Extensional tectonics during the Tyrrhenian back‐arc basin formation and a new morpho‐tectonic map

We present a new tectonic map focused upon the extensional style accompanying the formation of the Tyrrhenian back‐arc basin. Our basin‐wide analysis synthetizes the interpretation of vintage multichannel and single‐channel seismic profiles, integrated with modern seismic images, P‐wave velocity models, and high‐resolution morpho‐bathymetric data. Four distinct evolutionary phases of the Tyrrhenian back‐arc basin opening are further constrained, redefining the initial opening to Langhian/Serravallian time. Listric and planar normal faults and their conjugates bound a series of horst and graben, half‐graben and triangular basins. Distribution of extensional faults, active throughout the basin since Middle Miocene, allows us to define an arrangement of faults in the northern/central Tyrrhenian mainly related to a pure shear which evolved to a simple shear opening. At depth, faults accommodate over a Ductile‐Brittle Transitional zone cut by a low‐angle detachment fault. In the southern Tyrrhenian, normal, inverse and transcurrent faults appear to be related to a large shear zone located along the continental margin of the northern Sicily. Extensional style variation throughout the back‐arc basin combined with wide‐angle seismic velocity models allows to explore the relationships between shallow deformation, faults distribution throughout the basin, and crustal‐scale processes as thinning and exhumation.     

Shallow earthquakes in a viscoelastic shear zone with depth-dependent friction and rheology

Summary. Most crustal earthquakes of the world are observed to occur within a seismogenic layer which extends from the Earth's surface to a depth of a few tens of kilometres at most. A model is proposed in which the shear zone along a transcurrent plate margin is represented as a viscoelastic medium with depth-dependent power-law rheology. A frictional resistance linearly increasing with depth is assumed on a vertical transcurrent fault within the shear zone. Such a model is able to reproduce a continuous transition from the brittle behaviour of the upper crust to the ductile behaviour at depth. Assuming that the shear zone is subjected to a constant strain rate from the opposite motions of the two adjacent plates, it is found that there exists a maximum depth H below which tectonic stress can never reach the frictional threshold: this may be identified as the maximum depth of earthquake nucleation. The value of H is consistent with observations for plausible values of the model parameters. The stress evolution in the shear zone is calculated in the linear approximation of the constitutive equation. A change in rigidity with depth, which is also introduced in the model, may reproduce the high vertical gradient of shear stress, which has been measured across the San Andreas fault, and the fact that most earthquakes are nucleated at some depth in the seismogenic layer. A crack which drops the ambient stress to the dynamic frictional level is then introduced in the model. To this aim, a crack solution is employed without a stress singularity at its edges, which is compatible with a frictional stress threshold criterion for fracture. A constraint on the vertical friction gradient is obtained if such cracks are assumed to be entirely confined within the seismogenic layer.     

Discrete element modelling of extensional,growth, fault‐propagation folds

Extensional fault‐propagation folds are now recognised as being an important part of basin structure and development. They have a very distinctive expression, often presenting an upward‐widening monocline, which is subsequently breached by an underlying, propagating fault. Growth strata, if present, are thought to provide a crucial insight into the manner in which such structures grow in space and time. However, interpreting their stratigraphic signal is neither straightforward nor unique. Both analogue and numerical models can provide some insight into fold growth. In particular, the trishear kinematic model has been widely adopted to explain many aspects of the evolution and geometry of such fault‐propagation folds. However, in some cases the materials/rheologies used to represent the cover do not reproduce the key geometric/stratigraphic features of such folds seen in nature. This appears to arise from such studies not addressing adequately the very heterogenous mechanical stratigraphy seen in many sedimentary covers. In particular, flexural slip between beds/layers is often not explicitly modelled but, paradoxically, it appears to be an important deformation mechanism operative in such settings. Here, I present a 2D discrete element model of extensional fault‐propagation folding which explicitly includes flexural slip between predefined sedimentary units or layers in the cover. The model also includes growth strata and shows how they may reflect the various evolutionary stages of fold and fault growth. When flexural slip is included in the modelling scheme, the resultant breached monoclines and their growth strata are strikingly similar to some of those seen in nature. Results are also compared with those obtained using simple, homogeneous, frictional‐cohesive and elastic cover materials. Both un‐lithified and lithified growth strata are considered and clearly show that, rather than just being passive recorders of structural evolution, growth strata can themselves have an important effect on fault‐related fold growth. Implications for the evolution of and strain within, the resultant growth structures are discussed. A final focus of this study is the relationship that trishear might have with the upward‐widening zone of flexural slip activation away from a fault tip singularity.     

