Fakultät für Geowissenschaften - Digitale Hochschulschriften der LMU Archiv

Abstract Exploration activities outlined a shear zone-hosted gold and base metal occurrence in low-grade metasedimentary rocks near the town of Workamba, Tigray State, northern Ethiopia. Gold resources are estimated at ~2 t Au with concentrations reaching up to 8 g/t Au in the ore. The geology of the study area is dominated by foliated or sheared, lower greenschist facies metavolcanic and metasedimentary rocks, which are correlated to the lower island-arc metavolcanic rocks of the ~860 to 750 Ma Tsaliet Group and upper carbonate and metasedimentary rocks of the ~740 Ma Tambien Group, respectively. The Tsaliet and Tambien groups represent the southern parts of the Arabian-Nubian Shield. The Tsaliet Group, which is exposed in the north-western parts of the study area, consists mainly of metavolcaniclastic rocks. The overlying slate, phyllite, sericite-chlorite schists and marbles of the Tambien Group occupy the south-eastern part of the area. A steeply dipping NE trending ductile shear zone occurs in the metasediments along the contact with the Tsaliet Group. It is intruded by monzogranite and lamprophyre dikes or sills. The shear zone is correlated with an early regional deformation event (D1), which also caused NE foliations and ENE trending folds. A second regional deformation phase (D2) resulted in NNE oriented weakly developed dextral shear bands and N-S trending parasitic folds. NW striking brittle faults postdate D1 and D2 ductile structures. Trace element patterns of the metasedimentary rocks support findings of previously published works suggesting that they are derived from the rocks of the Tsaliet Group. Major, trace, and rare earth element characteristics of the monzogranite dikes/sills permit the conclusion that they are related to the ~620 to 520 Ma post-tectonic magmatism in the Tigray region. The post-tectonic granitoids are resulted from mantle-derived magmas, which are modified by fluid components of the subducted slab or involvement of continental crust. Petrographic and geochemical results of the lamprophyres show that they are calc-alkaline in nature. The monzogranite dikes/sills have 208Pb/204Pb, 207Pb/204Pb, and 206Pb/204Pb values between 37.176 to 37.310, 15.508 to 15.525, and 17.799 to 18.310, respectively. These lead isotope ratios are compatible with a significant mantle component in these rocks. Lead isotope ratios of the metasedimentary and metavolcanic rocks at Workamba are heterogeneous, suggesting that not all samples did retain their original Pb isotope signatures. However, the original Pb isotope composition of these rocks tends to be less radiogenic as those of the post-tectonic dikes/sills. Field and petrographic observations show that the metavolcanic rocks are locally affected by propylitic alteration and sericitization. The metasedimentary rocks suffered from pervasive silicification, sericitization, and carbonatization. The monzogranite and lamprophyre dikes/sills locally experienced pervasive sericitization, carbonatization, epidotization, and chloritization. Two generations of quartz veins occur cutting and/or parallel to D1 foliation on the Tsaliet and Tambien groups. The first generation quartz veins are folded and less abundant as compared to the unfolded second generations. The metasedimentary rocks and the dikes/sills are also cut by calcite ±quartz veinlets in the mineralized zone. Mass balance calculations of the metasedimentary rocks suggest that Na2O, and Sr are removed by hydrothermal fluids from the original composition of the rocks. K2O, MnO, CaO, Ba, and Pb are variably added or removed. The dikes/sills retained near original geochemical composition. The shear zone hosted metallic