joint two dimensional dc resistivity and seismic travel time inversion with cross gradients constraints it is now common practice to perform collocated dc resistivity and seismic refraction surveys that complement each other in the search for more accurate characterization of the subsurface although conventional separate dc resistivity and seismic models can be diagnostic we posit that better results can be derived from jointly estimated models we make the assumption that both methods must be sensing the same underlying geology and have developed an innovative resistivity velocity cross gradients relationship to evaluate the structural features common to both methods the cross gradients function is incorporated as a constraint in a nonlinear least squares problem formulation which is solved using the lagrange multiplier method the resultant iterative two dimensional 2 d joint inversion scheme is successfully applied to synthetic data serving as validation tests here and to field data from collocated dc resistivity and seismic refraction profiling experiments and also compared to conventional separate inversion results the joint inversion results are shown to be superior to those from separate 2 d inversions of the respective data sets since our algorithm leads to resistivity and velocity models with remarkable structural agreement

joint two dimensional cross gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification summary collocated magnetotelluric mt and seismic profiling is emerging as a necessary combined approach for deep and near surface imaging but the resulting experimental data are typically interpreted separately since no production programs exist for multidimensional joint inversion of mt and seismic data we present a joint 2 d inversion approach for imaging collocated mt and seismic refraction data with cross gradient structural constraints we describe the main features of the algorithm and first apply it to synthetic data generated for a hypothetical complex geological model for the synthetic data we find that the scheme leads to models with remarkable structural resemblance and improved estimates of electrical resistivity and seismic velocity we apply the scheme to near surface field data to test the consistency of a previously suggested resistivity velocity interrelationship and its potential use for subsurface lithofacies discrimination or structural classification the mt seismic relationship is found to be in excellent accord with that derived previously for dc resistivity and seismic data set at the test site our results suggest that joint mt seismic cross gradient imaging leads to improved characterization of heterogeneous geological targets at near surface to mantle depths

viscosity in transition zone and lower mantle implications for slab penetration 1 the evolution of a subducting slab is strongly influenced by the viscosity of the mantle which it overlies however there is still no consensus about the viscosity in the transition zone and shallower lower mantle we use a numerical self consistent subduction model and run a set of experiments in order to find critical patterns of viscosity that would allow the evolution of the different subduction styles that can actually be found in nature our results show that a jump in viscosity of 5 times from transition zone to lower mantle gives the most reasonable results optimal values of viscosity in the transition zone are in the range of 3 1020 1021 pa s higher values would produce piling up of the slab and later sinking or even slab flattening lower viscosities result in velocities 30 cm yr that are too high while the new slab subducts through the upper mantle and transition zone a phenomenon that is rarely seen in nature reduction of the clapeyron slope related to the spinel perovskite transition variations in oceanic crustal thickness and in the age of the slab do not influence much the style of subduction when overriding velocity is applied to the upper plate the previously penetrating slab tends to lay at the 660 km boundary but does not substantially change the subduction velocity

effects of latent heat release at phase boundaries on flow in the earth s mantle phase boundary topography and dynamic topography at the earth s surface abstract mantle flow models that do not consider the effects of latent heat on phase boundaries typically predict dynamic surface topography too large to be compatible with observations here these effects were implemented in a mantle flow model and resulting changes in dynamic topography and topography of phase boundaries were computed inclusion of these effects was found to reduce the rms amplitude of dynamic topography by about 50 60 m still leaving a substantial misfit from observations in most cases considered generally it also leads to a slight improvement of correlation with dynamic surface and phase boundary topography constrained by observations results thus indicate that the model implemented here is applicable to the earth but that other effects need to be considered as well in order to fully explain phase boundary and dynamic surface topographies

rheology and strength of the lithosphere abstract mechanical properties of lithosphere are of primary importance for interpretation of deformation at all spatial and time scales from local scale to large scale geodynamics and from seismic time scale to billions of years depending on loading conditions and time scale lithosphere exhibits elastic brittle plastic or viscous ductile properties as can be inferred from rock mechanics data a large part of the long term lithospheric strength is supported in the ductile or ductile elastic regime while it also maintains important brittle strength yet at short seismic time scale s the entire lithosphere responds in elastic brittle elastic regime even though rock mechanics experiments provide important insights into the rheological properties of the lithosphere their conditions e g time scales strain rates temperature and loading conditions are too far from those of real earth therefore these data cannot be reliably extended to geological time and spatial scales strain rates 10 17 to 10 13 s 1 without additional parameterization or validation based on geological time scale observations of large scale deformation for the oceanic lithosphere the goetze and evan s brittle elastic ductile yield strength envelopes yses were validated by geodynamic scale observations such as the observations of plate flexure however oceanic lithosphere behavior in subduction zones and passive continental margins is strongly conditioned by the properties of the continental counterpart whose rheology is less well understood for continents and continental margins the uncertainties of available data sources are greater due to the complex structure and history of continental plates for example in a common continental rheology model dubbed jelly sandwich the strength mainly resides in crust and mantle while in some alternative models the mantle is weak and the strength is limited to the upper crust we address the problems related to lithosphere rheology and mechanics by first reviewing the rock mechanics data te flexure and ts earthquake data and long term observations such as folding and subsidence data and then by examining the physical plausibility of various rheological models for the latter we review the results of thermo mechanical numerical experiments aimed at testing the possible tectonic implications of different rheology models in particular it appears that irrespective of the actual crustal strength the models implying weak mantle are unable to explain either the persistence of mountain ranges for long periods of time or the integrity of the subducting slabs although there is certainly no single rheology model for continents the jelly sandwich is a useful first order model with which to parameterize the long term strength of the lithosphere it is concluded that dry olivine rheology laws seem to represent well the long term behavior of mantle lithosphere in oceans margins and continents as to the continent and margin crust rheology analysis of the results of thermo mechanical models and of te data based on the most robust variants of flexural models suggests that continental plates with te 30 50 smaller than their theoretical mechanical thickness hm i e te 20 60 km should be characterized by a weak lower or intermediate crustal rheology enabling mechanical decoupling between crust and mantle older plates such as cratons are strong due to crust mantle coupling and specific properties of the cratonic mantle lithosphere