High-frequency radiation from crack (stress drop) models of earthquake faulting

We present a theory for the radiation of high-frequency waves by earthquake faults. We model the fault as a planar region in which the stress drops to the kinematic friction during slip. This model is entirely equivalent to a shear crack. For two-dimensional fault models we show that the high frequencies originate from the stress and slip velocity concentrations in the vicinity of the fault's edges. These stress concentrations radiate when the crack expands with accelerated motion. The most efficient generation of high-frequency waves occurs when the rupture velocity changes abruptly. In this case, the displacement spectrum has an ω^-2 behaviour at high frequencies. The excitation is proportional to the intensity of the stress concentration near the crack tips and to the change in the focusing factor due to rupture velocity. We extend these two-dimensional results to more general three-dimensional fault models in the case when the rupture velocity changes simultaneously on the rupture front. Results are similar to those described for two-dimensional faults. We apply the theory to the case of a circular fault that grows at constant velocity and stops suddenly. The present theory is in excellent agreement with a numerical solution of the same problem.
Our results provide upper bounds to the high-frequency radiation from more realistic models in which rupture velocity does not change suddenly. The ω^-2 is the minimum possible decay at high frequencies for any crack model of the source.     

Small-scale mantle flows and induced lithospheric stress near island arcs

Summary. This paper explores the middle ground between complex thermally-coupled viscous flow models and simple corner flow models of island arc environments. The calculation retains the density-driven nature of convection and relaxes the geometrical constraints of corner flow, yet still provides semianalytical solutions for velocity and stress. A novel aspect of the procedure is its allowance for a coupled elastic lithosphere on top of a Newtonian viscous mantle. Initially, simple box-like density drivers illustrate how vertical and horizontal forces are transmitted through the mantle and how the lithosphere responds by trench formation. The flexural strength of the lithosphere spatially broadens the surface topography and gravity anomalies relative to the functional form of the vertical flow stresses applied to the plate base. I find that drivers in the form of inclined subducting slabs cannot induce self-driven parallel flow; however, the necessary flow can be provided by supplying a basal drag of 1–5 MPa to the mantle from the oceanic lithosphere. These basal drag forces create regional lithospheric stress and they should be quantifiable through seismic observations of the neutral surface. The existence of a shallow elevated phase transition is suggested in two slab models of 300 km length where a maximum excess density of 0.2 g cm⁻³ was needed to generate an acceptable mantle flow. A North New Hebrides subduction model which satisfies flow requirements and reproduces general features of topography and gravity contains a high shear stress zone (75 MPa) around the upper slab surface to a depth of 150 km and a deviatoric tensional stress in the back arc to a depth of 70 km. The lithospheric stress state of this model suggests that slab detachment is possible through whole plate fracture.     

