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Estimating crustal deformation from geodetic dataCheloni, Daniele <1979> 09 June 2008 (has links)
By the end of the 19th century, geodesy has contributed greatly to the knowledge of regional
tectonics and fault movement through its ability to measure, at sub-centimetre precision, the
relative positions of points on the Earth’s surface. Nowadays the systematic analysis of
geodetic measurements in active deformation regions represents therefore one of the most
important tool in the study of crustal deformation over different temporal scales [e.g., Dixon,
1991]. This dissertation focuses on motion that can be observed geodetically with classical
terrestrial position measurements, particularly triangulation and leveling observations. The
work is divided into two sections: an overview of the principal methods for estimating longterm
accumulation of elastic strain from terrestrial observations, and an overview of the
principal methods for rigorously inverting surface coseismic deformation fields for source
geometry with tests on synthetic deformation data sets and applications in two different
tectonically active regions of the Italian peninsula. For the long-term accumulation of elastic
strain analysis, triangulation data were available from a geodetic network across the Messina
Straits area (southern Italy) for the period 1971 – 2004. From resulting angle changes, the
shear strain rates as well as the orientation of the principal axes of the strain rate tensor were
estimated. The computed average annual shear strain rates for the time period between 1971
and 2004 are γ˙1 = 113.89 ± 54.96 nanostrain/yr and γ˙2 = -23.38 ± 48.71 nanostrain/yr, with
the orientation of the most extensional strain (θ) at N140.80° ± 19.55°E. These results
suggests that the first-order strain field of the area is dominated by extension in the direction
perpendicular to the trend of the Straits, sustaining the hypothesis that the Messina Straits
could represents an area of active concentrated deformation. The orientation of θ agree well
with GPS deformation estimates, calculated over shorter time interval, and is consistent with
previous preliminary GPS estimates [D’Agostino and Selvaggi, 2004; Serpelloni et al., 2005]
and is also similar to the direction of the 1908 (MW 7.1) earthquake slip vector [e.g., Boschi et
al., 1989; Valensise and Pantosti, 1992; Pino et al., 2000; Amoruso et al., 2002]. Thus, the
measured strain rate can be attributed to an active extension across the Messina Straits,
corresponding to a relative extension rate ranges between < 1mm/yr and up to ~ 2 mm/yr,
within the portion of the Straits covered by the triangulation network. These results are
consistent with the hypothesis that the Messina Straits is an important active geological
boundary between the Sicilian and the Calabrian domains and support previous preliminary
GPS-based estimates of strain rates across the Straits, which show that the active deformation
is distributed along a greater area. Finally, the preliminary dislocation modelling has shown
that, although the current geodetic measurements do not resolve the geometry of the
dislocation models, they solve well the rate of interseismic strain accumulation across the
Messina Straits and give useful information about the locking the depth of the shear zone.
Geodetic data, triangulation and leveling measurements of the 1976 Friuli (NE Italy)
earthquake, were available for the inversion of coseismic source parameters. From observed
angle and elevation changes, the source parameters of the seismic sequence were estimated in
a join inversion using an algorithm called “simulated annealing”. The computed optimal
uniform–slip elastic dislocation model consists of a 30° north-dipping shallow (depth 1.30 ±
0.75 km) fault plane with azimuth of 273° and accommodating reverse dextral slip of about
1.8 m. The hypocentral location and inferred fault plane of the main event are then consistent
with the activation of Periadriatic overthrusts or other related thrust faults as the Gemona-
Kobarid thrust. Then, the geodetic data set exclude the source solution of Aoudia et al. [2000],
Peruzza et al. [2002] and Poli et al. [2002] that considers the Susans-Tricesimo thrust as the
May 6 event. The best-fit source model is then more consistent with the solution of Pondrelli
et al. [2001], which proposed the activation of other thrusts located more to the North of the
Susans-Tricesimo thrust, probably on Periadriatic related thrust faults. The main
characteristics of the leveling and triangulation data are then fit by the optimal single fault
model, that is, these results are consistent with a first-order rupture process characterized by a
progressive rupture of a single fault system. A single uniform-slip fault model seems to not
reproduce some minor complexities of the observations, and some residual signals that are not
modelled by the optimal single-fault plane solution, were observed. In fact, the single fault
plane model does not reproduce some minor features of the leveling deformation field along
the route 36 south of the main uplift peak, that is, a second fault seems to be necessary to
reproduce these residual signals. By assuming movements along some mapped thrust located
southward of the inferred optimal single-plane solution, the residual signal has been
successfully modelled. In summary, the inversion results presented in this Thesis, are
consistent with the activation of some Periadriatic related thrust for the main events of the
sequence, and with a minor importance of the southward thrust systems of the middle
Tagliamento plain.
