venus topography a harmonic analysis a model of venusian global topography has been obtained by fitting an eighteenth degree harmonic series to pioneer venus orbiter radar altimeter data the mean radius is 6051 45 0 04 km the corresponding mean density is 5244 8 0 5 kg m 3 the center of figure is displaced from the center of mass by 0 339 0 088 km towards 6 6 10 1 n 148 8 7 7 e the figure of venus is distinctly triaxial but the orientation and magnitudes of the principal topographic axes correlate rather poorly with the gravitational principal axes however the higher degree harmonics of topography and gravity are significantly correlated the topographic variance spectrum of venus is very similar in form to those of the moon mars and especially earth we suggest that this spectral similarity simply reflects a statistical balance between constructional and degradational geomorphic processes venus and earth are particularly similar and differ from the moon and mars in that the larger bodies both exhibit a significant low degree deficit relative to the extrapolated trend of the higher harmonics

scale invariance of soil moisture variability and its implications for the frequency size distribution of landslides abstract power spectral analyses of soil moisture variability are carried out from scales of 100 m to 10 km on the microwave remotely sensed data from the washita experimental watershed during 1992 the power spectrum s k has an approximate power law dependence on wave number k with the exponent 1 8 this behavior is consistent with the behavior of a stochastic differential equation for soil moisture at a point and it has important consequences for the frequency size distribution of landslides we present the cumulative frequency size distributions of landslides induced by precipitation in japan and bolivia as well as landslides triggered by the 1994 northridge california earthquake large landslides in these regions despite being triggered by different mechanisms have a cumulative frequency size distribution with a power law dependence on area with an exponent ranging from 1 5 to 2 we use a soil moisture field with the above statistics in conjunction with a slope stability analysis to model the frequency size distribution of landslides in our model landslides occur when a threshold shear stress dependent on cohesion pore pressure internal friction and slope angle is exceeded this implies a threshold dependence on soil moisture and slope angle since cohesion pore pressure and internal friction are primarily dependent on soil moisture the cumulative frequency size distribution of domains of shear stress greater than a threshold value with soil moisture modeled as above and topography modeled as a brownian walk is a power law function of area with an exponent of 1 8 for large landslide areas this distribution is similar to that observed for landslides the effect of strong ground motion from earthquakes lowers the shear stress necessary for failure but does not change the frequency size distribution of failed areas this is consistent with observations this work suggests that remote sensing of soil moisture can be of great importance in monitoring landslide hazards and proposes a specific quantitative model for landslide hazard assessment

is the martian crust also the martian elastic lithosphere 1 correlations between topography gravity and areoid on mars are used to constrain the crustal and lithospheric thicknesses on the planet assuming that the hellas basin is in isostatic equilibrium with airy compensation point correlations between areoid anomalies and topography are used to obtain the mean crustal density and the crustal thickness we find that the crustal thickness at the reference zero elevation is 90 10 km we also find that the mean crustal density is 2960 50 kg m 3 we have also used several approaches to constrain the thickness of the elastic lithosphere using the spherical harmonic coefficients of the gravity potential and topography as a function of degrees a relatively weak constraint on the globally averaged thickness of the elastic lithosphere is obtained an improved constraint is obtained using wavelet transform analyses of great circle tracks of gravity and topography the gravity topography admittance as a function of wavelet wavelength constrains the globally averaged thickness of the elastic lithosphere to be in the range 90 10 km the observation that the mean thicknesses of the crust and elastic lithosphere are likely to be equal suggests that a rheologically tougher crust is the elastic lithosphere

summary of the results from the lunar orbiter laser altimeter after seven years in lunar orbit in june 2009 the lunar reconnaissance orbiter lro spacecraft was launched to the moon the payload consists of 7 science instruments selected to characterize sites for future robotic and human missions among them the lunar orbiter laser altimeter lola was designed to obtain altimetry surface roughness and reflectance measurements the primary phase of lunar exploration lasted one year following a 3 month commissioning phase on completion of its exploration objectives the lro mission transitioned to a science mission after 7 years in lunar orbit the lola instrument continues to map the lunar surface the lola dataset is one of the foundational datasets acquired by the various lro instruments lola provided a high accuracy global geodetic reference frame to which past present and future lunar observations can be referenced it also obtained high resolution and accurate global topography that were used to determine regions in permanent shadow at the lunar poles lola further contributed to the study of polar volatiles through its unique measurement of surface brightness at zero phase which revealed anomalies in several polar craters that may indicate the presence of water ice in this paper we describe the many lola accomplishments to date and its contribution to lunar and planetary science

fractal analysis of venus topography in tinatin planitia and ovda regio we have applied a one dimensional fractal analysis to magellan altimetry data for two 20 20 equatorial regions on venus for the ovda regio highlands the power spectra of the altimetry data correlate well with power law fractal statistics over the full range of wavelengths considered 36 km 703 km the mean fractal dimension is dovda 1 64 for the tinatin planitia lowlands the power spectra consistently show a rollover at long wavelengths 200 km the long wavelength topography in this region either never developed or has subsequently relaxed the mean of the best fit fractal dimension for tinatin is dtinatin 1 41 the measure of roughness ra correlates well with variations in relief especially at short wavelengths 50 km our quantitative analysis of venus topography can be applied on a global scale the one dimensional method can be extended to two dimensional space yielding two dimensional maps of regional d and ra allowing a more complete use of regional two dimensional altimetry data

crustal thickness and support of topography on venus united states national aeronautics and space administration nasa planetary geology and geophysics program grant