Post-seismic reloading and temporal clustering on a single fault

Geological studies show evidence for temporal clustering of large earthquakes on individual fault systems. Since post-seismic deformation due to the inelastic rheology of the lithosphere may result in a variable loading rate on a fault throughout the interseismic period, it is reasonable to expect that the rheology of the non-seismogenic lower crust and mantle lithosphere may play a role in controlling earthquake recurrence times. We study this phenomenon using a 2-D, finite element method continuum model of the lithosphere containing a single strike-slip fault. This model builds on a previous study using a 1-D spring-dashpot-slider analogue of a single fault system to study the role of Maxwell viscoelastic relaxation in producing non-periodic earthquakes. In our 2-D model, the seismogenic portion of the fault slips when a predetermined yield stress is exceeded; stress accumulated on the seismogenic fault is shed to the viscoelastic layers below and recycled back to the seismogenic fault through viscoelastic relaxation. We find that random variation of the fault yield stress from one earthquake to the next can cause the earthquake sequence to be clustered; the amount of clustering depends on a non-dimensional number, W , called the Wallace number defined as the standard deviation of the randomly varied fault yield stress divided by the effective viscosity of the system times the tectonic loading rate. A new clustering metric based on the bimodal distribution of interseismic intervals allows us to investigate clustering behaviour of systems over a wide range of model parameters and those with multiple viscoelastic layers. For models with   W ≥ 1  clustering increases with increasing W , while those with   W ≤ 1  are unclustered, or quasi-periodic.     

Relay zone evolution: a history of repeated fault propagation and linkage,central Corinth rift,Greece

Established models indicate that, before being breached, relay zones along rift borders can evolve either by lengthening and rotating during progressive overlap of growing fault segments (isolated fault model), or, by simply rotating without lengthening before breaching (coherent fault model). The spatio‐temporal distribution of vertical motions in a relay zone can thus be used to distinguish fault growth mechanisms. Depositional relay zones that develop at sea level and accommodate both deposition on the ramp itself as well as transfer of sediments from the uplifting footwall into the hangingwall depocentres and provide the most complete record of vertical motions. We examine the development of a depositional relay ramp on the border of the active Corinth rift, Greece to reconstruct fault interaction in time and space using both onshore and offshore (2D seismic lines) data. The Akrata relay zone developed over a period of ca. 0.5 Myr since the Middle Pleistocene between the newly forming East Helike Fault (EHF) that propagated towards the older, more established Derveni Fault (DF). The relay zone captured the Krathis River, which deposited prograding Gilbert‐type deltas on the sub‐horizontal ramp. Successive oblique faults record progressive linkage and basinward migration of accommodation along the ramp axis, whereas marine terraces record diachronous uplift in their footwalls. Although early linkage of the relay zone occurs, continuous propagation and linkage of the EHF onto the static DF is recorded before final beaching. Rotation on forced folds above the upward and laterally propagating normal faults at the borders of the relay zone represents the ramp hinges. The Akrata relay zone cannot be compared directly to a simple fault growth model because (1) the relay zone connects two fault segments of different generations; (2) multiple linkages during propagation was facilitated by the presence of pre‐existing crustal structures, inherited from the Hellenide fold and thrust belt. The linkage of the EHF to the DF contributed to the westward and northward propagation of the southern rift border.     

Structural evolution of the Gediz Graben,SW Turkey: temporal and spatial variation of the graben basin

The structural evolution of the Miocene to Recent Gediz Graben is intimately related to the evolution of its southern margin. This margin is shaped by a time‐transgressive, composite structure that possesses flat‐ramp geometry with three separate dip domains: a low‐angle shallow segment; a steeper middle segment; and a low‐angle deeper segment. This geometry was probably produced by one of two mechanisms, which operated perpendicular to the general trend of the graben, resulting in gradual back‐rotation followed by abandonment of the shallow segment as it was dissected by the high‐angle normal fault(s). The geometry of the southern margin structure is not simple along‐strike. It includes broad undulations and discrete fault segments, developed by large‐scale fault growth processes through segment linkage. The along‐strike growth of the southern margin‐bounding structure is responsible for the composite character of the Gediz Graben and controls the observed stratigraphic variability. Two sub‐basins aligned with the major segments of the southern graben margin structure have been investigated. The Salihli and Ala?ehir sub‐basins comprising 3000 m sedimentary thickness are separated by an intervening basement high, that is covered by a thin veneer of post‐Miocene sediments. The two sub‐basins, which evolved as isolated basins during most of the graben history, amalgamated during post‐Miocene time to form the composite configuration of the graben. There is a general east to west trend of growth for the Gediz Graben.     

