stable isotope records of late quaternary climate and hydrology from mediterranean lakes the isomed synthesis lake isotope records can be used to assess the spatial coherency of late quaternary climate change across the circum mediterranean region we place modern and palaeo data within a simple conceptual lake response model to show that the isotope hydrology of most mediterranean lakes has been influenced strongly by water balance even in those systems that are chemically dilute i e freshwater 18o data on biogenic and endogenic carbonates from 24 lake basins are used to reconstruct multi millennial scale trends since the lgm while it is difficult to make direct comparisons between lake records in terms of single climatic parameters coherent regional isotopic trends can be identified during glacial times mediterranean lakes deposited carbonates isotopically heavier in 18o compared to the holocene partly due to source area effects isotopic enrichment was most marked during intervals corresponding to the h1 and younger dryas events confirming that late pleistocene cold stages in the north atlantic region were marked by aridity around much of the mediterranean almost all mediterranean lake records shifted to more depleted isotopic values during the last glacial interglacial transition lgit this shift is the reverse of the trend which characterised the same transition in lakes from northern and central europe and suggests that temperature changes were not an important direct driver of mediterranean lake isotopic records over glacial interglacial timescales in the early holocene many lakes in the eastern part of the region were more depleted isotopically than in recent millennia this corresponds with marine sapropel formation both chronologically and geographically and implies that increases in local rainfall contributed significantly to the creation of a freshwater lid and anoxia in the east mediterranean sea in contrast no such pattern is currently apparent from lake isotope records from the west mediterranean suggesting a possible nw se contrast in climate history during the holocene

preliminary experiments to evaluate the gassmann equation in carbonate rocks calcite and dolomite fluid substitution is used to predict potential changes in seismic data due to production in oil reservoirs the fluid changes in clastic rocks are often predicted by the gassmann equation however the applicability of gassmann s equation in carbonates is not well understood apparently part of this failure is due to the violation of the assumption of a constant shear modulus for different fluids baechle et al 2005 adam et al 2006 but it is not clear yet

gassmann s fluid substitution and shear modulus variability in carbonates at laboratory seismic and ultrasonic frequencies carbonates have become important targets for rock property research in recent years because they represent many of themajoroilandgasreservoirsintheworld someareundergoing enhanced oil recovery most laboratory studies to understand fluid and pressure effects on reservoir rocks have been performed on sandstones but applying relations developed for sandstones to carbonates is problematic at best we measure in the laboratory nine carbonate samples from the same reservoir at seismic 3 3000 hz and ultrasonic 0 8 mhz frequencies samples are measured dry humidified and saturated with liquid butane and brine our carbonate samples showed typical changes in moduli as a function of porosity andfluid saturation however we explore the applicability of gassmann s theory on limestone and dolomite rocks in the context of shear and bulk modulus dispersion andgassmann stheoryassumptions forourcarbonatesetat high differential pressures and seismic frequencies the bulk modulus of rocks with high aspect ratio pores and dolomite mineralogy is predicted by gassmann s relation we also explore in detail some of the assumptions of gassmann s relation especiallyrock framesensitivitytofluidsaturation our carbonate samples show rock shear modulus change from dry to brine saturation conditions and we investigate several rock fluid mechanisms responsible for this change to our knowledge these are the first controlled laboratory experimentsoncarbonatesintheseismicfrequencyrange

evidence of lateglacial and holocene climatic change and human impact in eastern anatolia high resolution pollen charcoal isotopic and geochemical records from the laminated sediments of lake van turkey annually laminated sediments from lake van spanning about 13000 varve years were sampled for stable isotopic geochemical pollen and charcoal analyses in order to find evidence of past regional climatic changes and human impact in the semi arid region of eastern anatolia turkey the lateglacial period was cold and dry with steppe vegetation and saline lake water during the younger dryas the lake level dropped dramatically and the vegetation turned to a semi desert geochemical and isotopic records indicate a strong increase in moisture at the onset of the holocene and artemisia chenopod steppes were partly replaced by grass steppe and pistachio scrub a delay of about 3000 years in the expansion of deciduous oak woodlands and high steppe fire frequencies suggest dry spring and summer weather during the early holocene at 8200 yr bp a shift in the regional climate regime facilitated the transport of more moisture into the interior areas of the taurus mountains and caused a change in the seasonal distribution of precipitation the steppe forests dominated by quercus advanced and reached their maximum extention at about 6200 yr bp all the proxy data indicate optimum climatic conditions low water salinity and high lake level between 6200 and 4000 yr bp after 4000 yr bp aridity increased again and the modern climatic situation was established human impact in the catchment of lake van started at 3800 yr bp and was intensified during the last 600 years