subducted slabs and the geoid 1 numerical experiments with temperature dependent viscosity one of the most powerful constraints on mantle viscosity comes from the correlation of the long wavelength degree 4 9 geoid with that predicted by a density model for subducted slabs the effect of lateral variations of viscosity should be most pronounced at subduction zones due to the strong effect of temperature on viscosity an idealized slab model with temperature dependent viscosity is considered with various lateral and vertical viscosity structures using a two dimensional finite element formulation the viscosity parameterization affects the amplitude of the long wavelength geoid anomaly but not the sign of the correlation between the geoid and density anomalies depth dependent viscosity models with a high viscosity lithospheric layer do not completely match the temperature dependent laterally varying results suggesting that the rheology of the slab does have an effect on the long wavelength surface topography and geoid however this affect is minor suggesting that the radial models of mantle viscosity inferred from surface observables are correct to first order in contrast the short wavelength features are dramatically affected by the rheology of the region surrounding the downwelling further study of the shorter wavelength geoid over subduction zones may provide better insight into subduction zone processes

cooperative inversion of geophysical data geophysical inversion by iterative modeling involves fitting observations by adjusting model parameters both seismic and potential field model responses can be influenced by the adjustment of the parameters of the rock properties the objective of this cooperative in version is to obtain a model which is consistent with all available surface and borehole geophysical data al though inversion of geophysical data is generally non unique and ambiguous we can lessen the ambiguities by inverting all available surface and borehole data this paper illustrates this concept with a case history in which surface seismic data sonic logs surface gravity data and borehole gravity meter bhgm data are ad equately modeled by using least squares inversion and a series offorward modeling steps the traditional analysis of various geophysical data sets has been termed integrated interpretation such analysis has traditionally involved much processing modeling and subjec tive interpretation in order to develop a geologic model which is consistent with various surface and borehole geophysical data a method which automates some of the above pro cedures is least squares inversion this procedure perturbs an initial set of model parameters in order to fit the observed data least squares inversion is described in many papers in cluding those of jackson 1972 wiggins 1972 jupp and vozoff 1975 and lines and treitel 1984 this inversion technique could also be termed automated iterative mod eling in terms of modeling different geophysical data sets there are many possible approaches which allow inversion of a given data set and it is doubtful whether one single recipe will prove suitable for all problems nevertheless by jointly invert ing various types of geophysical observations we may lessen the extent of some of the ambiguities inherent in individual data sets lafehr 1984 gives a germane discussion of several reasons for this type of coordinated geophysical effort in the present study we define cooperative inversion as the esti mation of a subsurface model which is consistent with various independent geophysical data sets in the case discussed in this paper these data sets include surface and borehole observa tions of the seismic and gravity responses in our definition cooperative inversion may include either joint inversion or sequential inversion

predicting plate velocities with mantle circulation models 1 we predict plate motions from a comprehensive inversion of theoretical estimates of tectonic forces in order to evaluate the relative importance of these and the uncertainties of such models plate driving forces from the mantle are calculated using global flow models that are driven by tomography and subduction derived density fields observed and predicted plate velocities agree well for a variety of models leading to varied conclusions about the relative importance of forces the dominance of the subduction related density pattern in the mantle is confirmed it appears that p wave models do not satisfactorily image all of the slab associated anomalies in the upper mantle furthermore lower mantle structure always improves the plate motion fit with respect to models that are based on upper mantle anomalies and lithospheric thickening only we show that the average torques from the lower mantle scale with the radial flow through the 660 km phase transition the amplitude of the lower mantle torques will be significant for a range of models if there is mass flux through 660 km we also evaluate parameterized edge forces and find that the additional inclusion of such torques does not significantly improve the model fit the main reason for the nonuniqueness of the inversions is plate boundary geometry since all plate motions are dominated by the trench ridge system and plates move from ridges to trenches

seismic activity and ground deformation associated with 1995 phreatic eruption of kuju volcano kyushu japan abstract kuju volcano lies near aso caldera in central kyushu after a few hundred years of dormancy a phreatic eruption began with the ejection of about 20 000 m 3 ash on 11 october 1995 a number of new vents have opened on a series of lines striking east west on the eastern slope of mt hossho one of the domes of the kuju complex a few hundred meters from a pre existing fumarolic area after the eruption there has been continuous steam emission from the new vents there was the second ash eruption in december 1995 before these eruptions seismic events were rarely observed either near the site of the new vents or elsewhere under kuju volcano in the nearly 2 years since the first eruption several thousand earthquakes have been recorded these events have been very horizontally concentrated just to the north of the new vents vertically between 800 m above sea level and 1000 m below sea level very few earthquakes have been located on the southern side of the new vents there was clearly a strong high frequency attenuation affecting the seismic waves which passed through the region beneath the new vents to the seismometers south of mt hossho this evidence possibly indicates a thermal fluid content beneath the new vents suggesting that there is a seismic attenuating zone in the feeding area of the new vents nearly all the earthquake spectra were of dominantly high frequency but the percentage of earthquakes with predominantly low frequency spectra increased at times of enhanced volcanic activity volcanic tremors were also observed around the times of peak activity slope distance measurements have been made since the eruption the main results of these measurements are a contraction of more than 200 ppm in distances between mt hossho and points further north the significant distance changes occurred during seismic swarms this indicated that the seismic activities influenced ground deformation even though some of these swarms were 3 or 5 km from mt hossho the slope distance changes indicate that an area near the top of mt hossho has been moving to the northeast

uncertainty reduction through geologically conditioned petrophysical constraints in joint inversion abstractwe have developed a joint geophysical inversion workflow that aims to improve subsurface imaging and decrease uncertainty by integrating petrophysical constraints and geologic data in this framework probabilistic geologic modeling is used as a source of information to condition the petrophysical constraints spatially and to derive starting models the workflow then uses petrophysical measurements to constrain the values retrieved by geophysical joint inversion the different sources of constraints are integrated into a least squares framework to capture and integrate information related to geophysical petrophysical and geologic data this allows us to quantify the posterior state of knowledge and to calculate posterior statistical indicators to test this workflow using geologic field data we have generated a set of geologic models which we used to derive a probabilistic geologic model in this synthetic case study we found that the integration of geologic information and petrophysical con