mineralization occurs within the metasedimentary rocks, in close spatial proximity to the dikes/sills. It took place under brittle conditions. Pyrite, sphalerite, galena, and chalcopyrite are the main sulfide phases, whereas pyrrhotite, arsenopyrite, and chalcocite are minor components. Gold is invisible and was only detected in geochemical analysis. Gangues include calcite, sericite, and quartz. The mineralized rocks are enriched in Au, As, Sb, and Ag. The Au/Ag ratio of all analyzed samples is less than 10. The paragenetic relationships show that pervasive sericitization and chlorite-epidote (propylitic) alteration occurred before an early quartz and/or calcite ±quartz veining event. The mineralization occurred roughly concomitant with carbonatization and calcite ±quartz veining, after the intrusion of the monzogranite and lamprophyre dikes/sills. Sulfur isotope signature of sulfides (δ34S(VCDT) = 1.8 to 9.1 ‰) is compatible with the hypothesis that S is derived from the country rocks through leaching by hydrothermal fluids. The carbon isotope signature of hydrothermal calcite (13C(VPDB) = –5.6 to +1.8 ‰) and that of a fluid in equilibrium with this calcite (13C(VPDB) = -3.7 to +3.7 ‰) are similar to those of Tambien Group carbonate rocks (13C(VPDB) = -4.5 to 7 ‰). Therefore, the C is dominantly derived from the Tambien Group. The calculated oxygen isotope signature (18O(VSMOW) values between 5.1 to 8.7 ‰) of a hydrothermal fluid in equilibrium with calcite is compatible with a fluid of magmatic or metamorphic origin. The 208Pb/204Pb, 207Pb/204Pb, and 206Pb/204Pb values of sulfides, which range between 36.94 to 36.99, 15.47 to 15.49, and 17.36 to 17.38 respectively, differ markedly from those of monzogranite dikes/sills. The data implies that the mineralization is unrelated to post-orogenic magmatism and that the Pb isotope signature of the sulfides represents the original Pb isotope signature of the metasedimentary and metavolcanic rocks. Overall evaluation of S, C, and Pb isotopic data permits to conclude that metals, sulfur, and other ore components are derived from the country rocks through leaching by metamorphic fluids. Petrographic studies of fluid inclusions show the presence of coexisting liquid-only, liquid-rich and vapour-rich two phase fluids. The fluid inclusions are predominantly secondary or pseudo-secondary in nature. Microthermometric measurments show that all fluid inclusions are of low-salinity (~1 to 8 wt. % NaClequiv.) aqueous types. Average homogenization temperatures of fluid inclusions in calcite are around 300ºC, i.e. close to temperatures found in orogenic gold systems. The mineralization at Workamba was likely generated by devolatilization and dehydration processes during metamorphism of the Tsaliet and Tambien Group rocks. The major collision orogeny which waned in Tigray at ~630 Ma might have caused eviction of the mineralizing fluids from deep regions. These mineralizing fluids were then channeled in the shear zone. Gold was presumably transported as Au(HS)2- complexes at intermediate oxidation states by near-neutral fluids, and sulfidation of host rocks is proposed as the likely gold deposition mechanism. The sub- to greenschist facies metamorphism of the Tambien and Tsaliet Group rocks, the enrichment in Sb, and As, the brittle-ductile shearing experienced by the rocks, and the mineralization under brittle conditions suggest a depth of formation between 4 to 6 km. Generally, the findings of this study suggest that the genesis of metallic mineralization at Workamba is of orogenic gold type and unrelated to post-orogenic magmatism in the area, although a close spatial proximity to post-orogenic dikes/sills exists. The age of the mineralization is estimated to be late Neoproterozoic.

