Residual Velocity Field Research Articles

A method for velocity modeling in a volcanic rock zone that integrates the amplitude envelope attribute and grid tomography: application to data from the North Jiangsu Basin

Abstract The complexity of volcanic rocks presents challenges in seismic data quality and fine characterization of structural morphology, making velocity modeling difficult. In this study, we propose a velocity modeling method for volcanic rock areas that combines the use of amplitude envelope attribute and grid tomography inversion. By exploiting the strong reflection characteristics of volcanic rocks, the amplitude envelope attribute is employed to identify volcanic rock structures, eliminating the need for labor-intensive manual interpretation. The grid tomography inversion technique is then used to derive background velocity fields for all strata. These are further refined by incorporating the residual velocity fields of volcanic rocks through fusion and superposition. This integrated approach significantly improves the efficiency and accuracy of velocity modeling in complex volcanic rock areas, overcoming the limitations associated with conventional volcanic rock structural models and resulting in more accurate velocity inversion. The effectiveness and feasibility of the proposed method for velocity modeling in volcanic rock zone are demonstrated through the application of seismic data from an oilfield in eastern China. The results highlight the method's strong industrial application value.

Influence of inter-river water diversion on estuary pollution control: A case study of Liaodong Bay

Long-term mass transport processes in offshore seas are controlled by seasonal residual currents. The Euler residual mass transport velocity field was calculated form seasonal residual current patterns in shallow sea area, comparing with polluted water changes in typical years. The following conclusions were made: closed local large loops of the Euler residual mass transport led to polluted waters in the northeast Liaodong Bay, and the bay's optimal physical self-purification occurred in winter (Euler residual mass transport diffuses polluted water masses) and spring (overall self-purification capacity of the bay plays a role after winter). The central waters were clean while pollutants were discharged into near-shore waters, leading to perennial pollution in some near-shore waters. Pollution in Liaodong Bay could be alleviated or eliminated via diversion of water from the Daliaohe River (flowing into the northeast corner of Liaodong Bay and carrying > 65% of the total amount of pollutants discharged into the top of the bay) into the Liaohe River and Daling River. The percentage of inorganic nitrogen carried by 10% of the flux of the Daliaohe River was 5.70% of that discharged into Liaodong Bay. If 10% of the flux of the Daliaohe River was discharged into the Daling River, the annual total environmental carrying capacity of inorganic nitrogen increased 4.48%. Many bays in the world have adjacent river flows, such as Gulf of Mexico, Gulf of Guinea, and Bay of Bengal. Based on the Euler residual mass transport field, the water transfer between adjacent rivers could make better use of the Euler residual mass transport capacity to mitigate the water pollution of the estuaries.

Measuring the streaming motion in the Milky Way disc with Gaia EDR3+

ABSTRACT We map the 3D kinematics of the Galactic disc out to 3.5 kpc from the Sun, and within 0.75 kpc from the mid-plane of the Galaxy. To this end, we combine high-quality astrometry from Gaia EDR3, with heliocentric line-of-sight velocities from Gaia DR2, and spectroscopic surveys including APOGEE, GALAH, and LAMOST. We construct an axisymmetric model for the mean velocity field, and subtract this on a star-by-star basis to obtain the residual velocity field in the Galactocentric components (Vϕ, VR, Vz), and Vlos. The velocity residuals are quantified using the power spectrum, and we find that the peak power (A/[km s−1]) in the mid-plane (|z| < 0.25 kpc) is (Aϕ, AR, AZ, Alos) = (4.2,8.5,2.6,4.6), at 0.25 < |z|/[kpc] < 0.5, is (Aϕ, AR, AZ, Alos) = (4.0,7.9,3.6,5.3), and at 0.5 < |z|/[kpc] < 0.75, is (Aϕ, AR, AZ, Alos) = (1.9,6.9,5.2,6.4). Our results provide a sophisticated measurement of the streaming motion in the disc and in the individual components. We find that streaming is most significant in VR, and at all heights (|Z|) probed, but is also non-negligible in other components. Additionally, we find that patterns in velocity field overlap spatially with models for spiral arms in the Galaxy. Our simulations show that phase-mixing of disrupting spiral arms can generate such residuals in the velocity field, where the radial component is dominant, just as in real data. We also find that with time evolution, both the amplitude and physical scale of the residual motion decrease.

