effects of stencil width on surface ocean geostrophic velocity and vorticity estimation from gridded satellite altimeter data 1 this paper examines the effect of stencil width on surface ocean geostrophic velocity and vorticity estimated from differentiating gridded satellite altimeter sea surface height products in oceanographic applications the value of the first derivative at a central grid point is generally obtained by differencing the sea surface heights at adjacent grid points this is called a three point stencil centered difference here the stencil width is increased from three to five seven and nine points using well known formulae from the numerical analysis literature the discrepancies between velocities computed with successive stencils decreases with increasing stencil width suggesting that wide stencil results are more reliable significant speed dependent biases up to 10 20 are found between results computed from three point stencils versus those computed from wider stencils the geostrophic velocity and the variance of geostrophic velocity are underestimated with thin stencils similar results are seen in geostrophic velocities computed from high resolution model output in contrast to the case when three point stencils are used wider stencils yield estimates of theanisotropy of velocity variance that are insensitive to the differences in grid spacing between two widely used altimeter products three point stencils yield incorrect anisotropies on the 1 4 anisotropic aviso grid we recommend the use of 7 point stencils despite the demonstrated inadequacies of the three point stencils the conclusions of earlier studies based on them that the zonally averaged midlatitude eddy kinetic energy field is nearly isotropic are found to pertain also with wider stencils finally the paper also examines the strengths and limitations of applying noise suppressing differentiators versus classic centered differences to altimeter data

dynamic uplift of the himalaya it has become widely accepted that the himalaya is the product of collision between the indian landmass and the eurasian continent holmes1 conjectured that the indian shield was carried northwards by sub lithospheric mantle flow to cause a double thickening of crust beneath the himalayas and the tibetan plateau wager2 hypothesized that the extra height of the great peaks of the himalaya over tibet was due to isostatic readjustment following the removal of load by intense erosion molnar et al 3 relate the uplift to the shear stress on the boundary faults beneath the himalayas relevant data have recently become available from the northern flank of the himalaya and the tibet plateau of which especially important are 1 a gravity profile across central tibet 2 seismic crustal structures of the region from explosion seismology 3 seismicity 4 geothermal activities 5 geodetic palaeogeographical and radiometric data bearing on the uplift rate of the region and 6 field observation of the surface fault patterns the combined data set has imposed strong constraints on theories of the dynamic processes in this region we summarize here the relevant observations and discuss the results and implications of our model analysis details of the modelling procedure are given elsewhere4

eddy activity and mixing in upwelling systems a comparative study of northwest africa and california regions a comparative modeling approach is used to study the mesoscale dynamics of coastal transition zones in the upwelling systems of western sahara and central california it is shown that large differences in eddy activity and mixing exist between the two systems since upwelling favorable winds off central california and western sahara have similar amplitudes we suggest that observed and modeled differences in eddy activity are due to differences in configuration parameters it is argued that two of these parameters stratification and topography eventually affect the energy available for the mesoscales through baroclinic instability the large difference in stratification appears to be linked to the salinity structure formed by the large scale circulation and is directly related to available potential energy the shape of the continental shelf affects the position structure and scale of the ekman divergence hence upwelling intensity and frontal formation the potential impact of mesoscale eddy mixing and its variability on upwelling ecosystems is discussed

the role of a heterogeneous inclusion during continental collision abstract we study a simple model of the deformation due to collision between two continental plates the model is patterned after the geometry of the india asia collision but it may be applicable to more general situations the collision is modelled by the indentation of a viscoplastic plate asia by a rigid punch india a finite element approach capable of dealing with finite deformation heterogeneity and non linear rheologies is used to study the role of an inclusion of increased rigidity on the viscoplastic flow of the plate the heterogeneous zone was chosen to approximate the shape and position of the tarim basin behind tibet the lateral boundaries of the plate were defined so as to approximate those that are believed to apply for the asian plate i e fixed boundaries to the west and north free boundaries to the west and south several geometries and contrasts of rheology were analyzed to verify the general validity of our results the purpose was to determine the main kinematic features of the flow not to model the particular case of tarim it is found that the heterogeneity affects the flow in a drastic way even for small contrasts of rigidity and for small size heterogeneities the main effect of the heterogeneity is to create two important shear zones or internal boundary layers the most important is in front of the inclusion separating the main flow from the inclusion as the flow proceeds the inclusion rotates and the shear zone progressively bends in qualitative agreement with the bending of the large strike slip faults like the altyn tagh that separates the tarim from tiber our model of continuous deformation does not allow for the formation of faults or fractures but the shear zones may be understood as the initial stages for the generation of fractures or velocity discontinuities another shear zone develops to the left of the inhomogeneity near the fixed boundary and in the wake of the punch the role of these shear zones is to isolate the heterogeneity from the main flow to facilitate its rigid rotation inside the flow of the softer plate a final observation is that in the presence of the heterogeneity the lower left hand corner rotates almost like a rigid block producing a sharp bend on the left hand side of the plate as the inclusion rotates pushed by the punch this rigid block rotates clockwise to open up the space necessary for the homogeneity

