Testing the effects of basic numerical implementations of water migration on models of subduction dynamics

Subduction of oceanic lithosphere brings water into the Earth's upper mantle. Previous numerical studies have shown how slab dehydration and mantle hydration can impact the dynamics of a subduction system by allowing a more vigorous mantle flow and promoting localisation of deformation in the lithosphere and mantle. The depths at which dehydration reactions occur in the hydrated portions of the slab are well constrained in these models by thermodynamic calculations. However, computational models use different numerical schemes to simulate the migration of free water. We aim to show the influence of the numerical scheme of free water migration on the dynamics of the upper mantle and more specifically the mantle wedge. We investigate the following three simple migration schemes with a finite-element model: (1) element-wise vertical migration of free water, occurring independent of the flow of the solid phase; (2) an imposed vertical free water velocity; and (3) a Darcy velocity, where the free water velocity is a function of the pressure gradient caused by the difference in density between water and the surrounding rocks. In addition, the flow of the solid material field also moves the free water in the imposed vertical velocity and Darcy schemes. We first test the influence of the water migration scheme using a simple model that simulates the sinking of a cold, hydrated cylinder into a dry, warm mantle. We find that the free water migration scheme has only a limited impact on the water distribution after 1 Myr in these models. We next investigate slab dehydration and mantle hydration with a thermomechanical subduction model that includes brittle behaviour and viscous water-dependent creep flow laws. Our models demonstrate that the bound water distribution is not greatly influenced by the water migration scheme whereas the free water distribution is. We find that a bound water-dependent creep flow law results in a broader area of hydration in the mantle wedge, which feeds back to the dynamics of the system by the associated weakening. This finding underlines the importance of using dynamic time evolution models to investigate the effects of (de)hydration. We also show that hydrated material can be transported down to the base of the upper mantle at 670 km. Although (de)hydration processes influence subduction dynamics, we find that the exact numerical implementation of free water migration is not important in the basic schemes we investigated. A simple implementation of water migration could be sufficient for a first-order impression of the effects of water for studies that focus on large-scale features of subduction dynamics

Analogue modelling of basin inversion: a review and future perspectives

Basin inversion involves the reversal of subsidence in a basin due to compressional tectonic forces, leading to uplift of the basin's sedimentary infill. Detailed knowledge of basin inversion is of great importance for scientific, societal, and economic reasons, spurring continued research efforts to better understand the processes involved. Analogue tectonic modelling forms a key part of these efforts, and analogue modellers have conducted numerous studies of basin inversion. In this review paper we recap the advances in our knowledge of basin inversion processes acquired through analogue modelling studies, providing an up-to-date summary of the state of analogue modelling of basin inversion. We describe the different definitions of basin inversion that are being applied by researchers, why basin inversion has been historically an important research topic and what the general mechanics involved in basin inversion are. We subsequently treat the wide range of different experimental approaches used for basin inversion modelling, with attention to the various materials, set-ups, and techniques used for model monitoring and analysing the model results. Our new systematic overviews of generalized model results reveal the diversity of these results, which depend greatly on the chosen set-up, model layering and (oblique) kinematics of inversion, and 3D along-strike structural and kinematic variations in the system. We show how analogue modelling results are in good agreement with numerical models, and how these results help researchers to better understand natural examples of basin inversion. In addition to reviewing the past efforts in the field of analogue modelling, we also shed light on future modelling challenges and identify a number of opportunities for follow-up research. These include the testing of force boundary conditions, adding geological processes such as sedimentation, transport, and erosion; applying state-of-the-art modelling and quantification techniques; and establishing best modelling practices. We also suggest expanding the scope of basin inversion modelling beyond the traditional upper crustal “North Sea style” of inversion, which may contribute to the ongoing search for clean energy resources. It follows that basin inversion modelling can bring valuable new insights, providing a great incentive to continue our efforts in this field. We therefore hope that this review paper will form an inspiration for future analogue modelling studies of basin inversion.</p

A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the ‘sticky air' method

Calculating surface topography in geodynamic models is a common numerical problem. Besides other approaches, the so-called ‘sticky air' approach has gained interest as a free-surface proxy at the top boundary. The often used free slip condition is thereby vertically extended by introducing a low density, low viscosity fluid layer. This allows the air/crust interface to behave in a similar manner to a true free surface. We present here a theoretical analysis that provides the physical conditions under which the sticky air approach is a valid approximation of a true free surface. Two cases are evaluated that characterize the evolution of topography on different timescales: (1) isostatic relaxation of a cosine perturbation and (2) topography changes above a rising plume. We quantitatively compare topographies calculated by six different numerical codes (using finite difference and finite element techniques) using three different topography calculation methods: (i) direct calculation of topography from normal stress, (ii) body-fitting methods allowing for meshing the topography and (iii) Lagrangian tracking of the topography on an Eulerian grid. It is found that the sticky air approach works well as long as the term (ηst/ηch)/(hst/L)3 is sufficiently small, where ηst and hst are the viscosity and thickness of the sticky air layer, and ηch and L are the characteristic viscosity and length scale of the model, respectively. Spurious lateral fluctuations of topography, as observed in some marker-based sticky air approaches, may effectively be damped by an anisotropic distribution of markers with a higher number of markers per element in the vertical than in the horizontal directio

How ‘demos’ met ‘cracy’: debt, inequality, money

The recurrence of ever more destructive economic crises and patterns of pervasive indebtedness and inequality threaten the social fabric of our societies. Our main responses to these trends have been partial, focusing on symptoms rather than causes, often exacerbating rather than improving the underlying socio-economic dynamics. To reflect on these conditions and on ‘what needs to be done’ this article turns to a similar socio-economic malaise faced by the city-state of Athens in the 6th century BC. Most historical studies dealing with this crisis focus on the comprehensive debt relief policy (seisachteia) implemented by Solon. We argue that this debt relief, although necessary, was the least important of Solon’s reforms. Solon read the problem of debt as a problem of money so he went on to reform the monetary and exchange system. However, he did not think that these reforms alone could restore socioeconomic sustainability. For this, a redefinition of what was counted as valuable economic activity and as income had also to take place. Moreover, for all these to work, citizens had to be involved more in the commons. Far from only achieving socioeconomic sustainability, these reforms gave rise gradually to the demos that we meet in the golden age of Democracy. Such a broad historical horizon may help us grasp better the problems, stakes and challenges of our times

New Economy, Old Central Banks?

Proponents of the so-called New Economy claim that it entails a structural change of the economy. Such a change, in turn, would require the central bank to rethink its monetary policy to the extent that traditional relationships between inf1ation and economic growth are no longer valid. But such a rethinking presupposes that prospective advances in information technology and other factors associated with the new economy do not threaten the capacity of central banks to stabilise the general level of prices. It is the aim of this paper to shed some light on the latter, by analysing the monetary transmission mechanism in a 'new economy' environment. We argue that, although the form of central bank instruments and current methods for implementing monetary policy may change, the goals that the policy makers try to achieve by employing these instruments remain valid, and achievable