Macro- and meso- failure mechanism analysis for shale-like brittle materials under uniaxial compression

Understanding the failure mechanisms of the widespread shale-like brittle materials is of great significance to engineering safety. In this research, the discrete element model which can reflect the real rock mechanical properties and failure mode of shale specimens with different bedding angles has been reconstructed. First, microcrack has been introduced to characterize the meso-damage. The relationship between the microscopic crack numbers in the material and the macroscopic stress has been revealed. In addition, the relative movement between different deformed blocks has been analyzed by introducing the residual velocity field. The control factor of material failure varies with the bedding angle (β) in the macro scale. It manifests from the bedding plane and the matrix synergistically control the failure mode of rocks to mainly the bedding plane and then back to the bedding plane and the matrix synergistically control the rock failure mode. The competitiveness of the shear and tensile damages in the failure mechanism varies with the bedding angle in the meso scale. When 30°<β<75°, Shear damage dominates the failure mechanism. The established numerical model is capable of predicting the mechanical behavior of brittle rock, which may have guiding merits to the application of shale-like brittle materials.

Bending waves in velocity space: a first look at the THINGS sample

ABSTRACT Detection of bending waves is a highly challenging task even in nearby disc galaxies due to their sub-kpc bending amplitudes. However, simulations show that the harmonic bending of a Milky Way-like disc galaxy is associated with a harmonic fluctuation in the measured line-of-sight (los) velocities as well, and can be regarded as a kinematic signature of a manifested bending wave. Here, we look for similar kinematic signatures of bending waves in H i discs, as they extend too much beyond the optical radii. We present a multipole analysis of the H i los residual velocity fields of six nearby spiral galaxies from the THINGS sample, which uncovers the bending wave-induced velocity peaks. This allows us to identify the radial positions and amplitudes of the different bending modes present in the galaxies. We find that all of our sample discs show a combined kinematic signature of superposition of a few lower order bending modes, suggesting that bending waves are a common phenomenon. The identified velocity peaks are found to be of modes m = 2, 3, and 4, not more than 15 km s−1 in amplitude and spread across the entire H i disc. Interestingly, they appear to be concentrated near the optical edge of their host galaxies. Also, m = 2 appears to be more common than the other two modes.

A Tidally Induced Global Corrugation Pattern in an External Disk Galaxy Similar to the Milky Way

Abstract We study the two-dimensional (2D) line-of-sight velocity (V los) field of the low-inclination, late-type galaxy VV304a. The resulting 2D kinematic map reveals a global, coherent, and extended perturbation that is likely associated with a recent interaction with the massive companion VV304b. We use multiband imaging and a suite of test-particle simulations to quantify the plausible strength of in-plane flows due to nonaxisymmetric perturbations and show that the observed velocity flows are much too large to be driven either by a spiral structure or by a bar. We use fully cosmological hydrodynamical simulations to characterize the contribution from in- and off-plane velocity flows to the V los field of recently interacting galaxy pairs like the VV304 system. We show that, for recently perturbed low-inclination galactic disks, the structure of the residual velocity field, after subtraction of an axisymmetric rotation model, can be dominated by vertical flows. Our results indicate that the V los perturbations in VV304a are consistent with a corrugation pattern. Its V los map suggests the presence of a structure similar to the Monoceros ring seen in the Milky Way. Our study highlights the possibility of addressing important questions regarding the nature and origin of vertical perturbations by measuring the line-of-sight velocities in low-inclination nearby galaxies.

Quantifying Truncation-Related Uncertainties in Unsteady Fluid Dynamics Reduced Order Models

In this paper, we present a new method to quantify the uncertainty introduced by the aggressive dimensionality reduction commonly practiced in the field of computational fluid dynamics, the ultimate goal being to simulate accurate priors for real-time data assimilation. Our key ingredient is a stochastic Navier-Stokes closure mechanism that arises by assuming random unresolved flow components. This decomposition is carried out through Galerkin projection with a Proper Orthogonal Decomposition (POD-Galerkin) basis. The residual velocity fields, model structure and evolution of coefficients of the reduced order's solutions are used to compute the resulting multiplicative and additive noise's correlations. The low computational cost of these consistent correlation estimators makes them applicable to the study of turbulent fluid flows. This stochastic POD-ROM is applied to 2D and 3D DNS wake flows at Reynolds 100 and 300, respectively, with Uncertainty Quantification (UQ) and forecasting outside the learning interval in mind. The proposed stochastic POD-ROM approach is shown to stabilize the unstable temporal coefficients and to maintain their variability under control, while exhibiting an impressively accurate predictive capability.