self affine gravity covariance model for the bay of bengal summary an anisotropic covariance model embedded with self affine characteristics of gravity and bathymetry anomalies is proposed high resolution free air gravity data obtained from the high density satellite altimetry data have been used to study the self affinity of the gravity measurements the digital terrain model 5 dtm 5 is used for the bathymetry data the hurst coefficients h are calculated using 2 d power spectral density of the free air gravity and bathymetry data from 140 blocks of 1 1 the hurst coefficients h are also determined for free air gravity data along 24 orthogonal profiles using rescaled range r s analysis further the estimated h values are used in order to find the appropriate gravity and bathymetry covariance model for the area the average value of h is more for 2 d free air gravity data as compared with the bathymetry data the h values from the 1 d free air gravity profiles are found to be 0 75 and 0 77 along the n s and e w directions respectively the von karman covariance model with different correlation lengths is found to be suitable for 2 d and 1 d free air gravity and 2 d bathymetry data

the southernmost margin of the tethys realm during the mesozoic and cenozoic initial geometry and timing of the inversion processes 1 along the northern border of africa pangea breakup has been diachronic during the jurassic the alpine tethys propagated northeastward from the atlantic to the alps during the permian the neo tethys propagated westward from oman to northwestern arabia then a secondary and late branch of neo tethys gave birth to the east mediterranean basin finally the two oceans connected at end of jurassic times achieving the development of africa northern plate boundary by the late cretaceous convergence between africa and eurasia led to the progressive closure of the tethys realm the continental collision is not completely achieved and the different segments of the confrontation zone maghreb central and east mediterranean zagros and oman expose different stages of the process however we emphasize the existence of synchronous geodynamic events from one end of the system to the other although they do not have the same meaning two of them are particularly important the campanian santonian c s event corresponds to 1 obduction and exhumation of high pressure low temperature metamorphic rocks around the arabian promontory 2 inversion along the margins of the east mediterranean basins and 3 lithosphere buckling in the atlas system maghreb and adjacent sahara platform the middle late eocene mle event corresponds to 1 the onset of collision at the northern corner of arabia 2 the onset of slab retreat in the mediterranean and 3 inversion along the margin of the east mediterranean as well as in the atlas the c s event coincides with a change in plate kinematics resulting in an abrupt increase of convergence velocity the mle event coincides with a period of strong coupling between the africa and eurasia plates and an abrupt decrease of convergence velocity in the middle of the system the central mediterranean seems to escape to the effects of convergence and is the site of quite permanent extensional movements since the triassic

topographic meteorologic and canopy controls on the scaling characteristics of the spatial distribution of snow depth fields 1 in this study lidar snow depths bare ground elevations topography and elevations filtered to the top of vegetation topography vegetation in five 1 km 2 areas are used to determine whether the spatial distribution of snow depth exhibits scale invariance and the control that vegetation topography and winds exert on such behavior the one dimensional and mean two dimensional power spectra of snow depth exhibit power law behavior in two frequency intervals separated by a scale break located between 7 m and 45 m the spectral exponents for the low frequency range vary between 0 1 and 1 2 for the one dimensional spectra and between 1 3 and 2 2 for the mean twodimensional power spectra the spectral exponents for the high frequency range vary between 3 3 and 3 6 for the one dimensional spectra and between 4 0 and 4 5 for the mean two dimensional spectra such spectral exponents indicate the existence of two distinct scaling regimes with significantly larger variations occurring in the larger scale regime similar bilinear power law spectra were obtained for the fields of vegetation height with crossover wavelengths between 7 m and 14 m further analysis of the snow depth and vegetation fields together with wind data support the conclusion that the break in the scaling behavior of snow depth is controlled by the scaling characteristics of the spatial distribution of vegetation height when snow redistribution by wind is minimal and canopy interception is dominant and by the interaction of winds with features such as surface concavities and vegetation when snow redistribution by wind is dominant

mars topography lessons learned from spatial and spectral domain comparisons of mars orbiter laser altimeter and u s geological survey data the topography of mars has been mapped several times by a variety of techniques we compare the recent mars orbiter laser altimeter version with the earlier u s geological survey compilation of photogrammetry and earth based radar we compare them in terms of their respective representations on 1 1 grids though both data sets contain substantially higher spatial resolution we find that the differences between the two mars topography models though locally quite large are generally quite small the difference variance is 4 of the data variance the difference between the two models is also quite notably anisotropic with substantially more variation north south than east west the variance in the difference between the models is a very small fraction of the data variance at the longest wavelengths and approaches a constant value of 30 at harmonic degrees above 20

stochastic parameterization of processes leading to convective initiation in kilometer scale models abstractkilometer scale models allow for an explicit simulation of deep convective overturning but many subgrid processes that are crucial for convective initiation are still poorly represented th

fractals in geology and geophysics the definition of a fractal distribution is that the number of objectsn with a characteristic size greater thanr scales with the relationn r d the frequency size distributions for islands earthquakes fragments ore deposits and oil fields often satisfy this relation fractals were originally introduced by mandelbrot to relate the length of a coastline to the length of the measuring stick this application illustrates a fundamental aspect of fractal distributions scale invariance the requirement of an object to define a scale in photographs of many geological features is one indication of the wide applicability of scale invariance to geological problems scale invariance can lead to fractal clustering geophysical spectra can also be related to fractals these are self affine fractals rather than self similar fractals examples include the earth s topography and geoid

self organization and scaling relationships of evolving river networks the power spectra s of linear transects of earth s topography is often observed to be a power law function of wave number k with exponent close to 2 s k k 2 in addition river networks are fractal trees that satisfy several power law relationships between their morphologic components a model equation for the evolution of earth s topography by transport limited erosional processes which produces fractal topography and fractal river networks is presented and its solutions are compared in detail to real topography the model is the diffusion equation for sediment transport on hillslopes and channels with the diffusivity constant on hillslopes and proportional to the three halves power of discharge in channels the dependence of diffusivity on discharge is consistent with sediment rating curves we study the model in two ways in the first analysis the diffusivity is parameterized as a function of elevation and a taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which includes the spatially variable diffusivity to first order in the elevation the solution to this equation is a self affine or fractal surface with linear transects that have power spectra s k k 1 8 independent of the age of the topography consistent with observations of real topography the hypsometry produced by the model equation is skewed such that lowlands make up a larger fraction of the total area than highlands as observed in real topography in the second analysis we include river networks explicitly in a numerical simulation by calculating the discharge at every point we characterize the morphology of real river basins with five independent scaling relations between six morphometric variables scaling exponents are calculated for seven river networks from a variety of tectonic environments using high quality digital elevation models river networks formed in the model match the observed scaling laws and satisfy tokunaga side branching statistics

