Correction to: a thin viscous sheet model for continental deformation

Summary. The governing equation derived by England & M c Kenzie for the deformation of a thin viscous shell contains an error. We give the correct derivation here and correct those figures where the change makes a visible difference. The correct results differ quantitatively from those of England & M c Kenzie but their conclusions are not affected.     

State of stress within a thin elastic wedge: a model of internal deformation of the continental plate at arc—arc junctions

Summary. Anomalous stress distributions near arc—arc junctions have been found in several parts of the world. As a simple two-dimensional model, a thin elastic wedge is introduced to model the continental side of the arc—arc junction, and the stress distribution within it is calculated to interpret those anomalies. Uniform normal and/or shear stress boundary conditions are given separately to each edge to approximate the effect of the two neighbouring converging plate boundaries; Stress components are obtained by numerical integration. Among the various results, the following features are predominant and seem to be actually taking place at arc—arc junctions.
(1) The anomaly in stress pattern within the wedge is basically due to the difference in stress conditions between the two boundaries.
(2) A large stress concentration takes place when symmetrical shear stresses are applied to the two edges.     

Thickening model of the continental lithosphere

Summary. The thickening plate theory proposed by Yoshii and Parker & Oldenburg for the oceanic lithosphere is extended to include the continental lithosphere. The theory is based on the assumption that the lithosphere—asthenosphere boundary is a solidus and that as a result solidification of the top of the asthenosphere is occurring. Observational data imply that the relationship between the plate thickness and basement age for the North American continent is y = 1.7 √ t + (50 ± 10), where y (km) is the plate thickness and t (Myr) is the basement age.
The theory is tested against changes with basement age of the observed surface heat-flow and seismic estimate of plate thickness. The following conclusions are inferred:
(1) The changes both of the observed heat flow and plate thickness with basement age are explained by this theory.
(2) The surface erosion and vertical distribution of radiogenic heat sources are important factors in controlling the thickening process of the continental lithosphere.
(3) The equality of the average surface heat-flow over the oceans and over the continents is a consequence of a faster release of latent heat at the lithosphere—asthenosphere boundary under the oceans, instead of a higher heat production in the continental crust.     

Generalized thin sheet analysis in magnetotellurics: an extension of Price's analysis

Summary. Price's thin sheet analysis for electromagnetic fields has been extended in order to model the effects of crustal resistivity and conductivity variations on magnetotelluric fields. These extensions allow for a general layered medium below the crust and also account for the vertical resistance of the crust as well as its horizontal conductance. An important parameter emerges from the analysis which determines the distance it takes for the crustal current levels to readjust to changes in the crustal conductance. This adjustment distance is given by the square root of the conductivity thickness product multiplied by the resistivity thickness product. Approximate analytical solutions were developed for two-dimensional geometries in order to demonstrate these effects as well as the modifications produced by finite source wavelengths.     

A confirmed earthquake in continental Antarctica

Summary. An earthquake of magnitude ( M _b) 4.5 has been located by the International Seismological Centre, near 81°S, 37°E in the continental platform of east Antarctica, about 1200 km from the coast of Dronning Maud Land, and 500 km from the Pole of Inaccessibility. The event was found by the Centre's 'search' procedure, which is undertaken with a deliberate delay of about two years. It occurred on 1982 November 4, and its position is well determined from five stations in Antarctica, and four farther afield. This is the first earthquake definitely located in the interior of the Antarctic continent, although there have been some earlier less well established claims, and other earthquakes have occurred near the coast, or associated with areas of volcanism or ice movement.     