late quaternary paleoclimate in the eastern mediterranean region from stable isotope analysis of speleothems at soreq cave israel abstract the eastern mediterranean continental paleoclimate during the past 25 000 years was determined by a high resolution petrographic stable isotopic and age study of speleothems from soreq cave israel 18o 13c trends indicate that all speleothems older than 7000 yr formed under conditions that differ from those of today the period from 25 000 to 17 000 yr b p was characterized by the highest 18o and 13c values which indicate deposition at temperatures of 12 16 c annual rainfall of 300 450 mm and vegetation typical of a mixed c3 c4type from 17 000 to 10 000 yr b p deglaciation in northern europe 18o values dropped progressively correlative with warming 2 3 c and a gradual increase in precipitation a simultaneous decrease in 13c gives a range expected for c3 type vegetation this period also shows significant 18o and 13c spikes which are correlatable with global events e g heinrich events and the younger dryas stade the speleothems that grew between 10 000 and 7000 yr b p have a unique petrography showing irregular thin laminae of various colors and much detritus they have the lowest 18o corresponding to 1000 mm rain coupled with the highest 13c caused by flooding events which stripped the soil cover from 7000 to 1000 yr b p conditions became closer to those of today this study demonstrates that global events which were recognized in northern europe and north africa are also evident in the eastern mediterranean and are reflected principally by large changes in the rainfall rate

seismic wave attenuation in carbonates 1 the effect of pore fluids on seismic wave attenuation in carbonate rocks is important for interpreting remote sensing observations of carbonate reservoirs undergoing enhanced oil recovery here we measure the elastic moduli and attenuation in the laboratory for five carbonate samples with 20 to 30 porosity and permeability between 0 03 and 58 1 mdarcy contrary to most observations in sandstones bulk compressibility losses dominate over shear wave losses for dry samples and samples fully saturated with either liquid butane or brine this observation holds for four out of five samples at seismic 10 1000 hz and ultrasonic frequencies 0 8 mhz and reservoir pressures attenuation modeled from the modulus data using cole cole relations agrees in that the bulk losses are greater than the shear losses on average attenuation increases by 250 when brine substitutes a light hydrocarbon in these carbonate rocks for some of our samples attenuation is frequency dependent but in the typical exploration frequency range 10 100 hz attenuation is practically constant for the measured samples

convolutional time lapse seismic modeling for co2 sequestration at the dickman oilfield ness county kansas abstracttime lapse seismic modeling is routinely used to detect the state of hydrocarbon reservoirs at periodic time intervals the dickman field located in the u s midcontinent provides two possible co2 sequestration targets a regional deep saline reservoir is the primary objective and a shallower mature depleted oil reservoir is a secondary objective the goal of this work is to characterize and simulate monitoring of the co2 movement before during and after its injection into these sequestration targets including fluid flow paths reservoir property changes co2 containment and postinjection stability seismic images before during and after injection would improve understanding of the carbonate sequestration process and management our seismic simulation for time lapse co2 monitoring was based on flow simulator output over a 250 year injection and simulation period the seismic response was accomplished via convolutional 1d forward modeling this work will provide an evaluation for the ef

holocene climate change in the eastern mediterranean region a comparison of stable isotope and pollen data from lake golhisar southwest turkey stable isotope and pollen data from golhisar golu a small intramontane lake located in southwest turkey provide complementary records of holocene climate change modern oxygen and hydrogen isotope water data are used as a means of comparing present day isotope composition of the lake water to the past oxygen isotope composition of the lake water as calculated from 18o 16o ratios in calcite precipitated in the summer months despite the lake system being chemically dilute the modern isotope data clearly establish that the lake water is evaporated in relation to its spring input suggesting that the palaeo data can be interpreted primarily in terms of changing precipitation evaporation ratios 18o and 13c values from authigenic calcite through the holocene show predominantly negative values indicating climatic conditions wetter than today particularly notable are low depleted isotope values during the earliest holocene ca 10 600 8800 cal yr bp a period for which pollen data imply drier conditions than at present this divergence between pollen inferred and stable isotope palaeoclimate data is found in other east mediterranean lake sediment records and suggests that vegetation may have taken several millennia to reach climatic equilibrium at the start of the holocene isotopic fluctuations during the early to mid holocene 8800 5100 cal yr bp suggest oscillations between aridity and humidity higher 18o and 13c values for the second half of the holocene indicate generally drier conditions than during the period before ca 5100 cal yr bp although there is some evidence for increased humidity coinciding with pollen evidence for increasing human impact and intensification of agriculture notably during the so called beyehir occupation phase classical and early byzantine periods the modern trend towards aridity started about 1300 yr ago

