crack fusion dynamics a model for large earthquakes the physical processes of the fusion of small cracks into larger ones are nonlinear in character a study of the nonlinear properties of fusion may lead to an understanding of the instabilities that give rise to clustering of large earthquakes we have investigated the properties of simple versions of fusion processes to see if instabilities culminating in repetitive massive earthquakes are possible we have taken into account such diverse phenomena as the production of aftershocks the rapid extension of large cracks to overwhelm and absorb smaller cracks the influence of anelastic creep induced time delays healing the genesis of juvenile cracks due to plate motions and others a preliminary conclusion is that the time delays introduced by anelastic creep may be responsible for producing catastrophic instabilities characteristic of large earthquakes as well as aftershock sequences however it seems that nonlocal influences i e the spatial diffusion of cracks may play a dominant role in producing episodes of seismicity and clustering

origin of the giant eruption cloud of pinatubo june 15 1991 the series of eruptions of june 15 1991 at mt pinatubo philippines were observed hourly by satellite a giant discshaped cloud covering an area of 60 000 km2 appeared in the satellite images at 14 40 philippine time the cloud expanded radially against wind of 20 m s and spread to an area of more than 120 000 km2 within an hour according to eyewitness accounts there was heavy fine ash fall after 14 00 intermittent lapilli fall started at about 14 20 and heavy and continuous lapilli fall widely started at about 15 00 the occurrence of the giant cloud roughly corresponded to the initiation of the intermittent lapilli fall the air fall deposits of the major eruption are widely distributed including upwind from the vent they are composed of 3 units a silt size fine ash layer layer b a lapilli layer commonly including pumice grains of 1 cm in diameter layer c a lapilli bearing volcanic sand layer layer d judging from its wide distribution and depletion of coarse grains most of the fine ash of layer b is not distal deposits of a small eruption but is originated from a large co ignimbrite cloud it is suggested that the major eruption started with the generation of a pyroclastic flow which was subsequently followed by a plinian eruption resulting in the formation of the giant cloud and the lapilli fall the results of calculations on the dynamics of eruption cloud indicate that the dimension and dynamics of the giant eruption cloud is accounted for by a plinian eruption with a magma discharge rate of the order of 109 kg s

fractal reconstruction of sea floor topography sea floor bathymetric profiles exhibit features at many different scales of length this suggests that they could be described as fractals an algorithm interpolating a fractal line between points has been used to reconstruct bathymetric profiles from a few data points in general this fractal line has the same fourier amplitude spectrum as real bathymetry and if the parameters of the interpolation are suitably chosen it has a very similar appearance the success of this fractal reconstruction algorithm for the sea floor raises the possibility that it could be used to extrapolate from data collected at one scale the properties of the sea floor at finer scales and that similar techniques could be used to interpolate a surface between bathymetric profiles the fractal character is a sign that the processes that shape the sea floor are scale invariant and suggests that the renormalization group technique could be used to model these processes

the statistical mechanics of earthquakes abstract we review recent theoretical developments on the physics of earthquakes in particular we focus on the rise of the statistical mechanical view of earthquakes as a kind of phase transition this view is appealing in light of the well known scaling relations such as the gutenberg richter magnitude frequency and omori s law of aftershock decay scaling relations such as these which are in reality power laws are known to be associated with dynamical systems residing near a critical point in the state space of the system these second order critical points are associated with second order transitions which are a result of gradual changes of the controlling parameters at the same time characteristic earthquakes which involve the entire fault segment sliding nearly at once are more reminiscent of a first order transition which is characterized by sudden widespread changes in the physical state of the system in this paper we review these ideas and show how recent developments are leading to a view of earthquake fault systems based on modern statistical mechanics

a model for repetitive cycles of large earthquakes the theory of the fusion of small cracks into large ones reproduces certain features also observed in the clustering of earthquake sequences by modifying our earlier model to take into account the stress release associated with the occurrence of large earthquakes we obtain repetitive periodic cycles of large earthquakes a preliminary conclusion is that a combination of the stress release or elastic rebound mechanism plus time delays in the fusion process are sufficient to destabilize the crack populations and ultimately give rise to repetitive episodes of seismicity

premonitory transformation of steel fracturing and seismicity abstract transformation of microfracturing preceding the break up of steel and rock samples is similar to transformation of earthquakes flow prior to strong earthquakes in southern california the break up in a sample is preceded by transition from formation of new microcracks to coalescence or expansion of existing cracks this is reflected in the relation between the length and the number of the cracks similar transformation of seismicity precedes southern california earthquakes with magnitude m 6 6 1935 1994 specifically magnitude frequency relation bends downward for magnitudes from 3 to 4 5 and upward for magnitudes from about 4 5 to 6 in the usual notations the b value becomes larger in the first interval and smaller in the second one this transformation is accompanied by the increased share of aftershocks in the earthquakes flow in such a way the approach of a strong earthquake is reflected in both major traits of seismicity magnitude frequency relation and earthquake clustering imprecision of the earthquake catalog and reasonable variations in its analysis do not change our conclusions this phenomenon explains so far qualitatively a wide set of premonitory seismicity patterns we give it a formal definition allowing to test whether it takes place in other seismic regions

thermal disequilibrium at the top of volcanic clouds and its effect on estimates of the column height satellite images of large volcanic explosions reveal that the tops of volcanic eruption columns are much colder than the surrounding atmosphere1 we propose that this effect occurs whenever a mixture of hot volcanic ash and entrained air ascends sufficiently high into a stably stratified atmosphere although the mixture is initially very hot it expands and cools as the ambient pressure decreases we show that cloud top undercoolings in excess of 20 c may develop in clouds that penetrate the stratosphere this is consistent with observations of the 4 april 1982 eruption of el chichon1 and the 18 may 1980 eruption of mount st helens2 furthermore from our model results we predict that for a given cloud top temperature variations in the initial temperature of 100 200 c may correspond to variations in the column height of 5 10 km we deduce that the present practice of converting satellite based measurements of the temperature at the top of volcanic eruption columns to estimates of the column height will produce rather inaccurate results and should therefore be discontinued

premonitory seismicity changes prior to the parkfield and coalinga earthquakes in southern california abstract in this work we apply the pattern informatics technique for evaluating one surface expression of the underlying stress field the seismicity in order to study the parkfield coalinga interaction over the years preceding the 1983 coalinga earthquake we find that significant anomalous seismicity changes occur during the mid 1970s in this region prior to the coalinga earthquake that illustrate a reduction in the probability of an event at parkfield while the probability of an event at coalinga is seen to increase this suggests that the one event did not trigger or hinder the other rather that the dynamics of the earthquake system are a function of stress field changes on a larger spatial and temporal scale

