seismic image quality beneath strongly scattering structures and implications for lower crustal imaging numerical simulations summary the aim of this paper is to analyse how the scattered wavefield in a highly heterogeneous structure influences the image quality of structures below it and how the velocity control during processing of data from highly heterogeneous areas is important in the imaging problem statistical 2 d two layer models are built based on deep borehole data the layers are characterized by a fractal dimension hurst exponent and by the standard deviation of the velocity fluctuations over a constant background velocity value shot gathers are generated in these models with a 2 d elastic and viscoelastic finite difference simulator the synthetic data are first stacked and migrated using an average background velocity function as would be done in a realistic situation during which only a smooth version of the velocity field can be resolved second the full heterogeneous velocity models are applied to the migration scheme the final sections are compared using a semblance based technique to quantify the amount of contamination from an upper heterogeneous structure of a lower heterogeneous structure in data that are not properly migrated multiple scattering in the upper layer seems to dominate the lower part of the section this contamination is controlled by the standard deviation of the velocity fluctuations and it is reduced when viscoelasticity is introduced in the simulations counterintuitively a low q value may improve deep imaging when the seismograms are migrated with the real complex velocity field this contamination is reduced to acceptable levels residual contamination cannot be corrected completely because of the single scattering assumption inherent to all migration techniques

underestimation of scale lengths in stochastic fields and their seismic response a quantification exercise summary the possibility that parts of the earth s continental lower crust can be described with stochastic geological models has been suggested for some time recent studies of deeper well logs also indicate a possible stochastic structure at mid crustal levels this motivates a closer examination of the relation between the statistics of reflection wavefields and that of the lower crust such a relation can put important constraints on possible lower crustal models this study follows up earlier efforts to quantify the statistics of both stochastic lower crustal models and the reflected wavefield since modelling of the seismic response of stochastic von karman fields implies the usage of the impedance contrast field of the latter we wish to compare the second order statistics of both types of fields velocity and impedance this study concludes that the vertical derivative operator on a von karman velocity field implicitly present in the impedance contrast field alters the second order horizontal von karman statistics of the velocity fields in a profound way wavefield effects undoubtedly present in observed seismic data which have earlier been proposed as possible causes for the aforementioned change seem to play a secondary role the vertical derivative operation inherent in the impedance contrast field reduces the estimated horizontal scale length and hurst number by a factor of 2 22 and 1 3 respectively original vertical scale length and hurst number of the velocity fields have a quasi linear influence on this underestimation horizontal scale lengths and hurst numbers were also estimated from the seismic response primary reflectivity section of the von karman fields the values obtained are close to those obtained from the causative impedance contrast fields and are similarly underestimated this suggests a dominant role for the vertical derivative operator in the underestimation of horizontal scale length and hurst number this attempt to quantify the relation between the horizontal spatial statistics of von karman fields and the estimates derived from their seismic response may be useful in upscaling the latter

mapping correlation lengths of lower crustal heterogeneities together with their maximum likelihood uncertainties abstract a novel statistical technique has been applied to the ag 48 seismic line from the lithoprobe dataset passing through the abitibi grenville province canada the method maps lateral stochastic parameters representing von karman heterogeneity distributions in the crust estimated from migrated deep reflection data together with these parameters viz lateral correlation length and power law exponent we also compute their associated maximum likelihood uncertainties combining normalised measurements of lateral correlation and their uncertainties objective profiles of crustal fabric can be made these profiles indicate significant spatial variations in macro scale petrofabric correlation length which carries useful information about structural scale lengths of heterogeneous bodies is an especially robust parameter with moderate associated uncertainties although the general outline of the profiles conforms to the earlier tectonic interpretations based on line drawings new features are visible too the macro scale petrofabric is seen to vary significantly within the tectonic terrains identified earlier in depth as well as laterally a consequence of this additional delineation is that we can explain an existing part of the ag 48 line equally well in terms of collisional deformation and in terms of the effects of a major shear zone projected onto a parallel segment of the line

origin of late variscan granitoids from ne bavaria germany exemplified by ree and nd isotope systematics sm nd isotopic results are presented for late and post tectonic granitoids comprising peraluminous granites and subordinate metaluminous dioritic rocks redwitzites from the fichtelgebirge fg and northern oberpfalz nop ne bavaria the data combined with a number of earlier geochromological studies on these granitoids place severe constraints on the crustal evolution of this region during the carboniferous and pre carboniferous epoch redwitzites range in nd t from 4 to 0 inclusive data from p k holl and coworkers the nd t values of the granites s s are restricted to overlapping ranges of 8 to 3 fg and 8 to 2 nop in both domains the older granites 330 325 ma are characterized by nd t values of 4 whilst the younger granites 315 305 and 290 ma have nd t values of 4 the diversity observed in nd isotopic characteristic is interpreted in terms of different source material the nd isotopic compositions of the redwitzites exhibit source heterogeneity suggesting mixing between mantle magma and crust the nd isotopic features of the older granites are consistent with the magmatic precursors having been generated by partial melting of pre existing mature crust variably contaminated by mantle material or alternatively by melting of chemically less evolved crust resembling paragneisses of teh zev structural unit the origin of the younger granites can be confidently linked to anatexis of common moldanubian and saxothuringian metasediments two stage nd model ages tdm of the granitoids are in the range 1 1 1 7 ga these ages provide further support of substantial involvement of pre phanerozoic crust in the generation of the granitoids the leuchtenberg granite and the g2 and g3 granites yield late variscan sm nd isochron ages which are concordant with previous rb sr data on these granites by contrast the nd isotopic data for barnau and flossenburg define pseudo isochrons suggestive of mixing between contrasting felsic melts