seismo acoustic evidence for an avalanche driven phreatic eruption through a beheaded hydrothermal system an example from the 2012 tongariro eruption abstract the 6 august 2012 te maari eruption comprises a complex eruption sequence including multiple eruption pulses a debris avalanche that propagated 2 km from the vent and the formation of a 500 m long arcuate chasm located 300 m from the main eruption vent the eruption included 6 distinct impulses that were coherent across a local infrasound network marking the eruption onset at 11 52 18 all times utc an eruption energy release of 3 1012 j was calculated using a body wave equation for radiated seismic energy a similar calculation based on the infrasound record shows that 90 of the acoustic energy was released from three impulses at onset times 11 52 20 20 of total eruption energy 11 52 27 50 and 11 52 31 20 these energy impulses may coincide with eyewitness accounts describing an initial eastward directed blast followed by a westward directed blast and a final vertical blast pre eruption seismic activity includes numerous small unlocatable micro earthquakes that began at 11 46 50 two larger high frequency earthquakes were recorded at 11 49 06 and 11 49 21 followed directly by a third earthquake at 11 50 17 the first event was located within the scarp based on an arrival time location from good first p arrival times and probably represents the onset of the debris avalanche the third event was a tornillo characterised by a 0 8 hz single frequency resonance and has a resonator attenuation factor of q 40 consistent with a bubbly fluid filled resonator this contrasts with a similar tornillo event occurring 2 5 weeks earlier having q 250 1000 consistent with a dusty gas charged resonator we surmise from pre eruption seismicity and the observed attenuation change that the debris avalanche resulted from the influx of fluids into the hydrothermal system causing destabilisation and failure the beheaded hydrothermal system may have then caused depressurisation frothing of the remaining gas charged system leading to the onset of explosive activity

seismic response of the fractured and faulted granite of soultz sous forets france to 5 km deep massive water injections summary the european enhanced geothermal system egs formerly hot dry rock hdr programme of soultz sous foris organized around three wells drilled to a depth of about 5000 m hydraulic stimulations were performed in the wells in 2000 gpk2 well 2003 gpk3 well and 2004 and 2005 gpk4 well the stimulation of gpk2 induced more than 700 seismic events with a magnitude greater than 1 0 the seismicity depicts a dense homogeneous cloud without any apparent structure medium size earthquakes represent more than 80 per cent of the cumulative seismic moment the b value of the gutenberg and richter law is larger than 1 2 the injectivity has been increased by a factor 20 these characteristics indicate that the stimulation reactivated a 3 d dense network of fractures the stimulation of gpk3 induced only about 250 events with a magnitude greater than 1 0 but with a greater proportion of large events up to 2 9 the hypocentres form clear structures identified as large faults the b value is about 0 9 and the large events m 2 0 account for the greater part of the cumulative seismic moment the injectivity of the well which was already high before the stimulation remained unchanged the stimulation of gpk4 was achieved in two stages this stimulation produced even less induced events making the interpretation difficult the differences between the seismic response of gpk2 and gpk3 are due to the presence of large faults cut by gpk3 or in its close vicinity and reached by the injected water once a seismic event occurs on a fault a sequence of earthquakes is triggered and the seismicity behaves for a large part independent of the injected flow rate the stimulations also show some evidence that creeping could be a major source of deformation if not the main one the future egs programme will have to drill wells in zones free of large faults to avoid poor hydraulic performance and inconvenience to the population

effects of lateral viscosity variations on the geoid 1 we investigate the effects of lateral viscosity variations lvvs on mantle circulation model predictions of the global geoid the present study is motivated in part by earlier findings that lvvs due to stiff slabs in the lower mantle have a strong influence on the geoid and that slabs in the lower mantle are perhaps no stronger than the ambient mantle however more recently it has been argued based on global seismic tomography models that lvvs are a minor effect on the geoid in the light of these seemingly contradictory results we re visit the problem of slab strength in the lower mantle we substantiate that the geoid calculated from tomography is hardly affected by the presence of lvvs whereas the geoid computed from global slab models yields a poor fit to the observed geoid when lvvs are considered however this degradation of fit only occurs for very long wavelengths of flow indicating inherent differences between the slab and tomography models we also investigate the effects on the geoid due to weak plate boundaries strong cratonic keels and a low viscosity region in the d layer due to post perovskite in addition to the geoid we attempt to fit plate motions with a circulation model that has prescribed weak zones at plate boundaries motions are matched well and taking into account lvvs the geoid with appropriate surface velocity boundary conditions agrees with the observed geoid as well as for free slip cases

sea level change glacial rebound and mantle viscosity fornorthern europe northwestern europe remains a key region for testing models of glacial isostasy because of the good geological record of crustal response to the glacial unloading since the time of the last glacial maximum models for this rebound and associated sea level change require a detailed knowledge of the ice sheet geometry including the ice thickness through time existing ice sheet reconstructions are strongly model dependent and inversions of sea level data for the mantle response may be a function of the model assumptions thus inverse solutions for the sea level data are sought that include both ice and earth model parameters as unknowns sea level data from fennoscandia the north sea the british isles and the atlantic and english channel coasts have been evaluated and incorporated into the solutions the starting ice sheet for fennoscandia is based on a reconstruction of a model by denton hughes 1981 that is characterized by quasi parabolic cross sections and symmetry about the load centre both global northwestern europe as a whole and regional subsets of the data solutions have been made for earth model parameters and ice height scaling parameters the key results are as follows 1 the response of the upper mantle to the changing ice and water loads is spatially relatively homogenous across scandinavia the north sea and the british isles 2 this response can be adequately modelled by an effective elastic lithosphere of thickness 65 85 km and by an effective upper mantle viscosity from the base of the lithosphere to the 670 km depth seismic discontinuity of about 3 4 1020 pa s the effective lower mantle viscosity is at least an order of magnitude greater 3 the ice thickness over scandinavia at the time of maximum glaciation was only about 2000 m much less than the 3400 m assumed in the denton hughes model 4 the ice profiles are asymmetric about the centre of the ice sheet with those over the western part being consistent with quasi parabolic functions whereas the ice heights over the eastern and southern regions increase much more slowly with distance inwards from the ice margin

mechanisms of the nyos carbon dioxide disaster and of so called phreatic steam eruptions abstract during the night of august 21 1986 a huge volume of concentrated co 2 was emitted by the crater maar of nyos cameroon it killed more than 1700 people and all animal life as far as 14 km away two hypotheses have been put forward to account for this disaster the chronologically first one imputes it to have been a phreatic eruption exceptionally co 2 rich as had been the case in february 1979 on the dieng plateau in central java indonesia where the erupting crater was lake less the second one claims a limnic origin for the co 2 release through an overturn of the 220 m deep lake nyos the hypolimnium of which was supposed to be oversaturated by dissolved gas of volcanic origin the present paper points to six observed facts for which the eruptive hypothesis easily accounts and which the authors of the limnic one do ignore

an inversion for radial viscosity structure using seismic tomography using a uniform velocity density scaling we have inverted the seismically inferred 3 dimensional structure of the whole manfie for the radial viscosity structure which best fits the geoid we are able to obtain 60 72 variance reductions for three different s wave tomographic models the resulting viscosity structures are remarkably similar showing a high viscosity lid a low viscosity zone in the transition region and a high viscosity lower manfie a resolution analysis indcates that the viscosity structure in the upper manfie is well resolved by the data however the resolution in the lower manfie is poorer our models axe in general agreement with previous studies except that our inversions prefer a low viscosity layer at 400 670 km as opposed to 100 400 kin

