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Co-auteur étranger; International audience; While major impacts during late accretion of a Mars type planet occur on a differentiated body, the characteristics of the shockwave propagation are poorly knownwithin these layered objects. Here, we use iSALE-2D hydrocode simulations to calculate shock pressure in a differentiated Mars type body for impact velocitiesranging from 5 to 20 km/s, impactor radii ranging from 50 to 200 km, and different rheologies. To better represent the distribution of shock pressure as a function ofdistance from the impact site at the surface, we propose two distinct regions in the mantle: a near field region that extends to 7–15 times the projectile radius into thetarget, where the peak shock pressure decays exponentially with increasing the distance from the impact site, and a far field region where the pressure decaysstrongly with the distance following a power law. At the core-mantle boundary, the peak shock pressure increases from the mantle side to the core side. The refractedshockwave travels within the core where the shock pressure decreases following a second power law. In this study, we fit the output obtained from iSALE hydrocodesimulations to determine scaling laws that illustrate the influence of the distance from the impact site, the ray angle, the target rheology, the impactor size and theimpact velocity. Finally we combine these shock-pressure scaling laws with the formalism proposed by Watters et al. [2009] to determine the impact heating inducedby large impacts within a differentiated Mars

The core dynamos of Mars and the Moon have distinctly different histories. Mars had no core dynamo at the end of accretion. It took ∼100 Myr for the core to create a strong dynamo that magnetized the martian crust. Giant impacts during 4.2–4.0 Ga crippled the core dynamo intermittently until a thick stagnant lithosphere developed on the surface and reduced the heat flux at the core–mantle boundary, killing the dynamo at ∼3.8 Ga. On the other hand, the Moon had a strong core dynamo at the end of accretion that lasted ∼100 Myr and magnetized its primordial crust. Either precession of the core or thermochemical convection in the mantle or chemical convection in the core created a strong core dynamo that magnetized the sources of the isolated magnetic anomalies in later times. Mars and the Moon indicate dynamo reversals and true polar wander. The polar wander of the Moon is easier to explain compared to that of Mars. It was initiated by the mass deficiency at South Pole Aitken basin, which moved the basin southward by ∼68° relative to the dipole axis of the core field. The formation of mascon maria at later times introduced positive mass anomalies at the surface, forcing the Moon to make an additional ∼52° degree polar wander. Interaction of multiple impact shock waves with the dynamo, the abrupt angular momentum transfer to the mantle by the impactors, and the global overturn of the core after each impact were probably the factors causing the dynamo reversal.

The youngest of the giant impact basins on Mars are either weakly magnetized or completely demagnetized, indicating that a global magnetic field was not present at the time those basins formed. Eight basins are sufficiently large that the impact heating associated with their formation could have penetrated below the core–mantle boundary (CMB). Here we investigate the thermal evolution of the martian interior and the fate of the global magnetic field using 3D mantle convection models coupled to a parameterized 1D core thermal evolution model. We find that the survival of the impact-induced temperature anomalies in the upper mantle is strongly controlled by the mantle viscosity. Impact heating from subsequent impacts can accumulate in stiffer mantles faster than it can be advected away, resulting in a thermal blanket that insulates an entire hemisphere. The impact heating in the core will halt dynamo activity, at least temporarily. If the mantle is initially cold, and the core initially superheated, dynamo activity may resume as quickly as a few Myr after each impact. However unless the lower mantle has either a low viscosity or a high thermal conductivity, this restored dynamo will last for only a few hundred Myr after the end of the sequence of impacts. Thus, we find that the longevity of the magnetic field is more strongly controlled by the lower mantle properties and relatively insensitive to the impact-induced temperature anomalies in the upper mantle.

The analysis of the Lunar Prospector magnetic data over South Pole Aitken basin reveals two categories of magnetic anomalies with distinctly different polarities. Modeling the anomalies in terms of vertical prism source bodies shows two separate true polar wander paths of the Moon. One is driven by the giant surface mass deficiency resulted from the formation of the South Pole Aitken basin and the other by the giant surface mass concentrations (mascons) formed inside the large impact basins, such as Serenitatis and Imbrium, and a vast volcanic deposit on Procellarum Terrane. A total of ~100o true polar wander path suggests that the source bodies are formed and magnetized during a long period. Moreover, the distinctly different polarities of the two categories of the anomalies supports the idea that the core dynamo underwent a reversal, or shutdown and started up with a different polarity, caused by the latter impacts. The impact-induced shock pressures of 10-20 GPa traveling inside the lunar core, the appreciable angular momentum transfer to the lunar mantle by the impacting bodies, and the impact-induced stratification of the core probably reversed the polarity of the core dynamo. We also model the north Crisium magnetic anomaly, extracted from the Lunar Prospector magnetic data. The paleomagnetic pole position obtained for the source body reveals that the north Crisium anomaly belongs to the first category of the anomalies.

The formation of an inner core during the accretion of Earth is investigated using self-gravitating and compressible Earth models formed by accreting a total of 25 or 50 Moon to Mars size planetary embryos. The impact of an embryo heats the proto-Earth's interior differentially, more below the impact site than elsewhere. The rotating core dynamically overturns and stratifies shortly after each impact, creating a spherically symmetric and radially increasing temperature distribution relative to an adiabatic profile. Merging of an embryo to the proto-Earth increases the lithostatic pressure that results in compressional temperature increase, while further enhances the melting temperature of the core causing solidification. A total of 36 thermal evolution models of the growing proto-Earth's core are calculated to investigate effects of major physical parameters. No solidification is considered in the first 21 models where modified two-body escape velocities are used as the impact velocities of the embryos. At the end of accretion, temperatures in the upper part of the core are significantly different among these models, whereas temperatures in the deeper parts are similar. The core solidification considered in the remaining 15 models, where impact velocities higher than the modified two-body escape velocities are adopted, drastically changes the temperature distribution in the deeper parts of the core. All of the models produce partially solidified stiff inner cores, 1000-2100 km in radius, at the end of accretion, where the solid fraction is larger than 50%. The innermost of the stiff inner cores are completely solidified to radii 250-1500 km.

The Rayleigh number-Nusselt number, and the Rayleigh number-thermal boundary layer thickness relationships are determined for the three-dimensional convection in a spherical shell of constant physical parameters. Several models are considered with Rayleigh numbers ranging from 1.1 x 102 to 2.1 x 105 times the critical Rayleigh number. At lower Rayleigh numbers the Nusselt number of the three-dimensional convection is greater than that predicted from the boundary layer theory of a horizontal layer but agrees well with the results of an axisymmetric convection in a spherical shell. At high Rayleigh numbers of about 105 times the critical value, which are the characteristics of the mantle convection in terrestrial planets, the Nusselt number of the three-dimensional convection is in good agreement with that of the boundary layer theory. At even higher Rayleigh numbers, the Nusselt number of the three-dimensional convection becomes less than those obtained from the boundary layer theory. The thicknesses of the thermal boundary layers of the spherical shell are not identical, unlike those of the horizontal layer. The inner thermal boundary is thinner than the outer one, by about 30- 40%. Also, the temperature drop across the inner boundary layer is greater than that across the outer boundary layer.