Theoretically, to fully describe the change in the medium around a point one needs three components of translation, six components of strain, and three components of rotation. It is expected that collocated measurements of translations and rotations may help (1) correcting translation signals recorded by classical seismometers for contamination by ground rotations, (2) extracting additional information on earthquake source properties, soil-structure interactions, and properties of the subsurface, and (3) providing additional ground motion information to earthquake engineers for seismic design. Thus, in addition to translations and strains, the rotational part of ground motions should also be recorded. However, the lack of instrumental sensitivity did not allow seismologists to observe rotational motions for decades. Recently, ring laser technology has provided the means to develop instruments that allow in principle the observation of rotational motions in a wide frequency band and epicentral distance range. Here we present the observations of rotational ground motions around a vertical axis in the P coda (the section between the onsets of direct P- and S- waves) of tele-seismic signals on a ring laser sensor at the Fundamental Observatory Wettzell, southeast Germany. The studies focus on finding the explanation for the observed P coda rotations as well as the way to extract additional information from the use of co-seismic rotational motions. First, the effects of co-seismic tilts on ring laser measurements are quantified based on magnitude-amplitude relations and translation derived tilts. Then the phenomenon of scattering assuming three dimensional random media and topography that may generate the observed P coda rotations is investigated through analysis of observations and forward modelling. The partitioning of P and S energy indicated by the stabilization of the ratio of energies of the two is used to constrain scattering properties. Finally, an analytical approach focusing on the solution of plane waves in linear elastic anisotropic media is used to quantify the anisotropic behavior through the variations of rotational wavefield. The focus is on quasi-P waves and transverse isotropic media. Kelvin-Christoffel equation and the Thomson parameters, descriptive of the degree of anisotropy, are used. The obtained results show that 1) P-SH scattering in the random crust is the main cause of the P-coda observations; and 2) rotational motions contain additional information (at least) about scattering properties and anisotropic coefficients and that joint measurements of translational and rotational motions at only one point allow the extraction of additional information. The results demonstrate the potential benefit not only of measurements of co-seismic rotational ground motions but also of the use of the amplitude content of seismic signals.

High-silica volcanic systems are considered to be the most devastating. Their highly viscous properties create a high pressurised non- fluent system which consequently relaxes the stress mostly by exploding through the brittle regime. Even if an explosion is avoided and the magma fl ows, it often generates lava domes at the top of the volcano; which, patiently, accumulate magmas that will rush down the slopes once the yield stress is crossed. Thus, such volcanoes have an explosive nature and often generate catastrophic pyroclastic flows. The modelling of magma ascent inside eruptive conduits is commonly based on fl uid mechanic principles. The difficulty of the approach is however not as much driven by the physical equations of the numerical model as the variability of the parameters of the magma itself. It is well established that the rheology of magma strongly depends on the temperature, the stress, the strain, the chemical composition, the crystal and the bubble contents. In other words, magmatic modelling involves a set of movement equations which call for a comportmental/rheological law. The movement equations give roughly equivalent results through the different models; however magma rheology is poorly controlled. The deformation of highly crystallised dome lavas is key to understanding their rheology and to fixing their failure onset. It is thus essential to adequately understand magma rheology before performing complex numerical models. Here we focus on the well studied Unzen volcano, in Japan, which had a recent period of activity between 1990 and 1995. The dome building eruptions in Unzen generate repeated dome failure and pyroclastic ows. They vary in character and behaviour from effusive domes to brittle pyroclastic events. Since then, the Unzen Scientic Drilling Project, initiated in April 1999, drilled through the volcano and sampled the eruptive conduit. This provides us with rare original samples for study and characterisation. The physico-chemical properties of these valuable samples were determined with an array of devices. Of these a large uniaxial deformation press, which can operate at high load (0 up to 300KN), and temperature (25-1200°C), will be of utmost importance. This press deforms the samples under known parameters and allows us to determine the viscosity of the melt. In this study we investigate the stress and strain-rate dependence on several glasses and Mt Unzen dome lavas. Their rheology has been determined for temperatures from 900 to 1010°C and stresses from 2 to 120 Mpa (60 MPa for crystal bearing melt) in uniaxial compression . This survey aims to distinguish the Non-Newtonian effects perturbing magmatic melts, also known as indicators of the brittle field. Towards our experiments we observed three majors viscosity decrease types: Two were dependant and typical of the solid fraction (Shear thinning & Time weakening effect). The first is instantaneous and on the whole recovered during stress release. The second is time dependent and non-recoverable. The