Supplementary material relevant to the manuscript: “Fast and spatially heterogeneous cooling rates at amphibolite-facies conditions reveal the significance of local heat sources: a case study from the Lepontine Alps (Switzerland)” by Tagliaferri, A., Moulas, E., Schmalholz, S. M., & Schenker, F. L. Submitted to American Journal of Science.
Computer-based numerical solutions of geomechanical problems are important to understand the processes forming rock structures as well as to quantify the associated pressure, stresses and strain rates. However, the development of such computer programs and the underlying mathematical methods are commonly not taught in a standard structural geology curriculum. Here, we present a simple computer program to calculate the stress, pressure, velocity and strain rate fields for two-dimensional (2D) viscous inclusion-matrix systems under pure shear and simple shear. The main aim of our contribution is to explain this computer program in a simple and transparent way, so that it can be used for introductory courses on geomechanical numerical modelling in structural geology. We present the governing equations of 2D viscous deformation and program the equations in the same order and style, so that the equations are still recognizable in the computer program. The computer program can treat stiff and weak inclusions of any shape and considers both linear and power-law viscous flow laws. We present numerical calculations for various inclusion-matrix scenarios. The program is written with the software MATLAB, is provided as supplementary material, and can also be run with the freely available software GNU Octave.
Abstract We investigate lithosphere necking using two‐dimensional thermo‐mechanical numerical simulations without strain softening or weakening mechanisms. The models have an initial small sinusoidal perturbation of the Moho depth, whose wavelength corresponds to the model width. Applied boundary conditions (constant extension velocity or bulk extension rate) and initial model width significantly impact the necking dynamics. For constant bulk extension rates, wider models generate more intense necking with locally higher strain rates, whereas for constant velocity extension, models evolution is similar independent on their initial width. However, the width of the final necking zones ranges consistently between 45 and 105 km, independent on the type of applied boundary conditions and the initial Moho wavelength. The modeled widths are similar to along dip necking zones widths of natural rifted margins that formed during a single, unidirectional, and relatively continuous extensional event (e.g., Iberia‐Newfoundland margins, Porcupine Basin, Gulf of Aden). When the crust is mechanically decoupled from the mantle by a weak ductile lower crust, models exhibit three characteristic stages: (1) distributed thinning and extension associated with progressive subsidence; (2) upper mantle necking compensated by flow of the weak lower crust, which hampers both crustal thinning and subsidence at the rift center; and (3) crustal necking associated with fast subsidence after the mantle has necked. Decoupled models display regions of relatively thick crust on one or both sides of the rift center, comparable to the Galicia, Rockall, Hatton, and Porcupine Banks along the North Atlantic rifted margins.
Abstract The Brossasco‐Isasca subunit ( BIU ) of the Dora Maira massif is currently the only known continental crustal ultrahigh‐pressure ( UHP ) unit in the Western Alps. The peak pressure/temperature conditions are 3.5–4.5 GPa/~730 °C; exhumation from ~3.5 GP a to ~1 GPa occurred within 2.2 ± 1.8 Ma, but the exhumation mechanism is incompletely understood. We present a conceptual model for the buoyancy‐driven exhumation of the BIU inside a low‐viscosity, dense mantle shear zone weakened by increased strain rates due to simultaneous strike‐slip and subduction (oblique‐slip) of the European plate. Two‐dimensional thermo‐mechanical models simulate such a buoyant uprise of an ellipse inside an inclined layer. Simulations (i) show the feasibility of the conceptual model, (ii) fit the pressure/temperature/time record and (iii) constrain effective viscosities. The model is compatible with the (i) small volume of continental crustal UHP rock in the Western Alps, (ii) minor erosion during exhumation and (iii) strike‐slip deformation during the exhumation period.
A method is presented to detect subsurface seismic tremor sources by analyzing surface data. Spectral attributes of the recorded seismic wave‐field at low frequencies are used to map the surface projection of the sources. We illustrate the concept on a synthetic data‐set generated with a homogenous forward model and show how spectral attributes can be used for detecting locations of seismic tremor sources. In a second part we apply the method to an example of hydrocarbon reservoir related tremors. The results show that increased complexity of the subsurface seismic properties and/or the presence of several tremor sources can strongly complicate the interpretation. In addition, the presence of dominant surface noise may mask the signals emitted by the subsurface tremor sources and make it impossible to detect them at the surface without additional processing. F‐K filtering is successfully applied to noise‐contaminated data and retrieves masked anomalies. Care has to be taken for using a proper data‐set and proper processing parameters in order to avoid artifacts introduced by the F‐K filter. Although we discuss an application for possible hydrocarbon reservoir related tremors, we believe that the methods can also be applied to any other type of seismic tremor signal.
Abstract. The shortening and extension of mechanically layered ductile rock generates folds and pinch-and-swell structures (also referred to as necks or continuous boudins), which result from mechanical instabilities termed folding and necking, respectively. Folding and necking are the preferred deformation modes in layered rock because the corresponding mechanical work involved is less than that associated with a homogeneous deformation. The effective viscosity of a layered rock decreases during folding and necking, even when all material parameters remain constant. This mechanical softening due to viscosity decrease is solely the result of fold and pinch-and-swell structure development and is hence termed structural softening (or geometric weakening). Folding and necking occur over the whole range of geological scales, from microscopic up to the size of lithospheric plates. Lithospheric folding and necking are evidence for significant deformation of continental plates, which contradicts the rigid-plate paradigm of plate tectonics. We review here some theoretical and experimental results on folding and necking, including the lithospheric scale, together with a short historical overview of research on folding and necking. We focus on theoretical studies and analytical solutions that provide the best insight into the fundamental parameters controlling folding and necking, although they invariably involve simplifications. To first order, the two essential parameters to quantify folding and necking are the dominant wavelength and the corresponding maximal amplification rate. This review also includes a short overview of experimental studies, a discussion of recent developments involving mainly numerical models, a presentation of some practical applications of theoretical results, and a summary of similarities and differences between folding and necking.
Abstract A two‐dimensional numerical simulation of lithospheric shortening shows the formation of a stable crustal‐scale shear zone due to viscous heating. The shear zone thickness is controlled by thermomechanical coupling that is resolved numerically inside the shear zone. Away from the shear zone, lithospheric deformation is dominated by pure shear, and tectonic overpressure (i.e., pressure larger than the lithostatic pressure) is proportional to the deviatoric stress. Inside the shear zone, deformation is dominated by simple shear, and the deviatoric stress decreases due to thermal weakening of the viscosity. To maintain a constant horizontal total stress across the weak shear zone (i.e., horizontal force balance), the pressure in the shear zone increases to compensate the decrease of the deviatoric stress. Tectonic overpressure in the weak shear zone can be significantly larger than the deviatoric stress at the same location. Implications for the geodynamic history of tectonic nappes including high‐pressure/ultrahigh‐pressure rocks are discussed.