Seismic fine imaging and its significance for natural gas hydrate exploration in the Shenhu Test Area, South China Sea

ABSTRACT Shenhu area in South China Sea includes extensive collapse and diapir structures, forming high-angle faults and vertical fracture system, which functions as a fluid migration channel for gas hydrate formation. In order to improve the imaging precision of natural gas hydrate in this area, especially for fault and fracture structures, the present work propose a velocity stitching technique that accelerates effectively the convergence of the shallow seafloor, indicating seafloor horizon interpretation and the initial interval velocity for model building. In the depth domain, pre-stack depth migration and residual curvature are built into the model based on high-precision grid-tomography velocity inversion, after several rounds of tomographic iterations, as the residual velocity field converges gradually. Test results of the Shenhu area show that the imaging precision of the fault zone is obviously improved, the fracture structures appear more clearly, the wave group characteristics significantly change for the better and the signal-to-noise ratio and resolution are improved. These improvements provide the necessary basis for the new reservoir model and field drilling risk tips, help optimize the favorable drilling target, and are crucial for the natural gas resource potential evaluation.

An Hα kinematic survey of the Herschel Reference Survey

Aims. We present new 2D high resolution Fabry–Perot spectroscopic observations of 152 star-forming galaxies that are part of the Herschel Reference Survey (HRS), which is a complete K-band selected, volume-limited sample of nearby galaxies that spans a wide range of stellar mass and morphological types. Methods. By using improved data reduction techniques, that provide adaptive binning based on Voronoi tessellation, and using large field-of-view observations, we derived high spectral resolution (R &gt; 10 000) Hα datacubes from which we computed Hα maps and radial 2D velocity fields that are based on several of thousand independent measurements. A robust method based on such fields allowed us to accurately compute rotation curves and kinematical parameters, for which uncertainties are calculated using a method based on the power spectrum of the residual velocity fields. Results. We checked the consistency of the rotation curves by comparing our maximum rotational velocities to those derived from H I data, and by computing the i-band, NIR, stellar, and baryonic Tully-Fisher relations. We used this set of kinematical data combined with those available at other frequencies to study, for the first time, the relation between the dynamical and the total baryonic mass (stars, atomic and molecular gas, metals, and dust) and to derive the baryonic and dynamical main sequence on a representative sample of the local universe.

CO Multi-line Imaging of Nearby Galaxies (COMING). VII. Fourier decomposition of molecular gas velocity fields and bar pattern speed

Abstract The 12CO (J = 1→0) velocity fields of a sample of 20 nearby spiral galaxies, selected from the CO Multi-line Imaging of Nearby Galaxies (COMING) legacy project of Nobeyama Radio Observatory, have been analyzed by Fourier decomposition to determine their basic kinematic properties, such as circular and noncircular velocities. On average, the investigated barred (SAB and SB) galaxies exhibit a ratio of noncircular to circular velocities of molecular gas larger by a factor of 1.5–2 than non-barred (SA) spiral galaxies at radii within the bar semimajor axis ab at 1 kpc resolution, with a maximum at a radius of R/ab ≈ 0.3. Residual velocity field images, created by subtracting model velocity fields from the data, reveal that this trend is caused by kpc-scale streaming motions of molecular gas in the bar region. Applying a new method based on radial velocity reversal, we estimated the corotation radius RCR and bar pattern speed Ωb in seven SAB and SB systems. The ratio of the corotation to bar radius is found to be in a range of $\mathcal {R}\equiv R_\mathrm{CR}/a_\mathrm{b} \approx 0.8$–1.6, suggesting that intermediate (SBb–SBc), luminous barred spiral galaxies host fast and slow rotator bars. Tentative negative correlations are found for Ωb vs. ab and Ωb vs. total stellar mass M*, indicating that bars in massive disks are larger and rotate slower, possibly a consequence of angular momentum transfer. The kinematic properties of SAB and SB galaxies, derived from Fourier decomposition, are compared with recent numerical simulations that incorporate various rotation curve models and galaxy interactions.