deep structure of the continental margin and basin off greater kabylia algeria new insights from wide angle seismic data modeling and multichannel seismic interpretation abstract during the algerian french spiral survey aimed at investigating the deep structure of the algerian margin and basin two coincident wide angle and reflection seismic profiles were acquired in central algeria offshore greater kabylia together with gravimetric bathymetric and magnetic data this 260 km long offshore onshore profile spans the balearic basin the central algerian margin and the greater kabylia block up to the southward limit of the internal zones onshore results are obtained from modeling and interpretation of the combined data sets the algerian basin offshore greater kabylia is floored by a thin oceanic crust 4 km with p wave velocities ranging between 5 2 and 6 8 km s in the northern hannibal high region the atypical 3 layer crustal structure is interpreted as volcanic products stacked over a thin crust similar to that bordering the margin and related to miocene post accretion volcanism these results support a two step back arc opening of the west algerian basin comprising oceanic crust accretion during the first southward stage and a magmatic and probably tectonic reworking of this young oceanic basement during the second westward opening phase the structure of the central algerian margin is that of a narrow 70 km magma poor rifted margin with a wider zone of distal thinned continental crust than on the other margin segments there is no evidence for mantle exhumation in the sharp ocean continent transition but transcurrent movements during the second opening phase may have changed its initial geometry the plio quaternary inversion of the margin related to ongoing convergence between africa and eurasia is expressed by a blind thrust system under the margin rising toward the surface at the slope toe and by an isostatic disequilibrium resulting from opposite flexures of two plates decoupled at the continental slope this disequilibrium is likely responsible for the peculiar asymmetrical shape of the crustal neck that may thus be a characteristic feature of inverted rifted margins

scaling properties and spatial organization of snow depth fields in sub alpine forest and alpine tundra this paper reports on a study analysing the spatial distribution functions the correlation structures and the power spectral densities of high resolution lidar snow depths 1 m in two adjacent 500 m 500 m areas in the colorado rocky mountains one a sub alpine forest the other an alpine tundra it is shown how and why differences in the controlling physical processes induced by variations in vegetation cover and wind patterns lead to the observed differences in spatial organization between the snow depth fields of these environments in the sub alpine forest area the mean of snow depth increases with elevation while its standard deviation remains uniform in the tundra subarea the mean of snow depth decreases with elevation while its standard deviation varies over a wide range the two dimensional correlations of snow depth in the forested area indicate little spatial memory and isotropic conditions while in the tundra they indicate a marked directional bias that is consistent with the predominant wind directions and the location of topographic ridges and depressions the power spectral densities exhibit a power law behaviour in two frequency intervals separated by a break located at a scale of around 12 m in the forested subarea and 65 m in the tundra subarea the spectral exponents obtained indicate that the snow depth fields are highly variable over scales larger than the scale break while highly correlated below based on the observations and on synthetic snow depth fields generated with one and two dimensional spectral techniques it is shown that the scale at which the break occurs increases with the separation distance between snow depth maxima in addition the breaks in the forested area coincide with those of the corresponding vegetation height field while in the tundra subarea they are displaced towards larger scales than those observed in the corresponding vegetation height field

new martian paradigms several interrelated paradigms concerning the nature and the evolution of mars are discussed these include an impact origin of the northern lowland mars as a water rich planet former oceans in the northern lowlands a warm wet climate on early mars and the possibility of ancient life on mars locations on mars suggested for the search of possible ancient life include the heavily cratered terrain dissected by valley networks possible lacustrine deposits in valles marineris the oxidizing layer below the surface sites along the fringes of the hypothetical northern circumpolar ocean and in evaporite deposits

grim gravity model improvement using lageos grim3 l1 improved modeling of the earth s geopotential is one of the major tasks of satellite geodesy the availability of a new set of precise lageos satellite laser ranging slr data as well as seasat acquired observations enabled us to compute an improved solution in the grim model series the new geopotential grim3 l1 recombined the satellite perturbation normals of the former grim3 solution with new normal equation subsystems derived from an additional 16 months of lageos slr data oceanic 1 1 mean free air anomalies recovered from seasat altimetry an updated set of terrestrial 1 1 mean free air anomalies and several condition equations for zonal and resonant harmonics the combined normal equations were solved for a complete set of spherical harmonics up to degree and order 36 and the coordinates of 109 tracking stations comparisons with altimetry derived quantities terrestrial gravity anomalies from satellite to satellite tracking longitude accelerations of 24 hour satellites and satellite orbit fits show a substantial improvement over previous grim solutions and indicate that the lageos data have contributed considerably to the reliable estimation of the long wavelength portion of the gravity field

self affine behavior of martian topography at kilometer scale from mars orbiter laser altimeter data 1 we used mars orbiter laser altimeter mola data from the current mars global surveyor mission to characterize the topographic roughness of the martian surface and to provide a mean to evaluate clutter at long 10 300 m wavelengths such wavelengths are relevant for the marsis and sharad subsurface radars which will be flown in future missions to mars the method of analysis is based on the assumption that topography can be described as a self affine fractal 30 km long segments of mola altimetry profiles have thus been reduced to the topographic parameters rms height rms slope and hurst exponent this last related to the fractal dimension which can be used as inputs to a near nadir radar scattering model the values of the hurst exponent are greater than 0 5 for most of the surface meaning a scaling behavior which is almost self similar maps of rms height and hurst exponent show that these two parameters have very different spatial distributions whereas the rms height is patterned after the north south dichotomy the hurst exponent follows a latitudinal trend we make use of a multivariate method called g mode to classify profiles in the three dimensional parameter space we find several roughness units some of which have a strong correlation with certain geologic units while others are bound by latitude however at scales between 300 m and 3 km large stretches of the surface of mars share common statistical properties of topography independent from the north south dichotomy