lithospheric deformation beneath the himalayan region abstract the structure of the highly seismic himalayan region is a consequence of continuing convergence of the indian and eurasian plates we have carried out plane strain elastic model calculations to examine a hypothesis on the likely interacting forces which are responsible for slow lithospheric deformation and seismicity in the himalayan region we conclude that the seismicity arises wholly from differential stresses which result from a significant force exerted by the tibetan plateau

vertical structure of mesoscale eddies in the eastern south pacific ocean a composite analysis from altimetry and argo profiling floats 1 the mean vertical structure of mesoscale eddies in the peru chile current system is investigated by combining the historical records of argo float profiles and satellite altimetry data a composite average of 420 526 profiles acquired by argo floats that surfaced into cyclonic anticyclonic mesoscale eddies allowed constructing the mean three dimensional eddy structure of the eastern south pacific ocean key differences in their thermohaline vertical structure were revealed the core of cyclonic eddies ces is centered at 150 m depth within the 25 2 26 0 kg m 3 potential density layer corresponding to the thermocline in contrast the core of the anticyclonic eddies aes is located below the thermocline at 400 m depth impacting the 26 0 26 8 kg m 3 density layer this difference was attributed to the mechanisms involved in the eddy formation while intrathermocline ces would be formed by instabilities of the surface equatorward coastal currents the subthermocline aes are likely to be shed by the subsurface poleward peru chile undercurrent in the eddy core maximum temperature and salinity anomalies are of 1 c and 0 1 with positive negative values for aes ces this study also provides new insight into the potential impact of mesoscale eddies for the cross shore transport of heat and salt in the eastern south pacific considering only the fraction of the water column associated with the fluid trapped within the eddies each ce and ae has a typical volume anomaly flux of 0 1 sv and yields to a heat and salt transport anomaly of 1 3 1011 w and 3 8 103 kg s 1 respectively

how did the foreland react yangtze foreland fold and thrust belt deformation related to exhumation of the dabie shan ultrahigh pressure continental crust eastern china during the triassic collision of the yangtze and sino korean cratons the leading edge of the yangtze crust subducted to mantle depths and was subsequently exhumed as a penetratively deformed coherent slab capped by a normal shear zone this geometry requires a reverse shear zone at the base of the slab and we suggest that the yangtze foreland fold and thrust belt constitutes this zone lower triassic rocks of the eastern foreland record nw se compression as the oldest compressional stress field onset of related deformation is indicated by middle triassic clastic sedimentation subsequent jurassic stress fields show a clockwise change of compression directions based on nearly coeval onset and termination of deformation and on a common clockwise change in the principal strain stress directions we propose that the foreland deformation was controlled by the extrusion of the ultra high pressure slab widespread cretaceous cenozoic reactivation occurred under regional extension to transtension which characteristically shows a large scale clockwise change of the principal extension directions during the lower cretaceous

