methodology for obtaining constraints on ground motion from precariously balanced rocks precariously balanced rocks provide constraints on the level of ground motion that could have occurred during the time the rocks have been in their current positions field measurements of the quasi static toppling accelerations of precariously balanced rocks provide information for computer modeling of the response of the rocks to given ground motion histories the quasi static toppling acceleration is determined by the ratio of the quasi static force through the center of mass whose moment about the rocking point counterbalances that of gravity and the mass of the rock for an estimate of dynamic toppling peak ground accelerations we use a finite difference numerical code to model the dynamic response of rocks to arbitrarily complex acceleration time histories we test our computational methodology and results using the university of nevada shake table the shake table tests of both idealized rectangular shapes and actual rocks confirm the accuracy of our methodology for estimating dynamic toppling accelerations of precarious rocks for different waveforms representing earthquake ground motion time histories a study of statistical variation of the dynamic toppling acceleration for a suite of seismograms provides constraints on the peak ground acceleration on hard rock sites in mojave desert about 15 km from the san andreas fault of about 0 5 g for synthetic seismograms with relatively high frequency content or about 0 4 g for seismograms with spectra similar to the recent izmit turkey earthquake a major source of uncertainty is the uncertainty in the spectrum of ground motion for large earthquakes waveforms with relatively more low frequencies can topple the rocks with lower peak ground accelerations we describe methods for reducing the uncertainties with further study and more data

a simple model of fjord and coastal circulation interaction abstract the dynamical interaction of a narrow fjord with a wind driven coastal regime is investigated using a linear two layer numerical model the coriolis acceleration is important in the coastal regime but assumed to he unimportant in the fjord dynamical because v 0 for a wide variety of wind conditions bottom topography and model parameters the wind forced coastal circulation with its geostrophic alongshore currants has a strong effect on the circulation within the fjord these geostrophic currents control the free surface and pycnocline displacement at the fjord mouth thereby strongly affecting fjord circulation this mechanism is an alternative to the classical idea of hydraulic control at the mouth by sills or constrictions model simulators also show that the free surface slope is a baroclinic effect and that alongshore and across shore winds affect the fjord differently alongshore winds produce flooding while up and down fjord winds simply sat up the surface we find that offshore win

mixing at camarinal sill in the strait of gibraltar during the gibraltar experiment in 1985 1986 observations of shear stratification microstructure and acoustic backscatter revealed a complex mixing regime at camarinal sill in the strait of gibraltar the mixing is forced by strong semidiurnal tidal currents and weaker but more steady baroclinic flows flows are characterized as outflow or inflow nearly equivalent to westward or eastward rising water at gibraltar coincides with outflow at all depths we observed two modes of outflow at the sill in may 1986 the transition layer separating atlantic and mediterranean water was between 0 75 mpa and 1 mpa when we sampled east of the sill near neap tide the transition turned down just before reaching the sill crest where the flow became critical increasing shear soon destabilized the transition producing billows which grew to 30 75 m on the west flank of the sill the overturning generated intense turbulence with peak dissipation rates e exceeding 10 2 w kg 1 this turbulence rapidly thickened the transition from z 30 50 m east of the sill to z 130 150 m within 1 2 km west of the sill from the rate of thickening we estimate the rate of formation of new transitional water during neap tide as 0 8 1 2 105 m3 s 1 this outflow mode did not release eastward propagating internal bores when outflow turned to inflow but the inflow did appear to arrest the deep outflow in may the largest average dissipation rate over and just west of the sill had the same magnitude as estimates of the net energy lost by adjustment of velocity and mass across the sill during outflow other averages are smaller than the energy loss presumably because the limited sampling severely underestimates the average dissipation rate during outflow strong shears were observed to rise to 100 times those in the background internal wave field however probably owing to spatial offsets between the ship s acoustic doppler current profiler and our tethered free fall profiler the only statistically significant correlations were found between overturning scales measured directly and those estimated from e in the same profile we observed the other outflow mode in october 1985 when we profiled over the sill near spring tide and the transition was east of the sill centered near 1 5 mpa after encountering the sill the transition rose sharply and remained within 10 20 m of the surface across the sill plunging steeply downward just past the west edge of the sill this was accompanied by intense turbulence and at least one rebound of the transition we did not observe release of eastward propagating bores when inflow turned to outflow but observations by armi and farmer 1988 in april 1986 found bores released at spring tide in regimes similar to the one we observed in october 1985