Quantitative analogue flume-model study of river–shelf systems: principles and verification exemplified by the Late Quaternary Colorado river–delta evolution

ABSTRACT Physical modelling of clastic sedimentary systems over geological time spans has to resort to analogue modelling since full scaling cannot be achieved within the spatial and temporal restrictions that are imposed by a laboratory set‐up. Such analogue models are suitable for systematic investigation of a sedimentary system's sensitivity to allocyclic changes by isolating governing parameters. Until now, analogue models of landscape evolution were mainly qualitative in nature. In this paper, we present a quantitative approach. The quantitative experimental results are verified and discussed by comparison with high‐resolution data from the Colorado river–shelf system of the Texas shelf that we used as a prototype. The model's dimensions are proportionally scaled to the prototype, except for a vertical exaggeration. Time is scaled using a Basin Response factor to maintain a similar ratio between the period of change and the system's equilibrium time for model and prototype. A Basin Fill factor was used to compare the ratio between the time‐averaged sedimentation rate and the rate of change in accommodation space of model and prototype. The flume‐model results are in the form of sediment budgets that are related to shelf cannibalism and fluvial supply, which are compared with the ancestral Colorado river–delta evolution of the last 40 kyr. Model and prototype have similarities in delta evolution in response to one cycle of sea‐level change. With sea‐level change as the isolated variable, the flume model generates a significant supply pulse caused by headward erosion of the shelf in response to the sea‐level fall. This pulse adds to the yield of the hinterland. The supply induced by sea‐level change persists during the early rise, although its rate declines. A similar trend is observed on the east Texas shelf. We argue that shelfal and fluvial degradation cycles induced by sea‐level changes can significantly influence the timing and amount of sediment supply to basins and must therefore be taken into consideration.     

Structure and recent evolution of the Hazar Basin: a strike‐slip basin on the East Anatolian Fault,Eastern Turkey

The Hazar Basin is a 25 km‐long, 7 km‐wide and 216 m‐deep depression located on the central section of the East Anatolian Fault zone (eastern Turkey) and predominantly overlain by Lake Hazar. This basin has been described previously as a pull‐apart basin because of its rhombic shape and an apparent fault step‐over between the main fault traces situated at the southwestern and northeastern ends of the lake. However, detailed structural investigation beneath Lake Hazar has not been undertaken previously to verify this interpretation. Geophysical and sedimentological data from Lake Hazar were collected during field campaigns in 2006 and 2007. The analysis of this data reveals that the main strand of the East Anatolian Fault (the Master Fault) is continuous across the Hazar Basin, connecting the two segments previously assumed to be the sidewall faults of a pull‐apart structure. In the northeastern part of the lake, an asymmetrical subsiding sub‐basin, bounded by two major faults, is cross‐cut by the Master Fault, which forms a releasing bend within the lake. Comparison of the structure revealed by this study with analogue models produced for transtensional step‐overs suggests that the Hazar Basin structure represents a highly evolved pull‐apart basin, to the extent that the previous asperity has been bypassed by a linking fault. The absence of a step‐over structure at the Hazar Basin means that no significant segmentation boundary is recognised on the East Anatolian Fault between Palu and Sincik. Therefore, this fault segment is capable of causing larger earthquakes than recognised previously.     