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The attenuation of seismic intensityPasolini, Chiara <1980> 20 June 2008 (has links)
No description available.
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Seismic wave modelling for large scale 3-D problems: method development and application to lateral heterogeneity imagingDanecek, Peter <1971> 20 June 2008 (has links)
No description available.
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Multiresolution spherical wavelet analysis in global seismic tomographyCarannante, Simona <1976> 20 June 2008 (has links)
Every seismic event produces seismic waves which travel throughout the Earth.
Seismology is the science of interpreting measurements to derive information about the structure of the
Earth. Seismic tomography is the most powerful tool for determination of 3D structure of deep Earth's
interiors. Tomographic models obtained at the global and regional scales are an underlying tool for
determination of geodynamical state of the Earth, showing evident correlation with other geophysical and
geological characteristics. The global tomographic images of the Earth can be written as a linear
combinations of basis functions from a specifically chosen set, defining the model parameterization. A
number of different parameterizations are commonly seen in literature: seismic velocities in the Earth
have been expressed, for example, as combinations of spherical harmonics or by means of the simpler
characteristic functions of discrete cells.
With this work we are interested to focus our attention on this aspect, evaluating a new type of
parameterization, performed by means of wavelet functions. It is known from the classical Fourier theory
that a signal can be expressed as the sum of a, possibly infinite, series of sines and cosines. This sum is
often referred as a Fourier expansion. The big disadvantage of a Fourier expansion is that it has only
frequency resolution and no time resolution.
The Wavelet Analysis (or Wavelet Transform) is probably the most recent solution to overcome the
shortcomings of Fourier analysis. The fundamental idea behind this innovative analysis is to study signal
according to scale. Wavelets, in fact, are mathematical functions that cut up data into different frequency
components, and then study each component with resolution matched to its scale, so they are especially
useful in the analysis of non stationary process that contains multi-scale features, discontinuities and
sharp strike. Wavelets are essentially used in two ways when they are applied in geophysical process or
signals studies: 1) as a basis for representation or characterization of process; 2) as an integration kernel
for analysis to extract information about the process.
These two types of applications of wavelets in geophysical field, are object of study of this work.
At the beginning we use the wavelets as basis to represent and resolve the Tomographic Inverse
Problem. After a briefly introduction to seismic tomography theory, we assess the power of wavelet
analysis in the representation of two different type of synthetic models; then we apply it to real data,
obtaining surface wave phase velocity maps and evaluating its abilities by means of comparison with an
other type of parametrization (i.e., block parametrization).
For the second type of wavelet application we analyze the ability of Continuous Wavelet Transform
in the spectral analysis, starting again with some synthetic tests to evaluate its sensibility and capability
and then apply the same analysis to real data to obtain Local Correlation Maps between different model
at same depth or between different profiles of the same model.