the dynamics and thermodynamics of volcanic clouds theory and observations from the april 15 and april 21 1990 eruptions of redoubt volcano alaska on april 15 1990 and april 21 1990 two relatively small explosive eruptions occurred at redoubt volcano alaska lasting about 4 and 8 minutes respectively on both occasions the erupted material travelled as a pyroclastic flow down an ice canyon on the north flank of the volcano using slow scan television recordings of the eruption and the seismic record in both the near and far field we deduce that after a few minutes the upper parts of these pyroclastic flows became buoyant and a large and hot ash cloud ascended off the flow these thermals rose to a height of about 12 km at which point they began to spread laterally as umbrella clouds using a simple thermodynamic model we estimate that the clouds had a temperature in the approximate range 600 700 k as they rose buoyantly from the flow after entraining and heating air and melting and vaporizing ice we also estimate that in each eruption approximately 109 kg of fine ash was injected into the atmosphere during the april 15 eruption a slow scan television camera recorded the ascent of the cloud these observations are described analysed and compared with the predictions of a new model for the dynamics governing the ascent of such clouds in accord with the observations our model predicts that the cloud initially ascended rather sluggishly since it is only just buoyant on rising from the pyroclastic flow as it ascends it entrains and heats up more air and hence generates more buoyancy therefore it accelerates upwards only much higher in the cloud does the velocity decrease again as the thermal energy of the cloud becomes exhausted the model also predicts that the height of rise of such coignimbrite thermals is a function of the initial mass and temperature of the cloud but is almost independent of the initial velocity during the april 21 eruption a sequence of photographs recorded the lateral spreading of the umbrella cloud during an interval of about 10 minutes after the eruption these photographs are analysed and successfully compared with a simple model for the spreading of the umbrella cloud as a gravity current in a stratified environment using an avhrr satellite image of the air fall deposit from the april 15 eruption combined with a simple model we suggest that the primary mechanism of ash dispersal was transport by the ambient wind

earthquake recurrence models and historical seismicity in the mexicali imperial valley abstract we have examined the historical seismicity of the mexicali imperial valley since about 1850 the largest observed earthquake in the area has been the magnitude m w 7 1 december 1934 event the magnitude distribution for large plate boundary rupturing earthquakes m 5 8 is not well fit by the gutenberg richter type b value model models which better fit the observed magnitude distribution are derived from a lognormal distribution of stress drops on faults of constant size and from an exponential distribution of rupture lengths as might be expected from randomly distributed rupture stopping asperities along the length of the fault this may be among the best data in the world for testing earthquake recurrence models e g time predictability slip predictability on a strike slip fault but the uncertainties are still too great to permit a unique interpretation

an observational test of the origin of accelerating moment release before large earthquakes 1 a progressive increase of seismic activity distributed over a wide region around a future earthquake epicenter is termed accelerating moment release amr this phenomenon has been observed in several studies over the last 15 years although there is no consensus about the physical origin of the effect in a recent hypothesis known as the stress accumulation sa model the amr is thought to result from the last stage of loading in the earthquake cycle in this view the increasing seismicity is due to minor stress release as the whole region becomes sufficiently stressed for the major event to occur the stress accumulation model makes specific predictions about the distribution of events in an amr sequence because the amr is predicted to be a result of loading on the main fault the precursory activity should be concentrated in the positive lobes of the far field stresses calculated by a backslip dislocation model of the main shock to test this model amr is first found in optimal circular regions around the epicenters of each of the m w 6 5 earthquakes in central and southern california since 1950 a backslip dislocation model is then used to determine which of the precursory events occur in the regions predicted by stress accumulation amr is shown to occur preferentially in the lobes of the backslip stress field predicted by the stress accumulation model

fractal dimension of fault systems in japan fractal structure in rock fracture geometry at various scales based on fault maps whether or not the fracture geometry of rocks is self similar was examined by using a box counting algorithm the statistical self similarity fractal structure of the fault fracture systems holds well at the scale of about 2 to 20 km the fractal dimension in japan varied from 1 05 to 1 60 the fractal dimension is about 1 5 1 6 at the central part of the japan arc and decreases with distance from the center at a smaller scale the fractal structure also holds well in the rock fracture geometry the fractal dimension of the north izu peninsula fault system branching faults is 1 49 at the scale of 0 625 to 10 km the fractal dimension of rock fracture geometry at the scale order of 10 1 to 10 2 meters is about 1 49 1 61 the upper limit of the fractal dimension of rock fracture geometry is about 1 6 judging from the estimation of fractal dimension on actual fracture geometry of rocks this value may impose a restraint on modeling of faulting and the fracture process of rocks

sliding with cavity formation we present a model for the determination of a sliding law in the presence of sub glacial cavitation this law determines the basal stress at a clean ice bedrock interf ace in terms of the velocity and effective pressure the method is based on an exact solut ion of the nye kamb linearly viscous sliding problem with cavities and uses ideas of lliboutry 979 to construct via re norma lization methods an approximate law for gene ral bedrock form we show that for a bedrock whose spectrum has a power law behaviour one obtains a sliding law which gives the basal shear stress proportional to a power of the velocity and to a power of the effective pressure the effect of subgl acial cavitation on the drainage system is exam ined using recent ideas of kamb for sufficiently high velocities drainage through a r6thlisberger tunnel system is unstable and drai nage takes place through the linked system of cavities this leads to a reduction of the effective pressure and by taking account of this one can rewrite the sliding law in terms of st ress and velocity only this sliding law can be multi v alued and it is suggested that this unde rlies the dynamic phenomenon of surges

statistical model for the stick slip behaviour of faults summary inspired by an earlier work by smalley turcotte solla 1985 in this paper we consider a fault consisting of large sets of asperities with a statistical distribution of strength it is argued that the principle of equal load sharing between asperities inside a segment is necessary to account for the stick slip behaviour this principle is responsible for amplifying or damping the effective probability for the displacement of crustal blocks the antecedents of this idea in the seismological literature are commented on

a gravity current model for the may 18 1980 mount st helens plume observations of the stratospheric plume from the may 18 1980 mount st helens eruption suggest that it spread in the crosswind direction as an intrusive gravity current as it was transported downwind grain size analyses of the plinian tephra are consistent with this model suggesting that to distances of many hundreds of kilometers turbulent atmospheric diffusion played a secondary role in plume spreading and tephra dispersal