slope instabilities in dolomieu crater reunion island from seismic signals to rockfall characteristics 1 the seismic signals of hundreds of rockfalls within dolomieu crater piton de la fournaise volcano reunion island have been analyzed to investigate a possible link between physical rockfall generating processes and associated seismic signal features moreover indirect observation of rockfalls via the seismic signals they generate can provide useful data for studying volcanoes and the temporal variations of their structure an increase in the number of rockfall events and their volumes might be an indicator of structural weakness and deformation of the volcano associated with potential eruptive activity the study focuses on a 10 month period following the 6 april 2007 crater floor collapse within dolomieu crater from may 2007 to february 2008 for granular flows a scaling law is revealed between seismic energy and signal duration a semiempirical approach based on both analytical analysis and numerical simulation of these flows shows that a similar scaling law exists between the difference of potential energy computed for an event and its propagation times and also emphasizes the effect of local topography on this scaling law simulated and observed data were compared to evaluate the proportion of potential energy dissipated in the form of seismic waves and confirm a direct link between the seismic energy and potential energy of a given granular flow the mean ratio of seismic to potential energy is of the order of 10 4 comparable to the range of values observed in previous studies a simple method based on these ratios is proposed to estimate the volumes of rockfalls from their seismic signal observed seismic energy and the frequency of rockfalls decreased at the beginning of the studied period and reached a stable level in july thus suggesting a postcollapse relaxation time of dolomieu crater structure of about 2 months from seismic signal analysis which is confirmed by deformation data the total rockfall volume over the study period is estimated to be 1 85 mm3

three dimensional gravity inversion model of the deep crustal structure of the central drake passage shackleton fracture zone and west scotia ridge antarctica 1 gravity and bathymetric data collected by the spanish r v hesperides over the shackleton fracture zone sfz and the west scotia ridge wsr were used to invert for the three dimensional 3 d structure of the deep crust data from the global gravity grid and global seafloor topography ggsft were also employed to enlarge the cruise area the merged data were analyzed to determine 3 d deep structure by numerical inversion water layer contribution to the gravity anomaly was eliminated taking into account the bathymetry spectral analysis of the reduced data yielded mean crust mantle interface cmi depths of 10 5 1 2 km inversion of the regional anomaly gave a 3 d detailed geometry of the cmi which generally agrees with the 2 d models established along profiles where gravity data and multichannel seismic lines are available the wsr shows an asymmetrical structure with a reverse fault located southeastward to the central valley this fault was developed probably as a consequence of the nw se compressive deformations which occurred following the spreading the 3 d view shows that the sw end of the spreading axis was affected more intensely by the compression the sfz represents an active sinistral transpressive fault zone of the scotia antarctica plate boundary and shows crustal thickening related to bathymetric highs the crustal thinning detected at the intersection with the inactive wsr suggests a complex interaction between these two structures

refinement of three dimensional multilayer models of basins and crustal environments by inversion of gravity and magnetic data abstract the sensitivity of gravity and magnetic data to deep structures and the broad availability of regional data sets and surveys of high resolution make them suitable for determining detailed three dimensional 3d models of the subsurface however the sole consideration of gravity and magnetic information cannot properly resolve heterogeneous 3d environments advocated to solve this problem we present an automated refinement technique for three dimensional multilayer models as conditioned by gravity and magnetic data and by meaningful geometrical and physical constraints we construct our model by an aggregate of rectangular prisms and aim to estimate their bottom depths which define the geological layers we summarize mathematically our concept of refinement in an objective function that includes the misfit to the data the similitude to an a priori geological geophysical model and the smoothness of the relief of the layers importantly our objective function also includes inequality constraints that prevent the superposition of layers and integrate the surface and borehole geology with the multilayer deep model the objective function is solved using quadratic programming in a stable iterative scheme the resulting algorithm is tested on synthetic data and applied to crustal and sedimentary basin environments from southern baja california mexico the assimilation of the geological and geometrical constraints to the inversion process produces models that correlate with the surface geology and reveal the three dimensional features of the subsurface

space geodesy constrains ice age terminal deglaciation the global ice 6g_c vm5a model a new model of the last deglaciation event of the late quaternary ice age is here described and denoted as ice 6g c vm5a it differs from previously published models in this sequence in that it has been explicitly refined by applying all of the available global positioning system gps measurements of vertical motion of the crust that may be brought to bear to constrain the thickness of local ice cover as well as the timing of its removal additional space geodetic constraints have also been applied to specify the reference frame within which the gps data are described the focus of the paper is upon the three main regions of last glacial maximum ice cover namely north america northwestern europe eurasia and antarctica although greenland and the british isles will also be included if peripherally in the discussion in each of the three major regions the model predictions of the time rate of change of the gravitational field are also compared to that being measured by the gravity recovery and climate experiment satellites as an independent means of verifying the improvement of the model achieved by applying the gps constraints several aspects of the global characteristics of this new model are also discussed including the nature of relative sea level history predictions at far field locations in particular the caribbean island of barbados from which especially high quality records of postglacial sea level change are available but which records were not employed in the development of the model although ice 6g c vm5a is a significant improvement insofar as the most recently available gps observations are concerned comparison of model predictions with such far field relative sea level histories enables us to identify a series of additional improvements that should follow from a further stage of model iteration

laboratory constraints on the rheology of the upper mantle the dynamics of convection and the mechanical behavior of the lithosphere are controlled by the rheology of upper mantle rocks for this reason experimental and theoretical studies on the rheology of olivine aggregates have been fields of active research for at least the last 35 years in this short course paper i briefly review some experimental and theoretical constraints on the rheology of upper mantle rocks and minerals and then discuss the application of these data for understanding the rheology of the upper mantle in different tectonic environments there is an expansive literature on the subject of mantle rheology extensive reviews and background can be found in several recent articles and books poirier 1985 ranalli 1995 karato and wu 1993 kohlstedt et al 1995 drury and fitzgerald 1998 hirth and kohlstedt 2003 as well as numerous references made throughout this chapter i focus the discussion of this chapter on the application of experimental data for constraining the rheology of the oceanic lithosphere and mantle constraints on mantle rheology based on extrapolation of laboratory experiments to deformation conditions in the oceanic lithosphere and asthenosphere are illuminating for several reasons first the composition of the mantle is relatively well constrained by analyses of peridotites from ophiolites and mid ocean ridges as well as chemical analyses of basalts second the oceanic lithosphere is comprised of rock that cooled from high temperature conditions at high pressure and is therefore not previously fractured in this way the lithosphere is similar to the ideal rocks we use in our experiments third the temperature of the lithosphere is constrained by a number of geophysical observations fourth microstructural observations on naturally deformed mantle rocks justify applying experimental flow laws at geologic conditions finally several independent geophysical observations such as constraints on viscosity based on analysis