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Sviluppo di metodologie di localizzazione nel contesto del Comprehensive Nuclear Test-Ban TreatyGiuntini, Alessandra <1976> 20 June 2008 (has links)
Since the first underground nuclear explosion, carried out in 1958, the analysis of seismic
signals generated by these sources has allowed seismologists to refine the travel times of seismic
waves through the Earth and to verify the accuracy of the location algorithms (the ground truth for
these sources was often known). Long international negotiates have been devoted to limit the
proliferation and testing of nuclear weapons. In particular the Treaty for the comprehensive nuclear
test ban (CTBT), was opened to signatures in 1996, though, even if it has been signed by 178
States, has not yet entered into force, The Treaty underlines the fundamental role of the
seismological observations to verify its compliance, by detecting and locating seismic events, and
identifying the nature of their sources. A precise definition of the hypocentral parameters represents
the first step to discriminate whether a given seismic event is natural or not. In case that a specific
event is retained suspicious by the majority of the State Parties, the Treaty contains provisions for
conducting an on-site inspection (OSI) in the area surrounding the epicenter of the event, located
through the International Monitoring System (IMS) of the CTBT Organization. An OSI is supposed
to include the use of passive seismic techniques in the area of the suspected clandestine
underground nuclear test. In fact, high quality seismological systems are thought to be capable to
detect and locate very weak aftershocks triggered by underground nuclear explosions in the first
days or weeks following the test.
This PhD thesis deals with the development of two different seismic location techniques: the
first one, known as the double difference joint hypocenter determination (DDJHD) technique, is
aimed at locating closely spaced events at a global scale. The locations obtained by this method are
characterized by a high relative accuracy, although the absolute location of the whole cluster
remains uncertain. We eliminate this problem introducing a priori information: the known location
of a selected event. The second technique concerns the reliable estimates of back azimuth and
apparent velocity of seismic waves from local events of very low magnitude recorded by a trypartite
array at a very local scale. For the two above-mentioned techniques, we have used the crosscorrelation
technique among digital waveforms in order to minimize the errors linked with incorrect
phase picking. The cross-correlation method relies on the similarity between waveforms of a pair of
events at the same station, at the global scale, and on the similarity between waveforms of the same
event at two different sensors of the try-partite array, at the local scale.
After preliminary tests on the reliability of our location techniques based on simulations, we
have applied both methodologies to real seismic events. The DDJHD technique has been applied to
a seismic sequence occurred in the Turkey-Iran border region, using the data recorded by the IMS.
At the beginning, the algorithm was applied to the differences among the original arrival times of
the P phases, so the cross-correlation was not used. We have obtained that the relevant geometrical
spreading, noticeable in the standard locations (namely the locations produced by the analysts of the
International Data Center (IDC) of the CTBT Organization, assumed as our reference), has been
considerably reduced by the application of our technique. This is what we expected, since the
methodology has been applied to a sequence of events for which we can suppose a real closeness
among the hypocenters, belonging to the same seismic structure. Our results point out the main
advantage of this methodology: the systematic errors affecting the arrival times have been removed
or at least reduced. The introduction of the cross-correlation has not brought evident improvements
to our results: the two sets of locations (without and with the application of the cross-correlation
technique) are very similar to each other. This can be commented saying that the use of the crosscorrelation
has not substantially improved the precision of the manual pickings. Probably the
pickings reported by the IDC are good enough to make the random picking error less important than
the systematic error on travel times. As a further justification for the scarce quality of the results
given by the cross-correlation, it should be remarked that the events included in our data set don’t
have generally a good signal to noise ratio (SNR): the selected sequence is composed of weak
events ( magnitude 4 or smaller) and the signals are strongly attenuated because of the large
distance between the stations and the hypocentral area.
In the local scale, in addition to the cross-correlation, we have performed a signal
interpolation in order to improve the time resolution. The algorithm so developed has been applied
to the data collected during an experiment carried out in Israel between 1998 and 1999. The results
pointed out the following relevant conclusions: a) it is necessary to correlate waveform segments
corresponding to the same seismic phases; b) it is not essential to select the exact first arrivals; and
c) relevant information can be also obtained from the maximum amplitude wavelet of the
waveforms (particularly in bad SNR conditions).
Another remarkable point of our procedure is that its application doesn’t demand a long time
to process the data, and therefore the user can immediately check the results. During a field survey,
such feature will make possible a quasi real-time check allowing the immediate optimization of the
array geometry, if so suggested by the results at an early stage.
