Apparent Depth Of Compensation Research Articles

Gravity analysis of Parga and Hecate chasmata: Implications for rift and corona formation

The two largest rift systems on Venus, Parga, and Hecate chasmata contain one third of all coronae. We map variations in elastic thickness and apparent depth of compensation (ADC) in these two regions using the admittance function for gravity and topography. We examine the relationship between rifting and coronae by comparing lithospheric structure with corona characteristics including volcanism, topographic shape, fracture pattern, diameter, and stratigraphic age. At Hecate chasmata, both ADC and elastic thickness correlate with two main rift branches, the fracture style and corona characteristics. Hecate chasma thus appears to be dominated by extensional processes. Parga chasma shows little correlation between lithospheric properties and the location of coronae or rift segments. The ADC at Hecate and Parga chasmata is mostly less than 75–100 km, implying that there is not large‐scale upwelling underlying the rift systems. The variations in the corona population sizes between Parga chasma, which has 131 coronae, and Hecate chasma, with 50 coronae, suggest differences in the evolution of the two rift systems. The much larger population of coronae at Parga contains more small coronae, many of which have relatively low volcanism and post date the rift. Further, many of the small coronae occur in chains and have similar diameters, as predicted by Rayleigh‐Taylor type instabilities. These characteristics suggest that the smaller coronae may form via a later, secondary decompression melting phase. Thus, Hecate chasma may be younger than Parga chasma and could experience a secondary stage of corona formation in the future.

Geoid height versus topography of the Northern Ninetyeast Ridge: implications on crustal compensation

In this paper we focused on understanding the isostatic compensation of the Ninetyeast Ridge in the overall context of the Bay of Bengal oceanic lithosphere and the interaction of the ridge system with the north Andaman subduction zone from north of 7–18°N. This region is characterized by the initial interaction of the Kerguelen hotspot with the Bay of Bengal oceanic lithosphere. We used satellite altimeter-derived marine geoid, as it should comprehensively reflect the compensations caused by large spatial wavelength dominated deeper anomaly sources in a hotspot affected lithospheric load like the Ninetyeast Ridge. Our analyses of the geoid-to-topography ratio (GTR), residual geoid, gravity-to-topographic kernel and upward continuation of anomalies show the existence of two different types of source compensation bodies beneath the northern (12–18°N) and southern (7–12°N) Ninetyeast Ridge. In the northern region, the geoid to topography ratio varies from 0.63 ± 0.05 to 0.44 ± 0.03, while in the southern region it ranges from 1.34 ± 0.09 to 1.31 ± 0.07 which resulted in a north to south increase in the apparent compensation depth from ~9 to 28 km. The presence of a shallow Moho, low GTR, broader gravity to topography kernel and the absence of a ridge anomaly from the mantle density dominated upward continued anomaly at z = 300 km indicates that at the northern segment the underplated low density crustal melt is the dominant isostatic compensating body. However, at the southern ridge segment the high GTR, strong gravity-to-topography kernel and the subsistence of the anomaly at long wavelengths, even at z = 300 km represents the existence of large volumes of hotspot related underplated dense material as the source of compensation. The proximity of the dense source compensating body of the southern Ninetyeast Ridge to the Andaman subduction zone affected the regional mantle driven density gradient flow, as observed from the z = 300 km continued gravity anomaly. The existence of a southern Ninetyeast Ridge in such a transpressional regime has caused the formation of a forearc sliver at its eastern flank, which is a major crustal deformational structure developed as a result of ridge-trench collision.

Topography and geoid anomalies due to density heterogeneities at the base of the thermal lithosphere: application to oceanic swells and small-wavelength geoid lineations

SUMMARY The surface topography, gravity and geoid associated with loads situated at the base of the thermal lithosphere are computed. The model lithosphere is composed of a viscous lower layer with depth-dependent viscosity overlain by an elastic lid. When the viscosity varies strongly with depth, the amplitude of the surface topography decreases rapidly as the wavenumber characterizing the mass anomaly increases. The response for this two-layer lithosphere differs substantially from the response computed for the loading from below of an elastic lid. If the 200km wavelength geoid anomalies observed in the oceans are due to convective instabilities at the base of the lithosphere, a positive geoid anomaly with an amplitude reaching 30 to 50cm is expected over a cold downwelling for ages greater than 10 Myr. No detectable topography associated with the lineations should be present for ages greater than 20 Myr. Our model predicts that some topographic anomalies might be visible for younger ages. If 1000 km broad swells are due to light material at a depth of about 100 km, the associated geoid-over-topography ratios are quite reduced compared to those predicted by the long-wavelength linear relationship usually employed for estimating the apparent compensation depth.