Kinematics of the Isolated Luminous Infrared Galaxy CIG 993

Abstract We present scanning Fabry–Perot interferometric observations of CIG 993, which is an apparently isolated luminous infrared galaxy that also exhibits luminous blue compact and Wolf–Rayet galaxy features, and which also has a high star formation rate. Our high-resolution observations of the Hα emission line allowed us to derive the radial velocity field (VF), the velocity dispersion σ, and the residual VFs of the galaxy. This galaxy exhibits several kinematical components. On the one hand, the velocity gradients detected on the VF can be associated with a rotating disk, which is in contrast to previous results with less spectral resolution. However, the VF, the σ and residual VF show significant deviations from circular motions in the central part of the galaxy that matches a region with high number of Wolf–Rayet and O stars, which is coincident with the blue luminous component of the galaxy. We find narrow and broad velocity components for the ionized gas in the central part of the galaxy. The broad component is evidence of a central outflow related with the ongoing burst of stellar formation. The morpho-kinematical analysis of the galaxy indicates we are only seeing the brightest parts of the galaxy, which correspond to the bulge, a central bar and the beginning of the disk. We believe that CIG 993 is a disk galaxy that harbors important star-forming processes, which are most likely caused by a relatively recent interaction. This could imply that small encounters can change the global characteristics of a galaxy without disturbing the main rotation disk motion or the morphology of the galaxy.

Laboratory experiment on the 3D tide-induced Lagrangian residual current using the PIV technique

The 3D structure of the tide-induced Lagrangian residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced Lagrangian residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the Lagrangian residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the Lagrangian and Eulerian residual currents shows that the Eulerian residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.

Monitoring geodynamic activity in the Victoria Land, East Antarctica: Evidence from GNSS measurements

GNSS networks in Antarctica are a fundamental tool to define actual crustal displacements due to geological and geophysical processes and to constrain the glacial isostatic models (GIA). A large network devoted to the detection and monitoring of crustal deformations in the Northern Victoria Land (Victoria Land Network for DEFormation control – VLNDEF), was monumented during the 1999–2000 and 2000–2001 field campaigns, as part of Italian National Program for Antarctic Research and surveyed periodically during the Southern summer seasons.In this paper, GPS observations of VLNDEF collected over a more than 15-year span, together with various selected POLENET sites and more than 70 IGS stations, were processed with Bernese Software, using a classical double difference approach. A solution was obtained combining NEQs by means of ADDNEQ2/FODITS tools embedded in Bernese Software. All the Antarctic sites were kept free and a subset of 50 IGS stations were used to frame VLNDEF into ITRF2008. New evidence provided by analysis of GPS time series for the VLNDEF network is presented; also displacements along the vertical component are compared with the recently published GIA models. The absolute velocities indicate an overall displacement of the northern Victoria Land region along the south-east direction (Ve=10.6mm/yr, Vn=−11.5mm/yr) and an average uplift rate of Vu=0.5mm/yr. Two GIA models have been analyzed: ICE-6G_C-VM5a proposed by Argus et al. (2014), Peltier et al. (2015) and W12A_v1 by Whitehouse et al. (2012a,b). Up rates, predicted over the VLNDEF sites by the mentioned GIA models, have been extracted and compared with those observed. A preliminary comparison with GPS-derived vertical rates shows that the Victoria Land ICE-6G_C-VM5 and W12A_v1 GIA models predict overestimated uplift rates of 0.7 and 0.9mm/yr weighted mean residuals respectively. The mean horizontal relative motions within the Victoria Land (VL) area are in most cases negligible, while only a few points exhibit horizontal velocities greater than the confidence level. Such a residual horizontal velocity field could represent some of the tectonic characteristics affecting VL, characterized by block faulting, tilting along NE striking and SE dipping extensional faults. Uplift rates, highlighted in the present paper depict a well defined spatial pattern in the investigated areas. Northward, all sites show a general positive trend up to 2.3mm/yr. In the central and southern areas small negative trends (up to −1.3mm/yr) were detected in the vertical displacements. Only the site VL06, located atop the Mt. Melbourne volcano, does not concord with such a general reading, as it is representative of the volcanic complex’s evolution. Observed and predicted uplift rates increase westward (inland) where the ice-load increases. The same behavior is predicted southward by the GIA models; whereas GPS values decrease toward the south pole, due to the movements of a few sites reflecting the neotectonic phenomena acting in the Victoria Land region.

The Local Spiral Arm in the LAMOST-Gaia Common Stars?