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Tecniche di elaborazione di dati macrosismici per la definizione di sorgenti sismogeneticheTripone, Daniele <1978> 22 June 2009 (has links)
La valutazione dell’intensità secondo una procedura formale trasparente, obiettiva e che permetta di ottenere valori numerici attraverso scelte e criteri rigorosi, rappresenta un passo ed un obiettivo per la trattazione e l’impiego delle informazioni macrosismiche. I dati macrosismici possono infatti avere importanti applicazioni per analisi sismotettoniche e per la stima della pericolosità sismica.
Questa tesi ha affrontato il problema del formalismo della stima dell’intensità migliorando aspetti sia teorici che pratici attraverso tre passaggi fondamentali sviluppati in ambiente MS-Excel e Matlab: i) la raccolta e l’archiviazione del dataset macrosismico; ii), l’associazione (funzione di appartenenza o membership function) tra effetti e gradi di intensità della scala macrosismica attraverso i principi della logica dei fuzzy sets; iii) l’applicazione di algoritmi decisionali rigorosi ed obiettivi per la stima dell’intensità finale. L’intera procedura è stata applicata a sette terremoti italiani sfruttando varie possibilità, anche metodologiche, come la costruzione di funzioni di appartenenza combinando le informazioni macrosismiche di più terremoti: Monte Baldo (1876), Valle d’Illasi (1891), Marsica (1915), Santa Sofia (1918), Mugello (1919), Garfagnana (1920) e Irpinia (1930). I risultati ottenuti hanno fornito un buon accordo statistico con le intensità di un catalogo macrosismico di riferimento confermando la validità dell’intera metodologia.
Le intensità ricavate sono state poi utilizzate per analisi sismotettoniche nelle aree dei terremoti studiati. I metodi di analisi statistica sui piani quotati (distribuzione geografica delle intensità assegnate) si sono rivelate in passato uno strumento potente per analisi e caratterizzazione sismotettonica, determinando i principali parametri (localizzazione epicentrale, lunghezza, larghezza, orientazione) della possibile sorgente sismogenica. Questa tesi ha implementato alcuni aspetti delle metodologie di analisi grazie a specifiche applicazioni sviluppate in Matlab che hanno permesso anche di stimare le incertezze associate ai parametri di sorgente, grazie a tecniche di ricampionamento statistico. Un’analisi sistematica per i terremoti studiati è stata portata avanti combinando i vari metodi per la stima dei parametri di sorgente con i piani quotati originali e ricalcolati attraverso le procedure decisionali fuzzy. I risultati ottenuti hanno consentito di valutare le caratteristiche delle possibili sorgenti e formulare ipotesi di natura sismotettonica che hanno avuto alcuni riscontri indiziali con dati di tipo geologico e geologico-strutturale. Alcuni eventi (1915, 1918, 1920) presentano una forte stabilità dei parametri calcolati (localizzazione epicentrale e geometria della possibile sorgente) con piccole incertezze associate. Altri eventi (1891, 1919 e 1930) hanno invece mostrato una maggiore variabilità sia nella localizzazione dell’epicentro che nella geometria delle box: per il primo evento ciò è probabilmente da mettere in relazione con la ridotta consistenza del dataset di intensità mentre per gli altri con la possibile molteplicità delle sorgenti sismogenetiche. Anche l’analisi bootstrap ha messo in evidenza, in alcuni casi, le possibili asimmetrie nelle distribuzioni di alcuni parametri (ad es. l’azimut della possibile struttura), che potrebbero suggerire meccanismi di rottura su più faglie distinte.
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Meccanismi di formazione dei tubi di lavaValerio, Antonella <1979> 05 June 2009 (has links)
Two analytical models are proposed to describe two different mechanisms of lava tubes formation.
A first model is introduced to describe the development of a solid crust in the central region of the channel, and the formation of a tube when crust widens until it reaches the leve\'es. The Newtonian assumption is considered and the steady state Navier- Stokes equation in a rectangular conduit is solved. A constant heat flux density assigned at the upper flow surface resumes the combined effects of two thermal processes: radiation and convection into the atmosphere. Advective terms are also included, by the introduction of velocity into the expression of temperature. Velocity is calculated as an average value over the channel width, so that lateral variations of temperature are neglected. As long as the upper flow surface cools, a solid layer develops, described as a plastic body, having a resistance to shear deformation. If the applied shear stress exceeds this resistance, crust breaks, otherwise, solid fragments present at the flow surface can weld together forming a continuous roof, as it happens in the sidewall flow regions.