quartz and feldspar zoning in the eastern erzgebirge volcano plutonic complex germany czech republic evidence of multiple magma mixing abstract zoned quartz and feldspar phenocrysts of the upper carboniferous eastern erzgebirge volcano plutonic complex were studied by cathodoluminescence and minor and trace element profiling the results verify the suitability of quartz and feldspar phenocrysts as recorders of differentiation trends magma mixing and recharge events and suggest that much heterogeneity in plutonic systems may be overlooked on a whole rock scale multiple resorption surfaces and zones element concentration steps in zoned quartz ti and feldspar phenocrysts anorthite content ba sr and plagioclase mantled k feldspars etc indicate mixing of silicic magma with a more mafic magma for several magmatic phases of the eastern erzgebirge volcano plutonic complex generally feldspar appears to be sensitive to the physicochemical changes of the melt whereas quartz phenocrysts are more stable and can survive a longer period of evolution and final effusion of silicic magmas the regional distribution of mixing compatible textures suggests that magma mingling and mixing was a major process in the evolution of these late variscan granites and associated volcanic rocks quartz phenocrysts from 14 magmatic phases of the eastern erzgebirge volcano plutonic complex provide information on the relative timing of different mixing processes storage and recharge allowing a model for the distribution of magma reservoirs in space and time at least two levels of magma storage are envisioned deep reservoirs between 24 and 17 km the crystallisation level of quartz phenocrysts and subvolcanic reservoirs between 13 and 6 km deflation of the shallow reservoirs during the extrusion of the teplice rhyolites triggered the formation of the altenberg teplice caldera above the eastern erzgebirge volcano plutonic complex the deep magma reservoir of the teplice rhyolite also has a genetic relationship to the younger mineralised a type granites as indicated by quartz phenocryst populations the pre caldera biotite granites and the rhyodacitic schonfeld volcanic rocks represent temporally and spatially separate magma sources however the deep magma reservoir of both is assumed to have been at a depth of 24 17 km the drastic chemical contrast between the pre caldera schonfeld westfalian b c and the syn caldera teplice westfalian c d volcanic rocks is related to the change from late orogenic geotectonic environment to post orogenic faulting and is considered an important chronostratigraphic marker

late collisional granites in the variscan erzgebirge germany the late collisional erzgebirge granites 325 318 ma were introduction emplaced at shallow crustal levels in the variscan metamorphic the erzgebirge is a ne sw trending antiformal structure basement shortly after large scale extension caused by orogenic exposing variscan crystalline basement rocks at the northcollapse these granites comprise mildly peraluminous transitional ern margin of the bohemian massif the region is famous i s types and strongly peraluminous s type rocks which can be among economic geologists for its extensive and highly subdivided into three major groups low f biotite granites low f variable metallic ore deposits which have been mined two mica granites and high f high p2o5 li mica granites the since the middle ages e g stemprok seltmann 1994 highest degree of differentiation is reached in the li mica granites tischendorf forster 1994 and for the classic studies which exhibit strongly elevated concentrations of p f li rb cs in the fields of economic geology mining and metallurgy ta sn w and u but very low ti mg co ni sr ba y zr chemistry and mineralogy e g werner 1791 breithaupt hf th and rare earth elements crystal melt fractionation is the 1849 agricola 1974 dominant process controlling the bulk composition of all groups of as in many of the other variscan provinces in central granites however metasomatic processes involving late stage residual europe granitic rocks make up a large proportion of the melts and high t orthomagmatic fluids became increasingly more exposed rocks in the erzgebirge and a great variety of important in highly evolved units and have modified the abundances compositional and textural types occur fig 1 knowof mobile elements p f li rb cs ba sr in the li mica ledge of the processes involved in the generation and granites particularly isotopic and geochemical characteristics suggest evolution of these silicic magmas is essential for underthat the three granite groups cannot be derived from a common standing heat and mass transport during the variscan precursor magma their discrete compositions are source related orogeny and also for the formation of metallic ore and are attributed to melting of quartzo feldspathic and pelitic deposits several lines of evidence indicate that early crustal lithologies in different proportions granites are common in high temperature sn w deposits are associated with the the central european variscides but the erzgebirge is unusual for emplacement of highly evolved volatile rich granitic the predominance of evolved li mica granites associated with melts tischendorf 1986 forster tischendorf 1992 economically important sn w and u deposits the abundance of stemprok 1993 the role of the granites in formation of li mica granites is attributed to a combination of favourable factors later permian u pb zn and younger ore mineralization 1 low degrees of anatectic melting of crustal protoliths 2 wide f ba is controversial but good evidence exists that the distribution of fertile lithologies rich in large ion lithophile elements vein type u deposits owe their uranium to leaching from and ore elements 3 extended magmatic differentiation by crystal the uraninite rich granites e g tischendorf forster melt fractionation and subsequent autometasomatism 1994

estimation of vertical stochastic scale parameters in the earth s crystalline crust from seismic reflection data 1 its been shown that the statistical properties of a reflected seismic wavefield can be related to the statistical properties of the crust in this paper we report on a method to invert a reflected seismic wavefield for vertical stochastic parameters the method is founded on a deconvolution thresholding and numerical integration procedure to estimate the earth s bi modal velocity perturbation we then fit a von karman autocorrelation function to the autocorrelation of the estimated velocity perturbation and record the von karman parameters which result in the minimum misfit tests show that our scheme is successful at recovering the vertical characteristic length in synthetic seismic reflection data

the broad band fractal nature of heterogeneity in the upper crust from petrophysical logs in situ measurements of petrophysical properties of the upper crust from wire line logs provide a direct means of assessing fluctuations in these properties with depth and thus allow for the statistical characterization of crustal heterogeneity wire line logs from a cluster of nine boreholes 1000 1500 m deep have been analysed using four different techniques autocorrelation semi variogram rescaled range and power spectra six of the boreholes are vertical the remainder inclined all penetrate clastic and pyroclastic rock the analysis techniques have been tested on synthetic data for which we have precise control on the scaling in order to assess their robustness the results for the borehole data show broad band fractal scaling with a fractal dimension of 1 62 to 1 97 autocorrelation 1 59 to 1 79 rescaled range and 1 61 to 2 0 power spectra the use of different techniques to estimate the fractal dimension provides an excellent constraint on the results furthermore it allows us to determine which model for crustal heterogeneity best describes the data a band limited von karman function or unbounded fractal scaling in order to test the possible anisotropy in the scaling parameters the horizontal scaling properties for this area have been calculated by correlation spectra analysis of neighbouring wells this suggests that upper crustal correlation lengths are of the order of kilometres and anisotropic being over four times greater in the horizontal direction the origins of the observed power law scaling are complex analysis of long term correlations between logs and televiewer data points towards the influence of fracture porosity within the pyroclastics but a fractal distribution of pore spaces within the clastics also controls the log fluctuations separating the logs into clastic and pyroclastic subsets reveals slight differences in fractal scaling as determined by autocorrelation and semi variogram these differences are attributed to the dominance of either primary or fracture porosity within each geological unit