We investigate the possibility that a strong core dynamo of the Moon has magnetized the lunar crust. The magnetic data from two missions, Lunar Prospector and Kaguya, are used and the magnetic fields of two different features are examined: The isolated small magnetic source bodies with almost no topographic signatures, and the impact craters with diameters larger than 100 km. Five data sets are examined separately for each of the isolated magnetic anomalies: the r, θ, and φ components of the Lunar Prospector data, the r component of a 150-degree spherical harmonic model of the lunar magnetic field, and the r component of the Kaguya data. The r component of the Lunar Prospector data is also used to derive the magnetic field over the impact craters. We conclude that most of the ancient lunar far side crust is heterogeneously magnetized with coherency wavelength about a few hundred km. The paleomagnetic north poles determined from modeling the magnetic field of both features show some clustering whereas the source bodies are widely distributed, suggesting that the magnetizing field may have been a core dynamo field. Paleointensity data suggest that the core field intensity was at least 1 mT at the core mantle boundary. There is also evidence for core field reversals, because further clustering occurs when the south poles of some features are considered.

The propagation of impact-induced shock wave inside a planetary embryo is investigated using the Hugoniot equations and a new scaling law, governing the particle velocity variations along a shock ray inside a spherical body. The scaling law is adopted to determine the impact heating of a growing embryo in its early stage when it is an undifferentiated and uniform body. The new scaling law, similar to other existing scaling laws, is not suitable for a large differentiated embryo consisting of a silicate mantle overlying an iron core. An algorithm is developed in this study on the basis of the ray theory in a spherically symmetric body which relates the shock parameters at the top of the core to those at the base of the mantle, thus enabling the adoption of scaling laws to estimate the impact heating of both the mantle and the core. The algorithm is applied to two embryo models: a simple two-layered model with a uniform mantle overlying a uniform core, and a model where the pre-shock density and acoustic velocity of the embryo are radially dependent. The former illustrates details of the particle velocity, shock pressure, and temperature increase behind the shock front in a 2D axisymmetric geometry. The latter provides a means to compare the results with those obtained by a hydrocode simulation. The agreement between the results of the two techniques in revealing the effects of the core–mantle boundary on the shock wave transmission across the boundary is encouraging.

Several giant impact basins of mid-Noachian age have been identified on Mars, and the global magnetic field appears to have vanished at about the same time. The impacts that formed these basins delivered a large amount of heat to the planetary interior, modified the pattern of mantle convection, and suppressed core cooling, potentially contributing to the cessation of dynamo activity. Here we investigate the thermal evolution of Mars in response to the largest basin-forming impacts, using a new method of coupling models of mantle convection with parameterized core cooling. We find that heating by a large impact generates a strong hemispheric upwelling in the mantle, which quickly spreads into a warm layer beneath the stagnant lid. The impact heating of the core leads to spherically symmetric stratification of the core; the outermost layers are strongly heated. This acts as a thermal “blanket” that prevents cooling of the interior and shuts down core convection. While the hottest part of the thermal blanket in the outermost core disappears relatively quickly, dynamo activity does not restart for ~100 Myr, and the core does not return to a fully convective state for ~1 Gyr following the impact.

A giant impact is an increasingly popular explanation for the formation of the northern lowland on Mars. It is plausible that at the impact time both Mars and the impactor were differentiated with solid silicate mantles and liquid iron cores. Such a large impact likely resulted in merging of the cores of both bodies, a process which will have implications on the thermal state of the planet. We model the evolution of the Martian mantle following a giant impact and characterize the thermochemical consequences of the sinking of an impactor's core as a single diapir. The impact heating and the viscous heating induced during the core merging may affect the early thermal state of Mars during several tens of million years. Our results show that large viscosity contrasts between the impactor's core and the surrounding mantle silicates can reduce the duration of the merging down to 1 kyr but do not modify the merging temperature. When the viscosity contrast between the diapir and the surrounding silicates is larger than a factor of 1000, the descent of the diapir can lead to some entrainment of the relatively shallow silicates to deepest regions close to the core-mantle boundary. Finally, the direct impact heating of Martian core leads to thermal stratification of the core and kills the core dynamo. It takes on the order of 150–200 Myr to reinitiate a strong dynamo anew. The merging of the impactor's core with the Martian core only delays the reinitiation of the dynamo for a very short time.

A meteorite impact capable of creating a 200 km diameter crater can demagnetize the entire crust beneath, and produce an appreciable magnetic anomaly at satellite altitudes of ∼400 km in case the pre-existing crust is magnetized. In this study we examine the magnetic field over all of the craters and impact-related Quasi-Circular Depressions (QCDs) with diameters larger than 200 km that are located on the highlands of Mars, excluding the Tharsis bulge, in order to estimate the mean magnetization of the highland crust. Using the surface topography and the gravity of Mars we first identify those QCDs that are likely produced by impacts. The magnetic map of a given crater or impact-related QCD is derived using the Mars Global Surveyor high-altitude nighttime radial magnetic data. Two extended ancient areas are identified on the highlands, the South Province and the Tempe Terra, which have large number of craters and impact-related QCDs but none of them has an appreciable magnetic signature. The primordial crust of these areas is not magnetized, or is very weakly magnetized at most. We examine some plausible scenarios to explain the weak magnetization of these areas, and conclude that no strong dynamo existed in the first ∼100 Myr of Mars’ history when the newly formed primordial crust was cooling below the magnetic blocking temperatures of its minerals.

When the core dynamo of Mars initiated and when and why it ceased is not well understood. Attempt is made in this study to constrain the active period of the core dynamo, assuming that it was powered by vigorous thermal convection in the liquid iron core. Two distinct periods of the planet are investigated: the latest stage of accretion when the growing Mars embryo likely experienced high-velocity embryo–embryo collisions, and during the late bombardment at ∼4 Ga that created 20 giant basins on Mars. The impact heating of Mars embryo by a large embryo, 1000 or 1500 km diameter, results in thermal stratification of the core where temperature increases with radius. The thermally stratified core requires 50–120 Myr to cool and regain vigorous convection, powering a strong core dynamo. The almost non-magnetic extended area of the primordial crust in the southern hemisphere supports this likely scenario. The impact heating of Mars by the seven largest of the 20 impacts is studied in detail. The collective battering the core dynamo by the impacts probably kills the dynamo. A strong core dynamo existed for ∼350 Myr, until Ares and the following Amazonis impacts introduced substantial perturbations to the core temperature and constrained the core convection to the upper ∼200 km for ∼28 Myr, during which no strong core dynamo was generated in this part of the core. However, it is possible that the strong dynamo that existed deep in the core prior to Ares impact retained its strength while the condition gradually changed from supercritical to subcritical until Acidalia impact which likely killed the dynamo.

The lack of distinct magnetic signatures observed by Mars Global Surveyor (MGS) over the impact craters and impact-related Quasi-Circular-Depressions (QCDs) with diameters greater than 200 km located on South Province, south of 30S and from almost the west of Hellas to Argyre basins, implies a weakly magnetized crust. Using MOLA topography and the recent JPL gravity model of Mars we determine the structure of the crust beneath the craters and impact-related QCDs, and show that the impacts that have created these features were capable of strongly disturbing the crust directly beneath. On the basis of theoretical magnetic anomaly modeling and shock demagnetization models, we demonstrate that the impacts are capable of demagnetizing the entire crust beneath and creating distinct magnetic anomalies at the satellite altitude of 400 km in case the crust was appreciably magnetized prior to the impacts. We derive the magnetic anomalies of these features using the radial component of the high-altitude nighttime MGS data. An upper limit of 4 A for the bulk magnetization of the crust beneath South Province is estimated, which is about 30 times less than that underlying Terra Cimmeria and Terra Sirenum. Similar weak bulk magnetization is obtained for part of the crust surrounding Hellas, Isidis, and Argyre basins.