goes weather satellite observations and measurements of the may 18 1980 mount st helens eruption we demonstrate the use of geostationary operational environmental satellite goes images of the may 18 1980 mount st helens volcanic plume in providing details of the dynamics and changing character of this major explosive eruption visible and thermal infrared ir data from a sequence of images at 30 min intervals from 0850 to 1720 local time lt give information on dispersal and plume top temperature initial visible and ir images at 0850 show the top of a spreading co ignimbrite like umbrella plume and an overshooting column emerging from it both rising off the ground hugging pyroclastic gravity flow generated by the opening directed blast the overshooting column had a minimum temperature significantly colder than local ambient atmosphere indicating substantial undercooling and a maximum altitude of 31 2 km at 0920 this large plume system then formed a high velocity radially spreading gravitationally driven current before becoming advected in the wind field at an average downwind velocity of 29 m s within 30 to 60 min the undercooled plume adjusted to ambient temperatures after this initial event the eruption column fluctuated over the next 8 hours between stable plinian column rise and unstable conditions favoring column collapse leading to pyroclastic flows and further development of co ignimbrite ash columns over this period of observation profiles of plume top temperatures derived from ir data versus distance along the downwind axis have distinctive patterns with steep slopes associated with co ignimbrite plumes and shallower slopes associated with plinian plumes moreover reflectance values from visible goes data change from lower to higher during periods of transition from darker toned plinian to lighter toned coignimbrite plumes indicating that in this case satellite data resolved changes in eruptive style from plumes with a coarser to a finer dominant particle size

a model of propagating brittle failure in heterogeneous media i consider a nonelastodynamic model for the propagation of brittle failure in a heterogeneously stressed medium numerical simulation shows a power law distribution of failure sizes with a slope not far different from the size distribution of seismic events the time history of calculated failure activity is not consistent with observed seismic behavior and some explanations and implications are discussed

the interpretation of the b and the b0 values and its implications on the regional deformation of the crust summary after reviewing the model and the interpretation of the negative power laws which represent the statistical distributions of the linear dimension of faults l and of the stress drops p of the earthquakes it is seen that the coefficient of the law log m0 m increases with m for smaller m it is verified that the parameters l and p of california earthquakes are independent and also it is suggested that one may consider a fractal dimension of earthquakes associated with p it is shown how these statistical distributions may allow distribution of slips in the seismic regions to be inferred where all the slips occur approximately in the same horizontal direction from the density distribution of the length of the faults it is found that in california 50 per cent of the regional displacement is due to the faults with linear lengths larger than 63 per cent of the maximum linear length of the faults similar results are obtained using the seismic moment m0 or the magnitude m instead of l in these cases however the density distribution of p is also needed for the exact computation of the displacement assuming that in california the regional displacement has been 5 cm yr 1 as measured with ground observations and space techniques it is tentatively estimated that the displacement due to earthquakes with m0 larger than 1027 1 may be as large as 4 2 cm yr 1 and that a cumulative displacement of at least 170 cm due to earthquakes with m0 larger than 1027 1 may have not been released since the great 1906 san francisco earthquake it is finally discussed how the variation in the density distribution of stress drops may be a precursor to earthquakes

the 2009 l aquila central italy seismic sequence as a chaotic process abstract in this paper we demonstrate that the seismic sequence of foreshocks culminating with the recent m w 6 3 main shock on april 6 2009 in l aquila central italy evolved as a chaotic process to do this we apply a nonlinear retrospective prediction to this seismic sequence and look at the temporal behaviour of the error between predicted and actual occurrence of the main shock when gradually increasing parts of the sequence are considered this is a generalisation of the typical nonlinear approach which is quite powerful to detect chaos in relatively short time series the method of prediction is based on the accelerated strain release asr analysis in time and on the nonlinear forecasting approach in a reconstructed phase space we find that i the temporal decay of the prediction error is consistent with an exponential function with a time constant of about 10 days and ii at around 6 days before the main shock asr analysis is quite powerful for anticipating the time of occurrence with an uncertainty of about a day due to its retrospective characteristics the latter result could be affected by changes on some a priori parameters used in the application of the asr technique however we consider these findings together with those obtained from the phase space analysis to be strong evidence that the studied sequence of foreshocks was produced by a physical process dominated by a significant chaotic component characterised by a k entropy 1 of about 0 1 day 1 this result could have important implications for the predictability of the possible main shock for those seismic sequences showing analogous nonlinear chaotic properties

the initial giant umbrella cloud of the may 18th 1980 explosive eruption of mount st helens abstract the initial eruption column of may 18th 1980 reached nearly 30 km altitude and released 10 17 joules of thermal energy into the atmosphere in only a few minutes ascent of the cloud resulted in forced intrusion of a giant umbrella shaped cloud between altitudes of 10 and 20 km at radial horizontal velocities initially in excess of 50 m s the mushroom cloud expanded 15 km upwind forming a stagnation point where the radial expansion velocity and wind velocity were equal the cloud was initiated when the pyroclastic blast flow became buoyant the flow reduced its density as it moved away from the volcano by decompression by sedimentation and by mixing with and heating the surrounding air observations indicate that much of the flow covering an area of 600 km 2 became buoyant within 1 5 minutes and abruptly ascended to form the giant cloud calculations are presented for the amount of air that must have been entrained into the flow to make it buoyant assuming an initial temperature of 450 c and a magmatic origin for the explosion these calculations indicate that the flow became buoyant when its temperature was approximately 150 c and the flow consisted of a mixture of 3 25 10 11 kg of pyroclasts and 5 0 10 11 kg of air if sedimentation is considered these figures reduce to 1 1 10 11 kg of pyroclasts and 1 0 10 11 kg of air

premonitory spreading of seismicity over the faults network in southern california precursor accord 1 we establish a connection between geometry of the faults network in a region and seismicity preceding the strong earthquakes in the intermediate term timescale of years previous studies of observed and computer simulated seismicity demonstrated that strong earthquakes are preceded in that timescale by the rise of seismic activity in a lower magnitude range here we explore a complementary phenomenon spreading of activity over the fault network this phenomenon is depicted by the seismicity pattern accord defined as a simultaneous rise of seismicity in a sufficiently large number of fault zones hence its name pattern accord has been found recently in synthetic seismicity generated by the colliding cascades cc model the present study demonstrates this pattern in observed seismicity of southern california we applied to observations a prediction algorithm based on the pattern accord scaled to the target magnitude 7 5 the pattern accord emerges within a few years before each of the three largest earthquakes in southern california kern county 1952 landers 1992 and hector mine 1999 and at no other time scaled to the target magnitude interval from 6 5 to 7 4 the pattern accord precedes six out of nine earthquakes the duration of alarms in both cases is about 30 of the time considered we repeated prediction with different combinations of adjustable numerical parameters of the algorithm summing up the success and error scores on an error diagram this numerical experiment shows that the prediction results are stable under moderate variations of adjustable parameters the final test would be as always an advance prediction the pattern accord has a simple physical explanation connected with equilibrium of the crustal blocks system under the impact of tectonic driving forces at the same time accord is a manifestation of a broader phenomenon premonitory increase of earthquakes correlation range the latter phenomenon was found for the first time in the cc model although it was hypothesized by one of the authors much earlier

