensional Talwani's method to the modeling, assuming that the density structure is similar for all the five survey lines. All the Bouguer anomaly profiles are characterized by flat areas on the Rokko Mountains and Kobe Plain, with steep gradient between them. The gradient is most likely due to the fault scarps between the Rokko granite and the sedimentary layer of the Osaka and Kobe groups. It also indicates that the faults are vertical or reverse ones, at least just below their surface traces. This finding is consistent with the tectonic background of the Rokko Mountains that have upheaved under the east-west compression in the Quaternary. Moreover, we found the southwestward extension of the Koyo Fault underneath the sedimentary layer. The extension runs on the edge of the earthquake disaster zone. We inferred that the thickness of the sedimentary layer is 1-2 km near the sea, decreasing gradually toward the mountain side. The wedge-like structure and the hidden fault under the Kobe Plain may have served as a focusing lens of seismic rays during the earthquake.

With high-resolution continuous gravity recordings from a regional network of superconducting gravimeters, we have detected permanent changes in gravity acceleration associated with a recent large earthquake. Detected changes in gravity acceleration are smaller than 10 –8 meters seconds –2 (1 micro-Galileo, about 10 –9 times the surface gravity acceleration) and agree with theoretical values calculated from a dislocation model. Superconducting gravimetry can contribute to the studies of secular gravity changes associated with tectonic processes.

The geodetic evidence of the uplift and crustal thickness of the Tibetan Plateau has been presented for the first time (Sun et al. 2009) using gravity and GPS observations. In this paper, we reinvestigate this tectonic deformation in more detail using GRACE data and taking the GIA effect into account. We first summarize the previous gravity and GPS observations and a local gravity network in the Dali County. The comparison between the surface absolute gravity and space GRACE gravity measurements shows that they are harmonic, agree well. Finally, we assume that the residual gravity change reflects material transport accompanying vertical movements on the crustal bottom; the crustal thickening rate is inferred as 1.9 ¡_ 1.4 cm yr-1. As the crust thickens, the mass of a column of rock beneath the station decreases because mantle is displaced by crust, causing a reduction in gravity.

SUMMARY This paper studies the potential and gravity changes caused by dislocations in spherically symmetric earth models. We define dislocation Love numbers to describe the elastic deformation of the earth raised by point sources. We discuss the shear and tensile dislocations, which can be expressed by four independent components: a vertical strike-slip, a vertical dip-slip, a tensile opening on a horizontal plane, and a tensile opening on a vertical plane. The results for a homogeneous earth model agree very well, at least within lo, with those predicted from flat-earth theory. The far-field results indicate no larger than 10per cent difference within 10". It makes little difference whether we use the theory on a sphere or that for a flat earth in the near field, while it is reasonable to use the spherical theory for global calculation. We proceed to calculations with a radially heterogeneous earth model (Model 1066A). The results are as a whole similar to those for a homogeneous sphere. In some cases, however, the difference between the two becomes significant. For example, the locations of the nodal lines of the gravity change differ significantly between the two models. This indicates that the vertical layering can cause considerable effects on the deformation fields.

Unequivocal coseismic gravity change was detected for the first time by absolute gravimetry. The measurements were done just one day before and only 7 days after a M6.1 earthquake (M6.1). The absolute gravity change was −6 microgal, significantly larger than the observational error of about 1 microgal. Of particular interest is that the observed spatial gravity variations agree remarkably well with those expected from an elastic dislocation model constructed on displacement data alone. The result strongly encourages us to perform a simultaneous inversion of both gravity and displacements to have better insight of earthquakes.

[1] The gravity disturbance caused by groundwater is derived based on hydrological physics by solving nonlinear hydrological diffusion equations for three-dimensional and temporal groundwater distributions. The gravity disturbance is then estimated by the spatial integral of the groundwater distributions. This approach aims to resolve the problems of previous methods for the correction of groundwater disturbances in gravity data, such as instrumental drift of relative gravimeters, empirical estimation of gravity assuming a linear gravity response to precipitation, and the use of lower-dimensional water transfer models. The disturbance estimated using the proposed model is consistent with the observed gravity change at Asama Volcano in Central Japan during the rainy summer of 2006. The model reproduces the rapid increase and subsequent gradual decrease in gravity following rainfall events. The water mass within 150 m of the gravimeter is shown to dominate the observed gravity change during precipitation. It is also demonstrated that the use of adequately representative soil parameters is essential in order to accurately estimate the groundwater distributions and consequent gravity variations. This study shows that correcting for hydrological disturbances requires a more sophisticated model of water movements, particularly during heavy rainfall.

