An active fold‐and‐thrust belt is analogous to a wedge of soil or snow that forms in front of a moving bulldozer; such wedges exhibit a critical taper and a regional state of stress that is everywhere on the verge of Coulomb failure. The width of such a critically tapered fold‐and‐thrust belt does not depend on its brittle strength or frictional properties but rather on the accretionary influx rate of fresh material at its toe and on the rate of erosion; a steady state fold‐and‐thrust belt is one in which the accretionary influx is balanced by the erosive efflux. Rocks are accreted at the toe and then horizontally shortened as they are transported toward the rear; those that enter lower in the accreted section are more deeply buried before being uplifted by erosion. Mass balance and isotropy constrain the kinematics of this large‐scale deformation, enabling us to infer the trajectories, residence times, and stress‐strain histories of rocks incorporated into eroding fold‐and‐thrust belts. A typical rock resides in the steady state Taiwan wedge for 2–3 m.y. before it is uplifted and eroded; during its motion through the wedge, it experiences strain rates in the range 10−13 to 10−14 s−1. The mechanical energy budget of brittle frictional mountain building is described by the equation , where is the rate of work performed on the base and front of the fold‐and‐thrust belt by the subducting plate, is the rate at which energy is dissipated against friction on the decollement fault, is the rate at which energy is dissipated by internal frictional processes within the deforming brittle wedge, and is the rate of work performed against gravitational body forces in a reference frame attached to the overriding plate. The total mechanical power being supplied by the subducting Eurasian plate to the active fold‐and‐thrust belt in Taiwan is slightly over 3 GW. Approximately 60% of this work of steady state mountain building is being dissipated against friction on the decollement fault, and about another 25% is being dissipated against internal friction; this leaves only 15% or roughly half a gigawatt available to do useful work against gravity. In general, fold‐and‐thrust belts with moderate pore fluid pressures are dominated by work done against friction on the decollement fault; however, those with nearly lithostatic pore fluid pressures may be dominated by work done against gravity. Internal frictional dissipation is always less than basal frictional dissipation, as it is in Taiwan. An alternative and equivalent description of the mechanical energy balance of a steady state fold‐and‐thrust belt is provided by the equation . In this version the quantity on the left, , is the rate at which work is performed on the back of the wedge by the overriding plate and is the rate of work performed against gravity in a reference frame attached to the subducting plate. The latter quantity is always positive for any critically tapered fold‐and‐thrust belt whose decollement fault dips toward its rear, in contradiction to the cen...
This paper describes a simple thermal model of an actively deforming critically tapered fold-and-thrust belt. The model determines the steady state temperature distribution and heat flow, as well as the pressuretemperature-time histories of rocks that outcrop at the surface. The main parameters controlling the thermal structure are the accretion and erosion rates, the undisturbed geothermal gradient at the toe, and the amount of frictional heating. Both shear heating on the decollement fault and internal strain heating within the deforming brittle wedge are incorporated in a mechanically consistent manner, and they dominate the effect of radiogenic heating, except in fold-and-thrust belts with significantly overpressured pore fluids. The mean stresses, temperatures, and surface heat flow all increase with an increase in the basal and internal coefficients of friction, and this dependence is used to constrain the level of friction on the decollement fault beneath the steady state fold-and-thrust belt in Taiwan. Rocks outcropping in the core of the Central Mountain Range of Taiwan experience maximum theoretical temperatures in excess of 400 ø C and maximum mean pressures in excess of 500 MPa if the coefficient of basal friction is gt, = 0.5. Qualitatively, these conditions are in good agreement with the observed high greenschist facies metamorphism. The theoretical surface heat flow, which increases from 95 mW/m 2 at the front of the fold-and-thrust belt to 240 mW/m 2 at the rear, is in excellent agreement with the results of a recent geothermal survey of Taiwan, and theoretical cooling histories are in good agreement with fission track and other geochronologic studies. Taken together, these results provide strong evidence that sliding on the basal decollement fault beneath Taiwan is governed by a coefficient of friction in the range of typical laboratory measurements, gt, = 0.5 +_ 0. Approximately 35% of the total surface heat flux of 3 GW is heat conducted into the base of the wedge from the top of the basal decollement fault, and somewhat more than 30% is heat advected into the toe by accretion. The remaining heat is generated internally, about 25% by internal strain heating and about 10% by radiogenic heating. Either an increase in the coefficient of basal friction gh or a reduction in the pore fluid pressure ratio )• = )•h leads to an increase in the surface heat flow, because of the increased frictional heating within the wedge and on the basal decollement fault. The overall balance of energy in a steady state fold-and-thrust belt is described by the equation E = W G + Q, where E is the rate at which both mechanical and heat energy are added from external sources, 1• G is the rate at which work is performed against gravitational body forces in a referenceframe attached to the overriding plate, and Q is the rate at which waste heat flows out of both the upper and lower boundaries. The total power input into the Taiwan fold-and-thrust belt is approximately 4.2 GW. The mechanical work being done on the base and ...