Interplay between subduction and continental convergence: a three-dimensional dynamic model for the Central Mediterranean

The Mediterranean region is attracting considerable attention due to the complexities of its tectonic setting, which is considered, worldwide, a unique natural laboratory for studying the occurrence of extensional tectonics in a general context of continental convergence. The Tyrrhenian–Apennine system is controlled by the west-dipping subduction of the Adria-Ionian lithosphere and by the near north-south convergence between the African and Eurasian plates. We provide the first 3-D dynamic model of the Central Mediterranean that quantifies the effects of subduction and convergence on surface deformation, in simplified geometry. The axis of the model extends from Sicily to the Alps along the subduction hinge line. A convergence rate of 1 cm yr^-1parallel to the subduction hinge has been applied to the Tyrrhenian block, in agreement with global plate-motion models. Density contrasts within the slab cause the gravitational sinking and roll-back of the slab in the southern Tyrrhenian domain. Modelling results show a gradual decrease of hinge retreat from south to north, with values ranging between 8 and 2 mm yr^-1, indicating that the arculate geometry of the hinge line along the Italian peninsula is ultimately controlled by the interplay between subduction and convergence. The pattern of vertical velocity along directions perpendicular to the hinge, with subsidence in the foredeeps and uplift at the eastern border of the Tyrrhenian domain, is maintained along the whole Italian peninsula, with higher values in the southern areas.     

Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth

Summary. A new method for solving problems in three-dimensional electromagnetic induction in which the Earth is represented by a uniformly conducting half-space overlain by a surface layer of variable conductance is presented. Unlike previous treatments of this type of problem the method does not require the fields to be separated into their normal and anomalous parts, nor is it necessary to assume that the anomalous region is surrounded by a uniform structure; the model may approach either an E- or a B -polarization configuration at infinity. The solution is expressed as a vector integral equation in the horizontal electric field at the surface. The kernel of the integral is a Green's tensor which is expressed in terms of elementary functions that are independent of the conductance. The method is applied to an illustrative model representing an island near a bent coastline which extends to infinity in perpendicular directions.     

Quantifying the relationship between structural deformation and the morphology of submarine channels on the Niger Delta continental slope

The processes and deposits of deep‐water submarine channels are known to be influenced by a wide variety of controlling factors, both allocyclic and autocyclic. However, unlike their fluvial counterparts whose dynamics are well‐studied, the factors that control the long‐term behaviour of submarine channels, particularly on slopes undergoing active deformation, remain poorly understood. We combine seismic techniques with concepts from landscape dynamics to investigate quantitatively how the growth of gravitational‐collapse structures at or near the seabed in the Niger Delta have influenced the morphology of submarine channels along their length from the shelf edge to their deep‐water counterpart. From a three dimensional (3D), time‐migrated seismic‐reflection volume, which extends over 120 km from the shelf edge to the base of slope, we mapped the present‐day geomorphic expression of two submarine channels and active structures at the seabed, and created a Digital Elevation Model (DEM). A second geomorphic surface and DEM raster—interpreted to closer approximate the most recent active channel geometries—were created through removing the thickness of hemipelagic drape across the study area. The DEM rasters were used to extract the longitudinal profiles of channel systems with seabed expression, and we evaluate the evolution of channel widths, depths and slopes at fixed intervals downslope as the channels interact with growing structures. Results show that the channel long profiles have a relatively linear form with localized steepening associated with seabed structures. We demonstrate that channel morphologies and their constituent architectural elements are sensitive to active seafloor deformation, and we use the geomorphic data to infer a likely distribution of bed shear stresses and flow velocities from the shelf edge to deep water. Our results give new insights into the erosional dynamics of submarine channels, allow us to quantify the extent to which submarine channels can keep pace with growing structures, and help us to constrain the delivery and distribution of sediment to deep‐water settings.     

Two-dimensional induction in a thin sheet of variable integrated conductivity at the surface of a uniformly conducting earth

Summary. The forward solution of the general two-dimensional problem of induction in a model earth comprising a uniformly conducting half-space covered by a thin sheet of variable integrated conductivity is obtained. Unlike some previous treatments of similar problems, the method presented here does not require the field to be separated into its normal and anomalous parts. Both the E - and B -polarization modes of induction are considered and in each case the solution is expressed in terms of the horizontal component of the electric field satisfying, on the surface of the conductor, a singular integral equation whose kernel is a well-known analytic function. A recently published solution of the coast effect is included as a special case. The numerical procedure for solving the integral equations is described and some illustrative calculations are presented.