geometry of ophiolites in eastern cuba from 3d inversion of aeromagnetic data constrained by surface geology this study combined geophysical geologic and topographic information to investigate the mayari baracoa ophiolitic belt in eastern cuba a recently developed interpretation technique for 3d inversion of magnetic data was employed to determine the geometry at depth of ophiolitic and other rocks based on measured susceptibilities lithologies were divided into four groups the geophysical data allowed 3d imaging of ophiolites serpentinized peridotites and gabbros as well as sedimentary and volcanic rocks the study verified that both the pinares de mayari plateau and the sagua de tanamo basin have been strongly influenced by tectonic activity the modeling showed evidence of more east west structural deformation of the ophiolite belt than had been previously reported the depth of the depocenter of the sagua de tanamo basin and its rate of subsidence were determined we identified some areas with potential for economic deposits of chromium cobalt and nickel as well as precious metals these were related to the thickness of the peridotite layer the modeling also corroborated the presence of previously mapped faults and revealed other previously unrecognized faults

active continental rifting in southern baja california mexico implications for plate motion partitioning and the transition to seafloor spreading in the gulf of california three major earthquake series have occurred during the past 30 years on fault systems that are spatially and kinematically distinct from oceanic spreading centers and transform faults in the southern gulf of california focal mechanism solutions for earthquakes of the april 1969 and june 1995 series indicate nearly pure normal displacement across nnw striking planes this seismicity falls along different strands of a major system of normal faults that extends at least 300 km along strike and defines the western limit of the gulf extensional province the dominant normal faults control distribution of neogene basins and have been active since middle to late miocene time epicenters of the august 1969 earthquake series lie south of the baja california peninsula and focal mechanism solutions indicate strike slip displacement this seismic activity is likely related to active wnw striking faults in the continental borderland which isolate baja california as a microplate within the pacific north american plate boundary therefore modern pacific north america plate motion is partitioned into at least three distinct fault systems oceanic spreading centers and transforms in the gulf of california normal faults along the western margin of the gulf of california and faults along the pacific margin of the baja california peninsula kinematic partitioning of plate motion is required to accommodate the strongly three dimensional strain of transtensional rifting continental rifting and seafloor spreading have overlapped in time for the past 3 6 myr which also is likely attributed to the highly oblique kinematics of rifting

extensional tectonics at the geysers geothermal area california comparisons between the yearly volume of steam withdrawn from the geysers california geothermal reservoir and the number of earthquakes indicate that most of the seismicity is induced to establish the inducing mechanism an estimate of the stress field orientation was calculated from inversion of 210 fault plane solutions below 1 km depth the geysers is undergoing uniaxial extension with the least principal stress 3 oriented near horizontal at approximately 105 azimuth the consistency between the local and regional stress fields indicates that the regional tectonic stress is much larger than the stresses induced locally through geothermal activities the stress data are equivocal as to whether earthquakes are induced due to conversion of aseismic to seismic slip or by increased shear stresses arising from reservoir contraction the observed tendency for downward growth of seismicity may arise from a preferential fracture orientation that is near vertical in conjunction with a stress state where the gradient of 1 exceeds that of 3 evidence of extension at the geysers and in the surrounding clear lake region indicates a direct relationship to the presence of the quaternary clear lake volcanics

structural model of the san bernardino basin california from analysis of gravity aeromagnetic and seismicity data 1 the san bernardino basin is an area of quaternary extension between the san jacinto and san andreas fault zones in southern california new gravity data are combined with aeromagnetic data to produce two and three dimensional models of the basin floor these models are used to identify specific faults that have normal displacements in addition aeromagnetic maps of the basin constrain strike slip offset on many faults relocated seismicity focal mechanisms and a seismic reflection profile for the basin area support interpretations of the gravity and magnetic anomalies the shape of the basin revealed by our interpretations is different from past interpretations broadening its areal extent while confining the deepest parts to an area along the modern san jacinto fault west of the city of san bernardino through these geophysical observations and related geologic information we propose a model for the development of the basin the san jacinto fault related strike slip displacements started on fault strands in the basin having a stepping geometry thus forming a pull apart graben and finally cut through the graben in a simpler bending geometry in this model the san bernardino strand of the san andreas fault has little influence on the formation of the basin the deep central part of the basin resembles classic pull apart structures and our model describes a high level of detail for this structure that can be compared to other pull apart structures as well as analog and numerical models in order to better understand timing and kinematics of pull apart basin formation

joint modeling of lithosphere and mantle dynamics elucidating lithosphere mantle coupling 1 we provide new insights into the lithosphere mantle coupling problem through a joint modeling of lithosphere dynamics and mantle convection and through comparison of model results with the high resolution velocity gradient tensor model along the earth s plate boundary zones using a laterally variable effective viscosity lithosphere model we compute depth integrated deviatoric stresses associated with both gravitational potential energy gpe differences and deeper mantle density buoyancy driven convection when deviatoric stresses from horizontal basal tractions associated with deeper density buoyancy driven convective circulation of the mantle are added to those from gpe differences the fit between the model deviatoric stress field and the deformation indicators improves dramatically in most areas of continental deformation we find that the stresses induced by the horizontal tractions arising from deep mantle convection contribute approximately 50 of the magnitude of the earth s deviatoric lithospheric stress field we also demonstrate that lithosphere asthenosphere viscosity contrasts and lateral variations within the lithospheric plate boundary zones play an important role in generating the right direction and magnitude of tractions that yield an optimal match between deviatoric stress tensor patterns and the deformation indicators

thermochemical structure and dynamics of the african superplume 1 we present a new three dimensional 3 d model of the thermochemical structure of the african superplume region obtained from simultaneous inversion of global seismic and convection related data convection related observations include the global free air gravity field tectonic plate motions dynamic surface topography and the excess ellipticity of the core mantle boundary a 3 d image of the chemically induced density perturbations provides direct evidence that intrinsically dense material is entrained within the superplume and concentrated into a rounded structure 1000 km above the core mantle boundary the thermally induced density perturbations are greater in magnitude than the chemically induced implying overall positive buoyancy throughout the superplume the observed morphology and density signatures are consistent with a thermochemical plume that has risen from a compositionally distinct pile at the base of the mantle and may be currently deforming under the influence of its intrinsic negative chemical buoyancy citation simmons n a a m forte and s p grand 2007 thermochemical structure and dynamics of the african superplume geophys res lett 34 l02301 doi 10 1029 2006gl028009

predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics the way in which basal tractions associated with mantle convection couples with the lithosphere is a fundamental problem in geodynamics a successful lithosphere mantle coupling model for the earth will satisfy observations of plate motions intraplate stresses and the plate boundary zone deformation we solve the depth integrated three dimensional force balance equations in a global finite element model that takes into account effects of both topography and shallow lithosphere structure as well as tractions originating from deeper mantle convection the contribution from topography and lithosphere structure is estimated by calculating gravitational potential energy differences the basal tractions are derived from a fully dynamic flow model with both radial and lateral viscosity variations we simultaneously fit stresses and plate motions in order to delineate a best fit lithosphere mantle coupling model we use both the world stress map and the global strain rate model to constrain the models we find that a strongly coupled model with a stiff lithosphere and 3 4 orders of lateral viscosity variations in the lithosphere are best able to match the observational constraints our predicted deviatoric stresses which are dominated by contribution from mantle tractions range between 20 70 mpa the best fitting coupled models predict strain rates that are consistent with observations that is the intraplate areas are nearly rigid whereas plate boundaries and some other continental deformation zones display high strain rates comparison of mantle tractions and surface velocities indicate that in most areas tractions are driving although in a few regions including western north america tractions are resistive citation ghosh a w e holt and l m wen 2013 predicting the lithospheric stress field and plate motions by joint modeling of lithosphere and mantle dynamics

a simple global model of plate dynamics and mantle convection cooling and thickening of lithospheric plates with age and subduction result in large scale horizontal density contrasts tending to drive plate motions and mantle flow we quantify the driving forces associated with these density contrasts to determine if they can drive the observed plate motions first two dimensional models are computed to evaluate the effects of assumed rheologies and boundary conditions we are unable to obtain platelike behavior in viscous models with traction free boundary conditions the piecewise uniform velocities distinctive of plate motion can be imposed as boundary conditions and the dynamic consistency of the models evaluated by determining if the net force on each vanishes if the lithosphere has a newtonian viscous rheology the net force on any plate is a strong function of the effective grid spacing used leading to ambiguities in interpretation incorporating a rigid plastic lithosphere which fails at a critical yield stress into the otherwise viscous model removes these ambiguities the model is extended to the actual three dimensional spherical plate geometry the observed velocities of rigid plastic plates are matched to the solution of the viscous stokes equation at the lithosphere asthenosphere boundary body forces from the seismically observed slabs from the thickening of the lithosphere obtained from the actual lithospheric ages and from the differences in structure between continents and oceans are included interior density contrasts such as those resulting from upwellings from a hot bottom boundary layer are assumed to occur on a scale small compared to plate dimensions and are not included the driving forces from the density contrasts within the plates are calculated and compared to resisting forces resulting from viscous drag computed from the three dimensional global return flow and resistance to deformation at converging boundaries the rms residual torque is 30 of the driving torque the density contrasts within the plates themselves can reasonably account for plate motions body forces from convection in the interior may provide only a small net force on the plates at converging boundaries the lithosphere has a yield stress of 100 bars drag at the base of the plates is 5 bars and resists plate motion the net driving forces from subducting slabs and collisional resistance are localized and approximately balance driving forces from lithospheric thickening are distributed over the areas of the plates as is viscous drag the approximate balance of these two forces predicts plate velocities uncorrelated with plate area as observed the model represents a specific case of boundary layer convection the dynamical results are consistent with either upper mantle or mantle wide convection

crustal structure of the northern menderes massif western turkey imaged by joint gravity and magnetic inversion in western anatolia the anatolide domain of the tethyan orogen is exposed in one of the earth s largest metamorphic core complexes the menderes massif the menderes massif experienced a two stage exhumation tectonic denudation in the footwall of a north directed miocene extensional detachment followed by fragmentation by e w and nw se trending graben systems along the northern boundary of the core complex the tectonic units of the vardar izmir ankara suture zone overly the stage one footwall of the core complex the northern menderes massif in this study we explore the structure of the upper crust in the northern menderes massif with cross gradient joint inversion of gravity and aeromagnetic data along a series of 10 km deep profiles our inversions which are based on gravity and aeromagnetic measurements and require no geological and petrophysical constraints reveal the salient features of the earth s upper crust we image the northern menderes massif as a relatively homogenous domain of low magnetization and medium to high density with local anomalies related to the effect of interspersed igneous bodies and shallow basins in contrast both the northern and western boundaries of the northern menderes massif stand out as domains where dense mafic metasedimentary and ultramafic domains with a weak magnetic signature alternate with low density igneous complexes with high magnetization with our technique we are able to delineate miocene basins and igneous complexes and map the boundary between intermediate to mafic dominated subduction accretion units of the suture zone and the underlying felsic crust of the menderes massif we demonstrate that joint gravity and magnetic inversion are not only capable of imaging local and regional changes in crustal composition but can also be used to map discontinuities of geodynamic significance such as the vardar izmir ankara suture and the west anatolia transfer zone

analysis of the microseismicity induced by fluid injections at the egs site of soultz sous forets alsace france implications for the characterization of the geothermal reservoir properties in june july 2000 a hydraulic stimulation experiment took place at the geothermal egs site of soultz sous forets alsace france in order to enhance the permeability of the fractured granitic massif at 5 km depth as it is well known that fluid injections tend to induce microseismic events a downhole and a surface seismological network have been installed to monitor the seismic activity during the stimulation test 23400 m3 of fluid have been injected in the rock volume through the open hole section 4400 m 5000 m of the well gpk2 at increasing rates of 30 l s 1 40 l s 1 and then 50 l s 1 more than 7200 microseismic events in the magnitude range 0 9 to 2 6 have been precisely located through a simultaneous inversion of the seismic velocity structure and location parameters the analysis of the behavior of the seismicity relative to the hydraulic parameters gives important information about the geothermal reservoir it appears that the evolution of the seismicity strongly depends on the variations of the injection rate an increase or a decrease leads to changes of the velocity structure the number and magnitude of microseismic events this involves different hydro mechanical processes between the fluid flow and the fracture planes which will control the final shape of the microseismic cloud moreover the study of the variations of the b value with time suggests that the stimulation experiment produces a large proportion of small earthquakes but records of events of magnitude higher than 2 indicate that fluid injection could reactivate structures whose dimensions allow the generation of such earthquakes