Variations of channel width, ground slope and effusion rate are analyzed, as
parameters that strongly affect the shear stress values. Crust growing is favored when the channel widens, and tube formation is possible when the ground slope or the effusion rate reduce.
A comparison of results is successfully made with data obtained from the analysis of pictures of actual flows.
The second model describes the formation of a stable, well defined crust along both channel sides, their growing towards the center and their welding to form the tube roof. The fluid motion is described as in the model above. Thermal budget takes into account conduction into the atmosphere, and advection is included considering the velocity depending both on depth and channel width. The solidified crust has a non uniform thickness along the channel width. Stresses acting on the crust are calculated using the equations of the elastic thin plate, pinned at its ends. The model allows to calculate the distance where crust thickness is able to resist the drag of the underlying fluid and to sustain its weight by itself, and the level of the fluid can lower below the tube roof.
Viscosity and thermal conductivity have been experimentally investigated through the use of a rotational viscosimeter. Analyzing samples coming from Mount Etna (2002) the following results have been obtained: the fluid is Newtonian and the thermal conductivity is constant in a range of temperature above the liquidus. For lower temperature, the fluid becomes non homogeneous, and the used experimental techniques are not able to detect any properties, because measurements are not reproducible.
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The rupture process of recent tsunamigenic earthquakes by geophysical data inversionRomano, Fabrizio <1979> 09 June 2009 (has links)
Subduction zones are the favorite places to generate tsunamigenic earthquakes, where friction between oceanic and continental plates causes the occurrence of a strong seismicity. The topics and the methodologies discussed in this thesis are focussed to the understanding of the rupture process of the seismic sources of great earthquakes that generate tsunamis.
The tsunamigenesis is controlled by several kinematical characteristic of the parent earthquake, as the focal mechanism, the depth of the rupture, the slip distribution along the fault area and by the mechanical properties of the source zone. Each of these factors plays a fundamental role in the tsunami generation. Therefore, inferring the source parameters of tsunamigenic earthquakes is crucial to understand the generation of the consequent tsunami and so to mitigate the risk along the coasts.
The typical way to proceed when we want to gather information regarding the source process is to have recourse to the inversion of geophysical data that are available.
Tsunami data, moreover, are useful to constrain the portion of the fault area that extends offshore, generally close to the trench that, on the contrary, other kinds of data are not able to constrain.
In this thesis I have discussed the rupture process of some recent tsunamigenic events, as inferred by means of an inverse method.
I have presented the 2003 Tokachi-Oki (Japan) earthquake (Mw 8.1). In this study the slip distribution on the fault has been inferred by inverting tsunami waveform, GPS, and bottom-pressure data. The joint inversion of tsunami and geodetic data has revealed a much better constrain for the slip distribution on the fault rather than the separate inversions of single datasets.
Then we have studied the earthquake occurred on 2007 in southern Sumatra (Mw 8.4). By inverting several tsunami waveforms, both in the near and in the far field, we have determined the slip distribution and the mean rupture velocity along the causative fault. Since the largest patch of slip was concentrated on the deepest part of the fault, this is the likely reason for the small tsunami waves that followed the earthquake, pointing out how much the depth of the rupture plays a crucial role in controlling the tsunamigenesis.
Finally, we have presented a new rupture model for the great 2004 Sumatra earthquake (Mw 9.2). We have performed the joint inversion of tsunami waveform, GPS and satellite altimetry data, to infer the slip distribution, the slip direction, and the rupture velocity on the fault. Furthermore, in this work we have presented a novel method to estimate, in a self-consistent way, the average rigidity of the source zone. The estimation of the source zone rigidity is important since it may play a significant role in the tsunami generation and, particularly for slow earthquakes, a low rigidity value is sometimes necessary to explain how a relatively low seismic moment earthquake may generate significant tsunamis; this latter point may be relevant for explaining the mechanics of the tsunami earthquakes, one of the open issues in present day seismology.