Investigating the surface process response to fault interaction and linkage using a numerical modelling approach

In order to better understand the evolution of rift‐related topography and sedimentation, we present the results of a numerical modelling study in which elevation changes generated by extensional fault propagation, interaction and linkage are used to drive a landscape evolution model. Drainage network development, landsliding and sediment accumulation in response to faulting are calculated using CASCADE, a numerical model developed by Braun and Sambridge, and the results are compared with field examples. We first show theoretically how the ‘fluvial length scale’, L_f, in the fluvial incision algorithm can be related to the erodibility of the substrate and can be varied to mimic a range of river behaviour between detachment‐limited (DL) and transport‐limited (TL) end‐member models for river incision. We also present new hydraulic geometry data from an extensional setting which show that channel width does not scale with drainage area where a channel incises through an area of active footwall uplift. We include this information in the coupled model, initially for a single value of L_f, and use it to demonstrate how fault interaction controls the location of the main drainage divide and thus the size of the footwall catchments that develop along an evolving basin‐bounding normal fault. We show how erosion by landsliding and fluvial incision varies as the footwall area grows and quantify the volume, source area, and timing of sediment input to the hanging‐wall basin through time. We also demonstrate how fault growth imposes a geometrical control on the scaling of river discharge with downstream distance within the footwall catchments, thus influencing the incision rate of rivers that drain into the hanging‐wall basin. Whether these rivers continue to flow into the basin after the basin‐bounding fault becomes fully linked strongly depends on the value of L_f. We show that such rivers are more likely to maintain their course if they are close to the TL end member (small L_f); as a river becomes progressively more under supplied, i.e. the DL end member (large L_f), it is more likely to be deflected or dammed by the growing fault. These model results are compared quantitatively with real drainage networks from mainland Greece, the Italian Apennines and eastern California. Finally, we infer the calibre of sediments entering the hanging‐wall basin by integrating measurements of erosion rate across the growing footwall with the variation in surface processes in space and time. Combining this information with the observed structural control of sediment entry points into individual hanging‐wall depocentres we develop a greater understanding of facies changes associated with the rift‐initiation to rift‐climax transition previously recognised in syn‐rift stratigraphy.     

Analogue modelling of inverted domino‐style basement fault systems

Inversion of pre‐existing extensional fault systems is common in rift systems, back‐arc basins and passive margins. It can significantly influence the development of structural traps in hydrocarbon basins. The analogue models of domino‐style basement fault systems shown in this paper produced, on extension, characteristic hangingwall growth stratal wedges that, when contracted and inverted, formed classic inversion harpoon geometries and asymmetric hangingwall contractional fault‐propagation folds. Segmented footwall shortcut faults formed as the basement faults were progressively back‐rotated and steepened. The pre‐existing extensional fault architectures, basement fault geometries and the relative hangingwall and footwall block rotations exerted fundamental controls on the inversion styles. Digital image correlation (DIC) strain monitoring illustrated complex vertical fault segmentation and linkage during inversion as the major faults were reactivated and strain was progressively transferred onto footwall shortcut faults. Hangingwall deformation during inversion was dominated by significant back‐rotation as the inversion progressed. The mechanical stratigraphy of the cover sequences strongly influenced the fold and fault evolution of the reactivated fault systems. The implications of the experimental results for the interpretation and analysis of inversion structures are discussed and are compared with natural examples of inverted basement‐involved extensional faults observed in seismic datasets.     

Minimum work, fault activity and the growth of critical wedges in fold and thrust belts