new insights into the structural model of the makran subduction zone by fusion of 3d inverted geophysical models abstract geological modeling by geophysical data in the makran subduction zone is a challenging task which comes from its extreme structural and geological complexity different geological models were presented for this zone in previous studies by the use of various sources of information among these studies numerous geophysical models were introduced to illustrate depth geometry and location of the subduction zone and definition boundaries with adjacent zones however structural complexity of the media and high degree of variation in geological units reduce accuracy of geophysical model derivation in this study an integrated strategy via model fusion for geological model building of the makran subduction zone was presented using gravity and magnetic data in the presented strategy gravity and magnetic models were integrated through fusing procedure herewith airborne magnetic and gravity data were inverted by fine gridding and solving large scale problems for each set of potential field data while magnetic model inherently was able to reveal near surface structures gravity data modeled large depth anomalies afterwards a discrete wavelet transform rule was used for fusion magnetic and gravity models to derive a unique model containing advantage of both sets of data the fused model revealed more detail of the makran zone structure location of the subduction zone and steep dip faults the final models proposed depth of 40 km for the top of the oceanic crust with variation in thickness from 5 to 8 km basin ward the subduction zone located 200 km in the onshore and it shows a very low dip

subducted slabs and the geoid constraints on mantle rheology and flow geoid anomalies are primarily the result of the density contrasts driving mantle convection and plate motion the total geoid anomaly resulting from a given density contrast in a convecting earth is affected by the mass anomalies associated with the flow induced deformation of the upper surface and internal compositional boundaries as well as by the density contrast itself these boundary deformations and hence the total gravity field depend on the radial distribution of effective viscosity if the internal density contrasts can be estimated as is the case for subducted slabs useful constraints can be placed on the depth and on the variation of viscosity with depth of the convecting system the degree 4 9 components of the observed long wavelength geoid are highly correlated with those predicted by a density model for seismically active subducted slabs the positive sign of the correlation requires that the effective viscosity increases with depth by a factor of 30 or more the amplitude of the correlation cannot be explained by the density contrasts associated with just the seismically active parts of subducted slabs however the amplitude can be explained if the density contrasts associated with subduction extend into the lower mantle or if old lithosphere is piled up at the base of the upper mantle beneath subduction zones to a thickness in excess of 350 km over horizontal distances of thousands of kilometers mantlewide convection in a mantle that has a viscosity increasing with depth provides a simple explanation of the long wavelength geoid anomalies over subduction zones

cyclic processes and factors leading to phreatic eruption events insights from the 25 september 2007 eruption through ruapehu crater lake new zealand abstract a dangerous block ash eruption occurred without warning from ruapehu crater lake on 25 september 2007 ending a 6 month period of temperature decline in the lake the northerly directed blast sent ballistics of up to 2 m diameter more than 2 km from the source the ejecta comprised a variety of volcano lacustrine lithologies many showing evidence of intense hydrothermal alteration petrographic studies of the ballistics reveal numerous examples of pores vesicles being filled with assemblages of elemental sulphur anhydrite pyrite and natroalunite and many ballistics exuded liquid sulphur from their pores during cooling at atmospheric pressure up to 5 of the ash was comprised of fine grained juvenile glass material confirming the presence of magma in the shallow vent environment a long recognised characteristic of this volcano is the thermal cycling behaviour of the crater lake behaviour which has remained effectively unchanged through two magmatic eruption events in 1945 and in 1995 96 airborne measurements of co2 and so2 flux from the volcano since 2003 show a strong positive correspondence with temperature cycling in the lake pointing to a definitive link between heat and mass discharge through the system low so2 emission rates and c s mole ratios 30 were typical of the period 2003 to early 2007 and appear to reflect vigorous scrubbing of s gases in the hydrothermal system during this time to better understand the chemical and physical processes operating in this very dynamic volcanic hydrothermal system and its propensity to develop potentially dangerous hydrothermal seals we have developed an integrated finite difference tough2 heat mass transport simulation of the hydrothermal environment the model which is constrained by observed heat and mass flux characteristics of the volcano demonstrates the transient nature of the heating cycles on the vent lake system of particular interest is the role of co2 as a relatively inert pressure transmitting medium in the hydrothermal environment seal formation was simulated using the reactive transport code x1t which showed that condensation of magmatic vapour into a highly porous medium of andesitic composition leads to rapid formation of an elemental sulphur anhydrite natroalunite mineral assemblage and a drastic reduction in permeability we suggest that since the 1995 96 vent clearing eruptions a shroud of elemental sulphur and other alteration phases formed along the margins of the 2 phase liquid vapour region enclosing the conduit this effectively seals the upper portion of the vent from the adjacent hydrostatically controlled environment and allows for development of pressurised vapour static gas columns beneath the northern and central vents

large earthquakes during hydraulic stimulations at the geothermal site of soultz sous forets abstract several deep wells were drilled in the rhine graben soultz sous forets france to evaluate the geothermal hot dry rock potential of a deep fractured granite reservoir three main boreholes which reached about 5 km depth intersected a crystalline basement overlain by 1 4 km of cenozoic and mesozoic sediments stimulations of these three wells were carried out in 2000 for gpk2 2003 for gpk3 and 2004 and 2005 for gpk4 during these stimulations and other hydraulic activities a seismological surface network was installed in order to monitor the seismicity induced by the massive fluid injection here we analyse the seismicity of magnitude larger than or equal to 1 4 which is the lowest magnitude felt by the population based on a spectral analysis of the displacement recorded by a guralp velocimeter at a depth of 200 m we know that the source dimensions range from tens to hundreds of metres we analyse several parts of the reservoir where obvious correlation between the fluid path and tectonic features has been pointed out based on seismological arguments such as location and focal mechanisms we show that this activity is linked with tectonic features or at least with large fractures that control the behaviour of the geothermal reservoir to constrain the hypothesis we study 391 events and focal mechanisms to argue in favour of the existence and stability of tectonic features that can be compared to geological data we show that the largest events recorded on the site occurred after the shut in their spatial distribution appears not to be random within the reservoir and the focal mechanisms of these events also confirm the non randomness of their distribution given their source dimensions the largest events can only occur on large structures such as tectonic ones therefore the behaviour of the reservoir is controlled by these main fractured zones which either lead the fluid or hinder its path