third and last effect observed is attributed to the melt fraction and its self heating under stress (Viscous Heating Effect). We extensively investigated this last eect on pure silicate liquids and crystal bearing melts. Our findings suggest that most of the Non-Newtonians effects observed in silicate melts are linked to a self heating of the sample and can subsequently be corrected with the temperature without involving other laws than a pure viscous material. Moreover we observed that this self heating reorganise the energy distribution within the sample and by localising the strain may favours the formation of shear banding and the apparition of 'hot cracks'. Crystal bearing melts exhibit two more Non-Newtonian eects. The first one, the shear thinning, is typical of that observed in previous experiments on crystal-bearing melts. On crystal free melts, this viscosity decrease is observed at much lower magnitude. We infer that the crystal phase responds elastically to the stress applied and relaxes once the load is withdrawn. The second one, the time weakening effect, appears more complex and this regime depends on the stress (and/or strain-rate) history. We distinguish four different domains: Newtonian, non-Newtonian, crack propagation and failure domains. Each of these domains expresses itself as a dierent regime of viscosity decrease. Due to stress localisation, cracking appears in crystal-bearing melts (intra-phenocryst and/or the in the melt matrix) earlier than in crystal-free melts. For low stresses, the apparent viscosity is higher for crystal-bearing melts (as predicted by Einstein-Roscoe equations). However, while the stress (or strain rate) increases, the apparent viscosity is decreasing to that of the crystal-free melt and could be even lower if viscous heating effects are involved. Consequently, we emphasise that any numerical simulation performed without taking into account the strain-rate dependencies described above would overestimate the apparent viscosity by orders of magnitude. The magma dynamics will appears slower than in reality. Exaggerating the viscosity of a volcanic dynamic system would overestimate the time range available for a potential evacuation of the red zones. Applying a more realistic rheology would improve the early warning tools and improve the safety of the population surrounding volcanic systems.

A long-standing question in the study of Earth’s deep interior is the origin of seismic mantle heterogeneity. The challenge is to efficiently mine the wealth of information available in complex seismic waveforms and to separate the potential contributions of thermal anomalies and compositional variations. High expectations to gain new insight currently lie within the application of high-performance computing to geophysical problems. Modern supercomputers allow, for example, the simulation of global mantle flow at Earth-like convective vigor or seismic wave propagation through complex three-dimensional structures. The sophisticated computational tools incorporate a variety of physical phenomena and result in synthetic datasets that show a complexity comparable to real observations. However, it is so far not clear how to combine the results from the various disciplines in a consistent manner to obtain a better understanding of deep Earth structure from the expensive large-scale numerical simulations. In particular, it is important to understand how to build conceptual models of Earth’s mantle based on geodynamic considerations that can be quantitatively assessed and used to test specific hypotheses. One specific goal is to generate seismic heterogeneity from dynamic flow calculations that can be used in global wave propagation simulations so that synthetic seismograms can be directly compared to seismic data without the need to perform inversions. In the multi-disciplinary study presented here, a new method is developed to theoretically predict and assess seismic mantle heterogeneity. Forward modeling of global mantle flow is combined with information from mineral physics and seismology. Temperatures inside the mantle are obtained by generating a new class of mantle circulation models at very high numerical resolution. The global average grid spacing of ~25 km (around 80 million finite elements) allows for the simulation of flow at Rayleigh numbers on the order of 10^9 and to resolve a thermal boundary layer thickness of around 100 km. To assess the predicted present day temperature fields, the geodynamic flow calculations are post-processed with published thermodynamically self-consistent models of mantle mineralogy for a pyrolite composition to convert thermal structure into elastic parameters. Quantitative predictions of the magnitudes of seismic velocity and density variations are thereby possible due to the appropriately high numerical resolution necessary to obtain temperature variations that are consistent with the mineralogical conversion. The resulting structures are compared to tomographic models based on a variety of statistical measures taking into account the limited resolving power of the seismic data. In a final step, the geodynamic models are investigated with respect to the influence of strong convective mass transport on the stability of Earth’s rotation axis. This additional and independent analysis provides information on whether strongly bottom heated isochemical mantle circulation can be reconciled with paleomagnetic estimates of true polar wander. One specific question that can be addressed with this approach is the origin of two large regions of strongly reduced seismic velocities in the lowermost mantle. Several seismological observations are interpreted as being caused by compositional variations. However, a large number of recent geodynamical, mineralogical and also seismological studies argue for a strong thermal gradient across the core-mantle boundary that might