Elastic thickness estimates for the northern lowlands of Mars

The northern lowlands cover approximately one-third of Mars' surface and are a fundamental part of the geologic evolution of Mars. We examine the admittance signature, the ratio of gravity to topography data in the spectral domain, for four regions in the northern lowlands that are both well resolved in the gravity data and have well constrained lithospheric parameters. These regions also have topographic power spectra similar to many highlands regions. A Cartesian multitaper method is used to calculate admittance. We compare the observed admittance signatures to those predicted from models of lithospheric flexure. On the basis of these comparisons, we estimate the thickness of the Martian elastic lithosphere ( T e ) required to support the observed topographic load since the time of loading. We use both top and bottom loading models to derive values of elastic thickness and crustal thickness or apparent depth of compensation although all four regions are best fit by bottom loading models. We obtain best fit elastic thickness estimates between 10 and 25 km with an acceptable error range of 0 to 45 km. These low elastic thickness estimates are consistent with the formation in the Noachian, when heat flow was high. The consistency in T e estimates between the Noachian highlands and lowlands basement suggests that both regions of the crust formed at similar times. The paucity of crustal magnetization in the lowlands is thus more likely a result of demagnetization than formation following shut down of the dynamo.

Laufey Regio: A newly discovered topographic rise on Venus

Laufey Regio is a 0.5 km high, elongate topographic rise, measuring 1000 by 2000 km, located within northern Navka Planitia, Venus. It is dominated by two large volcanoes, Var and Atanua Montes, and numerous coronae with associated flow deposits. The area has been geologically mapped, showing that large‐scale edifice formation focused at Var and Atanua Montes and overlapped in time with the formation of smaller coronae. Several coronae and volcanoes have had complex and protracted histories with multiple episodes of volcanism and tectonism, supporting a nondirectional history for this region. The broad topography of the rise is surrounded by a concentric set of wrinkle ridges interpreted to have formed after the onset of centralized volcanism. Admittance studies indicate both bottom and top loading, but lithospheric parameters are not well constrained. Top‐loading models give a range of 0–48 km for elastic thickness (Te) and 35–115 km for crustal thickness. We interpret the Te range as most likely indicating isostatic compensation. Bottom‐loading models yield lower bounds of 30–75 km for Te and 32–74 km for the apparent depth of compensation (ADC). The combination of the large Te and low topography indicates that the plume is no longer active. Bottom loading and a small ADC may indicate that a layer of low‐density residuum, produced by pressure release melting in the now extinct plume, is partially supporting the topography. On the basis of its broad, regional topography, abundant volcanism, and gravity signature, we interpret Laufey to be a volcano‐dominated rise in a late stage of evolution.

Admittance survey of type 1 coronae on Venus

In this study, we analyze Magellan gravity and topography data for Type 1 coronae on Venus to estimate crustal thickness (Zc), elastic thickness (Te), and apparent depth of compensation (ZL). We examine the free‐air admittance for all 103 Type 1 coronae (defined as having greater than 50% complete fracture annuli) that are resolved in the gravity data. A spatio‐spectral method is used to calculate a localized admittance signature of each corona from a global admittance map. This method extracts spectral information from a region in space whose area is varied as a function of degree to make it large enough to yield robust results at every individual wavelength. Elastic flexure models with either bottom‐ or top‐loading compensation are used to fit the data. The estimated lithospheric flexural parameters span the range obtained for other topographic features on Venus, suggesting that the lithosphere on which coronae form is variable. We find no significant difference in lithospheric properties between Type 1 and 2 coronae. Fifty‐four percent of all coronae are consistent with local isostasy, which may indicate that they are no longer active. Very few coronae with dome or plateau morphologies have a bottom‐loading signature or the small Te and large ZL expected if a mantle plume were present. Approximately 71% have ZL estimates less than 70 km, indicating that compensation probably occurs within the crustal layer. We find no systematic relationship between Te or Zc and corona diameter, as would be expected for the spreading‐drop model of formation.