deep crustal structure of the north west african margin from combined wide angle and reflection seismic data mirror seismic survey the structure of the moroccan and nova scotia conjugate rifted margins is of key importance for understanding the mesozoic break up and evolution of the northern central atlantic ocean basin seven combined multichannel reflection mcs and wide angle seismic obs data profiles were acquired along the atlantic moroccan margin between the latitudes of 31 5 and 33 n during the mirror seismic survey in 2011 in order to image the transition from continental to oceanic crust to study the variation in crustal structure and to characterize the crust under the west african coast magnetic anomaly wacma the data were modeled using a forward modeling approach the final models image crustal thinning from 36 km thickness below the continent to approximately 8 km in the oceanic domain a 100 km wide zone characterized by rough basement topography and high seismic velocities up to 7 4 km s in the lower crust is observed westward of the west african coast magnetic anomaly no basin underlain by continental crust has been imaged in this region as has been identified north of our study area comparison to the conjugate nova scotian margin shows a similar continental crustal thickness and layer geometry and the existence of exhumed and serpentinized upper mantle material on the canadian side only the oceanic crustal thickness is lower on the canadian margin

gravitational and topographic isotropy of the earth moon mars and venus the internal structures and surface shapes of the terrestrial planets are expected to be dominantiy isotropic we attempt to test this hypothesis by developing a criterion for recognizing statistical isotropy of spherical scalar fields and applying that test to the nonhydrostatic components of the gravitational and topographic fields of the earth moon mars and venus the criterion for topographic or geoidal surfaces is that the directional variance should be independent of azimuth that is the mean square east west slopes should be equal to the mean square north south slopes all four planets generally pass the criteria with a few minor exceptions most of the exceptions are likely to be artifacts of the current generation of planetary gravity and topography models rather than real features of the planets of the several broad band departures from isotropy which we found the only one likely to be real is the tendency for the earth s gravity and topography to have only 80 as much variance in a north south direction as in an east west direction

quantitative methods for analyzing the roughness of the seafloor the bathymetry of the world ocean has been mapped using a variety of acoustic sounding instruments and traditional contouring methods prior to this study relatively few quantitative studies have been focused on the detailed morphology of the seafloor the work of most investigators has generally dealt with the analysis of seafloor relief without regard to spatial frequency or concern for obvious morphologic anisotropies a brief review of previous work is presented and is accompanied by an identification of the specific applications and limitations of those approaches the availability of more precise digital sounding data coupled with the development of higher resolution sonar mapping instruments e g deeptow seamarc now make it possible to investigate quantitatively many important aspects of seafloor relief and the geological processes responsible for its formation typical bathymetric contour maps represent a low frequency deterministic model of the seafloor to describe the higher frequency variability or roughness of the seafloor requires the development of an appropriate statistical method for generating a valid stochastic model new methods are developed herein which allow valid statistical models of the variability of oceanic depths to be derived from existing digital bathymetric soundings the smooth contoured surface often preserved as a geographic grid of depths when supplemented by such a roughness model can provide an essentially complete statistical description of the relief statistical models of seafloor roughness are also valuable tools for predicting acoustic scattering and bottom loss and in addition contain a wealth of information for more comprehensive interpretations of deep sea relief forming geological processes to allow the variability of depths to be described as a function of scale spatial frequency the amplitude spectrum is employed as the fundamental statistic underlying the model since the validity of the amplitude spectrum depends upon the assumption of a statistically stationary sample space a computer algorithm operating in the spatial domain was developed which delineates geographic provinces of limited statistical heterogeneity within each of these provinces a spectral model is derived by fitting the amplitude estimates with one or two two parameter power law functions using specialized regression techniques the distribution of resultant model parameters is examined for a large test area adjacent to the coast of oregon 42 45 n 130 124 w which includes several contrasting geologic environments the distribution of roughness corresponds generally with the various physiographic provinces observed in the region within some provinces additional complexities are apparent in the roughness model which cannot be inferred by simply studying the bathymetry these patterns are related to a variety of geological processes operating in the region such as the convergence of the continental margin and the presence of a propagating rift on the northern gorda rise in contrast a very large area of the continental margin off the east coast of the united states was found to have in common a single distinct amplitude spectrum this amplitude spectrum is almost identical to that found from the tufts abyssal plain region off the west coast of the united states spectra from both of these areas can be clearly separated into two straight line segments of different slope the two segments of these spectra are interpreted as reflecting two dominant relief forming processes the higher frequency band representing a sedimentary regime and the lower frequency band representing an underlying tectonic volcanogenic regime in many cases the calculated roughness statistics are not constant for data collected along different ship track directions this is due to the anisotropic nature of the seafloor relief a simple model is developed which describes the roughness statistics as a function of azimuth the parameters of this model quantify the anistropy of the seafloor allowing insight into the directionality of the corresponding relief forming processes and the physical meaning of the derived model statistical parameters finally the model is used to successfully predict the roughness of a surface at scales much smaller than those resolvable by surface sonar systems the model regression line derived from a hull mounted sonar is compared to data from deep towed sonars and bottom photographs the amplitude of roughness is predicted to within half an order of magnitude over five decades of spatial frequency and this prediction capability can probably be improved even further the stochastic models presented also demonstrate the potential for closely approximating the full two dimensional nature of some areas of the seafloor with only four statistical parameters these parameters can be estimated from random ship track data given a sufficient number of tracks and range of headings