statistical measures of crustal heterogeneity from reflection seismic data the role of seismic bandwidth in recent years there has been a growing realization that geological media vary over a broad scale range as such heterogeneity cannot be described in a deterministic way a parallel growth in stochastic analyses of geological geophysical data has emerged the stochastic description of these media is usually through some form of correlation function of which the von karman is the most widely employed using this form media can be described in terms of a characteristic scale size or correlation length l and a coloured scaling regime with scaling described by h the hurst exponent beyond the correlation length the material follows a white noise spectrum where material average properties dominate below the correlation length local heterogeneity dominates hence the correlation length is a fundamental parameter in a range of geodynamical problems in situ information about stochastic properties of deep crustal rocks can be obtained from the statistical analysis of reflection seismic data typical correlation distances within the crust are found to be several hundred metres here we show that correlation distances derived from reflection seismic data are strongly influenced by the spectral content of the source in particular we conclude that there is no reliable evidence for hundred metre scale correlation lengths for crustal heterogeneity

small scale heterogeneity and large scale velocity structure of the continental crust since conrad 1925 first identified a midcrustal refraction event in central europe seismologists have developed layered models of the continental crust with velocity steps at various levels modern analysis of crustal refraction data including automated inversion relies on ray theoretical techniques or wave theory for plane layered media which generally parameterize the earth as a series of grossly horizontal layers the bias toward layered models is in part based on physical and geologic intuition but it is to a large measure a result of available interpretation methods for example layer based reflectivity and ray tracing methods in contrast reflection seismology has produced a picture of a highly heterogeneous crust with wavelength scale variations in velocity existing at different levels of the crust in different tectonic regimes finite difference modeling shows that zones of small amplitude random velocity fluctuations not only produce short discontinuous reflection segments as observed on deep seismic reflection data but also produce strong wide angle reflections some of the events identified as crustal wide angle reflections in field data may in fact be the result of scattering from wavelength scale heterogeneities and need not result from reflection from a first or second order velocity discontinuity significant changes in the large scale velocity structure associated with zones of random velocity fluctuations produce relatively small changes in the dynamic properties of the backscattered wave field this observation is in disagreement with the common credo that the seismic refraction method is primarily sensitive to changes in the large scale velocity structure as a consequence the ray theoretical interpretation of such wide angle reflections as first order discontinuities leads to crustal velocity structures that are nonunique and may be erroneous in detail while correctly predicting average crustal velocity and thickness we are not suggesting that crustal velocity does not change with depth on the large scale rather we are proposing that crustal seismic events observed at intermediate and large offsets may be the result of scattering from wavelength scale velocity fabric rather than specular reflection or refraction from first order discontinuities

a laboratory investigation of assimilation at the top of a basaltic magma chamber the fluid dynamic processes affecting the mechanism and amount of assimilation of the roof of a magma chamber have been studied in a series of analogue laboratory experiments an aqueous solution of na 2 co 3 was first cooled and crystallized at the top of a laboratory tank to form a solid roof layer of prescribed composition the tank was then drained and refilled with warmer solution either na 2 co 3 of the same or different composition or in two experiments kno 3 the metal top in all cases was held below the eutectic temperature for the system na 2 co 3 h 2 o the experiments were continued until substantial crystallization and in some cases complete solidification were achieved starting with a dense solid roof layer of na 2 co 3 10h 2 o and ice on the na 2 co 3 side of the eutectic and a warmer eutectic na 2 co 3 solution below there was rapid convective cooling of the liquid layer accompanied by melting of the roof producing a compositional

mixing and chemical interdiffusion of trachytic and latitic magma in a subvolcanic complex of the tertiary westerwald germany abstract a special kind of magma mixing is extraordinarily well exposed in the bittersberg subvolcanic complex in the tertiary volcanic field of the german westerwald a trachytic melt has been penetrated by a latitic dyke which has been dispersed within the host magma as small spherical enclaves globules whole rock analyses of the globules show a change in composition that cannot be explained by a simple mechanical mixing between the endmembers the most evolved globules have a phonolitic composition microprobe measurements in the microlithic matrix of the host rock and the guest indicate a diffusive motion of the alkalis from the host into the globules on the other hand an opposite trend can be observed for ca mg fe and ti which are impoverished in the globules the trace elements and the middle rare earth elements mree has also been involved in the diffusive exchange the ree pattern of the most evolved phonolitic globules shows a characteristic trough in the area of the mree which is almost identical to the ree pattern of many phonolites the phonolites and the alkali rich trachytes of the westerwald show similar globular textures as the bittersberg volcanics therefore generation of these rocks involving diffusive element exchange during mixing processes in a magma reservoir situated on a deeper crustal level may be possible

erosive effects of the storm helena 1963 on basse terre island guadeloupe lesser antilles arc erosive effects of the tropical storm helena that hit the volcanic island of basse terre guadeloupe lesser antilles arc on 24 october 1963 has been measured using 80 aerial images acquired by the french geographic institute ign institut geographique national at the approximate scale of 1 8000 less than three months after the storm helena on these images 253 landslides triggered during the storm were identified and mapped these landslides were located in the central region of the island where catchments exhibit the highest relief even though the average thickness of the landslides was only 1 m i e less than the thickness of the weathered layer the total volume of displaced sediments corresponded to an average denudation of 2800 t km 2 i e 1 4 mm on the watersheds affected by landsliding to assess the erosional significance of this single climatic event we compare the volume of sediment mobilized by the storm helena to the long term denudation rate the latter estimated from a calculation of the total volume of material eroded since the emplacement of lavas using a digital elevation model is found to be 0 14 mm y assuming that helena is representative of the storms that hit basse terre island during the quaternary we find that a return period of about 10 to 15 years is enough to account for the long term denudation rate recorded for this island such a period is comparable with the actual return period of the tropical cyclones of the order of 4 to 5 years suggesting that the erosion of basse terre island is entirely controlled by tropical hurricanes