A gravity survey of Type 2 coronae on Venus

Coronae are roughly circular tectonic features believed to form as a result of small‐scale mantle upwellings. We examine the admittance signature for all the 32 Type 2 coronae (defined as having less than 50% complete fracture annuli) that are both well resolved in the gravity data and have fairly well constrained lithospheric parameters. We use top and bottom loading models to derive values of elastic thickness and crustal thickness or apparent depth of compensation. Both Cartesian and spatiospectral methods are used to calculate admittance. Overall we find reasonable agreement between the two methods. The shape of the filter used in the spatiospectral method [Simons et al., 1997] provides a means of isolating the signature of coronae that occur in close proximity to other geologic features. The narrow filters used in the Cartesian approach are useful for identifying transitions between different types of compensation, as well as for estimating error. We obtain a wide range of elastic thicknesses, from 25 to 80 km. Larger values are derived from bottom loading models, which have not been used in most prior studies of Venus. Fifteen of the coronae have elastic thickness values between 0 and 20 km and are probably isostatically compensated. Estimates of crustal and elastic thicknesses and apparent depth of compensation obtained for Type 2 coronae span the range obtained for Venus globally. Neither the thickness of the elastic lithosphere nor the crust appear to control whether Type 1 coronae, Type 2 coronae, or volcanoes form over small‐scale mantle upwellings.

Analysis and interpretation of high‐resolution topography and gravity of Ishtar Terra, Venus

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.

Yellowstone: A continental midplate (hot spot) swell

The Yellowstone hot spot has been identified mainly by its track of age‐progressive volcanics; many smaller scale tectonic features serve to hide the long‐wavelength hot spot‐related swell. By employing averaging and filtering techniques, we are able to identify a swell in both the gravity and topography and use them to constrain the apparent depth of compensation of the Yellowstone hot spot at 70±10 km. This value is comparable to the deepest compensation depths for swells on old oceanic lithosphere. A compensation depth within the mid‐ to lower lithosphere combined with the only 15 m.y. known duration of the hot spot suggests either dynamic thinning of the thermal plate or compensation by upwelling in a low‐viscosity asthenosphere, with some combination of the two explanations being consistent with seismic tomography results. Thus in many ways the Yellowstone hot spot appears quite similar to the oceanic analogues.

Gravitational spreading of high terrain in Ishtar Terra, Venus

Magellan altimetry measurements indicate that the mountain belts and plateau margins of Ishtar Terra have topographic slopes in the range 2–30°. Magellan radar images reveal that numerous sets of narrow, closely spaced troughs and lineations, which we interpret as graben and normal faults, are located in many of these regions of high slope. The orientation of many of these graben sets perpendicular to the downslope direction suggests that they formed as a result of gravitational spreading. In several of the mountain belts, the extensional structures are parallel to the apparent direction of shortening, consistent with the interpretation that gravitational spreading occurred while mountain building was still active. To explore the implications of this spreading for the tectonic evolution of Ishtar Terra, we model the process by means of a finite element algorithm for viscoelastic deformation in a vertical section of the crust at the margin of a plateau or broad mountain range. Flow in the crust is assumed to be governed by a nonlinear, depth‐dependent rheology. We predict brittle failure and relaxation of topographic relief as functions of time, for ranges of crustal thickness (10–30 km) and thermal gradient (5–25 K/km) and for observed ranges in topographic elevation (1–6 km) and slope (1–30°). This parameter range predicts a large spread in the time scales for initial failure and significant relaxation of relief. For a crustal thickness greater than 10 km, a thermal gradient of 15 K/km or more, and average values of relief (3 km) and slope (3°), the topography relaxes to 25% of its original height in less than 10 m.y. Although initial failure, in the form of normal faulting on the highlands and margin and occasional shallow thrusting in the lowlands, is predicted to occur much earlier, values of horizontal surface strain that are likely to be observable (∼1%) do not accumulate until significant relaxation of relief begins. Given the predicted rate of topographic relaxation, either the crust of Ishtar Terra must be anomalous in some way (either much stronger than predicted by standard flow laws or very thin or cold) or the topographic relief and high slopes have been actively built and maintained until times significantly younger than the average crater retention age for Venus of 500 Ma. The large apparent depth of compensation, the abundance of volcanism, and the uncertainty in the local age favor the view that mountain building in Ishtar Terra has occurred until times at least as recent as 10 Ma.

Geoid and topography associated with sublithospheric convection: negligible contribution from deep currents

The sources of geoid and topography anomalies in a convecting upper mantle with realistic temperature- and pressure-dependent viscosity are studied. The results differ from those obtained in previous studies with layered, depth-dependent viscosity. For a Newtonian viscosity, the topography and the geoid anomalies coming from below the low-viscosity zone (i.e., deeper than 250 km) amount to 30 m and 10 cm, respectively, while they are reduced to 10 m and 10 cm for a non-Newtonian viscosity. It represents at most 6% of the complete signal and affects very little the geoid over topography ratio. The weakness of the contribution from the lower part of the cell is due to both small kernels and small lateral temperature variations at depth. Yet, a linear regression of the complete geoid signal versus topography yields an apparent compensation depth shallower than the base of the lithosphere. The damping of the vertical stress through a lithosphere with a depth-dependent viscosity implies a departure from isostasy and is the cause of the shallow apparent compensation depths found in our model.