mass distribution and moments of inertia in the outer shells of the earth terra nova 25 38 47 2013 abstract different mass distributions within the lithosphere and the sub lithospheric mantle have been considered here to calculate the moment of inertia of the outer shell of the earth relative to many different axes in particular we seek for the maximum moment of inertia mmi which represents the theoretical rotation axis that the outer shell of the earth should attain for maintaining equilibrium for the present day distribution of mass at depth we consider the most updated crustal lithospheric and sub lithospheric models satisfying general geological and geophysical laws when considering only the lithospheric shell as if it were fully independent from the sub lithospheric mantle i e totally decoupled our numerical results show the complete lack of equilibrium in terms of moment of inertia with respect to the present day rotation axis in further calculations we also included the sub lithospheric mantle assuming different density values as well as different compensation depths among the numerous tests the mass distribution models showing theoretical axes of rotation closest to the present day one are those obtained with a compensation depth of 400 km the possible implications of these results in terms of westward plates drift and depth of possible decoupling layers within the mantle are discussed

wind driven dispersal of volcanic ash plumes and its control on the thermal structure of the plume top the dispersal of an ash plume as it propagates downwind with the ash settling under gravity is presented it is shown that wind shear the initial plume height and the plume grain size distribution have an important role in the dispersal of the ash in particular in determining the evolution of the upper surface and the leading edge of the ash cloud once the ash has thermally equilibrated with the atmosphere the temperature of the upper surface of the ash plume is directly related to its altitude as a result we can use the model to interpret satellite images of the temperature of the upper surface of ash plumes these calculations are compared with new analyses of satellite data from the 18 may 1980 eruptions of mount st helens in which both thermal infra red and visible goes satellite data were examined in accord with the data the model is able to predict the rate at which the mount st helens ash plume propagated downwind through a combination of the wind shear and gravitational settling of different size particles the model is also able to explain the observed thermal structure of the upper surface of the ash plume in which the temperature initially decreases but then increases with downwind distance as the ash falls through the tropopause

variations in architecture and cyclicity in fault bounded carbonate platforms early miocene red sea rift nw saudi arabia abstract the early miocene was a period of active rifting and carbonate platform development in the midyan peninsula nw saudi arabia however there is no published literature available dealing with the detailed characterization of the different carbonate platforms in this study area therefore this study aims to present new stratigraphic architectural models that illustrate the formation of different carbonate platforms in the region and the forcing mechanisms that likely drove their formation this study identified the following features formed during active rifting a a late aquitanian n4 fault block hangingwall dipslope carbonate ramp b a late burdigalian n7 n8 isolated normal fault controlled carbonate platform with associated slope deposits and c a late burdigalian n7 n8 attached fault bounded platform with reef buildups rimmed shelf developed on a footwall fault tip within a basin margin structural relay zone that formed coinciding with the second stage of rifting variations in cyclicity have been observed within the internal stratigraphic architecture of each platform and also between platforms high resolution sequence stratigraphic analysis shows to be parasequences the smallest depositional packages metre scale cycles within the platforms the hangingwall dipslope carbonate ramp and the attached platform demonstrate aggradational progradational parasequence stacking patterns these locations appear to have been more sensitive to eustatic cyclicities despite the active tectonic setting the isolated fault controlled carbonate platform reveals disorganized stratal geometries in both platform top and slope facies suggesting a more complex interplay of rates of tectonic uplift and subsidence variation in carbonate productivity and resedimentation of carbonates such that any sea level cyclicity is obscure this study explores the interplay between different forcing mechanisms in the evolution of carbonate platforms in active extensional tectonic regions characterization of detailed parasequence scale internal architecture allows the spatial variation in syn depositional relative base level changes to be inferred and is critical for understanding the development of rift basin carbonate platforms such concepts may be useful for the prediction of subsurface facies relationships beyond interwell areas in hydrocarbon exploration and reservoir modeling activities

asperity distribution and percolation as fundamentals of an earthquake cycle abstract a seismic cycle model is proposed based on the existence of an asperity space strength distribution along the fault plane and the applicability of the percolation theory to earthquakes as suggested by vrancea seismotectonic data two seismic regions somewhat decoupled are emphasized in the lower lithosphere roughly between 80 and 110 km and between 120 and 170 km depth and an asperity magnitude quasi independent dimension of 0 3 0 4 km is determined for small to moderate earthquakes accordingly two concepts are introduced 1 the active zone a distinct fault region able to generate a major earthquake by percolation and characterized by a specific background seismicity total area and maximum possible magnitude 2 the asperity cell an elementary local stress inhomogeneity of an active zone generating weak to moderate events percolation requires the presence of a critical stress free surface 44 of the active zone area the model explains the non linearity of the frequency magnitude relationship and enables the estimation of the major earthquake magnitude domain in each zone the computed maximum possible magnitudes are mw 7 6 and mw 7 8 respectively in agreement with historical data a complex form of the recurrence period of earthquakes in the major magnitude domain is determined ranging from about 40 to 100 years irrespective of the seismic zone it follows that the seismic activity per unit area is invariant in both zones this result is considered to be a consequence of an intrinsic material property the scale invariance of the fragmentation process in the lithospheric material different aspects related to the discrete structure of the active zone and the fractal dimension of faulting are also discussed from the point of view of this model

high frequency spectral falloff of earthquakes fractal dimension of complex rupture b value and the scaling of strength on faults the high frequency falloff omega sup minus gamma of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones the author assumes that the high frequency energy of a main shock is produced by a self similar distribution of subevents where the number of subevents with radii greated than r is proportional to r sup minus d d being the fractal dimension in this model an earthquake is composed of a hierarchical set of smaller earthquakes the static stress drop is parameterized to be proportional to r sup eta and strength is assumed to be proportional to static stress drop he finds that a distribution of subevents with d 2 and stress drop independent of seismic moment eta 0 produces a main shock with an omega sup minus 2 falloff if the subevent areas fill the rupture area of the main shock by equating subevents to islands of high stress of a random self similar stress field on a fault he relates d to the scaling of strength on a fault such that d 2 minus eta thus d 2 corresponds to constant stress drop scaling eta 0 and scale invariant fault strength amore self similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value the size distribution of aftershock rupture zones and the scaling of strength on a fault the b value for aftershock sequences on a fault is found to equal 3 minus 1 5 eta 3 eta therefore this model indicates that the typically observed spectral falloffs of omega sup minus 2 and b values of 1 can be entirely caused by scale invariant strength eta 0 along fault zones less