Many studies of critical wedges treat the interior of the wedge as continuous and do not address the manner in which it grows from the undeformed state to a typical imbricate wedge. In this paper we present a 2D kinematic–mechanical model which attempts to explain the development of a critical wedge in a fold and thrust belt in terms of both gravitational and frictional work. In the undeformed model a series of thrust faults are defined which have the potential to take up an external displacement. The active fault at a given time is that which minimizes gravitational and frictional work as a result of displacement. Displacement on the active fault causes a change in topography and deformation of other faults which may favour an alternative fault at the next time step. The model is a mixed Lagrangian–Eulerian scheme in which the upper surface, in addition to being deformed, is also subject to erosion, transport and sedimentation. The model predicts propagation of thrust fault activity towards the foreland through time as a result of increasing topographic (gravitational) loads and frictional work on deformed hinterland faults. As the zone of fault activity progresses through the developing critical wedge several faults are active over time-scales of ≈1 Myr. However, a simple chronology or sequence of fault activity cannot be assumed as out-of-sequence thrusting occurs during this overall foreland propagation. The detailed spatial and temporal activity of faults is complex and reflects the interaction between the development of topography, the contrast between basal (décollement) and internal coefficients of friction and the effects of erosion and sedimentation. In particular, rates of erosion and sedimentation are found to be important controls on fault activity both spatially and temporally. Erosion, by locally removing topography above a fault, reduces gravitational and frictional work enabling continued fault activity or reactivation. Sedimentation, conversely, acts to increase gravitational and frictional work on a fault, and therefore has the potential to blanket faults and render them inactive. Model results illustrate the complex feedbacks that can exist between tectonic and surficial mass transport processes.     

An improved method for the determination of the tectonic stress field from focal mechanism data

All conventional stress inversion methods, when applied to earthquake focal mechanism data, suffer from uncertainty as to which plane is the true fault plane. This paper deals with several problems in stress inversion brought about by this uncertainty. Our analysis shows that the direction of shear stress on the auxiliary plane does not coincide with the hypothetical slip direction unless the B -axis is parallel to one of the three principal stress directions. Based on this simple fact, we propose a new algorithm dealing with the ambiguity in fault/auxiliary plane identification. We also propose a method to handle the inhomogeneity problem of data quality, which is common and unique for focal mechanism data. Different inversion methods and algorithms are applied to two sets of 'focal mechanism' data simulated from field fault-slip measurement data. The inversion results show that, among the four stress parameters inverted, the stress ratio suffers the most from the ambiguity in fault/auxiliary plane identity, whereas the solutions for the principal stress directions are surprisingly good. The errors in inversion solutions resulting from the fault/auxiliary plane ambiguity can be significantly reduced by controlling subjectively the sample variance of the measurement errors. Our results also suggest that the fault plane cannot be distinguished correctly from the auxiliary plane with a high probability on the basis of the stress inversion alone.     

Geometry of growth strata in a transpressive fold belt in field and analogue model: Gosau Group at Muttekopf,Northern Calcareous Alps,Austria

The thrust sheets of the Northern Calcareous Alps were emplaced during Late Cretaceous thrust‐dominated transpression expressed by thrust sheets segmented by closely spaced tear faults. Thrust sheet‐top sediments were deposited during thrusting and associated fold growth and were controlled by active folding and tearing. We observe two types of angular unconformities: (1) Angular unconformities above folds between tear faults conform with the model of progressive unconformities. Across these unconformities dip decreases upsection. (2) Here, we define progressive unconformities that are related to tear faults and are controlled by both folding and tearing. Across these unconformities both strike and dip change. In growth strata overlying folds dissected by high‐angle faults, such unconformities are expected to be common. We used analogue modelling to define the geometry of the tear faults and related unconformities. Within the syn‐tectonic sediments, a steep, upward flattening thrust within a broader, roughly tulip‐shaped drag zone develops. The thrust roots in the tear fault in pre‐tectonic deposits and is curved upward toward the downthrown block. Vertical offset on the thrust is related to differential vertical uplift caused by, for example, growth of folds with different wavelength and amplitude on either side of the tear fault. Formation of progressive unconformities is governed by the relationship between the rates of deposition and vertical growth of a structure. Fault‐related progressive unconformities are additionally controlled by the growth of the vertical step across the tear fault. When the rates of vertical growth of two neighbouring folds separated by a tear fault are similar, the rate of growth across the tear fault is small; if the first differ, the latter is high. Episodic tear fault activity may create several angular unconformities attached to a tear fault or allow the generation of angular unconformities near tear faults in sedimentary systems that have a rate of deposition too high to generate classical progressive unconformities between the tear faults.     

