Discrete-element modelling of extensional fault-propagation folding above rigid basement fault blocks

We employed a discrete‐element technique to investigate the effects of cover strength and fault dip on the style of fault‐propagation folding above a blind normal fault. Deformation in the cover is initially characterised by an upward‐widening monocline that is often replaced, with continued slip on the basement fault, by a single, through‐going fault. Localisation on a single fault produces hangingwall synclines and footwall anticlines as a result of breaching of the earlier monocline and which do not represent ‘drag’ against the fault. As basement fault dip decreases the width of the monocline at the surface increases. Experiments varying the strength of the overburden material illustrate the control that cover strength has on both fault propagation and folding in the cover. Reduction of the strength of the cover results in: (1) the width of the monocline above the fault tip increasing, and (2) more marked footwall thinning and hangingwall thickening of beds. In contrast, an increase in cover strength results in a narrower monocline and rapid propagation of the basement fault into the cover. In multi‐layer (variable strength) experiments simultaneous faulting of competent layers and flow of weaker layers produces complex structural relationships. Faults in the cover die out up and down section and do not link to the basement fault at depth. Similarly, complex macroscopically ductile characteristics such as footwall thinning and hangingwall thickening can be juxtaposed against simple brittle fault cut‐offs. These relationships must be borne in mind when interpreting the field and seismic expression of such structures. We discuss the modelling results in terms of their implications for structural interpretation and the surficial expression of fault‐related folding in extensional settings.     

Multiple mechanisms driving detachment folding as deduced from 3D reconstruction and geomechanical restoration: the Pico del Águila anticline (External Sierras,Southern Pyrenees)

Three‐dimensional (3D) modelling allows observation of geological features that may not be evident by classical two‐dimensional approaches. This is particularly important in the Pico del Águila anticline (Central External Sierras, Southern Pyrenees, Spain), a structure characterized by important geometrical variability in 3D. The Pico del Águila is a N–S‐trending fold, transverse to the E–W‐trending South‐Pyrenean thrust front, with well‐exposed growth strata that record the evolution of the structure and the influence of the South‐Pyrenean thrust front. Fold kinematics is complex and not precisely quantified. It is characterized by multiple folding mechanisms acting simultaneously in a heterogeneous stratigraphic sequence. To better understand the fold's structural evolution, 3D reconstruction and geomechanical restoration of the structure were performed. The restoration takes into account rock mechanical properties without assuming a specific kinematic model. Our work suggests that the growth of the structure was characterized by variable uplift/sedimentation rates through time and between fold limbs. The restoration also reveals that a combination of multiple folding mechanisms operated simultaneously in different units and structural domains during anti‐clinal growth. This has major implications in the understanding of detachment folds with associated growth strata, as such structures are described in many settings as potential traps for hydrocarbons and natural resources.     

A stochastic modelling of earthquake frequencies

Summary. The frequency of earthquake occurrence in a given region can be formulated as

where n ( t ) is the number of earthquakes per unit time, and r, k and α are constants. Empirically determined values of α range from 0.67 to 1.0. This is a generalization of the modified Omori formula for aftershocks, the latter being an approximation of the former for n > k. This formula adequately describes the initial increasing and later decreasing activity of earthquakes during the Matsushiro and Wakayama swarms as well as aftershocks of large earthquakes.
When a random external force is added to this system as a driving mechanism, the equation above becomes

where v = l n ( n/k ) and R ( t ) is the random Gaussian noise. Repetitive seismic patterns with bursts, which are commonly observed in real earthquake sequences, are predicted from this formulation under stationary conditions. These formulations appear to be quite promising in helping to understand macroscopic features of the microearthquake activity.     

Wavelet modelling of broad-band receiver functions

We present a wavelet modelling approach to invert for S -wave velocities from broad-band receiver functions. Taking spline function as the basic wavelet, the broad-band receiver function is decomposed into five resolution scales by Mallat's pyramid algorithm. The linearized least-squares inversion procedure is applied to every resolution scale. The fifth-scale approximation of receiver function is first inverted to recover the slowly varying background velocity variations with respect to a reference model. This solution is then taken as the initial model for fitting the fourth-scale wavelet coefficients of receiver function to further tune the solution to resolve sharper variations. This procedure is iteratively carried out up to the first-scale wavelet coefficients of receiver function. In this manner, the model neighbourhood containing the global minimum is first searched from the coarsest-scale receiver function, and the search gradually focuses on the global minimum by introducing finer-scale information of receiver function. Noise-free synthetic receiver function tests show that wavelet modelling of receiver functions can guide a certain range of initial models to converge to the true velocity distribution. Tests on actual data indicate that wavelet modelling can provide results very similar to those inferred by joint inversion of receiver function and surface wave dispersion.     