earthquake size frequency relations from an analytical stochastic rupture model an analytical stochastic model of earthquake rupture is presented although the general formulation makes no a priori self similarity assumption scale independent earthquake size frequency esf statistics emerge from the interaction between fault strength heterogeneity and rupture mechanics the model also gives theoretical derivations for scale dependent esf statistics including gradual frequency saturation for small earthquakes and a continuum of possible transitions in the statistics of large earthquakes a model fault is characterized as a surface composed of a large number of asperities defined as small discrete contact surfaces of finite strength an earthquake rupture grows via successive asperity breaking subevents the probability of rupture to a certain size earthquake or greater is the total product of incremental rupture growth probabilities these are governed by a new asperity failure probability distribution derived as a mixture of weibull distributions by including fracture mechanics the resulting mixture distribution characterized by the scale and shape parameters and is written in terms of the rupture size the important difference between the mixture distribution and the weibull distribution is that the mixture results in power law esf statistics self similarity occurs when material heterogeneity and rupture mechanics are mutually tuned to give 1 frequency saturation for small earthquakes is shown to be a simple consequence of a general aseismic nucleation process the nucleation magnitude m defines the roll off point in esf statistics that occurs when the area of seismic rupture equals the area of precursory aseismic rupture growth by fitting the model to the parkfield earthquake data set m 0 9 is obtained the change in esf scaling for the transition from moderate to large earthquakes depends on the changes in stress at the growing rupture front the northern california earthquake data center seismicity data set is fitted for a transition at magnitude m 5 with 0 4 and 0 75 this result indicates that the change in the esf relation associated with the transition from moderate to large earthquakes in california and nevada is caused by surface rupture accompanied by partial width and slip saturation

experiments on gas ash separation processes in volcanic umbrella plumes abstract we present a series of analogue laboratory experiments which simulate the separation of ash and gas and the formation of secondary intrusions from finite volcanic umbrella plumes we examined the lateral spreading of mixtures of freshwater and particles released into a laboratory tank containing a uniformly stratified aqueous solution for times smaller than the sedimentation time of particles through the intrusion the current remains coherent and intrudes laterally as some of the particles settle into the underlying ambient fluid a layer of particle depleted fluid develops below the upper surface of the current and the density of the residual fluid is reduced over longer times the intrusion ceases to be coherent with small fingers of relatively buoyant particle depleted fluid rising from the upper part of the intrusion into the overlying fluid meanwhile the lateral motion of the injected solution induces a return flow in the ambient fluid which sweeps some of the particles sedimenting from the lower surface of the intrusion inwards as a result relatively dense particle laden fluid collects below the intrusion and then sinks into the underlying fluid eventually this fluid reaches a new neutral buoyancy height where it intrudes to form a second laterally spreading current below the original intrusion the process then repeats to form further weaker intrusions below these results of the separation of the ash and volcanic gas in an umbrella plume are consistent with field observations at sakurajima volcano where positively charged plumes thought to consist of volcanic gas have been observed above negatively charged plumes of ash this work also suggests that volcanic aerosols may form up to a kilometer above the original injection height of the ash in a strong wind shear this could result in very different trajectories of the ash and gas and so be important for evaluating the impact of ash plumes on both aviation safety and volcanic aerosol formation the separation of the ash from the umbrella plume after a time of order 10 3 10 4 s corroborates recent models of the may 18 1980 eruption at mount st helens that after a few hours the motion of the ash was simply controlled by wind dispersal and gravitational settling the complex motion of the sedimenting ash may also explain some of the observations of multiple intrusions in short lived umbrella plumes such as observed at redoubt alaska in april 1990

statistical physics approach to understanding the multiscale dynamics of earthquake fault systems 1 earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales in addition many aspects of regional seismicity appear to be stochastic both in space and time however within this complexity there is considerable self organization we argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models examples include sandpile models forest fire models and particularly slider block models these models exhibit avalanche behavior very similar to observed seismicity a fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts some of which show promise

seismicity based earthquake forecasting techniques ten years of progress abstract earthquake fault systems interact over a broad spectrum of spatial and temporal scales and in recent years studies of the regional seismicity in a variety of regions have produced a number of new techniques for seismicity based earthquake forecasting while a wide variety of physical assumptions and statistical approaches are incorporated into the various methodologies they all endeavor to accurately replicate the statistics and properties of both the historic and instrumental seismic records as a result the last ten years have seen significant progress in the field of intermediate and short term seismicity based earthquake forecasting these include general agreement on the need for prospective testing and successful attempts to standardize both evaluation methods and the appropriate null hypotheses here we differentiate the predominant approaches into models based upon techniques for identifying particular physical processes and those that filter or smooth the seismicity comparison of the methods suggests that while smoothed seismicity models provide improved forecast capability over longer time periods higher probability gain over shorter time periods is achieved with methods that integrate statistical techniques with our knowledge of the physical process such as the epidemic type aftershock sequence etas model or those related to changes in the b value for example in general while both classes of seismicity based forecasts are limited by the relatively short time period available for the instrumental catalog significant advances have been made in our understanding of both the limitations and potential of seismicity based earthquake forecasting there is general agreement that both short term forecasting on the order of days to weeks and longer term forecasting over five to ten year periods is within reach this recent progress serves to illuminate both the critical nature of the different temporal scales intrinsic to the earthquake process and the importance of high quality seismic data for the accurate quantification of time dependent earthquake hazard

satellite observations and interpretation of the 1991 mount pinatubo eruption plumes we demonstrate the use of hourly geostationary meteorological satellite gms and noaa polar orbiting advanced very high resolution radiometer avhrr satellite images of the june 1991 mount pinatubo volcanic eruption plumes in providing details of the timing changing eruptive style and umbrella plume movement and dynamics a chronology of explosive events which culminated in a 9 hour long climactic phase on june 15 has been determined from satellite data and favorably compared to ground based and other ancillary information maximum eruption column altitudes of 40 km and column top undercooling in excess of 55 c below the ambient atmosphere occurred during the climactic phase phases dominated by plinian versus coignimbrite eruptive plumes can be distinguished on the images analysis of the spreading umbrella plume during the climactic phase suggests that over the first 4 5 hours the plume spread laterally as a gravitational intrusion before becoming advected in the ambient winds we compare the rate of plume growth to a model of a radially symmetric continuously fed intrusion to describe the motion the rate of plume growth shows good agreement with this simple model for the first 4 5 hours from column top heights we determine eruption rates and obtain an independent estimate of the total volume of magma erupted from june 12 16 of 5 5 km3 dense rock equivalent dre in good agreement with an independent estimate of the total eruptive volume made from deposits on land and submarine ash fall of up to 5 3 km3 dre we also show that secondary explosions in the pinatubo ignimbrite deposits produced ash plumes reaching altitudes as high as 19 km in september 1991 this study indicates that realistic interpretation and monitoring of major eruption plumes can be accomplished by analysis of high temporal resolution satellite data