subtidal circulation in a deep silled fjord douglas channel british columbia douglas channel a deep fjord on the west coast of british columbia canada is the main waterway in the fjord system that connects the town of kitimat to queen charlotte sound and hecate strait a 200 m depth sill divides douglas channel into an outer and an inner basin this study examines the low frequency from seasonal to meteorological bands circulation in douglas channel from data collected at three moorings deployed during 2013 2015 the deep flows are dominated by a yearly renewal that takes place from may june to early september a dense bottom layer with a thickness of 100 m that cascades through the system at the speed of 0 1 0 2 m s 1 which is consistent with gravity currents estuarine flow dominates the circulation above the sill depth and the observed landward net volume flux suggests that it is necessary to include the entire complex channel network to fully understand the estuarine circulation in the system the influence of the wind forcing on the subtidal circulation is not only at the surface but also at middepth the along channel wind dominates the surface current velocity fluctuations and the sea level response to the wind produces a velocity signal at 100 120 m in the counter wind direction overall the circulation in the seasonal and the meteorological bands is a mix of estuarine flow direct wind driven flow and the barotropic and baroclinic responses to changes to the surface pressure gradient caused by the wind stress

consistency of precariously balanced rocks with probabilistic seismic hazard estimates in southern california abstract the overturning fragility of a freestanding block such as a precariously balanced rock pbr has been parameterized as a function of a vector of ground motion intensity measures methodologies are outlined to estimate the failure probabilities of such objects given their residence times for deterministic seismic hazard analyses dshas a pbr is exposed to the scenario earthquakes that occur during its exposure time providing an estimate of the probability that the pbr survives the ensemble of events for probabilistic seismic hazard analyses pshas the pbr overturning fragility is multiplied by the ground motion occurrence rate from a vector valued probabilistic seismic hazard analysis vpsha yielding the marginal overturning rate for each ground motion bin summing the marginal rates over all ground motion bins produces the total overturning rate for time independent poisson based psha estimates the probability of block failure can be easily calculated as a function of exposure time this latter method is used to test vpsha estimates similar to the 2002 u s geological survey usgs national seismic hazard maps via pbr residence times pbr overturning fragilities are estimated at sites in southern california near the san andreas fault between the san jacinto and elsinore faults and near the white wolf fault the resulting failure probabilities for several of the pbrs are very high suggesting that they are inconsistent with the 2002 usgs ground motions an investigation of the hazard calculated with zero aleatory variability in the ground motion prediction equations gmpes suggests that the median ground motions or the earthquake rupture rates are too high at certain pbr sites

shelf fjord exchange driven by coastal trapped waves in the arctic in this article we show that the class of low frequency subinertial waves known as coastal trapped waves ctws are a significant agent of water volume exchange in a west svalbard fjord and by extension more widely along the west svalbard and east greenland margins where similar conditions prevail we show that ctws generated by weather systems passing across the sloping topography of the shelf break propagate into the fjord steered by the topography of an across shelf trough the ctws have characteristic periods of 2 days set by the passage time of weather systems phase speeds and wavelengths vary seasonally by a factor of two according to stratification winter summer values are cp 0 25 ms 1 0 5 ms 1 and 40 km 84 km ctw induced flow velocities in excess of 0 2 ms 1 at 100 m water depth are recorded observationally scaled ctw model results allow their explicit role in volume exchange to be quantified of the estimated exchange terms estuarine exchange is weakest qest 0 62 103 m3s 1 followed by barotropic tidal pumping qbt 2 5 103 m3s 1 with intermediary exchange dominating qi 2 4 104 m3s 1 oscillatory flows display greatest activity in the 1 5 day period band and ctw activity is identified as the likely source of variability in the 40 60 h period band within that band intermediary exchange driven by ctws is estimated as qictw ave 0 82 104 m3s 1 an exchange rate exceeding both barotropic and estuarine exchange estimates