estimates of upper crustal heterogeneity in the baltic shield from seismic scattering and borehole logs abstract constraints on small scale heterogeneity in the upper crust of the baltic shield were obtained from stochastic modelling of a variety of seismic data from the babel and siljan ring surveys a non linear least squares inversion scheme was applied to wavefield fluctuations in seismic reflections to obtain statistical parameters of the medium through which the wave energy propagated the reflections are from dolerite sills intruded at depths of 6 12 km into the palaeoproterozoic upper crust of the central baltic shield analysis of the babel data set reveals that the upper crust is a weakly scattering stochastic medium with velocities characterised by an exponential autocorrelation function with a correlation length of 150 50 m and rms velocity perturbation of 1 5 0 5 further inversions show that most of the scattering occurs within the upper few kilometres of the crust analysis of the sijan seismic data set reveals heterogeneity with length scales of 210 50 m and a velocity perturbation of about 1 0 the autocovariance and power spectrum of the sonic log and studies of frequency dependent q in vsp data from the gravberg 1 borehole give consistent estimates of basement heterogeneity the upper crust in this region is characterised by a correlation distance of 35 5 m and rms velocity perturbation of 4 6 in the uppermost 1 2 km of crust associated with near surface fracturing and a correlation distance of 140 50 m and rms velocity perturbation of 1 5 0 5 in the uppermost 6 8 km associated with compositional heterogeneity

significant p wave attenuation for a specific frequency range beneath kirishima volcano japan the three dimensional p wave attenuation structure beneath kirishima volcano southwest japan was obtained through tomographic inversion of 469 p wave seismograms from 41 regional events recorded at 14 stations using band pass filtered p wave amplitude data the inversion determined the deviatoric attenuation constants of 4 km 4 km 5 km sw ne se nw depth blocks in the study volume as a function of seismic wave frequency the result delineates strikingly high attenuation at the depth of about 5 km beneath the highest cinder cone karakuni dake in the central region of kirishima volcano the attenuation constant in this region shows strong frequency dependence with greatest absorption around 8 hz this result is interpreted to represent the absorption of seismic waves by an 80 m thick sill like magma body there

plagioclase xenocrysts and mafic magmatic enclaves in some granitoids of the sierra nevada batholith california plagioclase phenocrysts from mafic magmatic enclaves and plagioclase crystals from host granitoids of some plutons of the central part of the sierra nevada batholith are complexly zoned and commonly divided into three neatly distinct parts an oscillatory locally patchy zoned andesine or more calcic core a ring with dusty calcic plagioclase and a normally zoned rim of sodic plagioclase although aspect of the calcic rings and width and zoning of the rims may slightly vary from the enclaves to the hosts cores of both phenocrysts and large plagioclase crystals show similar zoning and composition the andesine or more calcic cores are interpreted to have crystallized in the felsic or the mafic magma respectively and been incorporated into the coeval magma when the two magmas mixed introduction of the xenocrystic cores into a magma where they were not in equilibrium resulted in partial dissolution development of abundant patchy zoning and coating with dusty calcic plagioclase in both granitoids and mafic magmatic enclaves composition and zoning contrast between cores and rims of the plagioclase crystals reflect drastic changes in conditions of crystallization before and after the mechanical mixing event mixing of two magmas with contrasted compositions is suggested to be the major mechanism for generating complexly zoned plagioclase xenocrysts in granitoids and mafic magmatic enclaves this hypothesis is consistent with many recent models in which mixing of two contrasting components is proposed to play a fundamental part in the generation of calc alkaline granitoids and mafic magmatic enclaves of the sierra nevada batholith plagioclase xenocrysts may also provide information on the timing of the different mixing processes and on the magmatic evolution of the plutons

time of formation and peak of variscan hp ht metamorphism of quartz feldspar rocks in the central erzgebirge saxony germany the variscan erzgebirge represents an antiform with a core of gneisses and mica schists surrounded by a phyllitic mantle the gneiss eclogite unit geu in the central part is a composite tectonometamorphic assemblage characterized by a hp ht imprint and comprises migmatitic para and orthogneisses ht mylonites hp granulites eclogites and garnet peridotites it is tectonically sandwiched between two major units with distinctly lower pt histories the geu experienced a characteristic kinked retrograde pt path after hp ht equilibration with 1 strong near isothermal decompression at high temperatures 2 extensive re equilibration at medium pressures followed 3 by rapid cooling during continued uplift we dated zircons pb pb evaporation from granitoid orthogneisses and metapelites of the geu the orthogneisses contain euhedral long prismatic zircons of igneous origin that provided protolith ages between 470 and 524 ma metapelites retain well preserved granulite facies mineral assemblages and contain spherical multifaceted metamorphic zircons that grew near the peak of hp ht metamorphism inclusions of prograde hp phengite 15 kbar and rutile are included in one such zircon metamorphic zircons of three samples from different localities yielded identical 207pb 206pb ages of 340 5 0 7 ma 341 2 0 5 ma and 341 6 0 5 ma respectively consideration of these zircon ages with published 39ar 40ar white mica ages suggests fast cooling and uplift rates in excess of 50 c ma and 4 km ma this is typical for large scale extensional tectonic unroofing of the ultra deep part of a fossil thickened variscan continental crust 60 km during continuing continental collision and orogenic collapse

variscan silicic magmatism and related tin tungsten mineralization in the erzgebirge slavkovský les metallogenic province integration of geochemical mineralogical isotopic and geochronological data with geodynamic considerations suggests that the variscan granites in the erzgebirge slavkovsk les domain originated from repeated melting events and were emplaced over a period of about 40 ma 330 290 ma several lines of evidence exist supporting the idea that erzgebirge granites assigned to different types biotite granites two mica granites strongly peraluminous p rich li mica granites and slightly peraluminous p poor granites are in most cases not genetically related via continuous fractional crystallization from a common magmatic reservoir the genesis of the slavkovsky les granites however might be discussed in terms of an uninterrupted fractionation series geological models of sn w deposits based upon geochemical and structural results imply that the main ore depositional events followed immediately the emplacement and solidification processes of melt via fluid melt immiscibility breccia pipe formation and or pervasive rock fluid interactions

