Extensional Models Research Articles

Rolling hinge or fixed basin?: A test of continental extensional models in Death Valley, California, United States

Two models are typically offered to explain severe continental extensional tectonism: low-angle detachment faults with alloch thonous sedimentary basins above a crustal “rolling hinge,” or differential displacement on systems of distinct, deeply rooted normal faults with in-place sedimentary basins. Structural and stratigraphic relationships between the Badwater turtleback and the adjacent Furnace Creek basin in Death Valley provide a test of these contrasting models. There, ductile extensional deformation of basement rock at the Badwater turtleback coincided with brittle extensional deformation and local uplift in the adjacent Furnace Creek basin between 13 and 18 Ma. In the Furnace Creek basin, crustal extension of this age is evident as (1) greater fault density and offset in pre–13 Ma rocks relative to post–13 Ma rocks and (2) the presence of laterally variable sedimentary breccias and conglomerates, which indicate a syndepositional paleotopographic high. This high is approximately on line with the likely projection of an early Badwater turtleback fault, the surface expression of the turtleback mylonites. These relationships indicate that the Badwater turtleback and Furnace Creek basin were contiguous prior to 13 Ma and that the basin formed in place relative to the Black Mountains basement. These findings support arguments for extension in the Death Valley area by distinct, deeply rooted fault zones rather than by a rolling-hinge detachment fault.

Active detachment faulting above the Peruvian flat slab

The Cordillera Blanca detachment fault in the Peruvian Andes is, to our knowledge, the first active detachment to be documented above a modern flat slab. Crustal detachment has unroofed the ca. 8 Ma Cordillera Blanca batholith, now the backbone of the highest mountain range in Peru. Large-magnitude slip along the fault was thermally enhanced by emplacement of the batholith, the penultimate magmatic event prior to flattening of the Nazca slab. However, extensional models based on arc magmatism and crustal thickening alone do not adequately explain the scale or structural asymmetry of a series of young, deep-seated, west-dipping normal faults across Peru. Here we show that the onset of detachment faulting coincided with subduction of the aseismic Nazca Ridge and consequent flattening of the Nazca slab. We propose that slab buoyancy from ridge subduction triggered extensional collapse of the prethickened continental crust, and that this buoyancy drove footwall uplift that exceeds basin subsidence. The west-dipping asymmetry of late Cenozoic extensional faults in Peru may be controlled by a preexisting crustal anisotropy (older thrusts), and/or formation of Riedel-like shears kinematically linked to the flat Nazca slab.

Post-Permian evolution of the Central North Sea: a numerical model

A dynamic thermomechanical model is presented for the post-Permian evolution of the Central North Sea including the Central Graben. Permo-Carboniferous and Jurassic thermal events, as well as Triassic and Jurassic extensional phases and Late Cretaceous shortening, are considered. The equations of force balance for a continuum and the transient heat equation are solved using the finite element method. The lithosphere responds to applied forces by elastic deformation at low deviatoric stress levels, fracture at low temperature and pressure conditions and nonlinear viscous flow at high temperature and pressure. A first-order rheological strain softening is incorporated to simulate a transition from strong to soft material behaviour, such as a change from dislocation creep to diffusion creep. Seismic refraction and reflection data indicate crustal thinning below the Central Graben by a factor of ∼2. While the Triassic rifting appears to have been associated with a more distributed deformation pattern, the Upper Jurassic rifting is more localised. Pure shear extensional models have been advocated to explain this. However, dipping seismic reflectors in the upper mantle indicate that simple shear could be important. The strain softening of the present model allows for modelling of strain localisation during the Upper Jurassic rifting phase and detailed modelling of Moho structures. The present model accounts for the main structural and stratigraphic observations in the Central North Sea. Furthermore, the results indicate that in the part of the Central North Sea investigated in this paper, a pure shear regime in Triassic changed into a simple shear-dominated regime with mantle shear zones developing during Late Jurassic extension.