Depth and geoid anomalies over oceanic hotspot swells: A global survey

The broad depth and geoid anomalies associated with 23 hotspot swells in oceanic areas have been analyzed. Maximum height and geographical extent of the topographic swell, and of the geoid anomaly as well, have been measured for each hotspot. The results indicate a clear increase of the topographic swell height with age of the underlying lithosphere, from values in the range 300–500 m at young ages to values in the range 1500–2000 m at ages larger than 100 Ma. The geoid anomaly amplitude also increases with plate age from nearly zero close to mid‐ocean ridges, to 6–8 m over old plates. On the other hand, the geographical extent of the swell does not show any clear relationship with plate age. The mean lateral extent of swells range from 1000 to 1500 km. Swells located close to spreading ridges show a significant non zero depth anomaly but are associated with negligeable geoid signal. These results complete those of a previous study where the apparent compensation depth of oceanic hots pot swells was showed to increase linearly with the square root of plate age and coincide roughly with the base of the thermal lithosphere. This trend may either be interpreted in terms of lithospheric thinning or dynamical support. Besides both seem necessary to explain the observed bathymetry, in proportion evolving with aging of the lithosphere.

Western Ishtar Terra and Lakshmi Planum, Venus: Models of formation and evolotion

Regional geologic mapping and gravity data reveal a variety of characteristics that must be accounted for in models for the formation and evolution of Western Ishtar Terra and Lakshmi Planum, including: 1) high elevation, 2) plateau‐shaped profile, 3) abnormally steep bounding slopes, 4) foredeeps, 5) polygonal outline, 6) adjacent orogenic belts, 7) volcanic plains, 8) plains emplaced synchronously with orogenic belts, 9) paterae, 10) variable topography of Lakshmi, 11) tessera‐like material underlying Lakshmi, and 12) a large apparent depth of compensation. A tessera/peripheral deformation model, in which a preexisting block of tessera is the locus of convergence of adjacent thinner crust and lithosphere, underthrusting, mountain building, subsurface melting, and plateau uplift, is interpreted to account for most of the characteristics. The apparent depth of compensation is not simply explained by this model and appears to require a second, deeper mantle anomaly component, such as broad mantle upwelling or a hot spot.

Variation of the apparent compensation depth of hotspot swells with age of plate

Most oceanic hotspot swells are associated with anomalously shallow seafloor and broad geoid anomalies. These depth and geoid anomalies are generally positively correlated and linearly related. The linear relationship can be used to infer an apparent depth of isostatic compensation of the swell. We have analysed geoid and depth anomalies over 23 oceanic hotspot swells (almost the majority of oceanic hotspots) and deduced the apparent depth of compensations of these features. The data indicate a linear increase of the compensation depth with the square root of seafloor age t, on the order of 7 km/(m.y.) 1/2. This trend is comparable to that predicted by conductive cooling models for the deepening of the isotherms inside the oceanic lithosphere.

The effect of a shallow low viscosity zone on the apparent compensation of mid-plate swells

A simple model for mid-plate swells is that of convection in a fluid which has a low viscosity layer lying between a rigid bed and a constant viscosity region. Finite element calculations have been used to determine the effects of the viscosity contrast, the layer thickness and the Rayleigh number on the flow and on the perceived compensation mechanism for the resulting topographic swell. As the viscosity decreases in the low viscosity zone, the effective local Rayleigh number for the top boundary layer of the convecting cell increases. Also, because the lower viscosity facilitates greater velocities in the low viscosity zone, the low viscosity layer produces proportionally greater horizontal flow near the conducting lid, causing the base of the conducting lid to appear like a free boundary. The change in the local Rayleigh number and in the effective boundary condition both cause the top boundary layer to thin. Through a Green's function analysis, we have found that the low viscosity zone damps the response of the surface topography to the temperature anomalies at depth, whereas it causes the gravity and geoid response functions to change sign at depth counteracting the positive contributions from the shallower temperature variations. By increasing the viscosity contrast, the conbined effects of the thinning of the boundary layer and the behaviour of the response functions allow the apparent depth of compensation to become arbitrarily small. Therefore, shallow depths of compensation cannot be used to argue against dynamic support of mid-plate swells. Furthermore, we compared the distribution of the effective compensating densities, which is used to obtain the geoid, to that of Pratt compensation, which is often used to calculate the depth of compensation from geoid and topography data for mid-plate swells. For all of our calculations including those with no low viscosity layer, the effective gravitational mass distribution is more complex than assumed in simple Pratt models, so that the Pratt models are not an appropriate gauge of the compensation mechanism.

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface‐density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.