a harmonic analysis of martian topography the topography of mars is represented by a spherical harmonic model complete to degree and order 50 the data source is a recently revised u s geological survey compilation which encompasses a diverse array of spacecraft measurements and earth based radar ranges because of the disparate nature of the original data sources it is difficult to obtain reliable estimates of the likely errors in martian topography however the variance spectrum has a shape similar to that found for other terrestrial planets and the topography correlates well with recent estimates of the gravitational field of mars both of these considerations suggest that the existing data provide a reasonable approximation to the true topography of mars nevertheless a detailed topographic mapping of the planet such as will be provided by the mars global surveyor will be required before significant advances are made in understanding the relationship between topography and gravity on mars

mountain volume control on deep convective rain amount during episodes of weak synoptic forcing abstractthermally driven upslope flows in mountainous areas provide favorable conditions for diurnal deep moist convection especially during episodes of weak synoptic forcing the present study inv

a fractal interpretation of topography and geoid spectra on the earth moon venus and mars global spectra are available for topography and geoid on the earth venus mars and the moon if the spectral energy density has a power law dependence on wave number a fractal is defined the topography spectrum for the earth is a well defined fractal with d 1 5 this corresponds to brown noise with the amplitude proportional to the wave length although there is more scatter for the other planetary bodies the data for mars and the moon correlate well with the data for the earth venus topography also exhibits a brown noise behavior but with a smaller amplitude the power law dependence of the earth s geoid is known as kaula s law we show that uncompensated brown topography gives a geoid with a power law dependence that is in quite good agreement with kaula s law however the required amplitude is only 8 of the observed topography a similar result is found for the other bodies with the ratio of the amplitude of topography required to explain the geoid to the observed topography increasing to 72 for the moon

harmonic and statistical analyses of the gravity and topography of vesta abstract we examine the gravity and topography of the asteroid 4 vesta as recently revealed by the dawn mission the observed gravity is highly correlated with the observed topography and suggests little lateral variation in density the variance spectra of both gravity and topography follow power laws which are very similar to those seen for the moon mars venus and earth a significant way in which vesta differs from these larger silicate bodies is that both gravity and topography are significantly anisotropic with more north south variation than east west variation rapid rotation plausibly contributes to this anisotropy but only at harmonic degree two the remainder of the anisotropy appears related to the large impacts which formed the rheasilvia and veneneia basins we note that as usual gravitational inverse problems are non unique while the observed gravity and topography of vesta do not preclude existence of a metallic core they certainly do not require it

constraints on vesta s interior structure using gravity and shape models from the dawn mission abstract we use the shape and gravity field of vesta determined from observations of the dawn spacecraft to place constraints on the asteroid s interior structure we compute a three layer interior structure model by minimizing the power of the residual gravity anomaly the densities of the mantle and crust are based on constraints derived from the howardite eucrite diogenite hed meteorites vesta s present day shape is not in hydrostatic equilibrium the rheasilvia and veneneia impact basins have a large effect on vesta s shape and are the main source of deviation from hydrostatic shape constraining a pre giant impact rotation rate and orientation of the spin axis from an ellipsoidal fit to the parts of vesta unaffected by the giant impacts and using the theory of figure we can constrain the shape of the core our solution for vesta s crust mantle interface reveals a belt of thick crust around rheasilvia and veneneia the thinnest crust is in the floor of the two basins and in the vestalia terra region our solution does not reveal an uplift of the crust mantle boundary to the surface in the largest basins this together with the lack of olivine detected by the visible and infrared spectrometer vir data in rheasilvia and veneneia indicates that vesta s presumed olivine mantle was either not brought to the surface by these large impacts or was covered by ejecta from subsequent impacts

topography of the lunar south polar region implications for the size and location of permanently shaded areas we analyze clementine altimetry to constrain the size and location of proposed permanently shadowed regions in the vicinity of the lunar south pole long and short wavelength topography in the vicinity of the pole in combination with measurements of depths of well preserved craters and basins and the lunar topographic power spectrum have direct bearing on the nature of elevations in the south polar region a criterion based on geometric considerations and altimetry demonstrates that the existence of permanent shadowing is not very sensitive to the elevation of the south pole in addition permanent shadowing cannot be a consequence of large structures such as the south pole aitken basin and or a 300 km degraded polar basin perennially dark regions if they exist are most likely associated with craters or other axisymmetric features with diameters of at most 80 km centered at the pole for structures displaced 2 from the pole the maximum allowable diameter decreases to 30 km

support of long wavelength topography on mercury inferred from messenger measurements of gravity and topography to explore the mechanisms of support of surface topography on mercury we have determined the admittances and correlations of topography and gravity in mercury s northern hemisphere from measurements obtained by nasa s mercury surface space environment geochemistry and ranging messenger spacecraft these admittances and correlations can be interpreted in the context of a number of theoretical scenarios including flexural loading and dynamic flow we find that long wavelength spherical harmonic degree l 15 surface topography on mercury is primarily supported through a combination of crustal thickness variations and deep mass anomalies the deep mass anomalies may be interpreted either as lateral variations in mantle density or as relief on compositional interfaces domical topographic swells are associated with high admittances and are compensated at 300 400 km depth in the lower reaches of mercury s mantle quasi linear topographic rises are primarily associated with shallow crustal compensation and are weakly correlated with positive mass anomalies in the mantle the center of the caloris basin features some of the thinnest crust on the planet and the basin is underlain by a large negative mass anomaly we also explore models of dynamic flow in the presence of compositional stratification above the liquid core if there is substantial compositional stratification in mercury s solid outer shell relaxation of perturbed compositional interfaces may be capable of creating and sustaining long wavelength topography