Sedimentary tectonics and subsidence modelling of the type Upper Cretaceous Gosau basin (Northern Calcareous Alps, Austria)

The Upper Cretaceous Gosau Group of the Austrian Northern Calcareous Alps records sedimentation and subsidence after Early Cretaceous thrusting. The Gosau basin in the Gosau-Russbach area is approximately 8 km wide and 10 km long. It is filled by more than 1000 m alluvial/shallow-marine deposits of the lower Gosau Subgroup (Upper Turonian–Lower Campanian). Facies and thickness changes within short horizontal distances suggest synsedimentary basin margin faulting. Extensional structures within the Triassic basement of the basin include fibrous gashes which indicate (W)NW–(E)SE directed extension of 6–18%. (W)NW-directed normal faults at the southeastern basin margin, a prominent SE-directed normal fault with a minimum fault throw of approximately 500 m at the NW basin margin, and dextral strike-slip at the southwestern margin suggest a pull-apart origin of the basin between NW/SE-trending, right-overstepping dextral strike-slip faults. Backstripped tectonic subsidence curves yield values of total subsidence of 700 m in approximately 6 Ma. Forward computer modelling based on extensional models results in stretching factors β between 1.09–1.15. Local extension along strike-slip faults is suggested as the main mechanism for basin formation.

CONTRIBUIÇÃO AO ESTUDO DA EVOLUÇÃO MECÂNICA DA BACIA DO PARANÁ

The aim of this paper to provide a geophysical contribution to the study of the processes involved in the mechanical evolution of the Paraná Basin 1 his Urdovicmn-Cretaceous sedimentary basin is intracrotonic and located in the S-SE portion of Brazil, also comprising part of Paraguay' Argentina and Uruguay and coversi approximately 1.4 million km 2 . In the thermomechanical study, 81 exploratory boreholes for hydrocarbon tolled by PETROBRAS and PAULIPETRO were used, applying pure shear extensional models. With this modeling, it was possible to locate a region of greatest stress, between 23,8 S, 53,8 W and 22,3 S, 52,0 W - which could reflect the existence of a paleo-structure representing the boundary between tectonic blocks. The results obtained, associated with the types of sedimentation described for the principal chronostratigraphic sequences, are also discussed.

CONTRIBUIÇÃO AO ESTUDO DA EVOLUÇÃO MECÂNICA DA BACIA DO PARANÁ

The aim of this paper to provide a geophysical contribution to the study of the processes involved in the mechanical evolution of the Parana Basin 1 his Urdovicmn-Cretaceous sedimentary basin is intracrotonic and located in the S-SE portion of Brazil, also comprising part of Paraguay' Argentina and Uruguay and coversi approximately 1.4 million km 2 . In the thermomechanical study, 81 exploratory boreholes for hydrocarbon tolled by PETROBRAS and PAULIPETRO were used, applying pure shear extensional models. With this modeling, it was possible to locate a region of greatest stress, between 23,8 S, 53,8 W and 22,3 S, 52,0 W - which could reflect the existence of a paleo-structure representing the boundary between tectonic blocks. The results obtained, associated with the types of sedimentation described for the principal chronostratigraphic sequences, are also discussed.

Isomorphism and Equational Equivalence of Continuous [lambda]-Models.

We will present several results on two types of continuous models of λ-calculus, namely graph models and extensional models. By introducing a variant of Engeler's model construction, we are able to generalize the results of [7] and to give invariants that determine a large family of graph models up to applicative isomorphism. This covers all graph models considered in the litterature so far. We indicate briefly how these invariants may be modified in order to determine extensional models as well.

An axiomatization of partial n-place operations

We propose a general theory of partial n-place operations based solely on the primitive notion of the application of a (possibly partial) operation to n objects. This theory is strongly selfdescriptive in that the fundamental manipulations of operations, that is, application, composition, abstraction, union, intersection and so on, are themselves internal operations. We give several applications of this theory, including implementations of partial n-ary λ-calculus, and other operation description languages. We investigate the issue of extensionality and give weakly extensional models of the theory.

Probability Bootstrapping: Improving Prediction by Fitting Extensional Models to Knowledgeable but Incoherent Probability Judgments

We propose a simple method for choosing a probability distribution as an approximation to a set of incoherent probability judgments. In two different domains we demonstrate that the resulting (coherent) probability estimates come closer to the observed relative frequencies than do the original incoherent judgments.