We test the consistency of 108 estimates of skewness (a measure of asymmetry that depends on the orientation of lithospheric magnetization) of magnetic anomaly 32 from the Pacific plate with a model for spreading-rate–dependent anomalous skewness formulated for data in the Arctic, Atlantic, and Indian Oceans. In a prior study, a chron 32 (71.6–73.0 Ma) paleomagnetic pole was determined that best fit these 108 skewness estimates while simultaneously solving for a third parameter, anomalous skewness, assumed to be independent of spreading rate. An analysis of the residuals in skewness was previously used to test for any dependence on spreading rate and indicated an increase in residual skewness with increasing spreading rate, which is opposite in trend to that observed in other ocean basins. In contrast with the prior analysis of residuals, we find the data to be consistent with anomalous skewness increasing with decreasing spreading half rate less than 50 mm yr −1 . Thus, the spreading-rate dependence of anomalous skewness in the Pacific is consistent with that found in other ocean basins and with the model for spreading-rate–dependent anomalous skewness. The resulting revised paleomagnetic pole lies only 1.2° from the prior pole. The revised pole, as was the case for the original pole, shows that the Hawaiian hotspot has shifted southward relative to the spin axis by 13° since ca. 72 Ma.

We investigate the effects of a huge impact called Borealis impact, possibly occurred at 4.5 Ga and created the northern lowland of Mars, on the thermal evolution of Mars using 2D axi-symmetric convection in a spherical shell of temperature- and pressure-dependent viscosity. A suite of models are calculated to study effects of different physical parameters on the impact-induced mantle dynamics. We use the conventional scaling laws of basin diameter and impactor size, the impact shock pressure in the interior of Mars and the foundering mechanism of impact heating to calculate the temperature increase in the mantle. The mantle is allowed to melt as its temperature surpasses the solidus. To assess the effects of the impact on the thermal evolution of Mars, we compare the thermal evolution of the models with impact to the equivalent models having no impact. It is shown that the impact increases the rate of crustal production for a period of about 50 m.y. after the impact. The initial impact-induced melt volume is about 3.44 × 108 km3, whereas the impact induced mantle upwelling beneath the impact site results in the production of an extra 8.8 × 108 km3 of melt. The models with no impact also produce melt in due time and the total volume of melt at 4.6 Gyr is not significantly sensitive to the impact. This observation suggests that large impacts can significantly alter the rate of crustal production of Mars but have minor effects on the total volume of crust or melt production.

Large impacts not only create giant basins on terrestrial planets but also heat their interior by shock waves. We investigate the impacts that have created the largest basins existing on the planets: Utopia on Mars, Caloris on Mercury, Aitken on Moon, all formed at � 4 Ga. We determine the impact-induced temperature increases in the interior of a planet using the ‘‘foundering’’ shock heating model of Watters et al. (Watters, W.A., Zuber, M.T., Hager, B.H. [2009]. J. Geophys. Res. 114, E02001. doi:10.1029/ 2007JE002964). The post-impact thermal evolution of the planet is investigated using 2D axi-symmetric convection in a spherical shell of temperature-dependent viscosity and thermal conductivity, and pressure-dependent thermal expansion. The impact heating creates a superheated giant plume in the upper mantle which ascends rapidly and develops a strong convection in the mantle of the sub-impact hemisphere. The upwelling of the plume rapidly sweeps up the impact-heated base of the mantle away from the core–mantle boundary and replaces it with the colder surrounding material, thus reducing the effects of the impact-heated base of the mantle on the heat flux out of core. However, direct shock heating of the core stratifies the core, suppresses the pre-existing thermal convection, and cripples a pre-existing thermally-driven core dynamo. It takes about 17, 4, and 5 Myr for the stratified cores of Mars, Mercury, and Moon to exhaust impact heat and resume global convection, possibly regenerating core dynamos.

We investigate the polar wander of Mars in the last ∼4.2 Ga. We identify two sets of basins from the 20 giant impact basins reported by Frey [Frey, H., 2008. Geophys. Res. Lett. 35, L13203] which trace great circles on Mars, and propose that the great circles were the prevailing equators of Mars at the impact times. Monte Carlo tests are conducted to demonstrate that the two sets of basins are most likely not created by random impacts. Also, fitting 63,771 planes to randomly selected sets of 5, 6, or 7 basins indicated that the identified two sets are unique. We propose three different positions for the rotation pole of Mars, besides the present one. Accordingly, Tharsis bulge was initially formed at ∼50 N and moved toward the equator while rotating counterclockwise due to the influence of the two newly forming volcanic constructs, Alba Patera and Elysium Rise. The formation of the giant impact basins, subsequent mass concentrations (mascons) in Argyre, Isidis, and Utopia basins, and surface masses of volcanic mountains such as Ascraeus, Pavonis, Arsia and Olympus, caused further polar wander which rotated Tharsis bulge clockwise to arrive at its present location. The extensive polar motion of Mars during 4.2–3.9 Ga implies a weak lithosphere on a global scale, deduced from a total of 72,000 polar wander models driven by Tharsis bulge, Alba Patera and Elysium Rise as the major mass perturbations. Different compensation states, 0–100%, are examined for each of the surface loads, and nine different thicknesses are considered for an elastic lithosphere. The lithosphere must have been very weak, with an elastic thickness of less than 5 km, if the polar wander was driven by these mass perturbations.

We first show that 7 out of the 20 giant impact basins of Mars recently reported by Frey [Frey, H., 2008. Geophys. Res. Lett. 35. L13203] trace a great circle on Mars. The other five basins trace another great circle and still the other three basins trace yet another great circle. The latter great circle is in good agreement with the pre-Tharsis equator of Mars that is estimated from modeling crustal magnetic anomalies [Arkani-Hamed, J., 2001. Geophys. Res. Lett. 28, 3409–3412] and diagonalizing the moment of inertia of Mars after removing the loading effects of Tharsis bulge [Sprenke, K.F., Baker, L.L., Williams, A.F., 2005. Icarus 174, 486–489]. It is shown in this paper that the three great circles were likely the equatorial plane of Mars at certain times and Mars experienced appreciable polar wander. The great circles also indicate that the asteroids that created the basins were satellites of Mars whose orbits decayed in time through spin–orbit coupling with tidally deforming Mars, and eventually impacted on the planet creating the giant basins at around 4 Ga. The orbital dynamics of four largest asteroids show that they could have orbited Mars for several hundred million years if they were retrograde satellites. Continual elliptical straining of otherwise circular fluid streamlines of the liquid core of Mars by tidal deformation could have exerted a strong strain that was large enough to overcome dissipation and excite the elliptical instability inside the core. We investigate the physical properties of the martian core that are required to allow the tidal deformation to power the core dynamo, i.e., the growth time of the elliptical instability to become shorter than the dissipation time. The tidal energy dissipation rate inside Mars caused by even only one of the 4 largest asteroids is found to be over two orders of magnitude greater than the magnetic energy dissipation rate in the core, indicating that if only one of the 4 largest asteroids were orbiting in retrograde sense, it would have likely powered the core dynamo of Mars for several hundred million years.