fractal geometry in the san andreas fault system it has been noted that the spatial distribution of earthquakes and the mode of strain release in the san andreas fault system is related to the complexity of fault geometry because of their rough appearance over many length scales faults can be regarded as fractal surfaces direct estimates of fractal dimension d of portions of the san andreas fault system between the northern gabilan range and the salton sea including the postulated extent of the great 1857 fort tejon earthquake are obtained from measured fault lengths analogous to the lengths of coastlines as discussed by mandelbrot regions characterized by complicated fault geometry are associated with larger values of d based on fault traces mapped at a scale of 1 750 000 d is 1 3 for this reach of the fault defined as a 30 km wide band about a main fault trace for that part near parkfield which could be associated with the nucleation of the 1857 earthquake d is 1 1 at this same scale d is 1 4 for the san andreas and related faults near san bernardino where the 1857 rupture stopped compared to 1 2 for the san andreas san juan fault segments near the point of arrest of the 1966 parkfield earthquake at finer map scales 1 24 000 and 1 62 500 critical lengths of 500 m and 1 km are identified which might relate to the extent of off san andreas fault offsets the critical lengths also suggest that fault geometry is not self similar if this fractal geometry persists through the seismic cycle it may be possible to use a quantitative measure of complexity to explain the occurrence of great and characteristic earthquakes along a given reach of fault

omori s power law aftershock sequences of microfracturing in rock fracture experiment a time series of acoustic emissions ae in basalt was measured under constant uniaxial compression some bursts of ae events considered to be the main shock and aftershock sequences were observed two models describing the aftershock sequences the exponential decay model n t k exp pt and the omori s power law model n t k c t p where n t denotes the occurrence rate of aftershocks at time t were examined with the progress of the fracturing process the bursts changed from the exponential decay type to omori s power law type and the p value of omori s power law aftershock sequences decreased these results indicate that microfracturing gains a longer tail with the evolution of the fracture process the reproduction of omori s power law aftershock sequences of ae events suggests that the self similarity of rock fracturing holds good over a range from microfracturing to large earthquakes

a renormalization group approach to the stick slip behavior of faults we treat a fault as an array of asperities with a prescribed statistical distribution of strengths when an asperity fails the stress on the failed asperity is transferred to one or more adjacent asperities for a linear array the stress is transferred to a single adjacent asperity and for a two dimensional array to three adjacent asperities using a renormalization group rg method we investigate the properties of a scale invariant hierarchical model for the stochastic growth of fault breaks through induced failure by stress transfer an extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions bifurcate at stresses less than the critical stress virtually no asperities fail on a large scale and the fault is locked above the critical stress asperity failure cascades away from the nucleus of failure we interpret this catastrophic failure as an earthquake and it corresponds to the transition from stick to slip behavior on the fault thus the stick slip behavior of most faults can be attributed to the distribution of asperities on the fault we propose our stochastic mechanism as an alternative to the traditional hypotheses for the stick slip behavior of faults a major advantage of our approach is the inclusion of scale invariance thus the observed frequency magnitude relation for seismicity is a natural consequence of our basic hypothesis

aseismic slip in earthquake nucleation and self similarity evidence from parkfield california aseismic slip microearthquakes and moderate earthquakes all take place along the san andreas fault at parkfield california in this letter we discuss the relationship of these slip mechanisms by establishing and modelling the local microearthquake size frequency distribution by examining the effect of background noise on earthquake event detection we show that the distribution is complete for m 0 3 unlike the gutenberg richter law the distribution begins with a relatively small number of very small events further the scaling relation of the distribution changes continuously with event size noting that many parkfield aseismic slip or creep events have moments equivalent to the smaller microearthquakes we show that the nucleation of microearthquakes by this type of slip can account for the size frequency distribution such a model does not require a lower limit to either earthquake or creep event size rather it suggests that at parkfield a transition from creep dominated slip to earthquake dominated slip takes place in the range of moments equivalent to magnitudes close to m 0 9 this is well above the m 0 3 detection limit of the seismic network but right at the limit of current near surface strain instruments

on convection and mixing driven by sedimentation the sedimentation of small particles from a suspension and the concomitant release of light interstitial fluid may constitute a buoyancy source for the development of convective motions when the dense suspension is emplaced beneath a stratified fluid an intermediate convecting layer between the sedimenting front and the density gradient above gradually grows in depth by erosion of the overlying stratified fluid novel laboratory experiments involving sedimentation below a two layer stratified region show that turbulent mixing and entrainment across the top density interface is significant for a broad range of the richardson number a simple theoretical model predicting the rate of erosion of the stratification above the convecting layer agrees well with these experiments the model is then extended to include the case of an overlying continuous density gradient and compared successfully with both new experimental data and the original data of kerr 1991 owing to the effects of dispersion of grain sizes small particles in the convecting fluid may lower the efficiency of the interfacial mixing by the turbulent eddies our model calculations suggest that turbulent mixing and entrainment driven by sedimentation may be significant in the atmospheric and oceanic contexts in both of which stratification is weak such mixing may also occur in molten magma chambers following the sedimentation of suspended crystals and in this case it may suppress large scale overturning events

a physical model predicting instability of rock slopes with locked segments along a potential slip surface abstract better understanding the evolutionary mechanism of landslides is very important to predict their occurrence based on firm scientific grounds the stability of a rock slope is often dominated by one or more locked segments along a potential slip surface with a large bearing capacity to resist instability we propose three preliminary categories for locked segments and develop a physical model for predicting the instability of rock slopes with locked segments by coupling a one dimensional renormalization group model with a strain softening constitutive model based on the weibull distribution we found that the ratio of the strain at the peak strength point of a locked segment to the strain at its volume dilation point is exclusively dependent on the weibull shape parameter m and is approximately constant at 1 48 the accelerating displacement of the slope can be observed from the volume dilation point of the locked segment due to unstable fracture propagation the physical model for slopes with multiple locked segments is only related to the displacement corresponding to the volume dilation point of the first locked segment and the number of locked segments applying this model to two typical cases the yanchihe rockslide in china and the wedge rockslide in libby dam usa the results are in agreement with field records this work will help to better understand the failure mechanism of slopes with locked segments and may provide guidelines for disaster mitigation and prevention