provide an alternative explanation through the resulting large temperature variations. Here, the forward modeling approach is used to test the assumption whether the presence of a strong thermal gradient in isochemical whole mantle flow is compatible with a variety of geophysical observations. The results show that the temperature variations deduced from the new high-resolution mantle circulation models are capable of explaining gross statistical features of mantle structure mapped by tomography. The main finding is that models with strong core heating, which also give a surface heat flux consistent with observations, yield realistic depth profiles of root-mean-square (RMS) variations of shear wave velocity. Most importantly, only models with a large core contribution to the mantle energy budget are compatible with the strong negative seismic anomalies in the large low velocity provinces of the lower mantle. Taking into account the effects of limited resolving power of seismic data on the magnitudes of predicted seismic heterogeneity further improves this match to tomographic models. This illustrates that seismic heterogeneity is likely dominated by thermal variations and thus limits the possible role of chemical heterogeneity in the lower mantle. Altogether, the results strengthen the notion of strongly bottom heated isochemical whole mantle flow with a pyrolite composition. Furthermore, these findings give confidence in the consistency of the presented approach and demonstrate the great potential of geophysical large-scale high-performance simulations and their application to seismic data and tomographic models.

Many plate boundaries appear to be broad deformation zones, composed of several smaller microplates (e.g. California, Alaska, Mediterranean sea). To accurately address plate boundary deformation, as needed for seismic hazard assessment, it is important to study the motion of these microplates. Furthermore the dynamics of microplates, such as their driving forces and the implication of their motion on the surrounding plate boundary region are not well understood. Following suggestions from previous studies that Baja California is a microplate located within the North America – Pacific plate boundary region, a kinematic study using horizontal velocity data from Global Positioning System was performed. Building on the kinematic results and using numerical modelling techniques, a 2D mechanical model that simulates the transport of the Baja California microplate by lithospheric coupling with the Pacific plate was created. This model addresses the transport forces, and necessary preconditions in the North America – Pacific plate boundary region for rigid microplate transport. In addition, this model provides insights on the deformational response of western North America to Baja California motion, in particular the kinematic response of neighbouring microplates and the activation of passive fault systems. This latter was examined in more detail by separating the contribution of deformation from Baja California microplate motion and Sierra Nevada microplate motion to the formation of the Eastern California Shear Zone. Overall, it was found, that microplates play an important role for plate boundary kinematics and that their motion strongly influences the dynamics and fault evolution in plate boundary regions.

In the present work three topics are outlined which are connected via biomineralisation. The investigation of the mechanical response of brachiopod shell material, the macroscopic calcite crystal growth, and the microscopic calcite crystal growth are discussed. Brachiopod shells have been investigated with nanoindentation and scanning electron microscopy to determine the material properties and the effects of the microstructure on the material properties. Brachiopod shells are highly optimised fibre composite materials. The material properties are adapted to the local material demands. The calcitic brachiopod \emph{Megerlia truncata} exhibits a hard primary layer and a softer secondary layer with a tendency to higher hardness at the inner shell margin. At the hinge region the hardness is considerably higher and reflects the possibly high abrasive wear. The phosphatic brachiopod shells of \emph{Lingula anatina} and \emph{Discradisca stella} have laminated architecture with alternating hard and soft layers. They are harder in the center and have softer, more flexible regions at the margins. The macroscopic crystal growth of calcite was performed in gels. The obtained crystals were investigated with scanning electron microscopy. With inert pore solutions the $\left\{104\right\}$ rhombohedron is the dominating habit. Succinic acid and aspartic acid inhibit the acute steps of the calcite $\left\{104\right\}$ surface. In combination with $Mg^{2+}$ and $Sr^{2+}$ one side divergant forms are obtained. Pore solutions containing silicic acids produce catastrophic nucleation. Crystal aggregates from calcite, aragonite, and vaterite develop. The aggregates have morphological similarities with calcites from travertines. $Mg^{2+}$ and $Sr^{2+}$ counteract the effect of silicic acids. The microscopic crystal growth of the calcite $\left\{104\right\}$ surface was investigated with the atomic force microscope in the presence of silicic acids. The two dimensional nucleation is enhanced. The form of the hillocks change from the additive free rhomb to lenses with increasing silicic acids concentrations. The step velocities increase from 0 ppm to 20 ppm silicic acids and decrease after 20 ppm. Therefore silicic acids possess a promoter and a inhibitor effect on calcite crystal growth. The inhibitory effect can be fitted by a Langmuir isotherm. Both effects can be fitted together with a polynom of rank three. For supersaturation $\beta = 30$ the step velocities are constant. This means that the process follows the step pinning model.

