This study is concerned with the computation of seismic first-arrival traveltimes in anisotropic media using finite difference eikonal methods. For this purpose, different numerical schemes that directly solve the eikonal equation are implemented and assessed numerically. Subsequently, they are used for pre-stack depth migration on synthetic and field data. The thesis starts with a detailed examination of different finite difference methods that have gained popularity in scientific literature for computing seismic traveltimes in isotropic media. The most appropriate for an extension towards anisotropic media are found to be the so-called Fast Marching/Sweeping methods. Both schemes rely on different iteration strategies, but incorporate the same upwind finite difference Godunov schemes that are implemented up to the second order. As a result, the derived methods exhibit high numerical accuracy and perform robustly even in highly contrasted velocity models. Subsequently, the methods are adapted for transversely isotropic media with vertical (VTI) and tilted (TTI) symmetry axes, respectively. Therefore, two different formulations for approximating the anisotropic phase velocities are tested, which are the weakly-anisotropic and the pseudo-acoustic approximation. As expected, the pseudo-acoustic formulation shows superior accuracy especially for strongly anisotropic media. Moreover, it turns out that the tested eikonal schemes are generally more accurate than anisotropic ray tracing approaches, since they do not require an approximation of the group velocity. Numerical experiments are carried out on homogeneous models with varying strengths of anisotropy and the industrial BP 2007 benchmark model. They show that the computed eikonal traveltimes are in good agreement with independent results from finite difference modelling of the isotropic and anisotropic elastic wave equations, and traveltimes estimated by ray-based wavefront construction, respectively. The computational performance of the TI eikonal schemes is largely increased compared to their original isotropic implementations, which is due to the algebraic complexity of the anisotropic phase velocity formulations. At this point, the Fast Marching Method is found to be more efficient on models containing up to 50 million grid points. For larger models, the anisotropic Fast Sweeping implementation gradually becomes advantageous. Here, both techniques perform independently well of the structural complexity of the underlying velocity model. The final step of this thesis is the application of the developed eikonal schemes in pre-stack depth migration. A synthetic experiment over a VTI/TTI layer-cake model demonstrates that the traveltime computation leads to accurate imaging results including a tilted, strongly anisotropic shale layer. The experiment shows further that the estimation of anisotropic velocity models solely from surface reflection data is highly ambiguous. In a second example, the eikonal solvers are applied for depth imaging of two-dimensional field data that were acquired for geothermal exploration in southern Tuscany, Italy. The developed methods also produce clear imaging results in this setting, which illustrates their general applicability for pre-stack depth imaging, particularly in challenging environments.

This study is concerned with the computation of seismic first-arrival traveltimes in anisotropic media using finite difference eikonal methods. For this purpose, different numerical schemes that directly solve the eikonal equation are implemented and assessed numerically. Subsequently, they are used for pre-stack depth migration on synthetic and field data. The thesis starts with a detailed examination of different finite difference methods that have gained popularity in scientific literature for computing seismic traveltimes in isotropic media. The most appropriate for an extension towards anisotropic media are found to be the so-called Fast Marching/Sweeping methods. Both schemes rely on different iteration strategies, but incorporate the same upwind finite difference Godunov schemes that are implemented up to the second order. As a result, the derived methods exhibit high numerical accuracy and perform robustly even in highly contrasted velocity models. Subsequently, the methods are adapted for transversely isotropic media with vertical (VTI) and tilted (TTI) symmetry axes, respectively. Therefore, two different formulations for approximating the anisotropic phase velocities are tested, which are the weakly-anisotropic and the pseudo-acoustic approximation. As expected, the pseudo-acoustic formulation shows superior accuracy especially for strongly anisotropic media. Moreover, it turns out that the tested eikonal schemes are generally more accurate than anisotropic ray tracing approaches, since they do not require an approximation of the group velocity. Numerical experiments are carried out on homogeneous models with varying strengths of anisotropy and the industrial BP 2007 benchmark model. They show that the computed eikonal traveltimes are in good agreement with independent results from finite difference modelling of the isotropic and anisotropic elastic wave equations, and traveltimes estimated by ray-based wavefront construction, respectively. The computational performance of the TI eikonal schemes is largely increased compared to their original isotropic implementations, which is due to the algebraic complexity of the anisotropic phase velocity formulations. At this point, the Fast Marching Method is found to be more efficient on models containing up to 50 million grid points. For larger models, the anisotropic Fast Sweeping implementation gradually becomes advantageous. Here, both techniques perform independently well of the structural complexity of the underlying velocity model. The final step of this thesis is the application of the developed eikonal schemes in pre-stack depth migration. A synthetic experiment over a VTI/TTI layer-cake model demonstrates that the traveltime computation leads to accurate imaging results including a tilted, strongly anisotropic shale layer. The experiment shows further that the estimation of anisotropic velocity models solely from surface reflection data is highly ambiguous. In a second example, the eikonal solvers are applied for depth imaging of two-dimensional field data that were acquired for geothermal exploration in southern Tuscany, Italy. The developed methods also produce clear imaging results in this setting, which illustrates their general applicability for pre-stack depth imaging, particularly in challenging environments.