The thermal evolution of lithosphere extending on a low-angle detachment zone

Abstract Expressions are obtained for temperature as a function of depth, and for surface elevation and surface heat flow using a simplified model to represent lithosphere extending on a low-angle detachment surface. The geometry of the resulting basin is determined by the dip of the detachment surface φ and the original thickness of the crust, h. For small extension the width of the basin is h /tan φ and with increasing extension the width of the basin cannot exceed 2 h /tan φ before sea-floor spreading begins. The asymmetry of heat flow and subsidence profiles across the basin is described and the predictions of the model are compared with those of the model for uniform extension by pure shear. The amplitude of thermal subsidence for the detachment-zone model is typically half as great as for the pure-shear model with the same extension factor. As the total subsidence is the same for each model the initial subsidence is correspondingly greater for the detachment-zone model. The time-integrated anomalous heat flow in the detachment-zone model is also approximately half that in the pure-shear model.     

Stratigraphic signatures of translation of thrust-sheet top basins over low-angle detachment faults

Abstract Low‐angle detachment faults and thrust‐sheet top basins are common features in foreland basins. However, in stratigraphic analysis their influence on sequence architecture is commonly neglected. Usually, only eustatic sea level and changing flexural subsidence are accounted for, and when deformation is considered, the emphasis is on the generation of local thrust‐flank unconformities. This study analyses the effects of detachment angle and repetitive detachment activation on stratigraphic stacking patterns in a large thrust‐sheet top basin by applying a three‐dimensional numerical model. Model experiments show that displacement over low‐angle faults (2–6°) at moderate rates (～5.0 m kyr^?1) results in a vertical uplift component sufficient to counteract the background flexural subsidence rate. Consequently, the basin‐wide accommodation space is reduced, fluvio‐deltaic systems carried by the thrust‐sheet prograde and part of the sediment supply is spilled over towards adjacent basins. The intensity of the forced regression and the interconnectedness of fluvial sheet sandstones increases with the dip angle of the detachment fault or rate of displacement. In addition, the delta plain is susceptible to the formation of incised valleys during eustatic falls because these events are less compensated by regional flexural subsidence, than they would be in the absence of fault displacement.     

Multi-criteria modelling and clustering of spatial information

To improve the formal integration of verbally given spatial information in a geographical information system, a methodology for converting such information to a geographical representation was developed. This was applied to examples of a spatial-related analysis of natural language text messages in the domain of disaster management. This article presents an approach for such a conversion by using a suitable knowledge representation as well as formal modelling structures. The structures are provided by an ontology-supported knowledge base. With respect to spatial uncertainty, a formal representation based on possibility theory was defined. Moreover, a cluster algorithm was developed for handling information of different sources and building a spatial context.     

Spatial strategies for parallel spatial modelling

Abstract

Abstract. To achieve high levels of performance in parallel geoprocessing, the underlying spatial structure and relations of spatial models must be accounted for and exploited during decomposition into parallel processes. Spatial models are classified from two perspectives, the domain of modelling and the scope of operations, and a framework of strategies is developed to guide the decomposition of models with different characteristics into parallel processes. Two models are decomposed using these strategies: hill-shading on digital elevation models and the construction of Delaunay Triangulations. Performance statistics are presented for implementations of these algorithms on a MIMD computer.     

Multi-label class assignment in land-use modelling

During the last two decades, a variety of models have been applied to understand and predict changes in land use. These models assign a single-attribute label to each spatial unit at any particular time of the simulation. This is not realistic because mixed use of land is quite common. A more detailed classification allowing the modelling of mixed land use would be desirable for better understanding and interpreting the evolution of the use of land. A possible solution is the multi-label (ML) concept where each spatial unit can belong to multiple classes simultaneously. For example, a cluster of summer houses at a lake in a forested area should be classified as water, forest and residential (built-up). The ML concept was introduced recently, and it belongs to the machine learning field. In this article, the ML concept is introduced and applied in land-use modelling. As a novelty, we present a land-use change model that allows ML class assignment using the k nearest neighbour (kNN) method that derives a functional relationship between land use and a set of explanatory variables. A case study with a rich data-set from Luxembourg using biophysical data from aerial photography is described. The model achieves promising results based on the well-known ML evaluation criteria. The application described in this article highlights the value of the multi-label k nearest neighbour method (MLkNN) for land-use modelling.     

Logical data modelling for geographical applications

Abstract.

A formal, yet practical, GeoRelational Data Model (GRDM) is presented for the logical database design phase of the development of spatial information systems. Geographic applications are viewed in the context of information systems development. The generic needs of modelling spatial data are analyzed; it is concluded that they are not served satisfactorily by existing data models, so specifications of modelling tools for spatial application design are given. GRDM provides a set of representational constructs (relations and layers for the logical schema; virtual layers, object classes and spatial constraints for the user views) on top of well-established models. It constitutes part of a full, easily automated application design methodology. Extensive examples demonstrate the relevance, and ease-of-use of the platform-independent GRDM.