constraints on the structure of the himalaya from an analysis of gravity anomalies and a flexural model of the lithosphere the intracontinental subduction of india beneath the himalaya presents several similarities to that occurring at island arcs we study one of those similarities by analyzing gravity anomalies across the himalaya assuming that the topography is supported by the indian elastic plate flexed under the weight of both the overthrust mountains and the sediments in the ganga basin we first examine in detail the effects of each of the following parameters on the configuration of the elastic plate and on the gravity anomalies the flexural rigidity the position of the northern end of the elastic plate the amount of underthrusting of such a plate beneath the range and the density contrasts between the crust and mantle and between the sediments and the crust a plate with a constant flexural rigidity of about 0 7 1025 n m between 0 2 and 2 0 1025 n m allows a good fit to the data from the lesser himalaya and the ganga basin such a plate however cannot underthrust the entire himalaya instead the gravity anomalies show that the moho steepens from only about 3 beneath the lesser himalaya to about 15 beneath the greater himalaya this implies a smaller flexural rigidity beneath the greater himalaya 0 1 to 1 0 1023 n m than beneath the ganga basin and the lesser himalaya even with a thin weak plate beneath the greater himalaya the weight of the mountains depresses the plate too much unless an additional force or moment is applied to the plate the application of a bending moment unit length to the end of the plate of about 0 6 1018 n m is adequate to elevate the indian plate and to bring the calculated gravity anomalies in agreement with those observed both the smaller flexural rigidity and the bending moment can be understood if we assume that part or all of the indian crust has been detached from the lower lithosphere that underthrusts the greater himalaya we study the tectonic implications of these results by means of a series of idealized balanced cross sections from the collision to the present that reproduce several important features of the geology of the himalaya and predict an amount of eroded material comparable to that in the ganga basin and the bay of bengal these cross sections include high grade metamorphic rocks near the main central thrust and a steeper dip of it there than in the lesser himalaya they predict rapid uplift only in the greater himalaya and at the foot of the lesser himalaya

quantifying atlantic water transport to the nordic seas by remote sensing abstract in this study the variability of atlantic water aw entering the nordic seas from the north atlantic through the passage between iceland the faroe islands and scotland has been investigated the poleward transport of this warm aw is a key component in maintaining a relatively mild climate in the northwestern europe satellite remote sensing datasets from altimetry and the gravity field and steady state ocean circulation explorer goce mission in combination with surface drifters fixed current meter and hydrographic data are used the high resolution mean dynamic topography mdt is shown to resolve the time invariant surface currents in the inflow region in addition to the improved mdt we take benefit of the new reprocessed sea level anomaly data in the estimation of absolute dynamic topography analysis of the monthly surface velocities from 1993 to 2016 demonstrates significant influence of the large scale atmospheric forcing associated with the north atlantic oscillation nao furthermore a significant increase in surface velocities along the slope current front current and the norwegian coastal current are found during winter finally combining altimetry with hydrographic data we demonstrate that the variability in surface velocities of the inflow region is also reflected in the deeper layers and that altimetry therefore can be used to monitor the variability of the poleward transport of aw in this region

m2 internal tides and their observed wavenumber spectra from satellite altimetry abstracta near global chart of surface elevations associated with the stationary m2 internal tide is empirically constructed from multimission satellite altimeter data an advantage of a strictly empirical mapping approach is that results are independent of assumptions about ocean wave dynamics and in fact can be used to test such assumptions a disadvantage is that present day altimeter coverage is only marginally adequate to support mapping such short wavelength features moreover predominantly north south ground track orientations and contamination from nontidal oceanographic variability can lead to deficiencies in mapped tides independent data from cryosphere satellite 2 cryosat 2 and other altimeters are used to test the solutions and show positive reduction in variance except in regions of large mesoscale variability the tidal fields are subjected to two dimensional wavenumber spectral analysis which allows for the construction of an empirical map of modal wavelengths mode 1 wavelengths sho

north south extension within the convergent himalayan region recent work by burg et al 1984 indicates the presence of east west striking gently north dipping normal faults in the higher himalayas and southern tibet that formed during postcollisional convergence of india and tibet these faults extend for at least 800 km along strike we interpret these normal faults as probable late miocene extensional features with perhaps several tens of kilometres of down to the north displacement a simple elastic model suggests that these normal faults may have formed during gravitational collapse of the miocene topographic front between india and tibet in this interpretation gravitational collapse occurred by southward motion relative to india and tibet of a wedge of crustal rocks bounded above by gently north dipping normal faults and below by thrust faults that probably dip north north south extension produced in this way is probably confined to upper crustal levels only and does not reflect regional extension of the entire lithosphere