The investigation of these tsunamigenic earthquakes has underlined the importance to use a joint inversion of different geophysical data to determine the rupture characteristics.
The results shown here have important implications for the implementation of new tsunami warning systems – particularly in the near-field – the improvement of the current ones, and furthermore for the planning of the inundation maps for tsunami-hazard assessment along the coastal area.
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Tectonics and kinematics of curved mountain belts: examples from the Andes and the AlpsMaffione, Marco <1979> 22 June 2009 (has links)
Curved mountain belts have always fascinated geologists and geophysicists because of their peculiar structural setting and geodynamic mechanisms of formation.
The need of studying orogenic bends arises from the numerous questions to which geologists and geophysicists have tried to answer to during the last two decades, such as: what are the mechanisms governing orogenic bends formation? Why do they form? Do they develop in particular geological conditions? And if so, what are the most favorable conditions? What are their relationships with the deformational history of the belt? Why is the shape of arcuate orogens in many parts of the Earth so different? What are the factors controlling the shape of orogenic bends?
Paleomagnetism demonstrated to be one of the most effective techniques in order to document the deformation of a curved belt through the determination of vertical axis rotations. In fact, the pattern of rotations within a curved belt can reveal the occurrence of a bending, and its timing. Nevertheless, paleomagnetic data alone are not sufficient to constrain the tectonic evolution of a curved belt. Usually, structural analysis integrates paleomagnetic data, in defining the kinematics of a belt through kinematic indicators on brittle fault planes (i.e., slickensides, mineral fibers growth, SC-structures).
My research program has been focused on the study of curved mountain belts through paleomagnetism, in order to define their kinematics, timing, and mechanisms of formation. Structural analysis, performed only in some regions, supported and integrated paleomagnetic data. In particular, three arcuate orogenic systems have been investigated: the Western Alpine Arc (NW Italy), the Bolivian Orocline (Central Andes, NW Argentina), and the Patagonian Orocline (Tierra del Fuego, southern Argentina).
The bending of the Western Alpine Arc has been investigated so far using different approaches, though few based on reliable paleomagnetic data. Results from our paleomagnetic study carried out in the Tertiary Piedmont Basin, located on top of Alpine nappes, indicate that the Western Alpine Arc is a primary bend that has been subsequently tightened by further ~50° during Aquitanian-Serravallian times (23-12 Ma). This mid-Miocene oroclinal bending, superimposing onto a pre-existing Eocene nonrotational arc, is the result of a composite geodynamic mechanism, where slab rollback, mantle flows, and rotating thrust emplacement are intimately linked.
Relying on our paleomagnetic and structural evidence, the Bolivian Orocline can be considered as a progressive bend, whose formation has been driven by the along-strike gradient of crustal shortening. The documented clockwise rotations up to 45° are compatible with a secondary-bending type mechanism occurring after Eocene-Oligocene times (30-40 Ma), and their nature is probably related to the widespread shearing taking place between zones of differential shortening. Since ~15 Ma ago, the activity of N-S left-lateral strike-slip faults in the Eastern Cordillera at the border with the Altiplano-Puna plateau induced up to ~40° counterclockwise rotations along the fault zone, locally annulling the regional clockwise rotation. We proposed that mid-Miocene strike-slip activity developed in response of a compressive stress (related to body forces) at the plateau margins, caused by the progressive lateral (southward) growth of the Altiplano-Puna plateau, laterally spreading from the overthickened crustal region of the salient apex. The growth of plateaux by lateral spreading seems to be a mechanism common to other major plateaux in the Earth (i.e., Tibetan plateau).
Results from the Patagonian Orocline represent the first reliable constraint to the timing of bending in the southern tip of South America. They indicate that the Patagonian Orocline did not undergo any significant rotation since early Eocene times (~50 Ma), implying that it may be considered either a primary bend, or an orocline formed during the late Cretaceous-early Eocene deformation phase. This result has important implications on the opening of the Drake Passage at ~32 Ma, since it is definitely not related to the formation of the Patagonian orocline, but the sole consequence of the Scotia plate spreading.