meteorologically forced subinertial flows through the strait of gibraltar the observed transport due to subinertial flows with periods ranging from days to a few months through the strait of gibraltar reaches values up to 106 m3 s 1 and is well correlated with atmospheric pressure fluctuations over the mediterranean sea this transport is barotropic and accounts for 84 of the variance observed at these frequencies a second mode accounts for 12 of the variance and is characterized by a node zero amplitude located at the mean depth of the interface between atlantic and mediterranean waters this baroclinic mode is modulated by the spring neap tidal cycle corresponding to an increased exchange of waters between atlantic and mediterranean at neap tides a simple model of the mediterranean which includes two basins and two straits indicates that the system has two resonant frequencies at periods of 1 2 and 5 6 days the 1 2 day resonance corresponds to the eastern and western basins oscillating through the strait of sicily while that at 5 6 days is the resonance of the mediterranean sea with the north atlantic ocean a good approximation to the observed flows is obtained when this model is forced with the most energetic mode of the atmospheric pressure over the eastern and the western mediterranean and a friction term is included to limit the flow through the strait of gibraltar restricting the flow through the strait of sicily does not improve the agreement between the model and the observations for the flows at gibraltar

modelling failure of natural rock columns abstract natural rock columns often assume strange geometries that look unstable under the static loading of the rock mass itself and even more so under the resonance inducing dynamic loads of seismic shaking a two dimensional finite element stress model was applied to the analysis of six selected rock columns formed in welded horizontally jointed tuff in the chiricahua mountains arizona the columns were selected for precarious appearing geometries such as asymmetrical overhangs narrow aspect and severely incut hourglass profiles in none of the cases did the stress modelling indicate proximity to either compressional or tensile failure the modelling revealed that failure because of slip along inclined joints penetrating the rock was much more likely surprisingly columns with pronounced hourglass morphologies were found to be more stable than cylindrical columns in rock with non horizontal joints the uniformity of column heights suggests that either rare high velocity winds or prehistoric seismicity cropped the previous generation of columns an estimate of the resonant frequencies of a typical column provides some idea of the dynamic response of the columns to seismic shaking the question of seismic destruction is intriguing because the columns were apparently unaffected by a magnitude 7 2 earthquake 120 km away in 1887

the dynamics of shelf forcing in greenlandic fjords abstractthe fjords that connect greenland s glaciers to the ocean are gateways for importing heat to melt ice and for exporting meltwater into the ocean the transport of heat and meltwater can be

omak rock and the 1872 pacific northwest earthquake abstract omak rock is an about 40 ton granite boulder balanced on a narrow support the rock is located in northern washington state in the general vicinity of the 1872 pacific northwest m 7 earthquake the survival of the balanced rock has in the past been used to place limits on peak acceleration and intensity at its location and thus possibly on the epicenter of the earthquake using dynamical analysis i find that the rock could have survived far greater peak ground motion than previously concluded and might well have survived within a few kilometers of the epicenter thus invalidating the earlier conclusions

the rate of inflow and mixing during deep water renewal in a sill fjord we obtained high resolution data on a deep water renewal in the basin of gullmar fjord sweden using an autonomous profiling platform in the middle of the fjord where the platform is anchored renewal starts with the passage of a gravity current front and continues with a steady thickening of the new oxygen rich low nitrate bottom layer and an associated lifting of the old oxygen depleted high nitrate bottom water the basin continuously fills to sill level during a period of 10 d at the mouth of the fjord a three layer structure develops renewal is driven by the density difference between the intermediate water inside and the new deep water outside the fjord the volume flux is well predicted by a hydraulic exchange model in which the upper layer plays a passive role local upwelling and downwelling of the upper halocline cause fluctuating baroclinic currents during renewal but these seem to have little influence on the average volume flux of new deep water entrainment rates are small and the associated volume flux increase seems to be balanced by detrainment