cross shore transport variability in the california current ekman upwelling vs eddy dynamics abstract the low frequency dynamics of coastal upwelling and cross shelf transport in the central and southern california current system ccs are investigated using the regional ocean modeling system roms over the period 1965 2008 an ensemble of passive tracers released in the numerical model is used to characterize the effects of linear ekman upwelling and non linear mesoscale eddies circulation dynamics on the statistics of advection of coastal waters the statistics of passive tracers released in the subsurface show that the low frequency variability of coastal upwelling and cross shelf transport of the upwelled water mass are strongly correlated with the alongshore wind stress and are coherent between the central and southern ccs however the offshore transport of tracers released at the surface is not coherent between the two regions and is modulated by intrinsic mesoscale eddy activity in particular cyclonic eddies the transport of cyclonic eddies extends with depth and entrains water masses of southern origin advected by the poleward california undercurrent cuc the cuc water masses are not only entrained by eddies but also constitute a source for the central california upwelling system the interplay between intrinsic eddy activity and deterministic ekman upwelling dynamics in controlling the cross shelf exchanges in the ccs may provide an improved framework to understand and interpret nutrients and ecosystem variability

implications of refined altimetry on estimates of mesoscale activity and eddy driven offshore transport in the eastern boundary upwelling systems we investigate the extent to which the recently upgraded version of the ssalto duacs sea level anomaly product affects the description of mesoscale activity in the eastern boundary upwelling systems ebus drifter observations confirm that the new data set released by archiving validation and inter pretation of satellite oceanographic data aviso in april 2014 dt14 offers an enhanced description of mesoscale activity for the four ebus dt14 returns significantly higher eddy kinetic energy levels 80 within a 300 km coastal band where mesoscale structures are known to induce important lateral phys ical and biogeochemical fluxes when applied to dt14 an automatic eddy detection algorithm detects more eddies in the ebus 37 and lower eddy radius estimates in comparison with results using the for mer altimetry product dt10 we show that despite higher eddy densities the smaller eddy radii result in westward eddy transport estimates that are smaller than those obtained from dt10 12

high frequency response of wind driven currents measured by drifting buoys and altimetry over the world ocean 1 we investigate the wind driven current response over the world ocean using svp drifting buoys ers 1 and ers 2 and topex altimetry data and ecmwf wind stress fields wind driven ageostrophic currents are estimated from drifting buoys by removing altimetry deduced geostrophic currents from observed drifting velocities removing the geostrophic signal enhances the coherence with wind stress at periods longer than 10 days for superinertial periods lower than 20 days a two parameter i e angle and amplitude model is fitted to the isolated ageostrophic signal to study the upper ocean response to surface wind stress in that frequency band the model which can explain up to 30 of the variance in some areas indicates that the currents spiral to the right left of the wind with depth in the northern southern hemisphere in agreement with the ekman theory the absolute value of the angle parameter is found to exhibit significant spatial and seasonal variability the vertical eddy viscosity and the ekman layer depth as deduced from ekman theory are compared to previous results their seasonal variability is also studied model results are then used to compute the mean and standard deviation of ageostrophic currents in 5 boxes over the world ocean the equatorial divergence and the subpolar and subtropical convergence zones are well reproduced

satellite observations of chlorophyll phytoplankton biomass and ekman pumping in nonlinear mesoscale eddies nonlinear mesoscale eddies can influence biogeochemical cycles in the upper ocean through vertical and horizontal advection of nutrients and marine organisms the relative importance of these two processes depends on the polarity of an eddy cyclones versus anticyclones and the initial biological conditions of the fluid trapped in the core of the eddy at the time of formation eddies originating in the eastern south indian ocean are unique in that anticyclones typically associated with downwelling contain elevated levels of chlorophyll a enhanced primary production and phytoplankton communities generally associated with nutrient replete environments from analysis of 9 years of concurrent satellite measurements of sea surface height chlorophyll phytoplankton carbon and surface stress we present observations that suggest eddy induced ekman upwelling as a mechanism that is at least partly responsible for sustaining positive phytoplankton anomalies in anticyclones of the south indian ocean the biological response to this eddyinduced ekman upwelling is evident only during the austral winter during the austral summer the biological response to eddy induced ekman pumping occurs deep in the euphotic zone beyond the reach of satellite observations of ocean color