Die vorliegende Arbeit behandelt zwei unterschiedliche Anwendungen aus dem Bereich der numerischen Seismologie: Das erste Thema umfasst die Entwicklung und Anwendung eines Programms zur Berechnung der lokalen Wellenausbreitung in seismischen Störungszonen (Fault Zones) mit spezieller Fokussierung auf geführte Wellen (Trapped Waves). Dieser Wellentyp wird an vielen Störungszonen beobachtet und aus seinen Eigenschaften können Informationen über die jeweilige Tiefenstruktur abgeleitet werden. Das zweite Thema dieser Arbeit behandelt die Entwicklung und Anwendung zweier Verfahren zur Berechnung der globalen Wellenausbreitung, also der Ausbreitung seismischer Wellen durch die gesamte Erde einschließlich des äußeren und inneren Erdkerns. Die verwendeten Methoden ermöglichen es, kleinräumige Strukturen in großen Tiefen wie zum Beispiel die Streueigenschaften des Erdmantels oder die kleinskalige Geschwindigkeitsstruktur an der Kern-Mantelgrenze in knapp 2900 km Tiefe zu untersuchen. Wellenausbreitung in seismischen Störungszonen: Seismische Störungszonen, wie zum Beispiel der San Andreas Fault in Kalifornien, zeigen auf beeindruckende Weise, wie die Gestalt der Erdoberfläche durch seismische Aktivität als Folge tektonischer Prozesse geprägt wird. Die genaue Kenntnis der Tiefenstruktur einer Störungszone hingegen bietet zusätzlich einen Einblick in die vergangene Seismizität, die die Struktur der jeweiligen Störung geprägt hat. Neben den tektonischen Eigenschaften einer Region lassen sich aus der Tiefenstruktur auch Voraussagen über Häufigkeit und zu erwartende Stärke zukünftiger Erdbeben ableiten. Da Erdbeben vorzugsweise in solchen Störungszonen auftreten, ist eine möglichst genaue Kenntnis der Geometrie einer Schwächezone wichtig, um Regionen mit erhöhtem Gefährdungspotenzial zu erkennen. Für die Untersuchung der Tiefenstruktur einer Störungszone stehen in vielen Fällen ausschließlich Messungen von der Erdoberfläche zur Verfügung, etwa von seismischen Netzen, die in unmittelbarer Umgebung oder direkt auf einer Störung platziert wurden. Ereignet sich nun ein Erdbeben in einigen Kilometern Tiefe innerhalb der Störungszone, breitet sich ein Teil der angeregten seismischen Wellen durch die gesamte Störungszone bis zur Erdoberfläche aus, wo sie registriert werden. Die aufgezeichneten Signale werden somit entlang ihres gesamten Laufweges durch die Struktur der Störungszone beeinflusst, was die Ableitung der tiefenabhängigen Struktur aus den Messdaten erschwert. Um trotzdem ein genaues seismisches Abbild einer Störungszone zu bekommen, analysiert man unterschiedliche Wellentypen im Seismogramm, wodurch ein Maximum an Strukturinformation abgeleitet werden kann. Einer dieser Wellentypen, der sich durch besondere Eigenschaften auszeichnet, ist die geführte Welle (Trapped Wave). Diese entsteht, wenn eine Störungszone einen ausgeprägten vertikal ausgedehnten Bereich drastisch reduzierter seismischer Ausbreitungsgeschwindigkeit (Low Velocity Layer) und nicht zu komplexer Geometrie besitzt, der als seismischer Wellenleiter wirkt. In einem solchen Wellenleiter kann sich eine geführte Welle ausbreiten, die als mit Abstand