mid to late holocene climate change in central turkey the tecer lake record the mineralogy and grain size distribution of sediments from tecer lake in central anatolia provides a 6000 year record of mid to late holocene climate trends and events correspondences between k

changes of shear moduli in carbonate rocks implications for gassmann applicability in laboratory experiments we measured the saturation effects on the acoustic properties in carbonates and the results question some theoretical assumptions in particular these laboratory experiments under dry and wet conditions show that shear moduli do not remain constant during saturation this change in shear modulus puts gassmann s assumption of a constant shear modulus into question and also explains why velocities predicted with the gassmann equation can be lower or higher than measured velocities

a 4 decade record of elevation change of the amery ice shelf east antarctica 1 we report on long term surface elevation changes of the central amery ice shelf ais by comparing elevation records spanning 4 decades 1968 2007 we use elevation records acquired with the following methods optical leveling 1968 1969 ers radar altimetry 1992 2003 gps 1995 2006 and ice cloud and land elevation satellite icesat laser altimetry 2003 2007 we compute multidecadal elevation trend dh dt values at crossovers between the leveling route and each of the gps and icesat tracks as well as shorter period dh dt at ers ers gps gps and icesat icesat crossovers at gps leveling crossovers the mean long term dh dt is 0 003 m a 1 and at icesat leveling crossovers the mean dh dt is 0 013 m a 1 neither trend is significantly different from zero the data do however exhibit variable trends near zero change between 1991 and mid 1996 then thickening to 2003 followed by thinning 2003 2007 with 5 year dh dt averages exceeding 0 1 m a 1 the changes in dh dt pattern in mid 1996 and again in 2003 occur with unexpected speed the ice shelf exhibits different dh dt patterns than does the surrounding grounded ice suggesting that surface mass balance variations or longer term variations in firn densification processes are unlikely to be major causes we conclude that these observed multiyear elevation changes must be due to currently unexplained or presently poorly quantified phenomena involving surface or basal processes and or ice dynamics with the multidecadal stability of the ais established the short term fluctuations that we observe suggests that for other ice shelves observed strong dh dt signals over short time periods do not necessarily indicate ice shelf instability

the effect of micrite content on the acoustic velocity of carbonate rocks abstractwe have demonstrated the effect of micrite content on the acoustic properties of well controlled microstructures that are created in the laboratory to closely mimic those of carbonate rocks in particular we examined the effect of micrite content on the acoustic velocity sensitivity of velocity to pressure and changes in velocity resulting from dissolution upon saturation with a reactive fluid we followed dunham s classification and fabricated the samples by mixing coarse sand sized and very fine micrite sized calcite grains in different ratios and then cold compressing the mixture the acoustic velocities were measured under benchtop conditions and as functions of confining pressure before and after the injection of a co2 aqueous solution the benchtop measurements indicated that the addition of micrite made the frame of the carbonate samples stiffer because the sensitivity of velocity to pressure decreases as the content of micrite increases we hypothesized a stiffer pore structure in

stratigraphic variations in carbon and oxygen isotopes in the dolostone of the carswell formation proterozoic of northern saskatchewan petrographic and stable isotopic analyses of stromatolitic sediments deposited in nearshore environments provides us with some of the best information available on ancient environments diamond dri