Abstract Using the LAMOST-Gaia common stars, we demonstrate that the in-plane velocity fields for the nearby young stars are significantly different from those for the old ones. For the young stars, the probably perturbed velocities that are similar to the old population are mostly removed from the velocity maps in the X–Y plane. The residual velocity field shows that the young stars consistently move along Y with faster v ϕ at the trailing side of the local arm, while at the leading side, they move slower in the azimuth direction. At both sides, on average the young stars move inward with a v R of km s−1. The divergence of the velocity in the Y direction implies that the young stars are associated with a density wave near the local arm. We therefore suggest that the young stars may reflect the formation of the local spiral arm by correlating themselves with a density wave. The range of the age for the young stars is around 2 Gyr, which is sensible since the transient spiral arm can persist for that long. We also point out that alternative explanations of the peculiar velocity field for the young population cannot be ruled out if solely using this observed data.

Modeling 3‐D crustal velocities in the United States and Canada

AbstractA numerical model for three‐dimensional (3‐D) crustal velocities has been derived for most of the United States and Canada, primarily from repeated geodetic data. This model provides a foundation for a prototype of the TRANS4D software. TRANS4D is being developed to enable geospatial professionals and others to transform 3‐D positional coordinates across time. The derived model reveals several macroscopic features of the 3‐D velocity field, including the pervasive presence of the glacial isostatic adjustment associated with the past melting of the ice fields that formed more than 19,000 years ago during the Last Glacial Maximum. In this study, the present‐day 3‐D velocity field associated with this melting (as estimated via the recently published ICE‐6G_C (VM5a) model) was subtracted from this study's total 3‐D velocity field to identify features of the residual velocity field. In particular, this study introduces the NA_ICE‐6G reference frame in which residual horizontal velocities have magnitudes that are less than 2 mm/yr everywhere east of longitude 104°W and south of latitude 60°N, except in southern Texas. Residual horizontal velocities of greater magnitude are found west and/or north of these two boundaries, and they are due mostly to interactions among tectonic plates with localized pockets due to other geophysical phenomena. Large residual vertical velocities, some with values exceeding 30 mm/yr, are found in southeastern Alaska. The uplift occurring here is due to present‐day melting of glaciers and ice fields formed during the Little Ice Age glacial advance that occurred between 1550 A.D. and 1850 A.D.

Hydrodynamics response to planned human interventions in a highly altered embayment: The example of the Bay of Cádiz (Spain)

Many bays worldwide are influenced by human interventions performed in the coastal embayment. Despite advances during recent years, the assessment and prediction of present and future impacts on the hydrodynamics of bays are still challenging tasks for both managers and scientists. This work presents an observational and numerical study on the impacts of planned human interventions in the Bay of Cádiz, an example of a heavily impacted bay that would change the hydrodynamic and sedimentary patterns due to the newly deepened channel. The Delft3D model is calibrated and tested during a period of 59 days with water level (R = 0.99), tidal current (R = 0.88) and residual current (R = 0.8) data obtained through a field survey from December 2011 to January 2012. The measurements revealed that the estuary is short and tidally driven and the water levels and currents are in quadrature. At the subtidal scale, the circulation patterns of the inner (hypersaline) and outer (thermal) portions operate almost independently. The results indicate that dredging activities will enhance residual currents, increasing both the erosion and deposition rates at various locations along the main channel. The analysis of the divergence of the residual velocity field shows that erosion is expected to occur on the banks and close to the intervention, whereas deposition mainly affects near-channel areas. Given that the proposed methodology can be applied to simulate altered bays, our results highlight the importance of analyzing the effects that these interventions can produce in similar environments.

Water fluxes and renewal rates at Pertuis d'Antioche/Marennes-Oléron Bay, France

Water renewal is crucial for removal of pollutants (e.g. oil), organic loadings, and oxygen supply and within shellfish farms. This study presents a 3-D hydrodynamic model with local resolution of 500 m used to quantify water renewal and water fluxes at Pertuis d'Antioche/Marennes-Oléron Bay, France. Open boundary conditions were based on MyOcean products (http://www.myocean.eu/) downscaled using four nested domains with increasing resolution from the large to the local scale. Results from a six-month model run were compared with data giving a good agreement. The spatial variation of water renewal was characterized by dividing the coastal waters into boxes which grouped the main shellfish areas. A Lagrangian model was coupled to the hydrodynamic model to track the history of water renewal. The boxes were filled with tracers and the pattern of particles passing through them was quantified. Model results were integrated over the volume of the boxes to calculate the water fluxes across box boundaries. The results of the integration provide horizontal and vertical fluxes of water which were used to assess the renewal of surface and bottom waters in the bay. Depending on tide and freshwater conditions, the water renewal ranges between 2 and 18 days. Main current patterns were investigated by drawing streamlines in the residual velocity field. It was found that eddies can slow down renewal rates, and either favour transport of tracers or locally trap them inside the bay. An assessment of typical trajectories of water particles released at different locations and depths provided insights into the potential dispersion of passive tracers, including spilled oil, and larvae.