Eskers are long winding ridges that originate from gravel that has travelled in meltwater streams in glaciers. At the study site, Virttaankangas plane in southwest Finland, there are esker structures covered by sediments. One reason why it is important to study eskers is because they are used for purifying drinking water. The data used in the study were collected during a seismic survey in July 2014. During the survey a controlled source created seismic waves that travelled down through the earth and then reflected back up again. By detecting the travel time of the waves and estimating the velocity of the geologic layers, the depth to the reflecting structures could be calculated. There are two types of waves that travel through the body of the earth, pressure waves (P-waves) and shear waves (S-waves). In a previous study (Maries et al., 2017) P-wave data from the same survey have been analyzed, so this work focuses on S-wave data but also compares the result from the two. Some structures related to eskers were identifiable, such as fractures in the bedrock from the pressure of the main esker core. By comparing S- and P-wave results it was possible to see hints of the arched esker cores and esker fan lobes. Overall the result confirmed the model that was achieved of the profile in the previous study. The location of the bedrock both matched with the previous study, and added information about its orientation. An additional goal was to demonstrate the insensitivity of S-waves to water content by showing that if there was a water table reflection in the P-wave data, this reflection was missing in the S-wave data. The results showed water table reflections in the P-wave data, but there were no distinguishable water table reflections with appropriate velocity for S-waves in the S-wave data. / Rullstensåsar definieras som långa åsar med storlekssorterat grus som avlagrats av smältvattenströmmar i glaciärer. Vid undersökningsplatsen, Virttaankangasheden i sydvästra Finland, finns rullstensåsstrukturer som är begravda under sediment. En anledning till varför det är viktigt att undersöka rullstensåsar är att de används för filtrering vid framställning av dricksvatten. De data som användes i denna studie inhämtades under en seismisk undersökning i juli 2014. Undersökningen gick till på så vis att en kontrollerad källa skapade seismiska vågor som färdades ner i jorden för att sedan reflekteras tillbaka upp mot ytan. Genom att notera tiden det tog för vågorna att färdas, samt uppskatta hastigheten i de geologiska lagren, kunde djupet till de reflekterande strukturerna beräknas. Det finns två sorters vågor som kan färdas genom jorden, tryckvågor (P-vågor) och skjuvvågor (S-vågor). I en tidigare studie (Maries et al., 2017) analyserades P-vågsdata från samma seismiska undersökning, så detta arbete fokuserar på S-vågsdata men jämför också resultaten av båda två. Vissa strukturer kopplade till rullstensåsar kunde identifieras, så som sprickor i begrgrunden från trycket av den största rullstensåsen. Genom att jämföra resultat från S- och P-vågor kunde man se reflektioner från rullstensåsar och sediment. Sammantaget bekräftade resultatet den modell över profilen som framtagits i den tidigare studien. Berggrundens läge stämde överens med den förra studien och tillförde ny information om dess orientering. Utöver detta försökte man också demonstrera S-vågors okänslighet för vatten genom att visa att om det fanns reflektioner från grundvattenytan i P-vågsdatan så skulle de reflektionerna inte synas i S-vågsdatan. I P-vågsdatan visade det sig att det fanns grundvattenreflektioner, men det gick inte att urskilja några liknande reflektioner i S-vågsdatan.