dynamic carbon and sulfur cycling in the aftermath of the lomagundi jatuli event evidence from the paleoproterozoic hutuo supergroup north china craton abstract the unprecedented positive 13c excursion in carbonates deposited between 2 2 and 2 0 ga known as the lomagundi jatuli event lje has been documented globally and linked to the rise of atmospheric oxygen increasing oxidation inevitably changed the atmosphere hydrosphere system but few chemostratigraphic or quantitative constraints for the aftermath of this event exists here we describe a 200 m thick carbonate succession in the huaiyincun formation hutuo supergroup 2 0 1 9 ga from the north china craton there is a lithological transition from pink purple dolostones to grey dolostones at ca 91 6 m above the base of the huaiyincun formation the former are more enriched in hematite and detrital minerals whereas the latter contain more organic matter but almost no detrital phases meanwhile the frequent occurrence of tempesite structures along with the abrupt decline of stromatolites in the upper huaiyincun formation suggest a storm dominated environment these distinct features within the huaiyincun formation reveal increased water depth during a transgression event two types of raman spectra of organic matter were found in the lower and upper huaiyincun formation respectively which is proposed to be the result of variable oxidation at 65 6 m 26 m below the lithological transition 91 6 m remarkable decreases in both 13ccarb and 34scas are observed this discordance between c s isotopic excursions and sedimentological and mineralogical variations argues against a seawater depth gradient effect of the 13ccarb and 34scas curves instead the decline of 13ccarb rather correlates with the negative 13ccarb excursions in ca 2 0 ga carbonates from gabon and russia known as the shunga francevillian event sfe the result of the quantitatively constrained paleo seawater so42 sw suggests a crash of the seawater sulfate reservoir compared with that during the preceding lje however the decreased 34scas and increased cas concentration towards the top of the study unit represent the recovery of seawater sulfate reservoir the coordinated decline in 34scas and 13ccarb values is likely related to enhanced oxidation of continental pyrite and organic matter in the aftermath of the lje the huaiyincun formation therefore represents a critical interval that recorded dynamic carbon and sulfur cycles after the lje

the tempo of holocene climatic change in the eastern mediterranean region new high resolution crater lake sediment data from central turkey this study presents results from a multi proxy analysis of cores taken in a crater lake sequence from eski acigol in central turkey which cover the period from pre c 16000 cal yr bp to the present the sediments comprise an upper unit of generally non laminated banded to massive silts and peats of mid to late holocene age overlying a laminated unit of late pleistocene to early mid holocene age the laminae comprising mainly aragonite amorphous silica diatom frustules and organic matter were formed in a relatively deep dilute meromictic lake pollen data indicate an abrupt replacement of artemisia chenopod steppe by grass oak terebinth parkland during the period of laminae deposition marking the start of the holocene a gradual increase in tree pollen during the early holocene came to an end c 6500 cal yr bp u series and adjusted c 14 timescale when mesic deciduous taxa declined at the same time as lake levels fell human impact on regional vegetation is inferred from a sharp decline in oak around 4500 4000 cal yr bp diatom isotopic and mineralogical data indicate that during the second half of the holocene the lake became relatively shallow and oscillated between fresh and brackish evaporated water conditions the contrast between wetter early and drier late holocene climatic conditions is matched by other eastern and central mediterranean proxy climate data while the eski acigol sequence resembles holocene hydroclimatic changes in the saharo arabian zone and was also apparently linked to orbital forcing it is unlikely to have had the same direct cause i e an expansion and subsequent retreat of monsoon rainfall

modeling the paleoclimate ca 6000 3200 cal bp in eastern anatolia the method of macrophysical climate model and comparisons with proxy data abstract both paleoenvironmental and archaeological data provide mounting evidence of increasing aridification in the near east starting with the late early bronze age ca 4300 bp combining the methods of the macrophysical climate model mcm and gis it is possible to obtain quantifiable values across landscapes at 100 year resolution this research focuses on the methods of mcm a synoptic paleoclimate model that applies statistical downscaling and compares the results with proxy data the discussion addresses the divergent trends in precipitation and temperature in eastern anatolia between 6000 and 3200 bp the general climatic trends emerging from this research are then compared with those illustrated in various proxy data to verify the accuracy of the retrodictions for precipitation and temperature variables of the mcm results of this research are important as they may be integrated with the agent based land use and landscape evolution models these new approaches have great potential to demonstrate how multifaceted long term dynamic human environment relationships can be defined and readapted according to the changing levels of social organization which start a new cycle of social and economic responses with each ecological change