stärkstes Signal an der Erdoberfläche registriert wird, also deutlich stärkere Bodenbewegungen hervorruft als etwa die direkte Welle. Dieser Verstärkungseffekt hat unter anderem Konsequenzen für die Abschätzung der seismischen Gefährdung in der Nähe einer Störungszone, zum Beispiel wenn die Störungszone durch dicht besiedeltes Gebiet verläuft. Geführte Wellen beinhalten aufgrund ihrer hohen Sensitivität bezüglich der Eigenschaften von Niedergeschwindigkeitszonen Strukturinformationen, die aus anderen Wellentypen nicht abgeleitet werden können. Daher leistet das Verständnis dieses Wellentyps einen wichtigen Beitrag für die Ableitung möglichst vollständiger Modelle von Störungszonen. Ausbreitung von SH- und P-SV Wellen in Erdmantel und der ganzen Erde: Das allgemeine Verständnis der Struktur und Dynamik des tiefen Erdinneren basiert zu einem großen Teil auf den Ergebnissen der globalen Seismologie. Im Gegensatz zum ersten Teil dieser Arbeit haben diese Erkenntnisse keine unmittelbare Auswirkung auf unser tägliches Leben. Jedoch liefert die Kenntnis des inneren Aufbaus der Erde wichtige Erkenntnisse für die geophysikalische Grundlagenforschung bis hin zum Verständnis der Entstehungsgeschichte der Erde und unseres Planetensystems. Die Modellierung der globalen seismischen Wellenausbreitung unterscheidet sich von der lokalen Modellierungen in zwei wesentlichen Punkten: (1) die wesentlich größere Ausdehnung globaler Modelle, welche die gesamte Erde oder zumindest große Teile des Erdinnern beinhalten, und (2) der Eigenschaft seismischer Wellen, sich im globalen Maßstab hauptsächlich in der Ebene auszubreiten, die durch den Großkreis zwischen Quelle und Empfänger aufgespannt wird. Beide Punkte legen nahe, zur Verringerung des Rechenaufwands eine Symmetriebedingung einzuführen. In dieser Arbeit wird durch die Formulierung von Wellengleichung und Modell in einem sphärisch-achsensymmetrischen Koordinatensystem der – im globalen Maßstab im Allgemeinen geringe – Anteil von Variationen der seismischen Parameter und von Wellenfeldanteilen orthogonal zur Großkreisebene vernachlässigt. Diese Beschränkung führt zu einer enormen Einsparung an Rechenressourcen, da das zu berechnende seismische Wellenfeld nur noch zwei Dimensionen aufspannt. Eine Folge der Achsensymmetrie ist die Aufspaltung des seismischen Wellenfeldes in einen SH- und einen P-SV Anteil. Beide Wellenfeldanteile sind voneinander entkoppelt und breiten sich in unterschiedlichen Regionen des Erdinneren aus. Zur Berechnung des SH- und des P-SV Wellenfeldes wurden daher in dieser Arbeit zwei separate Programme SHaxi und PSVaxi entwickelt. Kapitel 3 behandelt die Berechnung des globalen SH Wellenfeldes für Achsensymmetrische Geometrien mit dem im Rahmen dieser Arbeit entwickelten Programm SHaxi. Das SH Wellenfeld besteht aus horizontal polarisierten Scherwellen, die sich in guter Näherung ausschließlich im Erdmantel, also zwischen Erdoberfläche und Kern-Mantelgrenze ausbreiten. Somit muss nur der Erdmantel als Modellraum abgebildet werden, was die Diskretisierung des Modells und die Implementierung der Wellengleichung deutlich vereinfacht. Um eine Anwendung auf modernen