main eddy vertical structures observed in the four major eastern boundary upwelling systems in the four major eastern boundary upwelling systems ebus mesoscale eddies are known to modulate the biological productivity and transport near coastal seawater properties toward the offshore ocean however little is known about their main characteristics and vertical structure this study combines 10 years of satellite altimetry data and argo float profiles of temperature and salinity and our main goals are i to describe the main surface characteristics of long lived eddies formed in each ebus and their evolution and ii to depict the main vertical structure of the eddy types that coexist in these regions a clustering analysis of the argo profiles surfacing within the long lived eddies of each ebus allows us to determine the proportion of surface and subsurface intensified eddies in each region and to describe their vertical structure in terms of temperature salinity and dynamic height anomalies in the peru chile upwelling system 55 of the sampled anticyclonic eddies aes have subsurface intensified maximum temperature and salinity anomalies below the seasonal pycnocline whereas 88 of the cyclonic eddies ces are surface intensified in the california upwelling system only 30 of the aes are subsurface intensified and all of the ces show maximum anomalies above the pycnocline in the canary upwelling system 40 of the aes and 60 of the ces are subsurface intensified with maximum anomalies extending down to 800 m depth finally the benguela upwelling system tends to generate 40 50 of weak surface intensified eddies and 50 60 of much stronger subsurface intensified eddies with a clear geographical distribution the mechanisms involved in the observed eddy vertical shapes are discussed

front eddy influence on water column properties phytoplankton community structure and cross shelf exchange of diatom taxa in the shelf slope area off concepcion 36 37 s in eastern boundary current systems ebcss submesoscale to mesocale variability contributes to cross shore exchanges of water properties nutrients and plankton data from a short term summer survey and satellite time series january february 2014 were used to characterize submesoscale variability in oceanographic conditions and phytoplankton distribution across the coastal upwelling and coastal transition zones north of punta lavapie and to explore cross shelf exchanges of diatom taxa a thermo haline front frn 1 flanked by a mesoscale anticyclonic intrathermocline eddy ite 1 or mode water eddy persisted during the study period and the survey was undertaken during a wind relaxation event at the survey time ite 1 contributed to an onshore intrusion of warm oceanic waters southern section and an offshore advection of cold coastal waters northern section with the latter forming a cold high chlorophyll a filament in situ phytoplankton and diatom biomasses were highest at the surface in frn 1 and at the subsurface in ite 1 whereas values in the coastal zone were lower and dominated by smaller cells diatom species typical of the coastal zone and species dominant in oceanic waters were both found in the frn 1 and ite 1 interaction area suggesting that this mixture was the result of both offshore and onshore advection overall front eddy interactions in ebcss could enhance cross shelf exchanges of coastal and oceanic plankton as well as sustain phytoplankton growth in the slope area through localized upward injections of nutrients in the frontal zone combined with ite induced advection and vertical nutrient inputs to the surface layer

the evolution and propagation of quasigeostrophic ocean eddies abstractthe long term evolution of initially gaussian eddies is studied in a reduced gravity shallow water model using both linear and nonlinear quasigeostrophic theory in an attempt to understand westward propagating mesoscale eddies observed and tracked by satellite altimetry by examining both isolated eddies and a large basin seeded with eddies with statistical characteristics consistent with those of observed eddies it is shown that long term eddy coherence and the zonal wavenumber frequency power spectral density are best matched by the nonlinear model individual characteristics of the eddies including amplitude decay horizontal length scale decay and zonal and meridional propagation speed of a previously unrecognized quasi stable state are examined the results show that the meridional deflections from purely westward flow poleward for cyclones and equatorward for anticyclones are consistent with satellite observations examination of the fluid transport properties of the eddies shows that an

a three dimensional eddy census of a high resolution global ocean simulation 1 a three dimensional eddy census data set was obtained from a global ocean simulation with one tenth degree resolution and a duration of 7 years the census includes 6 7 million eddies in daily data which comprise 152 000 eddies tracked over their lifetimes using a minimum lifetime cutoff of 28 days variables of interest include eddy diameter thickness vertical extent minimum and maximum depth location rotational direction lifetime and translational speed distributions of these traits show a predominance of small thin short lived and slow eddies still a significant number of eddies possess traits at the opposite extreme thousands of eddies larger than 200 km in diameter appeared in daily data each year a tracking algorithm found hundreds of eddies with lifetimes longer than 200 days a third of the eddies are at least 1000 m tall and many penetrate the full depth of the water column the antarctic circumpolar current contains the thickest and highest density of eddies thick eddies are also common in the gulf stream kuroshio current and agulhas ring pathway the great majority of eddies extend all the way to the surface confirming that eddy censuses from surface observations are a good proxy for the full depth ocean correlations between variables show that larger diameter eddies tend to be thicker and longer lived than small eddies