effects of fluids and dual pore systems on pressure dependent velocities and attenuations in carbonates theeffectsoffluidsubstitutiononp ands wavevelocitiesin carbonates of complex texture are still not understood fully the often used gassmann equation gives ambiguous results when compared with ultrasonic velocity data we present theoretical modelingofvelocityandattenuationmeasurementsobtainedata frequency of 750 khz for six carbonate samples composed of calcite and saturated with air brine and kerosene although porosities 2 14 and permeabilities 0 74 md are relatively low velocity variations are large differences between the highest and lowest p and s wave velocities are about 18 and 27 for brine saturated samples at 60 and 10 mpa effective pressure respectively s wave velocities are measured for two orthogonal polarizations forfourofsixsamples anisotropyisrevealed the gassmann model underpredicts fluid substitution effects by 2 for three samples and by as much as 5 for the rest of the six samples moreover when dried they also show decreasing attenuationwithincreasingconfiningpressure tomodelthisbehavior we examine a pore model made of two pore systems one constitutesthemainanddrainableporosity andtheotherismade ofundrainedcracklikeporesthatcanbeassociatedwithgrain tograincontacts inaddition thesedriedrocksamplesaremodeled to contain a fluid filled pore system of grain to grain contacts potentiallycausinglocalfluidflowandattenuation forthetheoretical model we use an inclusion model based on the t matrix approach whichalsoconsiderseffectsofporetextureandgeometry and porefluid global and local fluidflow by using a dualpore system we establish a realistic physical model consistently describingthemeasureddata

regional cooling in a warming world recent temperature trends in the southeast pacific and along the west coast of subtropical south america 1979 2006 1 while it is widely accepted that the global mean atmospheric temperature has increased in recent decades the spatial distribution of global warming has been complex in this study we comprehensively characterize the spatial pattern including vertical structure of temperature trends along the subtropical west coast of south america continental chile for the period 1979 2006 and examine their consistency with expectations based on the cmip 3 ensemble of coupled ocean atmosphere simulations for the late 20th century in central and northern chile 17 37 s the most notable feature is a strong contrast between surface cooling at coastal stations 0 2 c decade and warming in the andes 0 25 c decade only 100 200 km further inland coastal radiosonde data imply that the coast andes variation is largely due to strong vertical stratification of temperature trends in the atmosphere west of the andes the coastal cooling appears to form part of a larger scale la nina like pattern and may extend below the ocean mixed layer to depths of at least 500 m over continental chile the cmip 3 gcm ensemble predicts temperature trends similar to those observed in the andes the cooling along the chilean coast is not reproduced by the models but the mean sst warming is weaker there than any other part of the world except the southern ocean it is proposed that the intensification of the south pacific anticyclone during recent decades which is also a simulated consequence of global warming is likely to play a major role in maintaining cooler temperatures off the coast of chile

mid holocene climate variations revealed by high resolution speleothem records from soreq cave israel and their correlation with cultural changes mid holocene 7000 4000 yr bp paleoclimate conditions were reconstructed for the eastern mediterranean region through a high resolution 3 20 yr oxygen and carbon isotopic record in a speleothem

climatic interpretation of carbon isotope content of mid holocene archaeological charcoals from eastern anatolia abstract the 13c 12c ratio of juniper charcoals from the archaeological site of arslantepe malatya turkey was analysed for the mid holocene period spanning from 3350 to 2000 years bc in addition modern juniper and deciduous oak specimens were collected during a botanical survey around arslantepe in august 2008 after the evaluation of weather parameters the modern 13c 12c ratio was compared with the archaeological one to infer past seasonal precipitation relative magnitude patterns 13c values obtained from these samples suggest that the present day climate is on average drier than that recorded in the past comparing the 13c juniper record with the already published curve for archaeological charcoals of deciduous oaks from arslantepe it appears that the two curves show similar trends in the short period between ca 2850 and 2500 bc in which the curves are substantially parallel and the 13c difference between them is quite reduced but they are shifted by ca 50 150 years in the rest of the record for the interpretation of the arboreal curves however it was necessary to consider the autoecology of modern plants and the source of the water used for photosynthesis as the two selected trees show 13c curves with rather different patterns overall 13c 12c contrasting ratios in juniper and deciduous oaks suggest that seasonality in rainfall distribution and aquifer recharge played a complex role thus a consistent seasonal contrast in precipitation similar to the one in recent times took place at ca 3350 3100 and 2300 bc indicating that semi arid conditions have occurred in the past in alternation with periods characterised by minor differences in the distribution of annual precipitation in particular the period between ca 2850 and 2500 bc may suggest more humid conditions in late winter early spring the combination of the two records suggests that 1 two periods of drought are found at ca 3350 3100 and at ca 2300 2200 bc and 2 that at present winter precipitation is lower than that recorded during the period 3350 2000 bc and summer aridity less or equal to that recorded ca 2200 bc changes in precipitation seasonality and the complex and the peculiar hydrogeological situation hindered the interpretation of the isotope records the use of two taxa having different autoecology and different growing season allows interpretation of the data in terms of changes in precipitation seasonality and of specific habitat in this complex and peculiar hydrological setting