Influence of oblique basement strike–slip faults on the Mesozoic evolution of the south-eastern segment of the Mid-Polish Trough

A series of analogue models are used to demonstrate how the multistage development of the Mid‐Polish Trough (MPT) could have been influenced by oblique basement strike–slip faults. Based on reinterpretation of palaeothickness, facies maps and published syntheses of the basin development, the following successive stages in the Mesozoic history of the south eastern part of the MPT were simulated in the models: (1) Oblique extension of the NW segment of the MPT connected with sinistral movement along the Holy Cross Fault (HCF, Early Triassic–latest Early Jurassic). (2) Oblique extension of both NW and SE segment of the MPT, parallel to the HCF (latest Early and Middle Jurassic). (3) Oblique extension of the SE segment of the MPT and much lesser extension of its NW segment connected with dextral movement along the HCF (Early Oxfordian–latest Early Kimmeridgian). (4) Oblique extension of the SE segment of the MPT and much lesser extension of its NW segment connected with dextral movement along the Zawiercie Fault (ZF, latest Early Kimmeridgian–Early Albian). (5) Oblique inversion of the NW segment of the MPT connected with dextral movement along the HCF (Early Albian–latest Cretaceous). (6) Oblique inversion of the SE segment of the MPT along the W–E direction (latest Cretaceous–Palaeogene). The different sense of movements of these two basement strike–slip faults (HCF and ZF) resulted in distinct segmentation of the basin and its SW margin by successive systems of extensional en‐echelon faults. The overall structure of this margin is controlled by the interference of the border normal faults with the en‐echelon fault systems related to successive stages of movement along the oblique strike–slip faults. This type of en‐echelon fault system is absent in the opposite NE‐margin of the basin, which was not affected by oblique strike–slip faults. The NE‐margin of the basin is outlined by a typical, steep and distinctly marked rift margin fault zone, dominated by normal and dip–slip/strike–slip faults parallel to its axis. Within the more extended segment of the basin, extensive intra‐rift faults and relay ramps develop, which produce topographic highs running across the basin. The change in the extension direction to less oblique relative to the basin axis resulted in restructuring of the fault systems. This change caused shifting of the basin depocentre to this margin. Diachronous inversion of the different segments of the basin in connection with movement along one of the oblique basement strike–slip faults resulted in formation of a pull‐apart sub‐basin in the uninverted SE‐segment of the basin. The results of the analogue models presented here inspire an overall kinematic model for the southeastern segment of the MPT as they provide a good explanation of the observed structures and the changes in the facies and palaeothickness patterns.     

Chaotic ray behaviour in regional seismology

Rays propagating through strongly laterally varying media exhibit chaotic behaviour. This means that initially close rays diverge exponentially, rather than according to a power law. This chaotic behaviour is especially pronounced if the medium contains laterally varying interfaces. By studying simple 2-D and 3-D versions of models with laterally varying interfaces, the importance of chaotic ray behaviour is determined. A model of the Moho below Germany produces sharp variations with epicentral distance of the number of arrivals. In addition, the number of caustics grows dramatically: up to 1200 caustics are present between a distance of 0 and 800 km. Using the theory of Hamiltonian systems, a more in-depth study of the chaotic character of the ray equations is obtained. It is found that for realistic heterogeneous models most of the relevant rays will exhibit chaotic behaviour. The degree of chaos is quantified in terms of predictability horizons. Beyond the predictability horizons ray tracing cannot be carried out accurately. For the models under consideration, the length from the source to the predictability horizon has an order of magnitude of 1000 km. The chaotic behaviour of the rays makes it necessary to use extensions of asymptotic ray theory, such as Maslov theory, to compute seismic waveforms. It is shown that pseudo-caustics, an important obstacle in computing Maslov synthetics, are a generic feature of the 2-D laterally varying models that are studied. Eventually, the use of asymptotic methods is restricted because of the inaccuracy in the computation of the ray paths.