International audience; While major impacting bodies during accretion of a Mars type planet have very low velocities (

Following a detailed investigation of the Fourier-domain differential reduction-to-the-pole (DRTP) algorithm I compared the results to those obtained using a space-domain reduction-to-the-pole algorithm. I demonstrate that DRTP reduces magnetic anomalies to the pole more effectively than the space-domain algorithm. The DRTP operator has singularities at the geomagnetic equator and enhances north-south trending features at low latitudes. The operator is modified by slightly increasing the inclination of the core field at low latitudes to suppress the singularity. This space-domain modification only affects the anomalies very close to the equator. The modified DRTP operator successfully reduces the magnetic anomalies at low latitudes to the pole. The effects of random noise added to the original magnetic anomalies are investigated in some detail, and an appropriate directional low-pass filter is used to remove the resulting enhanced noise in the reduced-to-the-pole magnetic anomalies. Very simple bodies (uniformly magnetized, cubic, or rectangular) are considered to clearly illustrate the effects of the DRTP, its modified version, and the directional low-pass filter.

We use the mapping-phase high-altitude magnetic measurements provided by Mars Global Surveyor (MGS) between March 1999 and April 2003 to model nine relatively isolated magnetic anomalies of Mars. Each anomaly is modeled with an elliptical prism. Each component of the observed magnetic field is modeled independently using an elliptical prism in order to assess the reliability of the results and suppress non-crustal and nearby crustal source contaminations. The paleomagnetic pole positions are obtained from the magnetization vectors of the model source bodies. We clean the data by removing the bad tracks and then divide the entire data into two sets that are measured at different times. Applying covariance analysis in the Fourier domain to two maps of the same magnetic component that are derived from the two sets provides a means to extract the most common features of the maps. The quality of a model is evaluated and only good models are used in the final geophysical interpretation. Most poles that come from good models cluster in the Tharsis region, suggesting that Mars experienced polar motion since the magnetic source bodies were magnetized.

The lack of magnetic anomalies within the giant martian impact basins, Hellas, Argyre, and Isidis suggests that the impacts demagnetized the crust. Our analysis of the magnetic anomaly intensity shows that the interior parts of the basins are completely demagnetized, while the outer parts and surroundings are partially demagnetized. We investigate the shock pressure and impact heating resulting from the impacts. The crust has been completely demagnetized within ∼0.8 basin radius by a combination of thermal and shock effects, and the surroundings have been partially demagnetized by shock to a distance of at least 1.4 radii. We also investigate magnetic signatures of intermediate-size craters. From the pressures generated by both the large and intermediate-sized impacts, we conclude that the remanent magnetization is carried at least in part by high coercivity rocks. Since the crust beneath the basins does not appear to have been remagnetized as it cooled following the impacts, we conclude that the martian core dynamo was inactive or very weak for at least 100 Myr following the Hellas impact.

A self-gravitating, elastic, spherical thick shell model is used to derive the present state of the lateral variations of density and stress differences within the lunar lithosphere. The model is allowed to deform under the load of an initial surface topography and internal density distribution, such that the resulting deformed body gives rise to the observed surface topography and gravity specified by the spherical harmonics of degree up to 70. Two main models are considered, Model A and Model B, with elastic lithospheres of thickness 300 and 210 km, respectively. Model A displays density perturbations of generally less than ±200 kg/m3 within the crustal layers, reducing rapidly to less than ±20 kg/m3 at the base of the lithosphere. The density perturbations in Model B are similar in the crust and marginally higher at the base of the lithosphere. The major stress differences in the mantle are associated with the mascon basins and are found to reach maximums of 8–10 MPa within the lower lithosphere (150–270 km) of Model A and maximums of 12–16 MPa at 150 to 180 km depth for Model B. A moderate correlation exists between the modeled stress distributions and shallow moonquake epicenters. However, the overall results of this study imply that other remnant stresses, due to processes other than density perturbations, exist and play a critical role in the large shallow moonquakes.

Investigation of the flexural response of the oceanic plate subject to loading of New England seamounts provides an insight into the rigidity of the lithosphere. Fourier domain analysis of the bathymetry and gravity anomalies over New England seamounts suggests that internal density perturbations exist in the crust and/or uppermost mantle. The loads due to the topography of the seamounts and density perturbations must have been supported by the lithosphere. We group the seamounts into three representative ages and adopt a 3-D thin elastic plate model over an invicid mantle to assess the rigidity of the lithosphere under these loads. The rigidity values are about 3–7×10 23 N m for lithospheric ages ranging from 30 to 60 my. The base of the elastic part of the lithosphere follows an isotherm in the range of 750–850 °C, suggesting a strong lithosphere that makes the north Atlantic Ocean difficult to initiate subduction. However, the thermal blanketing by the thick sediments at Scotian basin reduces the rigidity by one to two orders of magnitude, and may facilitate initiation of subduction of the north Atlantic oceanic lithosphere at Scotian margin.

We consider two-dimensional thermo-chemical mantle convection models to investigate the deformation of the continental lithosphere that follows the oceanic lithosphere into the subduction zone. The models account for the compositional buoyancy forces by considering lithospheric plates with distinct crustal layers. Continental convergence results in crust–mantle detachment in the subducting plate and crustal thickening in both subducting and overriding plates. The depth of detachment ranges from 90 to 200 km, depending on the strength of the lithosphere and the density of the continental crust. As the crust thickens, the convergence velocity in the collision zone decreases and the locus of subduction gradually shifts toward the interior of the subducting plate. In models with greater viscosity, the subducting mantle lithosphere maintains its integrity and does not break up. In models with weaker rheology, the positive buoyancy of the thickened crust can overcome the strength of the subducting lithosphere, and causes the oceanic slab to break off and sink into the mantle. The breakoff occurs over a time interval of 10–20 million years, which is roughly the time needed for the crust to reach its maximum thickness. Crustal detachment takes place over a wide range of lithospheric strength, suggesting that crustal buoyancy has an important role in the dynamics of continental subduction.

SUMMARY The youngest volcanoes of the Foundation volcanic chain were built on a plate less than 5 Myr near the Pacific‐Antarctic ridge (PAR) axis. The progressive approach of the spreading ridge to the hotspot during the last 10 Myr resulted in the building of the edifices upon a progressively younger plate. Estimates of the effective elastic thickness, Te, using two independent methods show that the elastic thickness of the plate diminishes towards the spreading ridge, from 5‐3 km to 2‐0 km. The spatial variation of Te correlates with a significant change in both the morphology and the volume of the volcanoes, suggesting an important control of the elastic thickness on the volcanic processes. The reduction in Te also explains conveniently the reduction in the distance between the North and the South Systems, the double volcanic line that characterizes the young part of the Foundation chain, in the direction of young loading ages. The South System formed at the top of a flexural bulge created by the emplacement of the North System, the main volcanic line. The low Te estimate for the South System and the shape of the Bouguer anomalies confirm this model. The effective elastic thicknesses obtained in this study are well matched by isotherms between 200 ◦ C and 300 ◦ C and support the hypothesis of a weak plate. Three mechanisms possibly acted to lower the plate rigidity: Re-heating of a ‘normal’ plate by the hotspot (North System); local fracturing (South System) and the creation of a thin lithosphere at the PAR axis by the coupling of a hotspot and the ridge-related melting zones (near-ridge volcanoes).