global drainage patterns and the origins of topographic relief on earth mars and titan rivers have eroded the topography of mars titan and earth creating diverse landscapes however the dominant processes that generated topography on titan and to some extent on early mars are not well known we analyzed drainage patterns on all three bodies and found that large drainages which record interactions between deformation and erosional modification conform much better to long wavelength topography on titan and mars than on earth we use a numerical landscape evolution model to demonstrate that short wavelength deformation causes drainage directions to diverge from long wavelength topography as observed on earth we attribute the observed differences to ancient long wavelength topography on mars recent or ongoing generation of long wavelength relief on titan and the creation of short wavelength relief by plate tectonics on earth

isostatic compensation of equatorial highlands on venus abstract spherical harmonic models for venus global topography and gravity incorporating magellan data are used to test isostatic compensation models in five 30 30 regions representative of the main classes of equatorial highlands the power spectral density for the harmonic models obeys a power law scaling with spectral slope 2 brown noise for the topography and 3 kaula s law for the geoid similar to what is observed for earth the venus topography spectrum has lower amplitudes than earth s which reflects the dominant lowland topography on venus observed degree geoid to topography ratios gtrs on venus are significantly smaller than degree gtrs for uncompensated topography indicative of substantial compensation assuming a global airy compensation most of the topography is compensated at depths greater than 100 km suggesting a thick lithosphere on venus for each region considered we obtain a regional degree of compensation c from a linear regression of bouguer anomaly versus bouguer gravity data geoid anomaly n versus topography variation h data for each sample were compared in the least squares sense to theoretical correlations for pratt airy and thermal thinning isostasy models yielding regional gtr zero elevation crustal thickness h and zero elevation thermal lithosphere thickness y l 0 respectively we find the regional compensation to be substantial c 52 90 and the h n data correlations in the chosen areas can be explained by isostasy models applicable on the earth and involving variations in crustal thickness airy and or lithospheric thermal thinning thickness however a thick crust and lithosphere y l 0 300 km must be assumed for venus compensation mechanisms are distributed as follows for the high plateaus of ovda gtr 9 m km and thetis gtr 11 m km mainly airy isostasy with h 50 60 km for the chasmata area sample gtr 15 m km airy with perhaps a thermal component finally a very strong thermal component for the broad swells of beta gtr 32 m km and atla gtr 25 m km with the lithosphere thinned to 100 km aphrodite terra which shows a marked eastward increase in pratt and airy model parameter values could be a candidate for thermal isostasy decay from east to west

a new proposal for the late cenozoic geodynamic evolution of the western mediterranean a simple mechanism of arcuate fold belt and back arc basin formation is presented based on the opening of mega continental tension gashes along pre existing deep parallel and steep faults that separate lithospheric units with different properties if plate convergence is parallel to these faults the fault bounded units open at right angles to the convergence vector adopting an arcuate shape with thrusting in front of the bowed out units and extensional basin opening between the separated units this model is applied to the cenozoic geodynamic evolution of the western mediterranean after the iberian collision 35 30 ma several ellipsoidal basins valencia alboran north algerian and liguro provencal developed by 10 ma along the eastern margin of the iberian plate the formation of these basins is attributed to an increase in ne sw horizontal tectonic palaeostress during early middle miocene times resulting from the post subduction collision of the tethyan oceanic lithosphere

structure of the lake county uplift new madrid seismic zone abstract the central segment of the new madrid seismic zone lies within a left step over zone between two northeast striking right lateral strike slip fault systems within this compressional step over zone is the topographically and structurally high lake county uplift which includes the tiptonville dome and ridgely ridge we believe these structures are a consequence of deformation in the hanging wall above the northwest striking southwest dipping reelfoot reverse fault reelfoot fault dips 73 from the surface to the top of the precambrian at a depth of approximately 4 km from 4 to 12 km depth the fault dips 32 and is seismically active based on a fault bend fold model we believe that the reelfoot fault becomes horizontal and aseismic at the top of the quartz brittle ductile transition zone at approximately 12 km depth our data indicate that the western margin of the tiptonville dome ridgely ridge and the western margin of the lake county uplift are bounded by east dipping kink bands backthrusts recent work suggests that the reelfoot fault is responsible for the 7 february 1812 m 8 new madrid earthquake however the reelfoot fault has a surface area that is less than that necessary for an m 8 earthquake a possible solution to this discrepancy between magnitude and fault plane area is that the associated backthrusts are seismogenic

surface roughness and geological mapping at subhectometer scale from the high resolution stereo camera onboard mars express the quantitative measurement of surface roughness of planetary surfaces at all scales provides insights into geological processes a characterization of roughness variations at the scale of a few tens of meters is proposed that complements the analysis of local topographic data of the martian surface at kilometer scale as achieved from the mars orbiter laser altimeter mola data and at the subcentimeter scale using photometric properties derived from multi angular observations relying on a gabor filtering process an algorithm developed in the context of image classification for the purpose of texture analysis has been adapted to handle data from the high resolution stereo camera hrsc the derivation of roughness within a wavelength range of tens of meters combined with analyses at even longer wavelengths gives an original view of the martian surface the potential of this approach is evaluated for different examples for which the geological processes are identified and the geological units are mapped and characterized in terms of roughness