palaeoenvironment and carbon isotope stratigraphy of upper proterozoic carbonates of the yangtze platform the 13c values for phanerozoic marine carbonates display secular trends mainly in the range 1 to 2 1 these have been interpreted as primary features reflecting changes in the carbon isotope composition of dissolved bicarbonate in seawater brought about largely by variations in the proportions of carbon being sequestered in the oxidized and reduced carbon reservoirs1 2 carbon isotope trends are not as well established for the precambrian but there are indications that upper proterozoic sequences contain carbonates with unusually high 13c values3 9 here we present the results of the first carbon isotopic study of the upper proterozoic carbonate strata from the type locality of the sinian system in the yangtze gorges sections near yichang south china and discuss their implications for accumulation of organic matter we also compare the results for these chinese strata with 13c trends in other upper proterozoic cambrian sequences and assess the extent to which such isotopic data can be used to make stratigraphic correlations between widely spaced sequences

multi proxy records of quaternary fluvio lacustrine sediments around lakes eymir and mogan ankara central anatolia turkey this paper presents the mineralogical geochemical palynological and stable isotopic compositions of the late pleistocene holocene fluvio lacustrine sediments around lakes eymir and mogan ankara central anatolia it is based on the interpretation of the multi proxy records in conjunction with the geochronological data in eight different sections the comparison between the increase decrease in the abundances of carbonates and total clay assemblages is correlated with the changing abundance of coniferous forests and herbaceous plants mainly asteraceae and chenopodiaceae 13c and 18o values and molecular weathering ratios of the sediments revealing the hydrolysis evaporation and leaching together with chemical index of alteration cia provide insight into the climatic changes in the study area between 11 899 and 1428 cal year bp relatively higher total clay amount 18o of around 8 and higher cia 40 with higher hydrolysis suggest humid conditions during 11 899 6448 cal year bp between 6448 and 5763 cal year bp sediments show oscillations between high and relatively low values of the proxy data implying intercalation of dry and wet seasons the last period recorded between 5763 and 1428 cal year bp is realized with high calcite precipitation low total clay and low cia and relatively higher salinization which directly characterize aridity

the effect of chemical and physical processes on the acoustic properties of carbonate rocks carbonate rocks have major economic significance 60 of the world s oil reserves lie in carbonate reservoirs and the potential for additional gas reserves is huge however the relationship in carbonates between measured geophysical data and rock properties is complex due to the large variety of textures that arise during postdepositional diagenesis and to the chemical processes i e dissolution and replacement by newly formed phases that characterize carbonate forming minerals most experimental and theoretical rock physics research has focused on siliciclastic and shaly rocks however applying insights gained from clastics to carbonates is rarely straightforward and thus is questioned in the literature

bounds on low frequency seismic velocities in partially saturated rocks the most common technique for estimating seismic velocities in rocks with mixed pore fluid saturations is to use gassmann s relations with an effective fluid whose density and compressibility are averages of the individual pore fluid properties this approach is applicable only if the gas oil and brine phases are mixed uniformly at a very small scale so the different wave induced increments of pore pressure in each phase have time to diffuse and equilibrate during a seismic period in contrast saturations that are heterogeneous over scales larger than the characteristic diffusion length i e patchy saturation will always lead to higher seismic velocities than if the same fluids are mixed uniformly at a fine scale critical saturation scales separating uniform from patchy behavior are typically of the order 0 1 1 cm for laboratory measurements and tens of centimeters for field seismic frequencies for low seismic frequencies velocities corresponding to patchy and homogeneous saturations represent a