estimation of crustal stochastic parameters from seismic exploration data stochastic models for the crystalline crust produce synthetic seismograms that compare well with recorded data for a variety of crustal ages and tectonic environments in this paper we explore the parameter space describing such stochastic models as a basis for formulating the inverse problem that is we wish to estimate the parameters which define a stochastic model from the recorded backscattered wave field we base the estimation on approximate relations between the primary reflectivity series which is the ideal wave field response of a medium and various seismic gathers a two dimensional lateral correlation method is used to investigate the sensitivity of synthetic wave fields to horizontal characteristic length a derived empirical relationship relates the scale length to the half width of the correlation coefficient a horizontal wavenumber time domain spectral analysis successfully estimates the horizontal characteristic length ax and the fractal dimension d of the stochastic medium from which the wave field was backscattered we employ a monte carlo based optimization scheme to fit the observed spectral values to a one dimensional von karman function and simultaneously estimate values for ax and the hurst number the method yields consistent results when tested on synthetic data application of this technique to data sorted into different domains shows that zero offset sections yield the best estimate we also present results of our estimates using this method on a program for array seismic studies of the continental lithosphere passcal dynamite source shot gather and a vibroseis source consortium for continental reflection profiling cocorp data set recorded in the basin and range province

conservation of lateral stochastic structure of a medium in its simulated seismic response 1 mapping correlation lengths of continental lower crustal heterogeneity directly from deep reflection data can be a valuable additional interpretation tool for deep seismic imaging in this feasibility study we investigate the conservation of lateral correlation length and power law structure in the seismic response of lower crustal stochastic lithology the conservation of von karman power law heterogeneity in backscattered wavefields is evaluated in a range of challenging seismic scenarios we pay special attention to the limitations of this conservation due to the effect of spatial band limitation caused by limited seismic recording aperture and to the effect of complex seismic scattering conditions the comparison of average lateral correlations in von karman media and their modeled reflection responses reveals two important facts spatial band limitation by limited seismic illumination severely affects the estimated power law exponent the hurst number of the von karman heterogeneity distribution but the estimated correlation length is unaffected and scales linearly with the original value the original type of lateral power law distribution is conserved under nearly all seismic scattering conditions investigated albeit with an underestimated correlation length and overestimated hurst number our results can be quantitatively explained which allows for stable estimations of correlation length under various seismic scattering scenarios this study confirms the potential of utilizing estimates of lateral von karman structure to characterize the middle and lower crust from deep seismic reflection data

rupture dynamics and ground motions from earthquakes in 2 d heterogeneous media we perform 2 d simulations of earthquakes on rough faults in media with random heterogeneities with von karman distribution to study the effects of geometric and material heterogeneity on the rupture process and resulting high frequency ground motions in the near fault region out to 20 km variations in slip and rupture velocity can arise from material heterogeneity alone but are dominantly controlled by fault roughness scattering effects become appreciable beyond 3 km from the fault near fault scattering extends the duration of incoherent high frequency ground motions and at least in our 2 d simulations elevates root mean square accelerations i e arias intensity with negligible reduction in peak velocities we also demonstrate that near fault scattering typically occurs in the power law tail of the power spectral density function quantified by the hurst exponent and another parameter combining standard deviation and correlation length

deep borehole log evidence for fractal distribution of fractures in crystalline rock summary sonic velocity and electrical resistivity logs run to a depth of 3 5 km in crystalline rock near the san andreas fault at cajon pass in southern california correlate over scale lengths both small sub metre and large tens to hundreds of metres no such correlations are seen with the more lithologically sensitive natural gamma intensity log the correlation between the sonic velocity and electrical resistivity logs suggests that a non lithologic property of the crystalline rock controls fluctuations in situ fracture intensity is a logical candidate for the controlling rock property the fluctuations of the individual sonic velocity and electrical resistivity logs are examined with the hurst rescaled range parameter over borehole log intervals 1 5 m l 1500 m for log fluctuations arising from a scale invariant physical process the hurst rescaled range scales with data interval as lh 0 h 1 a purely random sequence of in situ fractures produces a scaling exponent h 0 50 fluctuations in the cajon pass sonic velocity and electrical resistivity logs yield h 0 70 evidence that in situ fracture sets tend to occur in clusters rather than at purely random intervals the tendency for fracture clustering over log intervals 1 5 m l 1500 m suggests that fracture formation is a fractal process independent of length scale in which larger fracture intervals form from clustering of numerous smaller fracture intervals seismic reflectivity derived from the borehole sonic velocity log is also scale independent over the range of data intervals 1 5m l 1500 m with a hurst exponent h 0 21 if we associate fracture clustering with crustal fault formation the cajon pass borehole sonic velocity and electrical resistivity logs predict that crustal faults scale fractally with fractal dimension d 2 30 the equivalent b value for earthquake size distribution is b d 2 1 15 on this hypothesis observed b values 1 15 indicate a tendency for earthquakes to cluster on existing weak faults a scale independent mechanics for crystalline rock fracture formation in which larger scale fractures form as clusters of smaller scale fractures provides a mechanical link between the small pervasive stress aligned flaws cracks and microfractures which can impart anisotropy to crystalline rock and the larger scale fractures associated with finite strain and faulting thus in crustal regions of active but low strain fracture anisotropy is observed to be aligned with the inferred maximum principal stress while in actively faulted crust fracture anisotropy is observed to be more nearly fault parallel as if the fractures are aligned by the finite strain faulting process