Parallelcomputern mit verteilter Speicherarchitektur zu ermöglichen, wurde der Modellraum durch vertikale Schnitte in gleichgroße Segmente geteilt, die von den einzelnen Elementen (Knoten) eines Parallelrechners getrennt bearbeitet werden können. Das Wellenfeld in den Randbereichen dieser Segmente muss dabei nach jedem Zeitschritt explizit zwischen benachbarten Knoten ausgetauscht werden, um die Ausbreitung durch das gesamte Modell zu ermöglichen. Ein wesentlicher Aspekt des Kapitels ist die Verifikation des Verfahrens unter besonderer Berücksichtigung der implementierten Ringquelle. Durch einen Vergleich mit analytisch berechneten Seismogrammen werden die Eigenschaften der implementierten achsensymmetrischen Ringquelle diskutiert und es wird gezeigt, dass das Programm korrekte Seismogramme berechnet, die mit einer realistischen Double-Couple Quelle vergleichbar sind. Abschließend werden bisherige Anwendungen des Programms gezeigt: (1) die Modellierung von Streuung im gesamten Erdmantel und (2) die Untersuchung von kleinskaliger Topographie der D“ Schicht im untersten Erdmantel. Kapitel 4 behandelt das Gegenstück des im vorherigen Kapitel behandelten Verfahrens: Das Programm PSVaxi zur Berechnung des globalen P-SV Wellenfeldes für achsensymmetrische Geometrien. Im Gegensatz zum SH Wellenfeld breitet sich das P-SV Wellenfeld nicht nur im Erdmantel sondern auch im äußeren und inneren Erdkern aus. Dies erforderte eine Erweiterung des Modellraums bis praktisch zum Erdmittelpunkt, die sich mit dem im SH Fall verwendeten gleichförmigen Gitter aufgrund von Grundsätzlichen Stabilitätsproblemen des verwendeten Finite Differenzen Verfahrens nicht durchführen lässt. Um diesen zusätzlichen Modellraum zu erschließen wurde eine Mehrgebietsmethode (Multi-Domain Method) implementiert. Diese füllt zusätzliche Tiefenbereiche mit neuen, jeweils gleichförmigen Gittern (Domains) aus, deren Gitterabstände an den jeweiligen Tiefenbereich angepasst sind, was für die notwendige Stabilität des Verfahrens sorgt. Zusätzlich zur tiefenabhängigen Aufteilung des Modellraumes in gleichförmige Gitter wurde eine Parallelisierung vorgenommen, um das Programm auf Parallelcomputern nutzen zu können. Dazu wurde der Modellraum durch horizontale Schnitte in einzelne Segmente zerlegt, die – analog zu den vertikalen Schnitten bei der SHaxi Parallelisierung – von den einzelnen Knoten eines Parallelrechners bearbeitet werden können. Die Kombination von Mehrgebietsmethode und Segmentierung führt zu einem recht aufwendigen Algorithmus, erlaubt jedoch die Berechnung des hochfrequenten globalen Wellenfeldes durch die ganze Erde auf Parallelrechnern mit vergleichsweise geringem Rechenaufwand. Erste Anwendungen des PSVaxi Programms werden am Ende des Kapitels diskutiert: (1) eine exemplarische Modellierung der Wellenausbreitung in einer angenommenen D“ Schicht mit Topographie (2) eine Studie des Einflusses von Niedergeschwindigkeitszonen mit Topographie auf seismische Phasen, die durch den untersten Mantel und den äußeren Kern verlaufen und (3) eine Arbeit, die die Streueigenschaften des Mantels aus an der Kern-Mantelgrenze diffraktieren Wellen ableitet.