crustal types and tertiary tectonic evolution of the alboran sea western mediterranean multichannel seismic reflection images across the transition between the east alboran and the algero balearic basins show how crustal thickness decreases from about 5 s two way traveltime twtt 15 km thick in the west east alboran basin to 2 s twtt typical of oceanic crust 6 km thick in the east algero balearic basin we have differentiated three different crustal domains in this transition mainly on the basis of crustal thickness and seismic signature boundaries between the three crustal domains are transitional and lack evidence for major faults tilted blocks related to extension are very scarce and all sampled basement outcrops are volcanic suggesting a strong relationship between magmatism and crustal structure stratigraphic correlation of lithoseismic units with sedimentary units of southeastern betic basins indicates that sediments onlap igneous basement approximately at 12 ma in the eastern area and at 8 ma in the western area linking seismic crustal structure with magmatic geochemical evidence suggests that the three differentiated crustal domains may represent from west to east thin continental crust modified by arc magmatism magmatic arc crust and oceanic crust middle to late miocene arc and oceanic crust formation in the east alboran and algero balearic basins respectively occurred during westward migration of the gibraltar accretionary wedge and shortening in the betic rif foreland basins arc magmatism and associated backarc oceanic crust formation were related to early to middle miocene subduction and rollback of the flysch trough oceanic basement subduction of this narrow slab beneath the alboran basin was coeval with collision of the alboran domain with the iberian and african passive margins and subsequent subcontinental lithosphere edge delamination along the betic rif margins

numerical assessment of the effects of topography and crustal thickness on martian seismograms using a coupled modal solution spectral element method abstract the past 4 decades of mars exploration have provided much information about the mars surface when its interior structure remains relatively poorly constrained today available data are compatible with a large range of model parameters seismology is able to provide valuable additional data but the number of seismographs will likely be quite limited specially in the early stage of future mars seismic networks it is thus of importance to be able to correctly isolate effects induced by the crust structure mars topography is characterized by spectacular reliefs like the tharsis bulge or the hellas basin and by the so called mars dichotomy the north hemisphere is made up of low altitude plains above a relatively thin crust when the south hemisphere is characterized by a thick crust sustaining high reliefs the aim of this paper is to study the effects induced on seismograms by the topography of the surface and crust mantle discontinuities synthetic seismograms were computed using the coupled spectral element modal solution method which reduces the numerical cost by limiting the use of the spectral element method to the regions where lateral variations like the presence of a topography are considered due to numerical cost this study is limited to long period and thus focuses on surface waves mainly on long period rayleigh waves we show that reliefs like the tharsis bulge or the hellas basin can induce an apparent velocity anomaly up to 0 5 when only the surface topography is introduced apparent anomalies can raise up to 1 0 when the surface topography is fully compensated by a mirror image topography of the crust mantle discontinuity travel time of surface wave are systematically increased for seismometers in the north hemisphere of mars and decreased in the south hemisphere when comparing effects on seismograms by the earth and mars topography we found them to be larger for the earth it is due to the fact that we work with a seismic velocity model of mars with a mean crust thickness of 110 km when the crust thickness has a mean value of 50 km for the earth when changing the mars model for a thinner crust with a mean thickness of 50 km effects by the topography on mars seismograms becomes of the same order when not larger than what is observed on the earth

the decay of the spectrum of the gravitational potential and the topography for the earth summary the spectrum of the earth s gravitational potential and topography as represented by spherical harmonic expansions to degree 180 have been computed modelling the decay in the form of al values of a and for several degree l ranges were computed for degree range 5 180 was 2 54 for the potential and 2 16 for equivalent rock topography the potential decay was somewhat slower than that i e 3 implied by kaula s rule however at high degree ranges the values were larger 3 20 for degrees 101 180 agreeing better with recent determinations from terrestrial gravity data and geoid undulations implied by satellite altimetric data the values imply that the potential decays faster at higher l values the values of for topography were fairly uniform around 2 which agrees with a suggestion made by vening meinesz in 1951 we also found that the value for the earth s potential agrees well with the value implied by the topography with airy isostatic compensation with the depth of compensation equal to 30 km however the magnitude of the power implied by the topographic isostatic potential was approximately one third of the observed potential

long wavelength topographic relaxation for self gravitating planets and implications for the time dependent compensation of surface topography the support of planetary surface topography is controlled by the thickness of the elastic lithosphere and thus has implications for the thermomechanical structure of shallow planetary interiors previous analyses of the support of long wavelength topography have generally utilized elastic formulations which preclude consideration of the time evolution of lithospheric stresses and thermal state here we formulate a viscoelastic model for the support of topography on a spherical planet our stress relaxation model employs a multilayer linear viscoelastic rheology and includes the effect of self gravitation in these models we approximate internal rheology with an olivine flow law and we estimate the internal thermal structure assuming simple conductive cooling we analyze how relief at the surface and internal density interfaces evolves with time in response to a surface or internal load our analysis demonstrates that crustal compensation is strongly dependent on planetary radius with a tendency for a large terrestrial planet like earth to reach complete airy isostasy at long wavelengths within a time scale controlled by the mantle viscosity the correlation of degree of compensation with planetary radius is consistent with previous work turcotte et al 1981 which showed that membrane stress can support significant long wavelength gravity anomalies applied to the moon the degree of compensation associated with loading of 100 ma lithosphere is less than 0 3 and the load love numbers are greater than 0 6 for all harmonics including degree 2 even after 109 years of relaxation this conclusion does not change significantly even with a moderately low viscosity for the crust the tendency for a small body like the moon to support long wavelength stresses may be relevant in understanding the anomalously large degree 2 terms in the lunar shape the results also suggest that major impact basins would not be compensated throughout lunar geological history 4 b y even if the surfaces on which the basins were initially formed were relatively young i e 100 300 ma the fact that the south pole aitken basin is largely compensated suggests that the lateral variations in thermal and or mechanical structure induced by impact processes play significant roles in the compensation of this structure

the spectra of the topography of the earth venus and mars the global topography of the terrestrial bodies has been more or less determined from past planetary missions and from ground measurements and the behaviour of their spectra studied over the low frequencies only except the earth s case we here perform new spherical harmonic analysis of the topography of the earth venus and mars by using existing sometimes recently made available data sets to the highest possible degree and order so as to establish the decay of these spectra over a larger range of frequencies than before study the limit of validity of the used data sets and provide some new inputs to further geophysical analysis