An active fold‐and‐thrust belt in unchanging tectonic and climatic conditions exhibits a dynamic steady state, with the flux of rocks accreted at the toe balanced by the flux of rocks eroded off the top. Rocks entering the toe are buried and heated before they are uplifted and eroded; this results in a characteristic map pattern of low‐grade metamorphism on the surface. Metamorphic isograds are generally parallel to the regional strike of a fold‐and‐thrust belt, with the grade increasing progressively from unmetamorphosed and zeolite facies near the deformation front up to greenschist facies in the highest mountains; such a pattern is observed in the active fold‐and‐thrust belt of Taiwan. This paper examines the origin of this low‐grade syntectonic metamorphism, using a previously developed mechanical and thermal model of a steady state fold‐and‐thrust belt as a basis. To model the metamorphism, we develop a petrogenetic grid for rocks of basaltic composition, considering phases within the chemical system CaO‐MgO‐Al2O3‐SiO2‐H2O. Equilibria diagnostic of stable low‐grade mineral assemblages are mapped onto a cross section of the Taiwan fold‐and‐thrust belt, using the calculated fluid pressure and temperature distributions within the wedge. The variation of metamorphic grade along the surface is predicted by assuming that there is no retrograde metamorphism. The most important mechanical factor controlling the degree of metamorphism in an active fold‐and‐thrust belt is the amount of frictional heating, both on the basal decollement fault and within the deforming brittle wedge. Frictional heating raises temperatures in the deepest portions of the Taiwan fold‐and‐thrust belt by 200° C to 250° C; the resulting high temperatures, in excess of 400° C, are responsible for the extensive greenschist facies metamorphism. The amount of heating is well constrained by the observed heat flow anomaly, geochronological data, and the critical wedge taper; the best‐fitting coefficient of basal friction in Taiwan is μb = 0.5 ± 0.2. Underplating of footwall rocks by the assimilation of duplexes along the decollement fault is not considered to be a significant process in Taiwan, because of the observed balance between the accretionary influx at the toe and the erosive efflux off the top. In other fold‐and‐thrust belts, however, underplating can significantly increase the outcrop width of higher metamorphic grades on the surface by increasing the flux of rocks through the higher fluid pressure and temperature regions within the wedge.
S U M M A R YThe geological record of deformation is often characterized by a combination of discontinuous deformation, in which strain is concentrated in faults, and continuous deformation, in which strain is distributed through the material. Where slip occurs on a fault that terminates, the surrounding material is deformed. In the lower crust and in cases where large strains occur over long geological time-scales, it is appropriate to model the deformation using a viscous (probably non-linear viscous) rheology. We describe a method for practical finite-element solution of this problem using a dynamically self-consistent formulation for stress and displacement on a fault of arbitrary geometry; the accuracy of the method is tested by comparison with an analytical solution for the linear rheology. We describe here the instantaneous deformation fields around a mode I1 fault under both plane-strain and plane-stress conditions, and a range of rheological exponents n (where strain rate is proportional to deviatoric stress to the nth power). The distributions of stress and strain rate around the fault tip are controlled primarily by the rheological exponent n. A localized zone of high strain rate projects beyond the end of the fault if n is about 3 or greater, and the degree of localization of deformation increases with the value of n. The zone of high shear-strain rate can be defined in practical terms by considering (1) the region in which the creep velocity differs by more than 20 per cent from the velocity on the nearby external boundary and (2) the region in which the maximum shear-strain rate is greater than about twice the externally imposed shear-strain rate. For n = 1, the volumes so defined differ considerably, but for large values of n, the two definitions both describe the same narrow zone of deformation beyond the end of the fault. Evaluation of the Navier-Coulomb criterion for brittle failure of the medium surrounding the fault tip shows first that brittle failure is much more likely on the extensional side of the fault than the compressional side. It also shows that the volume of material subject to brittle failure decreases rapidly with increasing n because of the relatively weaker stress singularity. We analyse previously published displacement versus distance data for faults terminating in sedimentary rocks at 0.1 to 100m length-scales under different tectonic conditions, in order to determine the rheological exponent n. These analyses result in n values between approximately 0.85 and 5 for the different faults, with error bounds on n typically rt 1. The variation in n values may result from differences in pressure, temperature and fluid conditions at the time of faulting. More importantly, the analysis demonstrates a new method for the determination of the effective rheological exponent under in situ geological conditions.
Abstract. A simple kinematic model is used to illustrate the vertical motions of rocks during convergent deformation and erosion at the surface. It is shown that rocks may move upward or downward in the crust, depending on the relative rates of erosion and thickening and depending on their initial depth in the crust. Exhumation during thickening can only occur if rapid denudation accompanies the thickening process. During homogeneous thickening with erosion that is elevation dependent, the initial depth from which rocks can be exhumed is only determined by the density distribution in the column and is independent of erosion or thickening rates. The maximum initial depth, from which rocks can be exhumed, is of the order of 30 km or less. There is therefore no conflict in the observation of synchronous exhumation and convergent deformation if the peak pressure of rocks is equivalent to no more than 30 km of burial. It is also shown that uplift (defined as vertical motion of the surface with respect to a reference level, for example the geoid) and exhumation (defined as vertical motion of rocks with respect to the surface) may follow different patterns in time and that the difference between the two evolutions may be a useful indicator of the exhumation process. The model serves to emphasize the important differences between uplift and exhumation which are often not distinguished in the literature.
In the Halls Creek Orogen of north-western Australia, the distance of melt migration through migmatitic metasedimentary rocks and adjacent metabasites is partly constrained by relationships of leucosomes and small mafic magma veins to rock boundaries and structural elements. Stromatic leucosomes in metasediments are cut by a network of small extensional fractures and shear zones, oriented steeply during melt migration. These shear zones allowed cm- to 10 m-scale migration of felsic magma derived by in situ anatexis. In the adjacent metabasite layers, a similar shear array allowed injection of H2O-undersaturated mafic to ultramafic magma, locally dehydrating and chemically modifying these rocks. However, these mafic to ultramafic veinlets are too mafic to be explained by in situ anatexis, necessitating an external magma source. Also, the lack of felsic veinlets cutting metabasites, and mafic veinlets cutting metasediments, requires that vertical inter-connectivity of these fracture systems was restricted. We propose along-layer migration of mafic to ultramafic magma through the metabasite, assisted by horizontal connection of the shear zones. This migration occurred independantly of metre-scale felsic magma migration in the adjacent metasediments, even though these two deformation-assisted magma migration systems may have been operating at the same time.
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