strong motion seismology strong motion seismology is concerned with earthquake ground motion in the amplitude range that poses the threat of human injury or property damage because the occurrence of strong motion cannot be predicted in advance and because the time between significant events at any one place may range from tens to thousands of years strong motion data is recorded on triggered instruments that typically must be maintained in readiness for years between periods of significant recording as a consequence the strong motion data set is sparse because of the engineering need for estimates of future ground motion the scope of the field of strong motion seismology encompasses seismic source theory and any other aspect of seismology that can provide insights helpful in making the best possible estimates given the limited data this relationship with the rest of seismology is a reciprocal one in that strong motion data gives perhaps the best information available on earthquake source processes

electric potential gradient changes during explosive activity at sakurajima volcano japan we report electric potential gradient measurements carried out at sakurajima volcano in japan during 1 explosions which generated ash plumes 2 steam explosions which produced plumes of condensing gases and 3 periods of ashfall and plume induced acid rainfall sequential positive and negative deviations occurred during explosions which generated ash plumes however no deflections from background were found during steam explosions during periods of ashfall negative electric potential gradients were observed while positive potential gradients occurred during fallout of plume induced acid rain from the same eruption these results suggest that a dipole arrangement of charge develops within plumes such that positive charges dominate in the volcanic gas rich top and negative charges in the following ash rich part of the plume the charge polarity may be reversed for other volcanoes hatakeyama and uchikawa 1952 we suggest that charge is generated by fracto emission donaldson et al 1988 processes probably during magma fragmentation within the vent rather than by frictional effects within the plume

sedimentation of tephra by volcanic plumes i theory and its comparison with a study of the fogo a plinian deposit sao miguel azores sedimentation of ejecta from volcanic plumes has been studied as a function of distance from the source in the fogo a plinian deposit sao miguel azores the fogo a trachytic pumice deposit is reversely graded and can be divided into two parts on the basis of pumice colour abundance of syenite accessory lithic clasts and distribution the lower syenite poor part was dispersed to the south and was clearly influenced by wind the upper syenite rich part is coarsegrained and has a nearly symmetrical distribution around the vent elongation of isopachs to the east indicate a weak wind influence the grain size variations of lithic and crystal components in the upper coarse part were studied total accumulation and accumulation per unit area expressed in kg m2 show good fits to a gaussian function at distances greater than 7 km for grain diameters less than 2 cm these results agree with a theoretical model for a radially spreading turbulent current moving over a quiescent fluid the gaussian coefficient is shown to be a function of grain size and the flow rate of material into the umbrella region of the eruption column the coefficient is therefore also a function of column height the column height deduced from these data is 21 km which is in broad agrrement with the column height of 27 km deduced from maximum clast dispersal using the method of carey and sparks 1986 the accumulation of clasts larger than 2 cm agrees with a theory for the fallout of clasts from the margins of the ascending eruption column which treats the plume as a succession of large eddies that decrease their mass of particles as an exponential function of time calculations are also presented for the influence of the radial inflow of surrounding air into the column on the deposition of clasts these calculations constrain the wind speed during the later part of the fogo a eruption to be at most a few metres per second the study has allowed four different dynamic categories of clast behaviour to be recognised in eruption columns

a laboratory study of ash flows hot ash flows propagate from volcanic vents during some explosive volcanic eruptions as a flow entrains and heats ambient air and simultaneously deposits pyroclasts part of the flow may become less dense than the air and ascend from the flow if entrainment of air is more important than sedimentation in controlling the flowbehaviour then a large buoyant ash cloud may form above the flow conversely if sedimentation of particles dominates then a much smaller fraction of the particles are able to ascend in the buoyant cloud we have carried out a series of analog laboratory experiments to simulate the motion and buoyancy generation in dilute ash flows propagating along the ground the first series of experiments investigated buoyancy generation through entrainment using mixtures of methanol ethylene glycol and water the second series examined the role of sedimentation upon the generation of buoyancy using particle laden fresh water currents propagating in a saline ambient fluid the experiments showed that the rate of entrainment increases while the sedimentation rate decreases as the downward slope of the terrain increases suggesting that massive ash laden clouds are more likely to rise from flows traveling on steeper slopes changes in slope angle also control the motion of ash flows the experiments suggest that flow separation and hydraulic jumps resulting from sudden changes in slope angle can enhance entrainment or sedimentation and increase buoyancy observations of the the interactions of ash flows with topography at redoubt volcano in april 1990 and at mount st helens on may 18 1980 are consistent with our laboratory observations

sedimentation from gravity currents generated by turbulent plumes sedimentation from radially spreading gravity currents generated at the top of ascending sediment laden plumes is described by a model which assumes that sediment is dispersed homogeneously by turbulence in the gravity current resulting in an exponential decrease in the concentration of sediment with time as particles settle out of the lower boundary of the current for radial spreading this model predicts a gaussian distribution of sediment accumulation away from the source with an exponential constant b which depends on flow rate q and particle settling velocity v b nv q in the experiments described sedimentation occurs from gravity currents generated by ascent of buoyant particle laden plumes of fresh water in a tank of salty water the sediment accumulation shows close agreement with the theoretical model and the gaussian decay constant b can be determined from a maximum in the accumulated mass of sediment per unit distance and from the slope of the line in s s0 br2 where r is the radial distance s is the sediment mass flux per unit area and s0 is the value of s at r 0 data from the dispersal of volcanic ejecta from a large c 24 km high plinian eruption column in the azores also show good agreement with the theory confirming that it is general and independent of scale and the nature of the fluid the experimental data also show a change in sedimentation behaviour at distances from the source corresponding to the corner of the plume where it diverts into a lateral gravity current and there is an abrupt decrease in vertical velocity sedimentation of coarse grain sizes between the source and the corner occurs from the inclined plume margins and does not behave as predicted by the theoretical model