To assess the possibility that the North Atlantic Ocean may subduct at Scotian basin east of Canada, we investigate the present compensation state of this deep basin. A Fourier domain analysis of the bathymetry, depth to basement and observed gravity anomalies over the oceanic area east of Nova Scotia indicates that the basin is not isostatically compensated. Moreover, the analysis emphasizes that in addition to the sediments, density perturbations exist beneath the basin. The load produced by the sediments and these density perturbations must have been supported by the lithosphere. We simulate the flexure of the lithosphere under this load by that of a thin elastic plate overlying an inviscid interior. It is shown that a plate with a uniform rigidity does not adequately represent the lithosphere beneath the basin as well as the oceanic lithosphere far from the basin, rather the rigidity of the lithosphere directly beneath the basin is about one to two orders of magnitude smaller than elsewhere. We relate this weakening to the thermal blanketing effects of the thick sediments and the fact that the lithosphere has a temperature-dependent rheology. We suggest that this weak zone would have a controlling effect on the reactivation of normal faults at the hinge zone of the basin, that were formed during the break-up of Africa and North America and were locked in the early stages after the break-up. The weak zone would facilitate reactivation of the faults if tensional stresses were produced by possible reorientation of the spreading direction of the North Atlantic Ocean in the future. The reactivation of the faults would create a free boundary condition at the hinge zone, allowing further bending of the lithosphere beneath the basin and juxtaposition of this lithosphere to the mantle beneath the continent. This may provide a favorable situation for initiation of slow subduction due to subsequent compressional forces.

This paper presents a 50-degree and order spherical harmonic model of the magnetic field of Mars derived at 120-km altitude using the three orthogonal components of the vector magnetic field data acquired by the Mars Global Surveyor within the 80- to 200-km-altitude range. The downward continued vector magnetic field components to the surface of Mars delineate details of the Martian magnetic field. The strong magnetic anomalies in the southern hemisphere do not show compelling evidence for magnetic lineations similar to those associated with the seafloor spreading on Earth. The anomalies are more or less equidimensional. The magnetic signatures surrounding the impact basins Hellas, Argyre, and Isidis show that the prominent magnetic anomalies are older than the impact events. An average magnetization of ∼2 A/m is estimated for the upper crust surrounding Hellas basin. Four isolated magnetic anomalies are modeled by vertical prisms with circular cross sections of 170- to 190-km radius and 20- to 30-km thickness. The magnetization of the model prisms is 5 A/m more than that of the surroundings.

The compensation state of 49 intermediate size (120 to 600 km diameter) lunar craters are investigated using the most recent spherical harmonic models of the lunar topography and gravity, truncated at degree n =110. The total mass anomalies per unit area (i.e., the lateral variations of the vertically integrated density perturbations per unit area) within an otherwise uniform crust of 60 km thickness are determined such that, together with the surface topography, give rise to the model gravity anomalies. Crustal thicknesses of 40 and 80 km are also considered, but the general results of this study are not significantly affected. Excess mass anomalies are obtained by subtracting from the total mass anomalies the mass anomalies that are required for the isostatic compensation of the surface topography. The excess mass anomaly of a crater denotes its particular state of compensation. Dependencies of the excess mass anomalies on crater location, size, and age are investigated, but in general few discernable trends are evident. Although the vast majority of craters indicate some compensation, no correlation exists between age or size and the state of compensation. Roughly 16% of the craters show no compensation, and in some cases have mass deficiencies most likely due to the shock fractured bedrock: the breccia lens of lower density. The crust in these regions was likely cold and rigid enough at the time of impact to rigidly support the stress caused by crater excavation. These features are seen throughout different geological periods, demonstrating that the lunar crust cooled quickly and strengthened soon after formation. A comparison of the compensation state of craters Apollo, Korolev, and Hertzsprung suggests that the thermal and mechanical properties of the crust prior to impact had an appreciable effect on the compensation, and that crustal thickness may be the single most important factor controlling the compensation of intermediate size craters. The characteristics of the excess mass a nomaly profiles of the eight well-known near side mascon basins are used to identify new mascon-like craters. Ten newly found mascons are confirmed: Humboldtianum, Moscoviense, Mendel–Rydberg, Lorentz, Hertzsprung, Korolev, Schrodinger, Freundlich–Sharonov, Coulomb-Sarton, and Schiller–Zucchius, while two more, Deslandres and Dirichlet–Jackson, are very plausible. These results show that mare flow is not necessarily required to produce mascon-like characteristics.

The D″ layer is a dense and chemically distinct layer at the base of the convecting mantle. Numerical modeling of the entrainment of this layer by mantle convection requires the solution of the advective transport equation without introducing numerical diffusion across sharp material boundaries. We use our improved second moment numerical method to solve the equation. The method conserves the amount of material and the first and second moments of material distribution in each control volume. We first consider two examples of isothermal Rayleigh–Taylor instability to illustrate the performance of our method by comparing our results with those of a number of field, tracer and marker chain methods. We show that the performance of our method in minimizing the numerical diffusion is better than the field methods and comparable to the tracer and marker chain methods. We then study the instability of the dense D″ layer and its interaction with the overlying mantle. A range of density contrast between the D″ layer and the mantle, layer thickness, and the Rayleigh number, Ra , is examined. We show that for higher values of these parameters, the amount of entrainment decreases and the layer remains stable over longer periods of time. For very thick D″ layers and high Ra values, internal convection can take place within the layer.

This paper provides an estimate of the thermal state of Martian lithosphere established since the formation of the shield volcanoes. Comparison of the spherical harmonic models of Martian topography derived using harmonics truncated at degrees 10, 11, 12, and 14 shows that the volcanoes have almost no contribution from harmonic coefficients of the topography less than degree 11. Therefore intermediate-scale surface topography and gravity anomalies of Mars, specified by harmonics of degree 11-50, are considered in this study. These harmonics are dominated by shield volcanoes, Alba Patera, and Isidis basin. The central part of Valles Marineris is also well defined by these harmonics. The strong correlation of the topography and gravity anomalies over these harmonics and the positive Bouguer anomalies of the volcanoes suggest significant excess masses beneath these surface features in addition to their topographic masses. This indicates that the Martian lithosphere has been strong enough to support both the topography and the internal excess masses. We determine the rigidity of the lithosphere beneath a given surface feature. The lithosphere is modeled by a thin elastic spherical shell that overlies an inviscid interior of higher density and is subjected to both surface and internal loads. The thickness of the shell and the magnitude of the internal load are calculated such that the deformed structure resulting from the flexure of the shell under both surface and internal loads gives rise to the observed topography and gravity anomaly. It is shown that the lithosphere beneath Elysium Mons, Alba Patera, and the central part of Valles Marineris can be modeled by elastic shells subjected to topographic loads alone, whereas the lithosphere beneath Olympus and Tharsis Montes cannot. Internal excess masses of at least 40%, and more likely 50%, of the topographic masses are required, and the lithosphere beneath must have an elastic core of ∼100-80 km to support these volcanoes. The mean thermal gradient beneath this region of Tharsis is estimated to be ∼7-10 K/km on the basis of the strength envelopes calculated using diabase rheology for the crust of 50 km thickness and olivine rheology for the underlying mantle.

The second moment numerical method (SMM) of Egan and Mahoney [Numerical modeling of advection and diffusion of urban area source pollutant. Journal of Applied Meteorology 1972; 11: 312–322] is adapted to solve for the pure advection transport equation in a variety of flow fields. SMM eliminates numerical diffusion by employing a procedure that takes into account the first and second moments of mass distribution in each grid element. For pure translational flow fields, the method is conservative, positive definite and shape-preserving. In rotational and/or shear flows, the accuracy of SMM is significantly reduced. Two improvements are presented to make the SMM applicable to a wider range of flow problems. It is shown that the improved SMM (ISMM) is less diffusive and more shape-preserving than the SMM in rotational and/or deformational flows. The ISMM can also be used to solve for a color function in compressible flow fields. The computational efficiency of this method is compared with that of other methods and, for a given accuracy, it is shown that ISMM is a cost-effective, non-diffusive and shape-preserving method. Copyright © 2000 John Wiley & Sons, Ltd.