new validation method for hydrodynamic fjord models applied in the hardangerfjord norway abstract we introduce a new intuitive evaluation method for comparison of fjord model results and current measurements the approach is tested using high resolution model simulations and measurements in the hardangerfjord a large fjord system in norway with huge aquaculture production the method is easy to interpret clearly distinguishes periods with good and poor model performance and relate them to physical driving forces this makes it possible to identify potential shortcomings in the models representation of physical processes the applied model mostly performs well in the hardangerfjord good performance often coincides with strong local fjord forcing i e strong winds in the fjord in periods with poor model performance internal waves induced by pressure perturbations on the coastal shelf tend to propagate erroneously into the fjord stratification biases in coastal waters connected to the applied model boundary conditions seems to be an important cause demonstrated flexibility of time frame and performance criteria suggests applicability of the validation method for a wide set of geophysical variables in various physical environments

eigenoscillations and stability of rocking stones the case study of the hus pulpit in the central bohemian pluton stability of precariously balanced rocks is employed in seismic hazard estimates standard toppling models of these rocks are based on a rigid body motion i e this approximation assumes that their eigenfrequencies are infinite in any position of a rock this assumption is however questionable in the case of rocking stones oscillating with lowest eigenfrequencies of only several hertz when resonance effects facilitating rolling wobbling due to a seismic signal cannot be a priori excluded an example demonstrating existence of such low frequencies is the hus pulpit rocking stone located in the central bohemian pluton 49 568n 14 363e the observed lowest frequencies recorded by a guralp cmg 40t seismometer located on the top of this rocking stone are 3 7 and 9 hz with the quality factors of 60 55 and 77 respectively using the comsol multiphysics software package we model the oscillations of this rocking stone numerically and demonstrate that these observed low frequencies and their dampings can be explained by a force interaction between the stone base and the bedrock that can formally be interpreted as the damped elastic response of the bedrock to its surface deformation by the stone we also numerically study stability of the stone under the presence of such an interaction and conclude that beginning of toppling requires very high horizontal pgv pga for input seismic frequencies even at the resonance frequencies however different numerical models where the seismic displacements are considered as the direct input at the rock base can result in rock instabilities under a presence of an hbox m 7 earthquake at a distance of about 150 km

the role of the interface in exchange through the strait of gibraltar five cross strait hydrographic sections repeated several times during the gibraltar experiment in 1985 1986 are used to examine the structure of the interface layer between the inflowing atlantic waters and outflowing mediterranean waters in the strait of gibraltar the interface is 60 100 m thick with a strong vertical salinity gradient identified by fitting individual salinity profiles to a piecewise linear three layer model the interface is deeper thicker fresher and colder on the west end of the strait than in the narrows where there is a minimum in thickness and a maximum in salinity gradient farther east the interface thickens again and continues to get saltier warmer and shallower property variations in all three layers are also cast in terms of the three principal water types involved in the exchange the traditional knudsen model of exchange is extended to three layers assuming that the interface is a transport carrying third layer with uniform vertical shear as much as half of the inflowing or outflowing transport occurs in the interface layer transport converges in both the upper and lower layers implying over the length of the strait vertical exchange between layers that is comparable to about half the horizontal exchange the richness of structure and complexity of interaction between the interface and the upper and lower layers argues against the use of two layer models to characterize exchange through the strait of gibraltar

rocking and overturning of precariously balanced rocks by earthquakes abstract precariously balanced rocks in seismically active regions may be used to provide constraints on probabilistic estimates of strong ground motion a computer program is developed to study the rocking response of models of precariously balanced rocks when subjected to various levels of ground accelerations the computer code validated by comparing the numerical and experimental results for simple shaped rigid blocks is used to study the rocking response of rectangular blocks with various aspect ratios to the el centro strong ground motion recording of the 18 may 1940 imperial valley earthquake results show that during earthquakes the horizontal components of ground motion play a dominant role in overturning rocking objects the rederived and corrected housner9s equation 1963 could be used to estimate the minimum overturning acceleration of precarious rocks at different frequencies by measuring the quasi static toppling acceleration in the field