SUMMARY Based on the authors' previous work, co-seismic deformations for a spherical symmetric earth model are summarized and reformulated. Unified expressions presented herein accommodate physical deformations: displacement, potential, gravity, geoid and strain changes. The corresponding Green's functions are derived by combining spheroidal and toroidal deformations. Sign errors in previous publications are corrected in these new formulas. These expressions are developed basically for a deformed earth surface because most traditional geodetic measurements are performed on the terrain surface. However, through development of space geodetic techniques, such as the satellite gravity missions, co-seismic gravity changes can be detected from space. In this case, the above dislocation theory (e.g., the co-seismic gravity change) cannot be applied directly to the observed data because the data do not include surface crustal deformation (the free air gravity change). Correspondingly, the contribution by the vertical displacement part must be removed from the traditional expressions. For this purpose, we present the corresponding expressions applicable to space observations. Some numerical technical problems are discussed. In addition, a smoothing technique is necessary to damp the high-frequency contribution so that the theory can be applied reasonably. Global co-seismic deformations caused by the 2004 Sumatra–Andaman earthquake (M9.3) are studied as an application of the new Green's function. That earthquake caused a global deformation detected by GPS, strain metres and even a satellite gravity mission. These global deformations are calculated based on the derived Green's functions and the seismic-wave derived earth model. A segment-summation scheme is used considering the slip distribution on a limited fault plane. The results are useful for interpreting observed deformations, especially those in the far field. The earthquake reveals global co-seismic deformations and effects of spherical curvature and the earth's layered structure. Comparisons between results for a spherical earth mode and a half-space model show a large discrepancy at an epicentral distance of about 1000 km, implying that effects of spherical curvature and layer structure are considerably large. In addition, the theoretical results are compared with the real observed strain steps, horizontal displacements and gravity changes caused by that earthquake. Good agreement validates the results of the current theoretical work. Finally, we discuss the application the above theory to the GRACE data through several case studies.

[1] Today, some tens of million years after its creation by the collision between India and Asia, the Tibetan Plateau is the highest and largest plateau on Earth. Results of geological and tectonic studies indicate that the plateau is extending. However, almost no quantitative evidence shows whether the plateau is still uplifting or thickening nowadays. Herein, we present geodetic evidence of mass loss beneath the Tibetan Plateau and increasing crust thickness. Combined absolute gravity and Global Positional System (GPS) measurements at three stations in southern and southeastern Tibet during two decades reveal uplifting of the Tibetan Plateau at a millimeter-per-year level, but its underlying mass is diminishing, indicating that the crustal thickness is increasing at an annual millimeter to decimeter level.

SUMMARY We derive expressions in closed form which give the gravity potential changes caused by point dislocations. They enable us to evaluate coseismic changes in surface gravity and geoid height. Numerical simulation shows that a great earthquake could cause a geoid height change of order 1 m.

We detect significant gravity change due to the 1989 earthquake swarm and the submarine eruption, off Ito. Simultaneous inversion of gravity, leveling and EDM data shows almost zero density of cavity-filling matter associated with the event. The analysis clearly favors dry tensile crack opening due to regional stress for the event of July 1989. We prefer rather small-scale magma intrusion confined to an area just around Teisi Knoll. We reject the possibility of magma intrusion as a principal driving force of opening cracks in this event.

A new theory is presented for calculating co-seismic strain caused by four independent types of seismic source in a spherically symmetric, non-rotating, perfectly elastic, and isotropic (SNREI) Earth model. Expressions are derived by introducing strain Green’s functions. A proper combination of these expressions is useful to calculate co-seismic strain components resulting from an arbitrary seismic source at any position in the Earth. Numerical computations are performed for four independent sources at a depth of 32 km inside the 1066A Earth model. Results in the near field agree well with that calculated for a half-space Earth model. A case study is performed and Earth model effects are investigated. Furthermore, the effects of spherical curvature and the stratified structure of the Earth in computing co-seismic strain changes are also investigated using the present dislocation theory and Okada’s (1985) formulation. Curvature effects are small for shallow seismic events, but they are larger for greater source depths. Stratified effects are very large for any depth and epicentral distance, reaching a discrepancy greater than 30% almost everywhere.

This paper presents a new approach to calculate dislocation Love numbers using observations of a satellite gravity mission (e.g. GRACE). The necessary condition is that the co-seismic potential change be sufficiently large to be detected by the gravity mission. Co-seismic deformations for each spherical harmonic degree n are decoupled. Therefore, dislocation Love numbers of degree n can be determined independently. The determinable maximum harmonic degree n depends on the seismic size, source type, magnitude, and the accuracy of a satellite gravity mission. For an arbitrary seismic source, all four types of dislocation Love numbers can be determined using data from only one seismic event because all deformation components are involved together. Only the concerned dislocation Love numbers can be computed for any one of the four types of sources. To prove the validity of the method proposed in this study, a simulation test is carried out by considering a similar case to the 2004 Sumatra earthquake (Mw 9.1). Results show that the method works well and guarantee the accuracy.