Summary Using a two-phase flow model, we investigate the formation of a high-percentage melt layer beneath the oceanic lithosphere and focusing of the melt towards the ridge axis, taking into account freezing and melt extraction. Melt migration is modelled dynamically within a viscous permeable media that includes the asthenosphere and viscous part of the lithosphere. Due to a much faster melt migration in the brittle part of the lithosphere, the melt migration is simulated by instantaneous melt extraction from an assigned melt extraction region beneath the ridge axis. It is shown that a high-percentage melt layer forms and successfully focuses melt to a narrow zone beneath the mid-ocean ridge. Performance of the melt focusing mechanism is not significantly sensitive to the size of the melt extraction region, the melt extraction threshold and the spreading rate. In all of our models, about half of the total melt production freezes beneath the base of the lithosphere and the rest is focused towards the ridge and forms the crust.

By lowering the altitude of Lunar Prospector to about 10–20 km the spacecraft will provide measures of the Moon's gravity field at very high resolution, enabling us to derive a spherical harmonic representation that includes harmonics of degree 360 and demanding precise calculation of the gravity field of the topography at such low altitudes. We present a method to determine the gravity field of the topography at low altitudes, which is very efficient even for higher degree harmonics and is also applicable for topography with laterally and radially varying density. The method is applied to three simple models; namely, an unfilled basin, a basin with mare filling, and a topography specified by a tesseral harmonic of degree 60 and order 30, before applying it to the actual topography of the Moon. It is shown that the gravity of the topography calculated by the surface-mass density approximation (a conventional method) is sufficient for harmonics of degree up to about 100 but becomes increasingly inadequate as the degree of the harmonics increases. The method is also applied to internal density interfaces, such as a possible Moho undulation, and it is concluded that the surface-mass density approximation becomes less appropriate once the degree of the harmonics exceeds about 20. We also calculate the free air gravity anomaly of the lunar topography at 10 km altitude using this method and the available 90 degree spherical harmonic model of the topography. Although the surface topography of Venus has been expanded in terms of the spherical harmonics of degree up to 360 [Rappaport and Plaut, 1994], its gravity field is measured at altitudes greater than 150 km [Sjogren et al., 1997], which is much larger than the surface topography or possible undulation of the crust-mantle boundary. The results of our method and the conventional method may not differ significantly for Venus.

The equipotential surface hypothesis suggests that lunar maria floors lie on a surface parallel to the selenoid. This is examined using the spherical harmonic representations of the Clementine topography and Lunar Prospector gravity data. It is demonstrated that the floors of both circular and noncircular maria significantly deviate from an equipotential surface. Deeper circular maria and the deeper part of the noncircular Maxe Tranquillitatis have been subsided under larger mass loads in the crust. We calculate the mass beneath the maria to be in excess to the mass required for isostatic compensation of the topography at 60 km depth. A global map of this excess mass shows that the noncircular maria are isostatically compensated, unlike the circular maria. The map also reveals seven new sizable mascons: the three largest are associated with Mendel-Rydberg, Mare Humboldtianum, and Mare Moscoviense.

Regional studies have shown that remanent magnetization of the Cretaceous quiet zones (CQZs), created during the long period of geomagnetic normal polarity at 118–84 Ma, produce well-defined magnetic anomalies at satellite altitudes. We investigate the effects of the remanent magnetization of the oceanic lithosphere on satellite magnetic anomalies on a global scale. We consider entire oceanic areas because oceanic lithosphere formed during periods other than CQZ, but with a predominant polarity, also have appreciable contributions to the satellite anomalies. The magnetic anomalies of the world's oceans are calculated from a distribution of vertically integrated remanent magnetization that is computed using age map, plate relative motions, and the apparent polar wander path of Africa. Three magnetization models are examined: thermoremanent magnetization confined to extrusive layer 2A, and thermoviscous remanent magnetization of the crust and uppermost mantle down to a maximum depth of 12 km or 30 km. Although all models lead to rather similar anomaly distributions, the amount of magnetization required suggests the need for deeper sources. All models produce the satellite anomalies associated with the CQZ in the North Atlantic and parts of the Indian and Pacific Oceans, with slight differences in location, depending on the models. Low-amplitude observed anomalies associated with areas created at fast and intermediate spreading rates in the Indian and Pacific Oceans are successfully modeled. A major difference between models and observation is the north-south elongated model anomalies associated, for instance, with the CQZs in the South Atlantic and the fast spreading East Pacific Rise. These elongated anomalies are systematically absent on the observed map, probably because they were removed by along-track filtering in the early stages of processing the satellite data. A careful comparison of the model anomalies with observation favors model with thermoviscous magnetization down to 12 km and saturation magnetizations of 4, 0, 1, and 0.6 A/m for the extrusive basalts, intrusive basalts, gabbros, and peridotites, respectively.

The power spectra and degree correlation of the surface topography and free-air gravity anomalies of eastern Canada show that the gravity anomalies are subdivided into three parts. The short-wavelength components (30-170 km, shorter than 30 km are not well resolved) largely arise from density perturbations in the crust and to a lesser extent from the surface topography and Moho undulation, whereas the contribution of intracrustal sources to the intermediate-wavelength components (170-385 km) is comparable with that of the topography. The long-wavelength components (385-1536 km) are overcompensated at the Moho. We present a crustal model for the intermediate- and long-wavelength components which takes into account the surface topography, density perturbations in the crust, and Moho undulation with a certain degree of isostatic compensation. The general characteristics of this model resemble the crustal structure revealed from seismic measurements. The reduced-to-pole magnetic anomalies of eastern Canada show no pronounced correlation with the topography and with the vertical gradient of the gravity anomalies, suggesting that the source bodies are within the crust and Poisson's relationship does not hold over the entire area. Assuming that the magnetic anomalies arise from induced magnetization, lateral variations of magnetic susceptibility of the crust are determined while taking into account the effects of the surface topography and the Moho undulation of our crustal model. The intermediate- and long-wavelength components of the susceptibility contrasts delineate major collision zones as low-susceptibility regions. We interpret this in terms of thermal demagnetization of the high-magnetic crustal roots beneath the collision zones.

Equivalent point source inversion in the rectangular coordinate system has been widely used to reduce satellite magnetic data collected at dier- ent altitudes to a common elevation over small areas. This method is based on the expression of the mag- netic anomaly caused by a magnetic dipole. Such an expression derived in a spherical coordinate system by von Frese et al. (1981) is found erroneous. We point out the errors in von Frese et al.'s (1981) formulas and present the correct expression for the magnetic eld of a magnetic dipole in a spherical coordinate system.