methodology for using precarious rocks in nevada to test seismic hazard models abstract fields of precariously balanced rocks indicate that strong earthquake motions have not occurred at that site since the precarious rocks developed these fields can be characterized with an estimate of the peak acceleration that would be sufficient to topple the rocks and an estimate of how long the rocks have been precarious this article uses this information to test the input to probabilistic seismic hazard analysis the fundamental assumption is that the probability of exceeding a ground motion capable of toppling a precarious rock during a time period equal to the age of the rock is equal to the confidence level at which the inputs to the probabilistic seismic hazard analysis can be rejected we performed a probabilistic seismic hazard analysis for 26 sites of observed precarious rocks in nevada using preliminary estimates of the toppling acceleration and the age of the features two standard models are rejected with over 95 confidence by most of the precarious rock observations we consider several possible explanations for the inconsistency a probabilistic seismic hazard analysis that eliminates the area sources and only includes faults is consistent with the precarious rock observations at most of the sites spatial clustering of small magnitude events could maintain this effect without contradicting the precarious rock observations however it may not be necessary to completely reject the area sources from our probabilistic seismic hazard analysis the physics of rock stability may allow increasing the minimum magnitude to 6 0 in the area sources because the short duration of high frequency accelerations in smaller events may not topple all precarious rocks the precarious rocks could generally have small site effects attenuation models may overestimate ground motions on the foot wall of normal faults and a different attenuation model in general might decrease the ground motion predictions the ergodic assumption that is made in estimating the uncertainty in attenuation models may be contributing to overestimate the hazard individually each of these effects might allow more of the precarious rock sites to be consistent with the area source zones

exchange through the strait of gibraltar to measure the exchange between the atlantic and mediterranean through the strait of gibraltar an array of current meter moorings was deployed for a year in the strait during 1985 1986 a novel aspect of these measurements is the inclusion of conductivity as well as temperature and pressure sensors on each current meter so that the salinity of the flows could be monitored continuously these salinity measurements determine the water mass characteristics of the flows crossing the sill they allow definition of the 37 psu isohaline as the interface between inflowing fresher atlantic water and outflowing saltier mediterranean water and they enable time series to be developed for the depth of this interface for the upper layer inflow and for the lower layer outflow from these measurements the time averaged outflow of mediterranean water is estimated to be 0 68sv 1sv 1 106m3s 1 and the outflow salinity transport defined to be the outflow times the salinity excess above a basic atlantic water salinity of 36 1 psu is estimated to be 1 50 103m3s 1 1sv 1psu 1 103m3s 1 equivalent to a net evaporation over the mediterranean basin of 52cm y 1 extrapolated measurements of the inflow from current meters generally deployed below 100m depth yield an estimate for the time averaged inflow of 0 93sv which is believed to be unrealistically high in view of the better measured outflow and net evaporation thus a more realistic estimate of the inflow is 0 72sv equal to the sum of the outflow and net evaporation as required by the mass budget for the mediterranean sea such estimates of the exchange are smaller by almost a factor of 2 than previous values for the exchange by lacombe and richez 1982 the exchange across the gibraltar sill is found to be due in nearly equal parts to the mean currents and to the tidal fluctuations the mean currents are smaller than had been expected reaching a peak value of only about 60 cm s 1 in the deep outflow over the sill the tidal exchange is due to a strong correlation over the tidal period between the depth of the interface and the strength of the inflowing currents for the m2 tide at the sill the amplitude of the interface depth is 51 m and the amplitude of the tidal currents is 1 2m s 1 furthermore the inflow and interface depth have similar phases as a consequence the upper layer is deep on the inflowing tide so that a large slug of atlantic water crosses the sill into the mediterranean on the outflowing tide the interface is shallow so that a large slug of mediterranean water crosses the sill into the atlantic similar processes occur for the s2 o1 and k1 tides though the amplitude are smaller in this manner tidal oscillations lead to a time averaged exchange of water masses across the gibraltar sill the inflow and outflow defined to be the instantaneous transports above and below the 37psu isohaline interface exhibit m2 tidal amplitudes of 2 3 sv and 1 3sv respectively thus the tides are large enough to reverse the mean upper layer inflow and lower layer outflow daily averaged inflow and outflow transports exhibit low frequency fluctuations with standard deviations of 0 37sv and 0 22sv respectively such low frequency fluctuations have been shown previously to be associated with barotropic flows through the strait of gibraltar compensating for sea level variations over the mediterranean due to atmospheric pressure fluctuations candela winant and bryden 1989 finally from these measurements there appear to be little fortnightly or annual period fluctuations in the exchange through the strait of gibraltar