introduction to special section on physical processes in geodynamics on may 16 and 17 1992 a meeting was held at cornell university as part of activities to honor donald l turcotte on the occasion of his 60th birthday which actually occurred on april 22 1992 the papers in the following special section are a result of that meeting which included invited presentations and posters representing the diverse areas of geology and geophysics to which donald turcotte has contributed three of the papers deal with aspects of mantle convection a c fowler addresses the problem of initiation of subduction by extending boundary layer theory to a viscoplastic rheology turcotte and oxburgh 1967 pioneered such studies by showing how boundary layer theory could be used to describe the dependence of geophysical observables such as heat flux on distance from a midocean ridge or age of the oceanic crust d w sparks et al use a model of three dimensional convection beneath a segmented ridge to explore how buoyancy effects and melt production beneath a spreading center influence ridge parallel variations in crustal thickness and gravity magma migration and the dynamics of midocean ridges have been major focuses of donald turcotte s research in papers dating back to 1978 e g turcotte and ahern 1978 ahern and turcotte 1979 turcotte 1982a kenyon and turcotte 1987 g a glatzmaier and g schubert calculate models of three dimensional two layer mantle convection in a spherical shell and compare with whole layer spherical shell three dimensional convection models these models represent the end member states of a spectrum of possible modes of mantle convection turcotte and oxburgh 1972 oxburgh and turcotte 1978 turcotte 1979a silver et al 1988

earthquake rupture as a critical point consequences for telluric precursors abstract earthquakes are related to rupture phenomena in complex statistical systems of cracks we first review some available information suggesting that rupture in earthquakes is a critical point the consequences of this hypothesis on several phenomena are then discussed in particular we focus our attention on a simple theory of electroseismic activity based on mechano electrical transduction effects such as the piezoelectric or the pressure induced polarization effect the neighbourhood of the rupture threshold is characterized by a specific response which could correspond to telluric wave activity observed as precursors of earthquakes

experimental studies of particle laden plumes experiments are described in which buoyant plumes of fresh water and solid particles are generated in a tank of salt water dependence of the behavior of the plumes on particle concentration and grain size was studied at low concentrations behavior was similar to single component plumes and the principal effect of the particles was to reduce the buoyancy flux measurements of particle concentration across the plumes demonstrated that there were substantial amounts of particle reentrainment from an outer sedimenting veil reentrainment caused the plume margins to become denser than the ambient fluid total particle flux in the plumes increased with height and can be several times greater than the flux at the plume source plumes with high particle concentration exhibit several kinds of convective instability which generated gravity currents and rapid sedimentation gravity currents were generated at the margins of concentrated plumes these flows are attributed to reentrainment causing the flow margins to have excess density when the plume density was close to but less than the density of the ambient fluid a fountain forms high in the plumes which collapsed asymmetrically to generate a gravity current on one side of the plume when the density of the particle laden flow was greater than the ambient fluid a symmetrical fountain formed and gravity currents moved across the tank floor depositing sediment at a well defined distance from the source buoyant fluid ascended from the flow fronts to form a ring of plumes around the central fountain these plumes coalesced to form a broad buoyant cloud the plumes are generated by the sedimentation from the gravity currents which resulted in the fresh water and some entrained particles being released all the experimental plumes ascended to the top of the tank and spread out as gravity currents beneath the upper surface particles often fall from this layer in discrete parcels of particle rich fluid with shapes similar to thermals the fall velocities were much greater than the terminal velocities of individual particles and the sedimenting region is inhomogeneous these observations indicate that sedimentation is enhanced by convective instabilities when particle rich fluid is emplaced above particle free fluid the experiments indicate that there may be several different mechanisms of generating pyroclastic flows and surges from the collapse of volcanic eruptions columns the experiments also demonstrate that the sedimentation of particles from a plume has an important influence on dynamical behavior

towards a new view of earthquake phenomena recent advances in the theory of fracture and fragmentation are reviewed empirical laws in seismology are interpreted from a fractal perspective and earthquakes are viewed as a self organized critical phenomenon soc earthquakes occur as an energy dissipation process in the earth s crust to which the tectonic energy is continuously input the crust self organizes into the critical state and the temporal and spatial fractal structure emerges naturally power law relations known in seismology are the expression of the critical state of the crust an soc model for earthquakes which explains the gutenberg richter relation the omori s formula of aftershocks and the fractal distribution of hypocenters is presented a new view of earthquake phenomena shares a common standpoint with other disciplines to study natural complex phenomena with a unified theory

a geodetic sign of the critical point of stress strain state at a plate boundary i found a curious oscillating behavior in secular variations of relative ground level in the tokai district central japan the period of the oscillation is becoming shorter acceleratedly with time which thereby predicts the existence of a critical point in near future the data variations can successfully be expressed by the general equation describing the near critical point behavior based on the discrete scale invariance theory the critical point may be interpreted as the occurrence of the maximum sized fracture i e the biggest earthquake in a given tectonic environment the time predicted is 2004 7 1 7 year

new quantitative displacement criteria for slope deformation process from the onset of the accelerating creep to brittle rupture and final failure abstract two quantitative displacement criteria for slope deformation were deduced through the combination of a one dimensional renormalization group model and the strain softening constitutive model of geological materials the criteria can be used to understand the mechanical process from the onset of the accelerating creep on a slope through brittle rupture to the final failure and landslides the study showed that according to the first criterion the displacement ratio between the brittle rupture and the onset of the accelerating creep is approximately 1 48 which can be used to predict the brittle rupture of a slope with continuous progressive deformation the second displacement criterion shows that the displacement ratio between the final failure and the onset of the accelerating creep is approximately 2 59 which can be used to predict the occurrence of the ultimate disaster thus the critical displacement prior to the failure of the slope can be predicted using a time series of monitoring displacement data the methodology proposed in this study was validated using data from two well known landslides the vajont landslide in italy and the xintan landslide in china the results verify the applicability of this method

search for direct empirical spatial correlation signatures of the critical triggering earthquake model summary we propose a new test of the critical earthquake model based on the hypothesis that precursory earthquakes are actors that create fluctuations in the stress field which exhibit an increasing correlation length as the critical large event becomes imminent our approach constitutes an attempt to build a more physically based time dependent indicator cumulative scalar stress function in the spirit of but improving on the cumulative benioff strain used in previous works documenting the phenomenon of accelerating seismicity using a simplified scalar space and time dependent viscoelastic green s function in a two layer model of the earth s lithosphere we compute spatiotemporal pseudo stress fluctuations induced by a series of events before four of the largest recent shocks in southern california through an appropriate spatial wavelet transform we then estimate the contribution of each event in the series to the correlation properties of the simplified pseudo stress field around the location of the mainshock at different scales this allows us to define a cumulative scalar pseudo stress function which reveals neither an acceleration of stress storage at the epicentre of the mainshock nor an increase of the spatial stress stress correlation length similar to those observed previously for the cumulative benioff strain the earthquakes we studied are thus either simple witnesses of a large scale tectonic organization or are simply unrelated and or the green s function describing interactions between earthquakes has a significantly longer range than predicted for standard viscoelastic media used here