the idea of magma mixing history of a struggle for acceptance abstract in 1851 chemist robert bunsen suggested that the mixing of two magmas one mafic and the other felsic in various proportions might account for the wide range of chemical compositions of igneous rocks based on flaws in several of its secondary provisions the whole hypothesis was rejected by a succession of influential critics and remained in disrepute for a hundred years meanwhile studies of composite dikes and sills indicated that indeed mafic and felsic magmas had coexisted at close quarters and had been emplaced in quick succession this interpretation was also used by some investigators to explain the intimate association of mafic and felsic rock types in the commonly occurring igneous complexes others believed that the mafic components of these complexes were derived from geologically older mafic formations by the early 1900s it had become apparent that mafic magmas crystallized at higher temperatures than felsic magmas this knowledge was not immediately applied to the problem of m

some remarks on the estimation of fractal scaling parameters from borehole wire line logs well logging provides a direct means of assessing fluctuations in petrophysical properties with depth and thus allows for the statistical characterisation of crustal heterogeneity using records from three super deep boreholes ktb and cajon pass and synthetic data we assess three different techniques for estimating fractal dimension and correlation length inaccurate correlation lengths may result from the way in which the autocorrelation is calculated for well logs leading to an incorrect application of the von karman function analysis of the rescaled range power spectra and autocorrelation allow us to model the data as k where k wavenumber and exponent 5 2d for fractal dimension d process with values of fractal dimension displaying anti persistence

delineating tectonic units beneath the donbas fold belt using scale lengths estimated from dobre 2000 2001 deep reflection data 1 a novel statistical analysis which augments conventional interpretation of deep seismic reflection refraction data is applied to the dobre 2000 2001 reflection profile the goal is to improve delineation of the lithosphere in terms of lithotectonic units and to compare these to existing interpretations after a successful validation of the method using synthetic data stochastic parameters estimated from windowed average lateral autocorrelations in the dobre data are compiled in a two dimensional profile of von karman type causative reflectivity these estimates in terms of lateral correlation lengths and power law exponents are accompanied by associated uncertainties given its low uncertainties the lateral correlation length ax turns out to be a robust delineator the profile of ax reveals systematic spatial variations in the lithospheric fabric below the donbas fold belt as in earlier interpretations based upon conventional processing of reflection refraction data both the sedimentary basin and moho discontinuity stand out clearly as well as a region indicating massive vertical intrusion in the crust from upper mantle sills and ultramafic underplating of the lower crust notable differences with conventional interpretations include the number and extent of supra moho rift pillow structures the lack of imaging a crust cutting dislocation feature and a laterally disturbed uppermost mantle von karman lateral correlation length provides new independent information at a scale between velocity models from wide angle reflection refraction data and line drawings from near vertical reflections and provides new insights and understanding of lithospheric evolution

origin of mantle rapakivi feldspars experimental evidence of a dissolution and diffusion controlled mechanism experiments designed to simulate the dissolution of alkali feldspar during magma mixing produced plagioclase mantles that are texturally and compositionally similar to those in some hybrid volcanic rocks in hydrous dacite melt 69 sio2 at 0 8 gpa 850 c orthoclase or93 and sanidine or30 partially dissolved and were mantled by sodic plagioclase an25 30 although plagioclase nucleated epitaxially as a thin shell on the alkali feldspar surface near the time of initial resorption plagioclase subsequently grew inward mostly in the form of parallel blades toaard the receding dissolution surface orthoclase dissolved at a rate approximately proportional to the square root of run duration indicating diffusional control plagioclase grew inward within a static boundary zone of melt that formed between the original crystal dacite interface and the dissolution surface during orthoclase dissolution this boundary zone rapidly and simultancously gained na by diffusion from dacite and lost k by diffusion into dacite ca diffused more slowly into this zone from which non feldspar species were mostly excluded plagioclase was stable where sufficient ca had diffused in that the boundary zone melt intersected the plagioclase saturation liquidus plagioclase subsequently grew toward the receding dissolution surface as the ca compositional gradient and hence the site of plagioclase saturation stepped inward crystallization of plagioclase in the form of parallel blades allowed continued diffusive exchange of melt components between the dissolution surface and the host melt bladed growth also served to maintain at blade tips proximity of plagioclase to the dissolution surface thereby apparently preserving locally a thin zone of low variance melt in natural systems mantling of alkali feldspar by plagioclase will occur in a similar manner when a p t or x are changed to induce alkali feldspar dissolution b sufficient ca is available in the host melt to drive by diffusion boundary zone melt compositions to plagioclase saturation and c temperatures are low enough to stabilize sodic plagioclase and to maintain a coherent boundary zone these reqjirements are satisfied in volcanic systems when alkali feldspar is juxtaposed during mixing with hybrid melts of dacitic composition mantled feldspars in some intrusive systems i e rapakivi granites may form by a similar dissolution and diffusion controlled mechanism textural evidence of a similar origin may be obscurred in intrusive rocks however by products of late stage magmatic and subsolidus processes

statistical approaches to interpretation of seismic reflection data abstract statistical approaches offer a potentially powerful tool for interpretation of the complex seismic reflection patterns typically recorded from the crystalline crust these methods focus on characterization of the complexity scaling characteristics and spatial variability of the wave field with the ultimate aim of recovering information on the geometric variation of the geology in this paper we examine the potential and limitations of statistical approaches focusing on the issues of quality of the statistical estimator how noise and migration affect spatial statistics and the potential for both qualitative and quantitative approaches to statistics based interpretation the limited spatial bandwidth of typical seismic data presently inhibits complete quantitative recovery of the spatial properties of the geology migration which should increase the spatial bandwidth has to date not proven particularly effective on complex wave fields mapping of relative variation in the spatial properties of the wave field reveals subtle differences that are directly associated with the geometric character of the geology such mapping allows identification and mapping of variations in the geologic fabric at scales significantly larger than the seismic wavelength and objective access to scaling information that has previously been unavailable