Finally, relying on the results and implications from the study of the Western Alpine Arc, the Bolivian Orocline, and the Patagonian Orocline, general conclusions on curved mountain belt formation have been inferred.
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Crustal heterogeneities and complexities of fault processesFerrari, Claudio <1975> 05 June 2009 (has links)
In this work we study the relation between crustal heterogeneities and complexities in fault processes.
The first kind of heterogeneity considered involves the concept of asperity. The presence of an asperity in the hypocentral region of the M = 6.5 earthquake of June 17-th, 2000 in the South Iceland Seismic Zone was invoked to explain the change of seismicity pattern before and after the mainshock: in particular, the spatial distribution of foreshock epicentres trends NW while the strike of the main fault is N 7◦ E and aftershocks trend accordingly; the foreshock depths were typically deeper than average aftershock depths. A model is devised which simulates the presence of an asperity in terms of a spherical inclusion, within a softer elastic medium in a transform domain with a deviatoric stress field imposed at remote distances (compressive NE − SW, tensile NW − SE). An isotropic compressive stress component is induced outside the asperity, in the direction of the compressive stress axis, and a tensile component in the direction of the tensile axis; as a consequence, fluid flow is inhibited in the compressive quadrants while it is favoured in tensile quadrants. Within the asperity the isotropic stress vanishes but the deviatoric stress increases substantially, without any significant change in the principal stress directions. Hydrofracture processes in the tensile quadrants and viscoelastic relaxation at depth may contribute to lower the effective rigidity of the medium surrounding the asperity. According to the present model, foreshocks may be interpreted as induced, close to the brittle-ductile transition, by high pressure fluids migrating upwards within the tensile quadrants; this process increases the deviatoric stress within the asperity which eventually fails, becoming the hypocenter of the mainshock, on the optimally oriented fault plane.
In the second part of our work we study the complexities induced in fault processes by the layered structure of the crust.
In the first model proposed we study the case in which fault bending takes place in a shallow layer. The problem can be addressed in terms of a deep vertical planar crack, interacting with a shallower inclined planar crack. An asymptotic study of the singular behaviour of the dislocation density at the interface reveals that the density distribution has an algebraic singularity at the interface of degree ω between -1 and 0, depending on the dip angle of the upper crack section and on the rigidity contrast between the two media. From the welded boundary condition at the interface between medium 1 and 2, a stress drop discontinuity condition is obtained which can be fulfilled if the stress drop in the upper medium is lower than required for a planar trough-going surface: as a corollary, a vertically dipping strike-slip fault at depth may cross the interface with a sedimentary layer, provided that the shallower section is suitably inclined (fault "refraction"); this results has important implications for our understanding of the complexity of the fault system in the SISZ; in particular, we may understand the observed offset of secondary surface fractures with respect to the strike direction of the seismic fault. The results of this model also suggest that further fractures can develop in the opposite quadrant and so a second model describing fault branching in the upper layer is proposed. As the previous model, this model can be applied only when the stress drop in the shallow layer is lower than the value prescribed for a vertical planar crack surface.
Alternative solutions must be considered if the stress drop in the upper layer is higher than in the other layer, which may be the case when anelastic processes relax deviatoric stress in layer 2. In such a case one through-going crack cannot fulfil the welded boundary conditions and unwelding of the interface may take place. We have solved this problem within the theory of fracture mechanics, employing the boundary element method. The fault terminates against the interface in a T-shaped configuration, whose segments interact among each other: the lateral extent of the unwelded surface can be computed in terms of the main fault parameters and the stress field resulting in the shallower layer can be modelled. A wide stripe of high and nearly uniform shear stress develops above the unwelded surface, whose width is controlled by the lateral extension of unwelding. Secondary shear fractures may then open within this stripe, according to the Coulomb failure criterion, and the depth of open fractures opening in mixed mode may be computed and compared with the well studied fault complexities observed in the field. In absence of the T-shaped decollement structure, stress concentration above the seismic fault would be difficult to reconcile with observations, being much higher and narrower.
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