new cnes cls09 global mean dynamic topography computed from the combination of grace data altimetry and in situ measurements 1 an accurate knowledge of the ocean mean dynamic topography mdt is mandatory for the optimal use of altimetric data including their assimilation into operational ocean forecasting systems a new global 1 4 resolution mdt was computed for the 1993 1999 time period with improved data and methodology compared to the previous rio05 mdt field first a large scale mdt is obtained from the cls01 altimetric mean sea surface and a recent geoid model computed from 4 5 years of grace gravity recovery and climate experiment data altimetric sea level anomalies and in situ measurements are then combined to compute synthetic estimates of the mdt and the corresponding mean currents while the rio05 mdt was based on 10 years of in situ dynamic heights and drifting buoy velocities the new field benefits from an enlarged data set of in situ measurements ranging from 1993 to 2008 and includes all hydrological profiles from the argo array moreover the processing of the in situ data has been updated a new ekman model was developed to extract the geostrophic velocity component from the drifting buoy measurements the handling of hydrologic measurements has also been revisited compared to the previous rio05 solution the new global mdt resolves much stronger gradients in western boundary currents with mean velocities being doubled in some places moreover in comparison to several other recent mdt estimates we find that the new cnes cls09 mdt is in better agreement with independent in situ observations

velocities and propagation characteristics of pn and sn beneath the himalayan arc and tibetan plateau possible evidence for underthrusting of indian continental lithosphere beneath tibet new seismological observations on velocities and propagation characteristics of pn and sn waves beneath tibet can be interpreted although not uniquely to indicate the shallow angle underthrusting of the greater indian continental lithosphere beneath the tibetan plateau this is inferred from available geological and geophysical data and is now supported by new seismological observations the most significant observation is that high frequency sn waves shear waves that travel in the mantle lithosphere propagate efficiently in the uppermost mantle beneath the tibetan plateau except beneath the north central part of tibet the chang thang terrane furthermore sn propagates efficiently across the stable block of the tarim basin along the tien shan and himalayan mountains and across the indian shield apparent velocities of pn and sn waves that traverse the uppermost mantle beneath the tibetan plateau are 8 42 and 4 73 km s respectively these velocities are very similar to those beneath the himalayan mountains and the indian shield the efficient propagation and the velocities of pn and sn waves beneath tibet are also similar to those commonly observed beneath shield and stable continental regions these results are consistent with the underthrusting model and do not favor the class of alternative models in which the tibetan plateau is formed by shortening and thickening of hot crustal and uppermost mantle material in response to the convergence of india and asia

subregional characterization of mesoscale eddies across the brazil malvinas confluence horizontal and vertical motions associated with coherent mesoscale structures including eddies and meanders are responsible for significant global transports of many properties including heat and mass mesoscale vertical fluxes also influence upper ocean biological productivity by mediating the supply of nutrients into the euphotic layer with potential impacts on the global carbon cycle the brazil malvinas confluence bmc is a western boundary current region in the south atlantic with intense mesoscale activity this region has an active role in the genesis and transformation of water masses and thus is a critical component of the atlantic meridional overturning circulation the collision between the malvinas and brazil currents over the patagonian shelf slope creates an energetic front that translates offshore to form a vigorous eddy field recent improvements in gridded altimetric sea level anomaly fields allow us to track bmc mesoscale eddies with high spatial and temporal resolutions using an automated eddy tracker we characterize the eddies across fourteen 5 5 subregions eddy centric composites of tracers and geostrophic currents diagnosed from a global reanalysis of surface and in situ data reveal substantial subregional heterogeneity the in situ data are also used to compute the evolving quasi geostrophic vertical velocity qg associated with each instantaneous eddy instance the qg eddy composites have the expected dipole patterns of alternating upwelling downwelling however the magnitude and sign of azimuthally averaged vertical velocity varies among subregions maximum eddy values are found near fronts and sharp topographic gradients in comparison with regional eddy composites subregional composites provide refined information about mesoscale eddy heterogeneity this article is protected by copyright all rights reserved

stochastic finite element calculation of seismic risk abstract the probable locations and the times of occurrence of earthquakes can be suggested if a reasonably accurate finite element model of the area is available this can be done by determining the unstable regions of the model and studying their evolution in time instability of a particular area depends on how close such a region is to a limiting strength and this closeness can be interpreted statistically