cathodoluminescence and micro structural evidence for crystallisation and deformation processes of granites in the eastern lachlan fold belt se australia trace elements al k ti fe growth and deformation pattern in quartz of the multiple deformed carcoar barry and sunset hills granites were investi gated by electron micro probe and cathodolumines cence zoned quartz phenocrysts with high ti concentrations 70 ppm that show blue cathodolu minescence originated from the early stage of magma crystallisation multiple deformation of quartz causes the redistribution of al and k in the quartz lattice which results in the accumulation of these elements in submicroscopic inclusions 0 5 lm of muscovite like composition in contrast structural ti in quartz is mostly kept in the lattice common halos of defect poor secondary quartz around fluid inclusions result from re equilibration of fluid inclusions because of differences between fluid pressure and lithostatic pressure e g duringuplift isothermal decompression and or a b transition of quartz duringhealing defect poor sec ondary quartz grows at the cost of the host quartz and releases or replaces defect centres the results of micro structural investigations combined with al in horn blende thermobarometry allow the reconstruction of regional processes carcoar and barry granodiorites and sunset hills granite were intruded in the late ordovi cian early silurian at depths of 4 8 6 and 10 12 km respectively in contrast to the continuous crystallisation of the granodiorite magmas the magma of the sunset hills granite ascended in a stepwise fashion causing multiple quartz nucleation the two granodiorites were multiple post magmatically deformed first during early devonian under more brittle conditions at temperatures of 350 400 c whereas the sunset hills granite experienced more ductile deformation at tem peratures of around 550 c

cellular plagioclase intergrowths as a result of crystal magma mixing in the proterozoic aland rapakivi batholith sw finland finely cellular plagioclase intergrowths have been studied in xenocrystic andesine an32 and andesine mantled k feldspars within mafic magmatic enclaves in a quartz feldspar porphyry from the proterozoic subvolcanic hammarudda complex aland rapakivi batholith sw finland the cellular intergrowths usually occur as 0 2 2 0 mm mantles around xenocrysts but also as entirely cellular grains and are built up of a network of two distinct phases one relatively na rich an31 and one relatively ca rich an50 the grains are also covered by a thin 0 08 0 12 mm continuous normally zoned rim outside the cellular mantle small inclusions 0 01 0 05 mm of fe mg minerals are concentrated in the ca rich part of the network compositionally the na rich phase of the network is close to the inner non cellular andesine of the xenocrysts however it has a lower or and a slightly lower an content the ca rich phase has the same composition as the inner part of the normally zoned rim which outwards grades into lower an contents that overlap the an content of the matrix plagioclases the cellular network was developed after the andesine xenocrysts or andesine mantled k feldspars were engulfed in mafic magmatic enclaves during a mixing event the xenocrysts became heated to a temperature just below the liquidus of the mafic magma dissolution of the xenocrysts developed a spongy cellular texture which was penetrated by enclave magma ca rich plagioclase crystallized in the cells in equilibrium with the enclave magma trapping fe mg rich melt as the enclaves cooled the outermost thin rim and matrix plagioclases crystallized from the mafic melt these processes operated in fairly large enclaves as the one studied here which has a diameter of 70cm smaller enclaves on the other hand were cooled more rapidly to temperatures close to the solidus of the enclave magma and consequently had no time to dissolve the xenoxrysts

extended fault inversion with random slipmaps a resolution test for the 2012 mw 7 6 nicoya costa rica earthquake inversions for the full slip distribution of earthquakes provide detailed models of earthquake sources but stability and non uniqueness of the inversions is a major concern the problem is underdetermined in any realistic setting and significantly different slip distributions may translate to fairly similar seismograms in such circumstances inverting for a single best model may become overly dependent on the details of the procedure instead we propose to perform extended fault inversion trough falsification we generate a representative set of heterogeneous slipmaps compute their forward predictions and falsify inappropriate trial models that do not reproduce the data within a reasonable level of mismodelling the remainder of surviving trial models forms our set of coequal solutions the solution set may contain only members with similar slip distributions or else uncover some fundamental ambiguity such as for example different patterns of main slip patches for a feasibility study we use teleseismic body wave recordings from the 2012 september 5 nicoya costa rica earthquake although the inversion strategy can be applied to any type of seismic geodetic or tsunami data for which we can handle the forward problem we generate 10 000 pseudo random heterogeneous slip distributions assuming a von karman autocorrelation function keeping the rake angle rupture velocity and slip velocity function fixed the slip distribution of the 2012 nicoya earthquake turns out to be relatively well constrained from 50 teleseismic waveforms two hundred fifty two slip models with normalized l1 fit within 5 per cent from the global minimum from our solution set they consistently show a single dominant slip patch around the hypocentre uncertainties are related to the details of the slip maximum including the amount of peak slip 2 3 5 m as well as the characteristics of peripheral slip below 1 m synthetic tests suggest that slip patterns such as nicoya may be a fortunate case while it may be more difficult to unambiguously reconstruct more distributed slip from teleseismic data

estimation of the lateral correlation structure of subsurface water content from surface based ground penetrating radar reflection images 1 over the past decade significant interest has been expressed in relating the spatial statistics of surface based reflection ground penetrating radar gpr data to those of the imaged subsurface volume a primary motivation for this work is that changes in the radar wave velocity which largely control the character of the observed data are expected to be related to corresponding changes in subsurface water content although previous work has indeed indicated that the spatial statistics of gpr images are linked to those of the water content distribution of the probed region a viable method for quantitatively analyzing the gpr data and solving the corresponding inverse problem has not yet been presented here we address this issue by first deriving a relationship between the 2 d autocorrelation of a water content distribution and that of the corresponding gpr reflection image we then show how a bayesian inversion strategy based on markov chain monte carlo sampling can be used to estimate the posterior distribution of subsurface correlation model parameters that are consistent with the gpr data our results indicate that if the underlying assumptions are valid and we possess adequate prior knowledge regarding the water content distribution in particular its vertical variability this methodology allows not only for the reliable recovery of lateral correlation model parameters but also for estimates of parameter uncertainties in the case where prior knowledge regarding the vertical variability of water content is not available the results show that the methodology still reliably recovers the aspect ratio of the heterogeneity