Co-seismic deformations cannot be compared directly with those observed by gravity satellite missions because of the spatial resolution limit of the missions and the signal attenuation of the gravity field. For this purpose, the conventional dislocation theory for a spherical earth model can be used because it is expressed in the form of a spherical harmonic. In this study, analytical expressions of degree variances of the co-seismic geoid and gravity changes for shear and tensile sources are derived and calculated for three real earthquakes. Those results are compared with expected errors of GRACE to elucidate whether or not co-seismic geoid and gravity changes are detectable by gravity satellite missions. Behaviors of the degree variances for four independent seismic sources are investigated. Results indicate that both the gravity and geoid changes are near two orders of magnitude larger than the precision of the gravity missions in low harmonic degrees. Based on these results, we derived the minimum magnitudes of earthquakes detectable by GRACE. We concluded that co-seismic deformations for an earthquake with a seismic magnitude above m =7.5 are expected to be detected by GRACE.

This study presents an asymptotic theory for calculating displacements excited by a point dislocation in a spherically symmetric earth model as an approximation of the dislocation theory for a spherical earth model (Sun et al., 1996), employing the reciprocity theorem (Okubo, 1993) and asymptotic solutions of an elastic earth to tidal, load and shear forces (Okubo, 1988). This theory is mathematically simple and physically reasonable since it reflects the earth’s sphericity and radial structure. Comparison of the asymptotic results with both the exact results and the corresponding flat-earth results shows that for any distances the exact results are approximated better by the asymptotic results than by the flat-earth results. Especially, the asymptotic theory is obviously superior to the flat-earth theory due to a big sphericity effect for the tensile opening on a vertical fault. Owing to its mathematical simplicity, this theory can be applied easily to calculate co-seismic displacements. The validity of the theory for a stratified earth needs to be further tested and discussed.

[1] Coseismic deformations observed on the Earth surface or modeled by conventional dislocation theory cannot be compared directly with those observed by gravity satellite missions because of the spatial resolution limit of the missions and the signal attenuation of the gravity field. Coseismic deformations in the spectrum domain should be considered instead. For this purpose the conventional dislocation theory [e.g., Sun and Okubo, 1993] for a spherical Earth model can be used because it is expressed in the form of a spherical harmonic. In this study, analytical expressions of degree variances of the coseismic geoid and gravity changes for shear and tensile sources are derived and calculated for three real earthquakes. Those results are compared with expected errors of the Gravity Recovery and Climate Experiment (GRACE) to elucidate whether or not coseismic geoid and gravity changes are detectable by gravity satellite missions. Behaviors of the degree variances for four independent seismic sources are investigated. Results indicate that both the gravity and geoid changes are near two orders of magnitude larger than the precession of the gravity missions in low harmonic degrees. On the basis of these results, we derived the minimum magnitudes of earthquakes detectable by GRACE. We concluded that coseismic deformations for an earthquake with a seismic magnitude above m = 7.5 are expected to be detected by GRACE.

[1] Calderas are ubiquitous topographic features of volcanos, yet caldera formation itself has not been recorded intensively by modern measurement techniques. Here we report the spatiotemporal gravity changes before and after caldera collapse at the Miyakejima volcano, Japan in 2000. A gravity decrease of as much as 145 μGal (1 μGal = 10−8 m/s2) at the summit area since June 1998 was detected 2 days prior to the collapse, interpreted as reflecting the formation of a large void beneath the volcano. Gravity changes detected after the initiation of collapse can mostly be corrected by the effect of collapsed topography, from which a rapid rate of collapse of more than 1.6 × 107 m3/d can be inferred. Correcting for the effect of topography change, we identified a temporal decrease in gravity from the middle of July to late August despite ground subsidence. The gravity decrease is interpreted as a reduction of the density in a cylindrical conduit, attributed to water inflow from an ambient aquifer that also promoted intensive magma-water interaction and subsequent explosive eruptions. From September to at least November 2000, gravity values at all sites increased significantly by a degree that cannot be explained by ground displacement alone. We interpret this temporal evolution as primarily due to magma ascent and refilling of the conduit.

[1] To the present, dislocation theories for a homogeneous half-space are often used to calculate or interpret displacements and gravity changes caused by an earthquake or to inverse a seismic fault model. However, far-field effects of spherical curvature and radial heterogeneity have to be considered. In this research, Okada [1985] and Sun et al. [1996] dislocation theories are used to calculate displacements caused by four independent dislocations in three earth models: a homogeneous half-space, a homogeneous sphere, and a heterogeneous sphere. Effects of spherical curvature and radial heterogeneity are investigated through comparison of displacements. Results show that effects of both sphericity and stratification are very large. The stratified effect reaches a discrepancy of more than 25% everywhere on the surface of the earth, including the near field.