studies on precarious rocks in the epicentral area of the ad 1356 basle earthquake switzerland summary for the first time precarious rocks have been analysed in the epicentral area of the ad 1356 basle earthquake in northern switzerland several cliff sites in flat lying thickly bedded upper jurassic coral limestones in the jura mountains were investigated seven blocks are regarded as precarious with respect to earthquake strong ground motions the age of these precarious rocks could not be determined directly as for instance by radiometric dating methods however based on slope degradation processes it can be concluded that the formation of these blocks predates the ad 1356 basle earthquake the acceleration required to topple a precarious rock from its pedestal is estimated using geometrical data for individual block sections and earthquake strong motion records from stations on rock sites in the european strong motion database as input data for the computer program rocking v1 0 from the seismological laboratory university of nevada reno the calculations indicate that toppling of a precarious rock largely depends on earthquake strength but also on the frequency spectrum of the signal although most investigated precarious rocks are surprisingly stable for ground motions similar to those expected to have occurred during the ad 1356 basle earthquake at least two blocks are clearly precariously balanced with peak toppling accelerations lower than 0 3 g possible reasons why these blocks did not topple during the ad 1356 basle earthquake include incomplete separation from their base sliding of precarious rocks their size lower than assumed ground accelerations and or duration of shaking

constraints on ground accelerations inferred from unfractured hoodoos near the garlock fault california abstract in the absence of long term instrumental data the presence of fragile geologic features near active faults can provide physical limits on the level of ground shaking that could potentially have significant implications for seismic hazards this paper introduces a multidisciplinary investigation that uses unfractured hoodoos in seismically active regions to constrain the level of ground accelerations at those locations although there is a large uncertainty associated with the age of the hoodoos because of their rapidly eroding nature they can still be useful in providing physical limits on ground motions associated with recent large events here we consider the fragilities of two hoodoos in the red rock canyon region within a few kilometers of the garlock fault which is an active strike slip fault in a transtensional region with at least a few large earthquakes in the holocene the hoodoos at these sites could be evidence of median or relatively low ground motions associated with large transtensional strike slip earthquakes results of our field and laboratory tests on two hoodoos provide constraints on peak ground accelerations pgas of and using the u s geological survey s usgs probabilistic seismic hazard psh deaggregation the dominant earthquake contributing to the hazard at the site of the hoodoos for the recurrence intervals of 475 975 and 2475 years is located at a distance of 4 8 km and has a magnitude of 7 63 consistent with the observed paleoearthquake evidence on the garlock fault the pgas corresponding to these three return periods are 0 26 0 40 and respectively therefore the survival of the more fragile hoodoo during a presumably large event on the garlock fault in the past 550 years would be consistent with the 2008 seismic hazard level if the ground motions during that event were below the median value

numerical treatment of cross shelf open boundaries in a barotropic coastal ocean model abstract using a barotropic coastal ocean model with a straight coastline and uniform cross shelf bottom slope seven different cross shelf open boundary conditions four of which are applied in either implicit or explicit form are compared in three numerical experiments 1 a mound of water is allowed to collapse and radiate waves toward the open boundaries 2 a uniform alongshelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment 3 a uniform cross shelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment the boundary condition which is most transparent to waves consists of a sponge at the outer edge of the model domain with an orlanski radiation condition at the outer edge of the sponge several open boundary conditions perform adequately in the wind stress experiments but the orlanski radiation condition alone without a sponge appears to give the best total performance of thes