upper crustal seismic velocity heterogeneity as derived from a variety of p wave sonic logs sonic log measurements provide detailed 1 d information on the distribution of elastic properties within the upper crystalline crust at scales from about one metre to several kilometres 10 p wave sonic logs from six upper crustal drill sites in europe and north america have been analysed for their second order statistics the penetrated lithological sequences comprise archean volcanic sequences proterozoic mafic layered intrusions and precambrian to phanerozoic gneisses and granites despite this variability in geological setting tectonic history and petrological composition there are notable similarities between the various data sets after removing a large scale deterministic component from the observed velocity depth function the residual velocity fluctuations of all data sets can be described by autocovariance functions corresponding to band limited self affine stochastic processes with quasi gaussian probability density functions depending on the maximum spatial wavelength present in the stochastic part of the data the deterministic trend can be approximated either by a low order polynomial best fit or by a moving average of the original sonic log data the choice of the trend has a significant impact on the correlation length and on the standard deviation of the residual stochastic component but does not affect the hurst number for trends defined by low order polynomial best fits correlation lengths were found to range from 60 to 160 m whereas for trends defined by a moving average the correlation lengths are dominated by the upper cut off wavenumber of the corresponding filter regardless of the trend removed the autocovariance functions of all data sets are characterised by low hurst numbers of around 0 1 0 2 or equivalently by power spectra decaying as 1 k a possible explanation of this statistical uniformity is that sonic log fluctuations are more sensitive to the physical state in particular to the distribution of cracks than to the petrological composition of the probed rocks

zoned quartz phenocrysts from the rhyolitic bishop tuff cathodoluminescence cl reveals growth zones in quartz phenocrysts from the rhyolitic bishop tuff melt inclusions occur in various zones and record the evolving melt composition during zonal growth the zones form an oscillatory pattern between bright and dark cl quartz there are three recognizable patterns of cl zoning in these crystals 1 weakly zoned cores and bright cl rims 2 weakly zoned cores and dark cl rims and 3 no cl intensity difference from core to rim dark cl quartz generally occurs at crystal edges contains most of the melt inclusions and is interpreted as fast growing zones that occur along recognizable crystal edges edge zones are thicker than the same zone on adjacent faces consistent with relatively fast growth of these zones in each successive zone these edge zones decrease in size toward the rim while the zones along the crystal faces increase some of the melt inclusions have bright cl quartz locally associated with them this is interpreted as the postentrapment crystallization of slow growing quartz in the melt inclusions many crystals display zone discordance from the weakly zoned interiors to the rims most of the discordant surfaces are rational and probably are primary growth features pumice clasts from the southern vents are largely compositionally and texturally distinct from those from the northern vents and this distinction is also evident in the quartz cl the crystals that have bright cl rims are all associated with the late erupted northern part of the bishop tuff melt inclusion compositions and cl zoning patterns suggest a common origin for early and middle erupted quartz and the interior zones of late erupted quartz however the bright cl rim on the late erupted quartz indicates an additional stage of crystallization in late erupted magma melt inclusions in individual early erupted crystals have small variations in ba whereas inclusions in late erupted crystals markedly increase in ba toward the rim which is opposite to the normal zoning of sequentially trapped melts expected during closed system crystallization differentiation the quartz zoning features are consistent with the hypothesis of crystal settling in evolving magma that erupted late from northern vents

geostatistical analysis of ground penetrating radar data a means of describing spatial variation in the subsurface we have investigated the use of ground penetrating radar gfr as a means of characterizing the heterogeneity of the subsurface radar data were collected at several sites in southwestern british columbia underlain by glaciodeltaic sediments a cliff face study was conducted in which geostatistical analysis of a digitized photograph of the face and the radar image of the face showed excellent agreement in the maximum correlation direction and the correlation length determined from these two data sets other two dimensional 2 d sections of radar data were divided into sedimentary architectural elements on the basis of the distinct radar appearance of these sedimentary units examples of four sedimentary units were used to obtain semivariograms from the radar data and resulted in maximum correlation lengths between 0 5 and 4 8 m a 3 d radar survey collected over a package of gravel and sand foresets was analyzed to determine the paleoflow direction a correlation length of 4 m was found in that direction

geostatistical inversion of seismic and ground penetrating radar reflection images what can we actually resolve 1 estimation of the spatial statistics of subsurface velocity heterogeneity from surface based geophysical reflection survey data is a problem of significant interest in seismic and ground penetrating radar gpr research a method to effectively address this problem has been recently presented but our knowledge regarding the resolution of the estimated parameters is still inadequate here we examine this issue using an analytical approach that is based on the realistic assumption that the subsurface velocity structure can be characterized as a band limited scale invariant medium our work importantly confirms recent numerical findings that the inversion of seismic or gpr reflection data for the geostatistical properties of the probed subsurface region is sensitive to the aspect ratio of the velocity heterogeneity and to the decay of its power spectrum but not to the individual values of the horizontal and vertical correlation lengths

statistical description of seismic reflection wavefields a step towards quantitative interpretation of deep seismic reflection profiles summary seismic modelling designed to compare the statistics of a realistic acoustic impedance field with a statistical description of the resulting backscattered wavefield demonstrates a strong correlation between the spatial properties of the impedance field and the resulting wavefield experiments in the weak and strong scattering regimes indicate significant and predictable differences in the spatial properties of the wavefield depending upon the scattering mode wavefields generated in a mixed scattering regime with concurrent weak and strong scattering are dominated by the strong scattering response the results of these experiments suggest that the statistical description of reflection wavefields may provide a basis for the quantitative interpretation of the complex reflection wavefields most commonly observed in seismic reflection profiles across crystalline basement rocks and a tool for extracting more of the information content of the seismic data

a stochastic view of lower crustal fabric based on evidence from the ivrea zone despite its complicated history the ivrea zone is considered to be a representative surface exposure of extended continental crust we have digitized two standard 1 25 000 geological maps from this area and evaluated their structural statistics because of the subvertical orientation of the ivrea zone these maps can be considered as small scale cross sections through the lower continental crust the autocorrelation functions of the digitized lithologies measured from these maps show a clear self similar or fractal rather than a gaussian or deterministic trend we found that an anisotropic von karman correlation function with an aspect ratio around 4 and a hurst number of 0 3 corresponding to a fractal dimension of 2 7 matches the observed data our results represent an explicit confirmation of previous indirect evidence for the fractal nature of lithospheric heterogeneities and provide the means to construct realistic crustal scale seismic models of ivrea type lower continental crust