Mantle convection under simulated plates: effects of heating modes and ridge and trench migration, and implications for the core—mantle boundary, bathymetry, the geoid and Benioff zones

Summary. Numerical convection models are presented in which plates are simulated by imposing piecewise constant horizontal velocities on the upper boundary. A 4 × 1 box of constant viscosity fluid and two-dimensional (2-D) flow is assumed. Four heating modes are compared: the four combinations of internal or bottom heating and prescribed bottom temperature or heat flux. The case with internal heating and an isothermal base is relevant to lower mantle or whole mantle convection, and it yields a lower thermal boundary layer which is laterally variable and can be locally reversed, corresponding to heat flowing back into the core locally. When scaled to the whole mantle, the surface deflections and gravity and geoid perturbations calculated from the models are comparable to those observed at the Earth's surface. For models with migrating ridges and trenches, the flow structure lags well behind the changing surface 'plate'configurations. This may help to explain the poor correlation between the main geoid features and plate boundaries. Trench migration substantially affects the dip of the cool descending fluid because of induced horizontal shear in the vicinity of the trench. Such shear is small for whole mantle convection, but is large for upper mantle convection, and would probably result in the Tonga Benioff zone dipping to the SE, opposite to the observed dip, for the case of upper mantle convection.     

Localization of gravity and topography: constraints on the tectonics and mantle dynamics of Venus

We develop a method for spatio-spectral localization of harmonic data on a sphere and use it to interpret recent high-resolution global estimates of the gravity and topography of Venus in the context of geodynamical models. Our approach applies equally to the simple spatial windowing of harmonic data and to variable-length-scale analyses, which are analogous to a wavelet transform in the Cartesian domain. Using the variable-length-scale approach, we calculate the localized RMS amplitudes of gravity and topography, as well as the spectral admittance between the two fields, as functions of position and wavelength. The observed admittances over 10 per cent of the surface of Venus (highland plateaus and tessera regions) are consistent with isostatic compensation of topography by variations in crustal thickness, while admittances over the remaining 90 per cent of the surface (rises, plains and lowlands) indicate that long-wavelength topography is dominantly the result of vertical convective tractions at the base of the lithosphere. The global average crustal thickness is less than 30 km, but can reach values as large as 40 km beneath tesserae and highland plateaus. We also note that an Earth-like radial viscosity structure cannot be rejected by the gravity and topography data and that, without a mechanical model of the lithosphere, admittance values cannot constrain the thickness of the thermal boundary layer of Venus. Modelling the lithosphere as a thin elastic plate indicates that at the time of formation of relief in highland plateaus and tesserae, the effective elastic plate thickness, T_e , was less than 20 km. Estimates of T_e at highland rises are consistently less than 30 km. Our inability to find regions with T_e > 30 km is inconsistent with predictions made by a class of catastrophic resurfacing models.     

珠穆朗玛峰重力值的推估──兼论推估方法的基本原理

在山区 ,尤其是在有全球第三极之称的喜马拉雅山区 ,当相邻点间距不大时 ,如何利用这些点上的重力与地形 (高程 )数据推估待求点的重力值 ,这对难以攀登和不能用仪器观测的山峰很有意义。研究指出 ,在地形负荷的波长很短时 ,具有一定强度的地壳足以能够支撑这种负荷 ,因此 ,不能用Airy Heiskanen和Pratt Hayford局部补偿模型作重力推估 ;由于空间异常主要受地形起伏制约 ,因此借助于邻近重力点的地形 (高程 )作推估会得到满意的结果。基于这一思路 ,我们采用了 4种有关公式 ,有效地推估了第三极之巅珠穆朗玛峰顶上的重力值 ,该值为(976 970± 7)× 1 0 - 5m·s- 2 。这一结果为精确推求珠峰大地水准面和正高提供了必要的数据 ,若用均衡的方法来推估 ,则可能相差近 1 0 0× 1 0 - 5m·s- 2 。     

The reduction of aliasing in gravity anomalies and geoid heights using digital terrain data

Observations of gravity can be aliased by virtue of the logistics involved in collecting these data in the field. For instance, gravity measurements are often made in more accessible lowland areas where there are roads and tracks, thus omitting areas of higher relief in between. The gravimetric determination of the geoid requires mean terrain-corrected free-air anomalies; however, anomalies based only on the observations in lowland regions are not necessarily representative of the true mean value over the topography. A five-stage approach is taken that uses a digital elevation model, which provides a more accurate representation of the topography than the gravity observation elevations, to reduce the unrepresentative sampling in the gravity observations. When using this approach with the Australian digital elevation model, the terrain-corrected free-air anomalies generated from the Australian gravity data base change by between 77.075 and −84.335 mgal (−0.193 mgal mean and 2.687 mgal standard deviation). Subsequent gravimetric geoid computations are used to illustrate the effect of aliasing in the Australian gravity data upon the geoid. The difference between 'aliased' and 'non-aliased' gravimetric geoid solutions varies by between 0.732 and −1.816 m (−0.058 m mean and 0.122 m standard deviation). Based on these conceptual arguments and numerical results, it is recommended that supplementary digital elevation information be included during the estimation of mean gravity anomalies prior to the computation of a gravimetric geoid model.     

Crustal structure of the Newfoundland rifted continental margin from constrained 3-D gravity inversion

The rifting history of the Atlantic continental margin of Newfoundland is very complex and so far has been investigated at the crustal scale primarily with the use of 2-D seismic surveys. While informative, the results generated from these surveys cannot easily be interpreted in a regional sense due to their sparse sampling of the margin. A 3-D gravity inversion of the free air data over the Newfoundland margin allows us to generate a 3-D density anomaly model that can be compared with the seismic results and used to gain insight into regions lacking seismic coverage. Results of the gravity inversion show good correspondence with Moho depths from seismic results. A shallowing of the Moho to 12 km depth is resolved on the shelf at the northern edge of the Grand Banks, in a region poorly sampled by other methods. Comparisons between sediment thickness and crustal thickness show deviations from local isostatic compensation in locations which correlate with faults and rifting trends. Such insights must act as constraints for future palaeoreconstructions of North Atlantic rifting.