The entire spectra of the surface topography and gravity field of lunar mascons are well presented by the high-resolution Clementine data. The negative correlation between the topography and gravitational potential of the mascons suggests that they are dynamically supported. Both elastic support and viscous decay models are examined. For the elastic support models, the spectral characteristics and the lateral variations of the thickness of the elastic layer are determined on the basis of the thin spherical shell flexure formulation and using only the antivarying harmonics of the topography and potential. An elastic layer thickness of about 50 km is required to support Imbrium, Serenitatis, and Nectaris mascons, about 35 km for Crisium mascon, and about 30 km for Smythii and Humorum mascons. A layer of about 20 km thickness can support Orientale mascon. The strength envelopes of the upper 100 km of the Moon within 4–3 Gyr ago show that the elastic layer was not thick enough to support the mascons in the early history. They decayed through viscous deformation of the lunar interior. A lower limit of 6×1024 Pa s is estimated for the lunar viscosity within 3.6–3 Gyr ago. We also determine the thicknesses of the crust and mare flows of the mascon basins on the basis of the assumption that the basins were isostatically compensated prior to the mascon formation. The crust beneath the mascon basins is about 30–40 km except for Crisium and Orientale, where the crust is about 20 km. The mare flows of about 3–6 km are obtained for almost all of the mascon basins. The topography and gravitational potential of Aitken basin shows that the basin is compensated at 52–54 km depth. The mantle beneath the basin has rebounded upward by about 20–30 km and is overlain by about 20–25 km of a mixture of the excavated crustal and mantle material. The lack of a mascon and pervasive mare flows in the basin brings into question the current models of the mascon formation.

Satellite magnetic anomaly maps show well-defined negative anomalies over some deep sedimentary marginal basins, such as the Nova Scotia marginal basin. A possible explanation would be the thermal demagnetization of the oceanic upper crust due to thermal blanketing by the sediments and the oceanic lower crust and uppermost mantle due to subsidence into hotter regions beneath. We examine this possibility by computing the thermoviscous remanent magnetization of the oceanic lithosphere beneath the Nova Scotia basin using a detailed thermal evolution model which takes into account the continental rifting, sea-floor spreading, and subsequent subsidence. It is concluded that the thermal demagnetization is not sufficient to explain the entire observed negative magnetic anomaly over the basin; it contributes ~40% to the anomaly. We suggest that a major part, ~60%, of the anomaly arises from the particular location of the early Mesozoic oceanic lithosphere beneath the basin, which has a relatively weaker bulk remanent magnetization compared with a highly magnetic continental crust in the west and north and the strong magnetic oceanic lithosphere of the Cretaceous Quiet Zone in the east.

SUMMARY Detailed characteristics of marine magnetic anomalies 33r and 20r suggest that the magnetization of the deeper magnetic layers, including the lower crust and possibly the uppermost mantle, is horizontally displaced with respect to that of the upper crust. We examine the possibility that serpentinization of ultramafics in the lower crust and possibly the uppermost mantle delays the acquisition of magnetization and introduces a shift between the upper- and lower-crustal magnetization patterns. Thermal evolution models and the resulting magnetization patterns of the oceanic lithosphere are calculated for a wide range of physical parameters such as the Nusselt number and the depth of hydrothermal circulation in the crust, and the temperature range of serpentinization. The models with moderate hydrothermal cooling of the whole crust and serpentinization temperatures ranging between 200 and 300 dC successfully explain the anomalous skewness and the ‘hook shape’ of observed sea-level magnetic anomalies created at slow and intermediate spreading rates.

SUMMARY The deformation of the Iranian plateau due to the Arabia-Eurasia convergence is studied numerically using the viscous thin-sheet model. The lack of deformation in central Iran and the south Caspian sea is taken into account by including lateral heterogeneities in the lithospheric strength. We present results for models of different rheologies. The results imply that the deformation of the plateau is primarily controlled by the convergence of Arabia and the presence of rigid central Iran and the south Caspian. Deformation reaches to the northern parts at the early stages for many of the rheologies we considered, and crustal thickening takes place over the entire plateau, suggesting that the geometry of the plateau has a dominant effect on the deformation and tends to overshadow the role of rheology. The presence of rigid central Iran can explain the development of the shear zones in eastern and northern Iran. Our results are in good agreement with the observation that in the Zagros the crust is deforming by a creep process, whereas in northern Iran most of the present-day deformation is being accommodated seismically.

The mechanism by which high-pressure metamorphosed continental material is emplaced at high structural levels is a major unsolved problem of collisional orogenesis. We suggest that the emplacement results from partial subduction of the continental margin which, because of its high flexural rigidity, produces a rapid change in the trajectory of the descending slab. We assume a two-fold increase in effective elastic thickness of the lithosphere as the continental margin approaches the subduction zone, and calculate the flexural profile of a thin plate for progressive downward migration of the zone of increased rigidity. We assess the effect of changes in the flexural profile on the overlying accretionary prism and mantle wedge as the continent approaches by estimating the extra stresses that are imposed on the wedge due to the bending moment exerted by the continental part of the plate. The wedges overlying the subduction zones, and the subducting slab itself, experience substantial extra compressional stress at depths of around 100 km, and extensional stress at shallower depths, as the continental margin passes through the zone of maximum curvature. The magnitudes of such extra stresses are probably adequate to effect significant deformation of the wedge and/or the descending plate, and are experienced in a time interval of less than 5 m.y. for typical subduction rates. The spatial variation of yield stresses in the region of the wedge and descending slab indicates that much of this deformation may be taken up in the crustal part of the descending slab, which is the weakest region in the deeper parts of the subduction zone. This may result in rapid upward migration of the crust of the partially subducted continental margin, against the flow of subduction. High-pressure metamorphosed terranes emplaced by the mechanism envisaged in this paper would be bounded by thrust faults below and normal faults above. Movement on the faults would have been coeval, and would have resulted in rapid unroofing of the high-pressure terranes, synchronous with arrival of the continental margin at the subduction zone and, therefore, relatively early in the history of a collisional orogen.

We have used spherical harmonic representations of the Venus topography and geopotential, obtained from Magellan data, to evaluate isostatic support in several areas within the Ishtar Terra highlands, including the Lakshmi plateau, its surrounding mountain belts, namely Akna and Freyja, and Maxwell Montes, and the Fortuna Tessera province. We find that topography in Ishtar is largely isostatically compensated (>80%). Regional geoid-topography variations in the subregions can be explained by a combination of Airy (crustal thickening) and thermal (lithospheric thinning) mechanisms, provided Venus has a thick reference thermal lithosphere (∼300–400 km). With the exception of eastern Fortuna, low elevation areas (h 4 km above MPR) with small GTRs are almost certainly Airy compensated via thickened crust. Relatively large (>60 km) total Airy crustal thicknesses obtained in the western Ishtar mountain belts, together with a probable basalt-eclogite phase change, suggest a possible silicic composition for these structures, provided they are older than ∼25–50 Ma. Lakshmi Planum seems essentially thermally supported, with the thermal lithosphere thinned to ∼100 km. We suggest, as one possibility, that the lithospheric thinning process under Lakshmi is delamination of a dense eclogite lower lithosphere layer into the mantle. The decrease in GTR observed in Ishtar between Lakshmi to the west (GTR ∼ 20 m/km), Maxwell and west Fortuna (GTR ∼ 8 m/km), and eastern Fortuna (GTR ∼ 4 m/km) may correspond to a decay in thermal compensation attributed to lithospheric delamination, which would be fairly recent (∼100 Ma) in Lakshmi, partially decayed in west Fortuna, and absent in east Fortuna, where a mostly Airy-supported topography is essentially relaxed with no thermal uplift. Alternatively, if surficial concentrations in radiogenic elements were prevalent throughout the crust, partial melting of a thickened crust could account for the thermal uplift in Lakshmi and west Fortuna. The zero-elevation basaltic crustal thickness H ∼ 24 km obtained for the east Fortuna Tessera region may be representative of the ambient crustal thickness in the Venus lowlands. Our findings support multicomponent models for tectonic and volcanic activity in Ishtar. The thick ambient crust and thermal lithosphere implied by this study agree with observational constraints such as support of extreme elevations, large topographic slopes, unrelaxed craters, and the thick elastic lithosphere suggested by flexure studies. If the ambient thermal lithosphere on Venus were to be relatively thin (∼100–200 km), with a cold mantle and radiogenic elements concentrated in the crust, then thermal evolution on Venus may be in quasi-steady state, with the geodynamic evolution in monotonic decline. However, if the ambient thermal lithosphere is very thick (∼300–400 km), as suggested by our thermal model fits, then it is consistent with the predictions of strongly unsteady state thermal evolution models and an interior which is currently heating up. This would support the view that catastrophic resurfacing on Venus might be episodic.