maximal two layer exchange over a sill and through the combination of a sill and contraction with barotropic flow the analysis of two layer exchange flow through contractions with a barotropic component treated by armi farmer 1986 is extended to include exchange flows over sills and through a combination of a sill and contraction it is shown that exchange over a sill is fundamentally different from exchange through a contraction control at the sill crest acts primarily through the deeper layer into which the sill projects and only indirectly controls the surface layer this asymmetry in the control results in asymmetrical flows the interface depth above the crest is not one half the total depth as assumed in other studies by analogy with flow through contractions but is somewhat deeper the maximal exchange rate is less than for flow through a contraction of equal depth when both a sill and a contraction are present the contraction influences control at the sill crest only if it lies between the sill and the source of denser water the response to barotropic flow is also asymmetrical the transition to single layer flow occurs at much lower speeds for a barotropic component in one direction than the other results of the analysis are applied to exchange flow through the strait of gibraltar which includes both a sill and a contraction it is shown that maximal exchange conditions apply throughout part of the tidal cycle and observations illustrate several of the analytical predictions for barotropic flows including the formation of fronts single layer flow submaximal exchange and reverse flow

numerical modeling of stalagmite vibrations recently it has been argued that natural intact stalagmites in caves give important constraints on seismic hazard since they have survived all earthquakes over their rather long life span this suggests that the pattern of oscillation should be fully understood including the splitting of eigenfrequencies that has occurred in recent cave observations in the present study we simulate the oscillation of a given stalagmite by setting up four simplified models of the stalagmite the dimensions of the intact stalagmite were measured in situ and the geo mechanical and elastic parameters of broken stalagmite samples determined in geo mechanical laboratory have been taken into account the eigenfrequencies of the stalagmite are then calculated numerically by the finite element method and compared with the measured in situ values the latter have shown splitting of eigenfrequencies which we were able to reproduce by the numerical model calculations taking into account the asymmetric shape of the stalagmite

band of precariously balanced rocks between the elsinore and san jacinto california fault zones constraints on ground motion for large earthquakes a spectacular band of precariously and semiprecariously bal anced rocks extends from riverside to near borrego valley cali fornia about halfway between the elsinore and san jacinto fault zones the rocks are distributed in a band a few kilometers wide midway between the san jacinto and elsinore fault zones an in dication that the distribution is caused by attenuation of strong ground motion from numerous large events along these two fault zones these rocks have apparently been in place for thousands of years and thus place important constraints on ground motions from earthquakes on the basis of field tests and photographic analysis the estimated quasi static toppling accelerations for the precariously balanced rocks are 0 32 6 0 10 g g 5 gravitational acceleration the dynamic toppling accelerations are within this range for earthquakes with waveforms similar to those recorded during the izmit and denali earthquakes these constraints are roughly consistent with the median predicted value of ground mo tion for m7 earthquakes but somewhat lower than 11s ground motion curves and much lower than the values from the 2 in 50 yr hazard maps the evidence from these rocks has importance for some of the assumptions that go into calculating probabilistic seismic hazard assessment including median and standard devia tion of ground motion attenuation curves especially for hard rock for which few instrumental data are available the possible exis tence of random background earthquakes and the smoothing dis tance for historical seismicity

toppling analysis of the echo cliffs precariously balanced rock toppling analysis of a precariously balanced rock pbr can provide insight into the nature of ground motion that has not occurred at that location in the past and by extension can constrain peak ground motions for use in engineering design earlier approaches have targeted 2d models of the rock or modeled the rock pedestal contact using spring damper assemblies that require recalibration for each rock here a method to model pbrs in 3d is presented through a case study of the echo cliffs pbr the 3d model is created from a point cloud of the rock the pedestal and their interface obtained using terrestrial laser scanning the dynamic response of the model under earthquake excitation is simulated using a rigid body dynamics algorithm the veracity of this approach is demonstrated through comparisons against data from shake table experiments fragility maps for toppling probability of the echo cliffs pbr as a function of various ground motion parameters rock pedestal interface friction coefficient and excitation direction are presented these fragility maps indicate that the toppling probability of this rock is low less than 0 2 for peak ground acceleration pga and peak ground velocity pgv lower than 3 m s 2 and 0 75 m s respectively suggesting that the ground motion intensities at this location from earthquakes on nearby faults have most probably not exceeded the above mentioned pga and pgv during the age of the pbr additionally the fragility maps generated from this methodology can also be directly coupled with existing probabilistic frameworks to obtain direct constraints on unexceeded ground motion at a pbr s location