Free objects and equational deduction for partial conditional specifications

Partial conditional specifications consist of conditional axioms, with equalities in the (possibly infinite set of) premises and in the consequence, which are interpreted in partial algebras. Equalities may be existential (= e ) or strong ( = ); t = e t′ holds in an algebra iff both t and t′ are defined and equal, while t = t′ holds in an algebra iff either t = e t′ holds or both t and t′ are undefined. Contrary to the well explored case of positive conditional axioms (only existential equalities in the premises), general partial conditional specifications do not always admit free models and the related theory is much more subtle. In this paper we fully investigate and solve the problem of existence of free and initial models, giving necessary and sufficient conditions, first from a model-theoretical and then from a logical deduction viewpoint. In particular we present a deduction system which is complete w.r.t. strong equalities between open terms. Since positive conditional partial specifications and conditional total specifications are special cases of the paradigm investigated here, the presented theory generalizes the related results about free models and the Birkhoff-like deduction theory. The system we exhibit handles also the case of infinitary conjunctions as premises of the axioms; it reduces to a classical one for the positive conditional case by just dropping one rule, and finally it solves the empty-carrier problem without using explicit quantification. The theory presented here also gives the basis for solving, via the usual first-order reduction, the problem of the existence of free and initial models for partial higher-order specifications of term-generated extensional models.

An intensional semantics for a hybrid language

One of the major assumptions in designing knowledge representation formalisms in the KL-One family, was the so-called ‘intensional representation’. An intensional representation is required when two descriptions have to be compared, or when they are interpreted by qualitative processes; in other words, many processes can be activated by using the global structure of a concept, and by interpreting its properties and the relationships between these properties. In this perspective, an intensional semantics for a typical terminological language has been designed, which is quite different from the extensional models proposed so far. The semantics of the language is similar to that of data types in programming languages. Primitive concepts are denoted by a set of values. Defined concepts are denoted by their properties. A denotation thus contains the minimum number of properties which are required for an individual to be an instance of a generic concept. More precisely, the denotation is the Cartesian product of the sets denoting the properties of the genetic concept (deduced from its syntax). A role is denoted by a function which, given a tuple, returns the values of the property which individuates the role. An individual is created by instantiating the properties of the relative generic concept, used as a guide. As a result, this process creates a tuple whose elements are the instantiating properties. The instantiation chain terminates by instantiating primitive concepts on the basis of their denotation. A deeper integration between the entire system and any programming language can be reached, which implicitly gives rise to an object-oriented system. In other words, it is possible to introduce an individual concept into a programming language, like any other data type. For instance, an individual concept is passed to a function as a parameter; once it has been verified that this individual is an instance of a generic concept, or of one of its subconcepts, the function will be executed. Furthermore, an increase in the expressive power is obtained, since it makes it possible to give a formal meaning to all kinds of recursive definitions of individual and generic concepts.

Strike-Slip Interpretation of Basin-Bounding Faults of the St. Lawrence Lowlands Basin in the Quebec City Area, Canada

Traditional structural interpretations of faults identified in the autochthonous, Ordovician platform rocks of the St. Lawrence Lowlands basin of Quebec, Canada, assert that the primary sense of faulting is normal, extensional, and dip-slip in motion. Interpretation of field observations such as the offset of facies boundaries in outcrop, fault surface features, fracture patterns, and fault volume considerations lead directly to difficulties with a mobile crustal bulge model for normal faulting. Newly reprocessed seismic data and well-log correlations support this interpretation and indicate a need for a different model for the deformation of the platform margin. A left-lateral, basement-involved wrench system resolves stratigraphic discordances across fault zones, contradictions in the observed geometry of hanging-wall blocks, problems concerning timing of tectonic events, and the difficulty of using extensional deformation models in a compressional setting. This reinterpretation places the timing of the platform faulting just prior to the arrival of the Taconic thrust sheet. The lateral offset of subsurface and surface depositional facies, fault trace features, well correlations, and seismic expressions document approximately 60 km of left-lateral strike-slip motion in the St. Lawrence Lowlands basin.

Extensional pluton-emplacement models: Do they work for large plutonic complexes?