The relationship between the surface topography and gravitational potential of Venus and the Earth is investigated over the spherical harmonics of degree and order up to 75. The covarying harmonics of the topography and the potential, i.e. the harmonics having nonnegative degree/order correlation coefficients, are treated separately from the antivarying harmonics, those with negative degree/order correlation coefficients. The covarying harmonics provide reliable estimates of the compensation depth of the surface topography. The surface topography of the Earth specified by spherical harmonics of degree higher than 11 is essentially compensated isostatically at the Moho discontinuity, whereas the lower-degree harmonics are largely supported by mantle dynamics. For Venus the harmonics of degree lower than 9 are probably supported by mantle dynamics, while those of degree higher than 35 are most likely supported isostatically at a depth of about 45 km. There is a gradual increase in the compensation depth of the surface topography as the degree of harmonics decreases from 35 to 9, implying a combination of isostatic and dynamic support of these harmonics. Part of the topography specified by antivarying harmonics of degree greater than about 20 cannot be maintained by an isostatic compensation or a steady state dynamic support ; it is more likely time dependent. Assuming that this part of the topography arises from viscous deformation of mantle under surface loading, the gravity and topography relationship provides a first-order estimate of 5x10 24 Pa s for the viscosity of the Venusian mantle. This high viscosity results in a Rayleigh number of about 12000 for the mantle, which is only about 17 times greater than the critical Rayleigh number for convection, implying a very slow quasi-steady convection in the mantle.

The apparent depth of compensation (ADC) of the topography of Venus, determined on a global scale using the Airy isostasy model, shows that the topography specified by the spherical harmonics of degree lower than 10 is compensated at depths greater than 150 km, that of degree higher than about 35 is compensated at a constant depth of about 35 km, and the compensation depths of the harmonics of degree 10–35 shoal as the harmonic degree increases. Based on these characteristics of the globally determined ADC, three different maps of the topography and gravitational potential of the Greater Ishtar Terra are derived using the harmonics of degree 1–75 (LW), 10–75 (IW), and 30–75 (SW), respectively. The LW maps of the topography and potential do not correlate well, but the IW and SW maps show good correlation, emphasizing that the long-wavelength components of the gravitational potential over the Ishtar Terra have contributions from sources broader than the Terra. The energy of the gravitational potential of the topography is about an order of magnitude greater than that of the observed potential, indicating that the topography is strongly compensated. The ADC of the topography is estimated by both spectral and space domain analysis. In the spectral domain, three independent procedures, the energy spectrum, the statistical method, and the wavelength-dependent method, are employed. The first two yield a mean ADC value for the entire spectrum, whereas the last one calculates the ADC for different wavelengths. The ADC decreases as the longer-wavelength components are excluded. The mean ADC values determined for the LW, IW, and SW maps by the energy spectrum method are 115, 65, and 40 km, respectively. Those calculated through the statistical method are 85, 55, and 34 km, respectively. These values reflect the upper and lower limits, because the energy spectrum method overestimates and the statistical method underestimates the ADC. The wavelength-dependent method shows that the ADCs of the wavelengths 500–1350 km are similar for all the maps but those of the longer wavelengths significantly differ among the maps. The mean ADC values also differ from the ADC of local topographic features. For example, the ADC of Maxwell Montes is about 55 km in both the LW and IW maps. In the space domain, the ADC is determined for Pratt and Airy isostasy models through fitting a linear and a quadratic function to the geoid height versus topography data, respectively. The ADC values determined show good agreement with the above-mentioned values. In addition, the relationship between the high-resolution topography and the line-of-sight acceleration residuals of the western Ishtar Terra specified by wavelengths of 300–500 km suggests that the high-resolution topography is compensated at a depth of about 25 km. We also determine the lateral density perturbations inside a surface layer so that together with the topography of the Greater Ishtar Terra they give rise to the observed gravitational potential over the Terra. Three layer thicknesses of 50, 100, and 200 km are examined. The resulting density perturbations are too large to be interpreted in terms of lateral temperature variations alone. This suggests lateral variations in the rock type; the crust beneath the mountain belts may contain considerable amounts of low-density material.

SUMMARY Two intermediate-wavelength magnetic anomaly maps of the North Atlantic Ocean are derived based on satellite and marine magnetic observations. The satellite map is produced from the covariant features of POGO and Magsat dawn and Magsat dusk magnetic anomalies. The marine map is compiled using shipborne data collected since 1965. The two maps are in excellent agreement over well-defined anomalies both in location and amplitude, suggesting that these anomalies are real and reflect magnetization contrasts in the oceanic lithosphere. Both maps show the intermediate-wavelength seafloor-spreading anomalies of the Cretaceous quiet zone of the central North Atlantic Ocean as well as the negative seafloor-spreading anomaly of the Labrador Sea caused by dominantly reversed polarity periods. The Iceland hotspot, Alpha Ridge, Azores High, King's Trough and the Rockall microcontinent have positive anomalies. There is no consistent magnetic signature associated with the ocean-continent boundary, although the deep sedimentary basin of Nova Scotia is delineated by a well-defined negative anomaly.

The highland region of Ishtar Terra on Venus has mountains that reach up to 11 km in height and are thought to be basaltic in composition. Assuming that dynamic uplift of crust to this height is unlikely, we examine the topography produced by an isostatically supported thickening basaltic crust. It is found that regardless of whether the crust thickens by crustal shortening or by volcanic construction, the high-density basalt-eclogite phase transition is the limiting factor for producing significant elevation of the mountains. The maximum height attained by basaltic mountains depends on the nature of the basalt-eclogite phase transition. Without a phase transition, a basaltic crust must thicken to greater than 100 km to reach heights over 10 km. An instantaneous phase transition of basalt to eclogite allows a maximum topographic height of less than about 2 km. However, with a time lag of 100 Ma owing to slow rates of solid-state diffusion, our calculations show that the mountains can reach elevations greater than 10 km only if they are less than 25 Ma old. Higher temperatures within the Venusian crust may decrease the extent of the stability fields of high-density basalt phases and allow high topography if the thickening crust melts. This can occur if the radioactive element concentrations measured on the surface of Venus are uniformly distributed throughout the crust, the crust thickens to greater than 65 km, and the thickened crust is older than about 400 Ma. The conflicting results of a young age predicted for high basaltic mountains and an almost uniform surface age of 500 Ma from crater populations, coupled with similarities in bulk physical properties of Venus and Earth, suggest that the basaltic surface composition found at several landing sites on the planet may not be representative of the entire crust. We suggest that Ishtar Terra formed from the collision of continent-like highly silicic cratons over a region of mantle downwelling. Lakshmi Planum resulted from the thickening of a basaltic crust and the peripheral mountain belts formed from the collision of granitic cratons that were pulled toward a downwelling region of mantle.