scale invariant topography and porosity variations in fluvial sedimentary basins we consider a model offloodplain evolving with channelvulsion deposition nd erosion avulsion is modeled asrndom process in spce and time sediment transport is modeled by the diffusion equation culling s model the power spectrum of vritions in the topographic profiles predicted by the model s k is proportional to k 2 where k is the wvenumber this is the brown noise often observed in topography the power spectrum of wristions in the local elevation in time is proportional to f s where f is the frequency the model prediction of brown noise floodplain topography is roughly consistent with spectralnlyses of microtopography measured with lserltimetry we inferred brown noise pleotopogrphy by comparing the pir correlation function of showing wells in the denvernd powder river basins with a synthetic oil field bsed on caprock with brown noise topography topographic control of variations in the grain size of deposited sediment suggests that porosity vritions my exhibit the scale invrince predicted for the topographic profile to illustrate vertical scale invariance in porosity vritions we computed the power spectrum of vertical porosity well logs in 15 offshore wells in the gulf of mexico at spatial scales bove 3 m we find anverge power spectral exponent of 1 4 close to our model prediction of 1 5

improved regional gravity fields on the moon from lunar prospector tracking data by means of localized spherical harmonic functions 1 an approach to enhance regional gravity fields of the planets using the line of sight los doppler range rate measurements is presented instead of representing the gravity fields as nonlocalized spherical harmonic functions i introduced a lumped harmonic representation for obtaining regionally concentrated orthogonal basis functions without any regularization or spectral power control the gravity fields over the four spherical cap regions with the radius of 20 on the nearside of the moon to degree and order 200 were estimated using all 8 months of the extended mission data from lunar prospector the regional models are variations on the initial global gravity model lp100j it was found that the regional estimates significantly improve the initial gravity model at all four regions of interest my improved gravity models fit the los doppler range acceleration data better than any other global lunar gravity model especially the data for when the satellite was at low altitude 40 km or less in addition a better cross correlation with the topography was obtained from the regional model the regional enhancement of the correlation was prominent in degrees greater than 100 and in polar regions characterized by clusters of medium or small size craters that are presumably uncompensated

an episodic hypothesis for venusian tectonics it is suggested that episodic plate tectonics occurs on venus episodes of rapid plate tectonics are separated by periods of surface quiescence for the last 500 200 m y it is postulated that the surface of venus has been a single rigid plate that has been thickening due to conductive cooling a near uniform surface age is consistent with observed crater densities and the relatively small number of craters modified by surface tectonics or embayed by lava flows a lithosphere that has conductively thickened for some 500 m y has a thickness of about 300 km nearly an order of magnitude greater than the thickness associated with steady state conductive heat loss such a thick lithosphere can support the high topography and associated gravity anomalies on venus as well as the unrelaxed craters studies of lithospheric flexure at coronae are also consistent with a thick elastic lithosphere incipient subduction associated with large coronae may represent the onset of a new episode of rapid plate tectonics on the earth 75 90 of mantle heat transport is attributed to the creation of new oceanic lithosphere at ocean ridges this process is not operative on venus this paper suggests that episodic plate tectonics on venus constitutes the primary mechanism for mantle heat transport on that planet

extent and resolution requirements for the residual terrain effect in gravity gradiometry s from the aseg pesa airborne gravity 2004 workshop geoscience australia record 2004 18 sydney australia pp 41 47 ed lane r j l geoscience australia canberra city australia turcotte d l 1987 a fractal interpretation of topography and geoid spectra on the earth moon venus and mars j geophys res 92 b4 e597 e601 tziavos i n sideris m g forsberg r schwarz k p 1988 the effect of the terrain on airborne gravity and gradiometry j geophys res 93 b8 9173 9186 veryaskin a 2003 string gravity gradiometer noise error analysis and applications in proceedings of the abstracts agu egs conference nice france

the interior structure of ceres as revealed by surface topography abstract ceres the largest body in the asteroid belt 940 km diameter provides a unique opportunity to study the interior structure of a volatile rich dwarf planet variations in a planetary body s subsurface rheology and density affect the rate of topographic relaxation preferential attenuation of long wavelength topography 150 km on ceres suggests that the viscosity of its crust decreases with increasing depth we present finite element fe geodynamical simulations of ceres to identify the internal structures and compositions that best reproduce its topography as observed by the nasa dawn mission we infer that ceres has a mechanically strong crust with maximum effective viscosity 10 25 pa s combined with density constraints this rheology suggests a crustal composition of carbonates or phyllosilicates water ice and at least 30 volume percent vol low density high strength phases most consistent with salt and or clathrate hydrates the inference of these crustal materials supports the past existence of a global ocean consistent with the observed surface composition meanwhile we infer that the uppermost 60 km of the silicate rich mantle is mechanically weak with viscosity 21 pa s suggesting the presence of liquid pore fluids in this region and a low temperature history that avoided igneous differentiation due to late accretion or efficient heat loss through hydrothermal processes

wavelet analyses of mars polar topography we have analyzed topography tracks over the mars northern polar cap composed of h2o ice co2 ice and sediments and the antarctic ice sheet on earth using a mexican hat wavelet transform the great utility of the wavelet transform is that it gives both spatial and spectral resolution we have used the variance of the wavelet output in order to quantify the spectral content of the topography tracks at short wavelengths for both the mars northern polar cap and the antarctic ice sheet we find a power law dependence of the wavelet transform variance on wavelength with a power law exponent of 3 5 3 7 this compares with a power law exponent of 2 0 brownian motion typical of topography on both mars and earth there is a power law smoothing of the ice topography at short wavelengths on both planetary bodies at long wavelengths we infer a similar power law dependence with 1 5 2 0 typical of planetary topography a transition is observed between the smooth short wavelength behavior high to rougher long wavelength behavior low this fairly sharp transition occurs at a wavelength of 24 km for mars and 11 km for antarctica the transitions appear to scale with ice thicknesses and suggest a relaxation of short wavelength topography by ice flows or surface processes