Shallow-crustal to mid-crustal magma-emplacement models commonly rely on local or regional extension to solve the room problem. We argue that existing extensional models explain the emplacement of sheeted-dike complexes or internally layered plutons but are not as easily reconciled with the emplacement of elliptically shaped plutons or batholiths for the following reasons: (1) rock strengths and crustal stresses prevent large voids from existing at depth and therefore require wall-rock extension to be balanced by magma influx; (2) rates of extension are controlled by fault slip rates of millimetres to centimetres per year and thus require numerous small injections of magma; and (3) because of their sheetlike shapes and small thicknesses, these small magma injections will cool rapidly and form sheeted plutons or dike swarms. Extension may, however, facilitate emplacement of elliptically shaped plutons in concert with other mechanisms if certain kinematic constraints are satisfied.

Partial Higher-Order Specifications1

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

TECTONIC CONTROL OF WORLD OIL RESERVES: AUSTRALIA'S POSITION

Although simple extensional clay models may be representative of grabens tens of kilometres in length, rotational divergence of continents on a sphere produces very different structures. Repeated periods of compression during separation result in wrench faults and compressional anticlines developing along major crustal fractures as a consequence of changes in momentum between a continent and adjacent smaller continental blocks along its rifted margin.The global distribution of rotationally divergent continental margins can be accounted for by asymmetric expansion of the earth. The southern bulge caused by expansion has emphasised non-marine deposition on southern continents with marine deposition more common in the northern hemisphere.Phanerozoic source rocks of the northern hemisphere account for 97 per cent of the world's produced and current reserves of oil. Australia's share of this extreme distribution asymmetry is less than one half of one per cent, yet the country covers five per cent of the Earth's continental crust.The proportion of undiscovered oil reserves outside OPEC and the former USSR is approximately 30 per cent, or some 12 per cent of the world's estimated ultimately recoverable reserve of 2 trillion (Tera) barrels. The majority of Australia's undiscovered reserves lie on the North West Shelf where about 12 per cent of the country's estimated ultimately recoverable reserve could be found.Although Australia is politically stable, lower petroleum taxes would attract exploration for smaller, structurally complex oil fields. While such taxes may be considered politically difficult at present, a by-product of concerted oil exploration would be an enormous increase in Australia's gas reserves to feed the national pipeline grid for the 21st century. Industry can assist increased success rates by greater attention to current technical deficiencies, such as the structural interpretation of seismic lines.

Variations in heat flow across the Goban Spur and Galicia Bank continental margins

We present the results of 44 new heat flow stations which were taken in 1984 and 1989 in profiles across the Goban Spur and Galicia Bank continental margins (NW Atlantic Ocean). Simple extensional models indicate that the heat flow across both these Early Cretaceous rifted margins should increase from values of 45–50 mW/m2 over oceanic crust to 65–80 mW/m2 on the continents. The rate of this increase should help to constrain the mechanism (simple versus pure shear) by which the upper, more radiogenic continental crust is thinned. Measurements across Goban Spur increase from values of 40–45 mW/m2 over oceanic crust to 50–55 mW/m2 near the continental shelf. They follow the predicted trend for pure‐shear rifting, but only if the value of upper crustal radiogenic heating is low (1–2 μW/m3). Otherwise, they would require the upper crust to thin more rapidly than the total crustal thickness, as with a lower plate, simple‐shear margin. Measurements across Galicia Bank show a very different pattern, with similar values over oceanic crust but much lower values (30–35 mW/m2) nearer land. This is difficult to reconcile with any simple, single rifting event but is more compatible with an origin as a pure‐shear or lower plate rather than upper plate margin. We also note that oceanic values of heat flow require asthenospheric temperatures 100°C lower than normal for both margins. This indicates that the triple junction in existance between these margin segments during the breakup of Iberia, Europe, and North America was not the site of a major mantle plume.

Basin analysis and hydrocarbon generation of the South Mozambique Graben using extensional models of heat flow

The northern South Mozambique Graben was assessed for hydrocarbon potential by reconstructing its structural, burial and thermal histories using a seismic line and an array of basin modelling techniques. The structural and depositional history was determined by simultaneously palinspastically restoring and backstripping a depth converted cross-section. The thermal history was predicted from extensional models which relate palaeoheat flow to basement subsidence. Maturation potential cross-sections were derived by applying a generation model to each of the pseudo-wells, assuming each layer to be a potential source rock. Considering the range of uncertainty when using these models, this analysis suggested that regardless of the extension model type used, and within the maximum and minimum limits of the palaeoheat flow, the eastern side of the northern South Mozambique Graben is more hydrocarbon prone than the west. In addition the timing of hydrocarbon generation, regardless of the palaeoheat flow possibilities modelled, is favourably after source and seal rock deposition, and after the development of trapping structures. It is apparent from this study that a stratigraphic well with down-hole thermal indicator measurements and bottom hole temperature information would greatly enhance the understanding of the hydrocarbon potential of this basin.