Kinematics and strain rates of the Eastern Himalayan Syntaxis from new GPS campaigns in Northeast India

Newly acquired GPS data along transects across Himalaya in Eastern Himalayan Syntaxis (EHS) reveal a clockwise rotation of rigid micro-plate comprising part of Brahmaputra valley, NE Himalaya and Northern Myanmar that rotates about a pole located at 14.5°N, 100.8°E at an angular rate of 1.75±0.12°/Myr. The EHS is being torn-off from the main Indian Plate as a rigid block around which the kinematic clockwise rotation of Tibetan GPS sites toward the Sichuan-Yunnan region occurs in the Eurasia fixed frame. The residual velocity field of the newly acquired data estimated after removing the rotation that minimizes the GPS rates around EHS show a clear NE motion of the EHS sites, indentation of the rigid Indian plate into a less rigid area of the Eurasian plate. The most extensive EHS zones of compression and shortening are in the direction of indenter convergence, with average values ranging between ~50–100 nanostrain/year. Along the frontal segment of EHS, from NW to SE, the shortening rate is reduced from the local maximum value of 160 to ~80 nanostrain/year, thus indicating a possibly locked fault patch of Mishmi or Lohit thrusts, the southernmost part of segment activated during the large 1950 Assam earthquake, Mw 8.6.An elastic block-model was invoked to infer the average slip rates of sections around EHS and to estimate an average locking depth of ~15km. The slip rate perpendicular to the locked sector of EHS reaches 32.4mm/year and permits to roughly infer a recurrence time of ~200year for an earthquake as energetic as the 1950 Assam event.

Mixed moving least-squares method for shakedown analysis

The elastic shakedown theory can be used to analyze and design structures under loads that change over time. Methods that use mixed interpolations provide simultaneous information regarding the kinematics and the equilibrium without the necessity of postprocessing. Meshless methods, as suggested by the name, do not require mesh generation or node connectivity and are an alternative to classical numerical methods. However, no current method exists that combines a mixed approximation of the kinematics and equilibrium with meshless methods for an elastic shakedown problem. In this paper, a discretization of a mixed variational principle for the elastic shakedown is presented based on the moving least-squares method, where stress and velocity approximation functions are used. The optimization problem, which comes from the mixed variational principle, determines the load factor and the residual stress and velocity fields. The stresses and velocities are approximated using linear and quadratic polynomial functions, respectively. The solution to the problem is obtained through a nonlinear algorithm based on Newton’s method. The results obtained for the load factor and the residual stress field approach those obtained from the analytical solution for the tested examples.

Geodetic evidence for low coupling on the Hellenic subduction plate interface

We develop a block model for the Aegean and surrounding areas, constrained by Global Positioning System (GPS), in order to investigate the degree of coupling on the Hellenic subduction interface (i.e., the fraction of the motion across the plate boundary accommodated by elastic strain accumulation). We use previously published models, and seismicity to define the geometry of the interface separating the down-going Nubian slab from the overriding Aegean. This model provides a good fit to the GPS observations; for the ∼200,000 km2 Aegean block the wrms of the residual velocities is 1.4 mm/yr for 80 GPS velocity estimates, approximately the 95% level of the GPS velocity uncertainties. We investigate the degree of coupling on the seismically active plate interface, the Hellenic trench splay fault (believed to be the source of the 365 AD Great Crete Earthquake and Tsunami), and the Kephalonia transform fault by comparing the modeled GPS residual velocity field for a range of coupling values. The GPS observations are almost insensitive to coupling on the Kephalonia transform fault, because of the vertical dip of the fault that creates interseismic deformation only close to the fault where few GPS sites exist. The absence of resolvable shortening of the leading edge of the Aegean Plate precludes coupling of more than 0.2 (20% of the full Nubia–Aegean convergence rate) on the modeled plate interface. Because of the shallow dip of the plate interface and trench splay fault, and high rate of convergence, if these boundaries were fully coupled, high elastic strain rates would be expected to extend well into the overriding Aegean plate. Based on our preferred value for the degree of coupling (0.1), and assuming characteristic earthquake behavior, we estimate a recurrence time for great earthquakes with slip similar to that for the 365 Crete event of 5700–8300 yr, consistent with the absence of subsequent great earthquakes on this segment of the subduction zone.