Die folgende Arbeit ist Teil des multidisziplinären Projektes DESERT (DEad SEa Rift Transect), welches seit dem Jahr 2000 im Nahen Osten durchgeführt wird. Dabei geht es primär um die Struktur der südlichen Dead Sea Transform (DST; Tote-Meer-Transformstörung), Plattengrenze zwischen Afrika (Sinai) und der Arabischen Mikroplatte. Seit dem Miozän beträgt der sinistrale Versatz an dieser bedeutenden aktiven Blattverschiebung mehr als 100 km. Das steilwinkelseismische (NVR) Experiment von DESERT querte die DST im Arava Tal zwischen Rotem Meer und Totem Meer, wo die Hauptstörung auch Arava Fault genannt wird. Das 100 km lange Profil erstreckte sich von Sede Boqer/Israel im Nordwesten nach Ma'an/Jordanien im Südosten und fällt mit dem zentralen Teil einer weitwinkelseismischen Profillinie zusammen. <br><br> Steilwinkelseismische Messungen stellen bei der Bestimmung der Krustenstruktur bis zur Krusten/Mantel-Grenze ein wichtiges Instrument dar. Obwohl es kaum möglich ist, steilstehende Störungszonen direkt abzubilden, geben abrupte Veränderungen des Reflektivitätsmuster oder plötzlich endende Reflektoren indirekte Hinweise auf Transformbewegung. Da bis zum DESERT Experiment keine anderen reflexionsseismischen Messungen über die DST ausgeführt worden waren, waren wichtige Aspekte dieser Transform-Plattengrenze und der damit verbundenen Krustenstruktur nicht bekannt. Mit dem Projekt sollte deshalb untersucht werden, wie sich die DST sowohl in der oberen als auch in der unteren Kruste manifestiert. Zu den Fragestellungen gehörte unter anderem, ob sich die DST bis in den Mantel fortsetzt und ob ein Versatz der Krusten/Mantel-Grenze beobachtet werden kann. So ein Versatz ist von anderen großen Transformstörungen bekannt. <br><br> In der vorliegenden Arbeit werden zunächst die Methode der Steilwinkelseismik und die Datenverarbeitung kurz erläutert, bevor die Daten geologisch interpretiert werden. Bei der Interpetation werden die Ergebnisse anderer relevanter Studien berücksichtigt. Geologische Geländearbeiten im Gebiet des NVR Profiles ergaben, dass die Arava Fault zum Teil charakterisiert ist durch niedrige Steilstufen in den neogenen Sedimenten, durch kleine Druckrücken oder Rhomb-Gräben. Ein typischer Aufbau der Störungszone mit einem Störungskern, einer störungsbezogenen Deformationszone und einem undeformierten Ausgangsgestein, wie er von anderen großen Störungszonen beschrieben worden ist, konnte nicht gefunden werden. Deshalb wurden zur Ergänzung der Reflexionsseismik, welche vor allem die tieferen Krustenstrukturen abbildet, ASTER (Advanced Spacebourne Thermal Emission and Reflection Radiometer) Satellitendaten herangezogen, um oberflächennahe Deformation und neotektonische Aktivität zu bestimmen. / Following work is embedded in the multidisciplinary study DESERT (DEad SEa Rift Transect) that has been carried out in the Middle East since the beginning of the year 2000. It focuses on the structure of the southern Dead Sea Transform (DST), the transform plate boundary between Africa (Sinai) and the Arabian microplate. The left-lateral displacement along this major active strike-slip fault amounts to more than 100 km since Miocene times. The DESERT near-vertical seismic reflection (NVR) experiment crossed the DST in the Arava Valley between Red Sea and Dead Sea, where its main fault is called Arava Fault. The 100 km long profile extends in a NW&mdash;SE direction from Sede Boqer/Israel to Ma'an/Jordan and coincides with the central part of a wide-angle seismic refraction/reflection line. <br><br> Near-vertical seismic reflection studies are powerful tools to study the crustal architecture down to the crust/mantle boundary. Although they cannot directly image steeply dipping fault zones, they can give indirect evidence for transform motion by offset reflectors or an abrupt change in reflectivity pattern. Since no seismic reflection profile had crossed the DST before DESERT, important aspects of this transform plate boundary and related crustal structures were not known. Thus this study aimed to resolve the DST's manifestation in both the upper and the lower crust. It was to show, whether the DST penetrates into the mantle and whether it is associated with an offset of the crust/mantle boundary, which is observed at other large strike-slip zones. <br><br> In this work a short description of the seismic reflection method and the various processing steps is followed by a geological interpretation of the seismic data, taking into account relevant information from other studies. Geological investigations in the area of the NVR profile showed, that the Arava Fault can partly be recognized in the field by small scarps in the Neogene sediments, small pressure ridges or rhomb-shaped grabens. A typical fault zone architecture with a fault gauge, fault-related damage zone, and undeformed host rock, that has been reported from other large fault zones, could not be found. Therefore, as a complementary part to the NVR experiment, which was designed to resolve deeper crustal structures, ASTER (Advanced Spacebourne Thermal Emission and Reflection Radiometer) satellite images were used to analyze surface deformation and determine neotectonic activity.