Basin analysis predictions of known hydrocarbon occurrences: The North Sea Viking Graben as a test case

Basin analysis can assimilate structural, burial and thermal histories to predict hydrocarbon-prone zones in speculative areas. The validity of the modelling approach was field tested in the North Sea Viking Graben, an area for which good data are available. A recent BIRPS, deep seismic reflection profile across tectonic strike of the graben was interpreted and depth-converted with good well control. The burial and structural histories were determined by backstripping the chronostratigraphic layers using a one-dimensional fluid flow/compaction model on pseudo-wells. After removal of each sequence, the section was manually reconstructed. The thermal history was examined using thermal indicator tomography, extensional models and calculations of depth to detachment. Lack of resolution required that three different paleo-heat flow trends be tested to encompass the range in variability: a gradual warming trend, a constant heat flow through time, and a low heat flow until the Cretaceous-Tertiary boundary where a heat pulse occurred. Basement subsidence, extension, depth to detachment calculations, and thermal indicator inversions all suggest that the UK side of the graben has developed differently to the Norwegian section. The generation modelling predicts the position of the oil window in the cross-section. The areas where this window enveloped the Draupne Formation (Kimmeridge Clay) source rock broadly correlate with the positions of the Gullfaks, Statfjord and Thistle oilfields of the UK sector. However, in the Norwegian sector the Draupne Formation was generally overmature, except in the area around the Troll oilfield. Predicted Middle to Late Cretaceous generation in the rift axis may have caused updip oil migration towards the Horda platform. The correct prediction of oil-prone zones validates the use of quantitative basin analysis as a tool for evaluating frontier areas where data are limited.

Deformation mechanics in analogue models of extensional fault systems

Abstract Scaled analogue models of fault structures are powerful tools for investigating the progressive development of extensional deformation. The results of a wide ranging programme of extensional modelling are briefly reviewed and are analysed in terms of the deformation mechanics and rheological behaviour of the modelling materials. Extensional models have been constructed using homogeneous dry quartz sand with isotropic behaviour; sand and dry china clay mixtures; with behaviour controlled by competency; and sand with dry vermiculite mica flakes to simulate anisotropic systems. Rheological tests show that these materials deform by Navier-Coulomb failure with friction angles between 30° and 35°. Extensional faults developed within the models are dilatant granular shear zones, whose widths are grain-size dependent, being widest in the sand models and narrowest in faults cutting the fine-grained clay layers. Initial fault-bedding cutoff angles are high, 60°–70°, but during progressive deformation shear strains may change this, depending upon the boundary conditions of the model. Measurements of angular shear strains within domino fault arrays show significant zones of shear either parallel to the basal detachment or parallel to bounding faults. Small bulk dilations are found in most models as a result of grain packing rearrangements during extension. The primary extensional architecture of the models is controlled by the underlying detachment configuration. Despite limitations to the models, it is believed that the rheologies, the modelling materials and the deformation mechanics within the models realistically simulate brittle deformation of sedimentary rocks in the upper crust.

Some consequences of compressional tectonics for extensional models of basin subsidence

Changes in intraplate stress levels have important consequences for the stratigraphy of rifted basins and provide a tectonic explanation for the generation of sequence boundaries. Late-stage compressional phases during the post-rift evolution of basins produce unconformities, with offlap phases that increase in magnitude with the age of the rifted basin. Late-stage compression has not only a strong bearing on the generation of unconformities, but also induces significant downbending of the centre of a basin. Ignorance of the vertical motions of the lithosphere induced by late-stage compression during post-rift evolution can, therefore, give rise to substantial errors in the estimates of crustal extension derived from analysis of basement subsidence using stretching models. Consequently, late-stage compression can be of great significance in estimates of depth and timing of the hydrocarbon-window inferred from extensional models of basin subsidence. Quantification of the subsidence induced by post-rift compression has important implications for integrated models of basin subsidence and hydrocarbon generation.