earthquake induced transformation of the lower crust the structural and metamorphic evolution of the lower crust has direct effects on the lithospheric response to plate tectonic processes involved in orogeny including subsidence of sedimentary basins stability of deep mountain roots and extension of high topography regions recent research shows that before orogeny most of the lower crust is dry impermeable and mechanically strong 1 during an orogenic event the evolution of the lower crust is controlled by infiltration of fluids along localized shear or fracture zones in the bergen arcs of western norway shear zones initiate as faults generated by lower crustal earthquakes seismic slip in the dry lower crust requires stresses at a level that can only be sustained over short timescales or local weakening mechanisms however normal earthquake activity in the seismogenic zone produces stress pulses that drive aftershocks in the lower crust 2 here we show that the volume of lower crust affected by such aftershocks is substantial and that fluid driven associated metamorphic and structural transformations of the lower crust follow these earthquakes this provides a top down effect on crustal geodynamics and connects processes operating at very different timescales during continent collision and associated mountain building a surprisingly large volume of the lower crust is shown to be affected by earthquake aftershocks producing a top down effect on crustal geodynamics

joint modeling of lithosphere and mantle dynamics sensitivity to viscosities within the lithosphere asthenosphere transition zone and d layers abstract although mantle rheology is one of the most important properties of the earth how a radial mantle viscosity structure affects lithosphere dynamics is still poorly known particularly the role of the lithosphere asthenosphere transition zone and d layer viscosities using constraints from the geoid plate motions and strain rates within plate boundary zones we provide important new refinements to the radial viscosity profile within the key layers of the lithosphere asthenosphere transition zone and d layer we follow the approach of the joint modeling of lithosphere and mantle dynamics ghosh and holt 2012 ghosh et al 2013b 2019 wang et al 2015 to show how the viscosities within these key layers influence lithosphere dynamics we use the viscosity structure sh08 steinberger and holme 2008 as a starting model the density variations within the mantle are derived from the tomography models which based on prior modeling had provided a best fit to the surface observables wang et al 2015 our results show that narrow viscosity ranges of moderately strong lithosphere 2 6 5 6 1022 pa s and moderately weak transition zone 5 9 3 1020 pa s as well as slightly large ranges of moderately weak asthenosphere 5 34 1019 pa s and d layer 4 8 18 1020 pa s are necessary to match all the surface observables we also find that a very strong lithosphere 8 6 1022 pa s along with a weak asthenosphere

characterization of rockfalls from seismic signal insights from laboratory experiments the seismic signals generated by rockfalls can provide information on their dynamics and location however the lack of field observations makes it difficult to establish clear relationships between the characteristics of the signal and the source in this study scaling laws are derived from analytical impact models to relate the mass and the speed of an individual impactor to the radiated elastic energy and the frequency content of the emitted seismic signal it appears that the radiated elastic energy and frequencies decrease when the impact is viscoelastic or elasto plastic compared to the case of an elastic impact the scaling laws are validated with laboratory experiments of impacts of beads and gravels on smooth thin plates and rough thick blocks regardless of the involved materials the masses and speeds of the impactors are retrieved from seismic measurements within a factor of 3 a quantitative energy budget of the impacts is established on smooth thin plates the lost energy is either radiated in elastic waves or dissipated in viscoelasticity when the impactor is large or small with respect to the plate thickness respectively in contrast on rough thick blocks the elastic energy radiation represents less than 5 of the lost energy most of the energy is lost in plastic deformation or rotation modes of the bead owing to surface roughness finally we estimate the elastic energy radiated during field scale rockfalls experiments this energy is shown to be proportional to the boulder mass in agreement with the theoretical scaling laws

what caused the denudation of the menderes massif review of crustal evolution lithosphere structure and dynamic topography in southwest turkey the deformation of earth s lithosphere in orogenic belts is largely forced externally by the sinking slab but can also be driven by internal delamination processes caused by mechanical instabiliti

what are the limitations of satellite altimetry radar altimeter measurements of the marine geoid collected during the seasat altimeter mission gave geophysicists hope of uncovering the gravity field over all the ocean basins however because of insufficient track density it has taken 16 years for the full potential of the satellite altimeter to be realized the high density coverage obtained by ers 1 during its geodetic mapping phase april 1994 march 1995 prompted the u s navy to declassify all of the geosat altimeter data in june 1995 the combination of these two high density data sets provided the first global view of all the ocean basins at a wavelength resolution of 20 30 km

gravity inversion of basement relief using approximate equality constraints on depths we present a gravity interpretation method for estimating the relief of an arbitrary interface separating two homogeneous media the upper medium is discretized into rectangular juxtaposed prisms whose thicknesses represent the depths to the interface and are the parameters to be estimated from the gravity anomaly the density contrast of each prism is assumed to be constant and known to stabilize the inversion we introduce two kinds of constraints on the depths the first one requires proximity between the observed and computed depths at isolated points such as those obtained from boreholes absolute equality constraint the second one requires that groups of depths approximately follow an established linear relationship among the depths relative equality constraint both kinds of constraints are imposed in the least squares sense we illustrate the method performance by applying it to a synthetic anomaly produced by a simulated basement relief consisting of four narrow and adjacent structural lows

magma compressibility and the missing source for some dike intrusions 1 dike intrusions are often accompanied by localized deflation interpreted as depressurizing magma chambers feeding the dike in some cases the inferred volume decrease is a factor of 4 or 5 less than the volume increase of the dike here we explore whether this discrepancy can be explained by compressibility of the magma combined with the fact that cracks are much more compliant than equidimensional magma chambers if pressure changes are small the magma compressibility m is constant and the dike ends up in hydrostatic equilibrium with an ellipsoidal magma chamber at the same depth the ratio rv of the volume of the crack to the volume lost by the chamber is rv 1 4 m 3 1 where is the host rock rigidity for gas poor magmas m 0 6 2 10 10 pa 1 and 3 25 gpa we find 1 2 rv 7 7 large changes in magma compressibility due to gas exsolution increase rv

modelling of sedimentary basins from gravity anomalies with variable density contrast summary the decrease of density contrast with depth in sedimentary basins could be approximated by a quadratic function the sedimentary basin is viewed as a number of outcropping vertical prisms put in juxtaposition at each observation point equations are derived for the gravity anomaly of a vertical prism for a quadratic density function the initial model is obtained by calculating the thicknesses of the prisms at each station by an infinite slab formula the differences between the observed anomalies and the anomalies of the initial model at each station are used to modify the initial model a computer program is developed for initial estimates and refinement of the model the method is applied to interpret the gravity anomaly of san jacinto graben california where sediments filling the graben have a density contrast that can be approximated to a quadratic function finally the convergence of the method is discussed