1. Global/regional wave propagation through complex 3D heterogeneous Earth models
Present / introduce / motivate
After Introduction to the topic
Answer the question why DG
Differences to the elaborated spectral element method
In detail stress the difference of approximation of material values between the methods
Give conclusion and outlook

2. Outline 1. Why do we develop global simulation tools?
2. Why do we use the Discontinuous-Galerkin method?
3. What are the experiences in applying the method?
4. How do we have to focus the developments?
At first a quick overview on my presentation outline.
After the motivation of the project i will answer the question why we are using DG.
So I will explain why and for which applications the dg method is useful.
And afterwards I will show some preliminary results on the application of the method to global scale simulations.
Finally i will conclude the important facts of my talk and give an outlook on the further development of the project.

3. Motivation Imaging the Earth/Study Earthquake physics
Computational power increases exponentially
Inversion of full waveforms
Numerical simulations for 3D heterogeneous Earth models
Focus on Finite-Element methods
High order accurate and fast enough
Different implementations for different applications
There is no all in one algorithm
SEM – “faster but simple models”
DG – “slower but complex models”
Many other…
Wir wollen etwas über dynamische Eigenschaften der Erde rausfinden
Nutzen von allen Bereichen der Geowissenschaften: Geophysik, Geodynamik, Geologie, Geochemie, Mineralogie
Daraus werden theoretische Erdmodelle abgeleitet für alle möglichen Parameter wie Temperatur, Druck, Viskosität
In Seismologie sind wir an elastodynamischen Parametern interessiert die wir von Beobachtungen ableiten können.
Diese Paramter bestimmen wie sich eine mechanische Welle in der Erde ausbreitet. Ändern wir also die Parameter verändern wir das Verhalten der Wellenausbreitung. Das führt zu Veränderungen in der Ankunftszeit von bestimmten Phasen oder zur Veränderung der Form der Welle.
Zu überprüfung der Modelle nutzen wir sogenannte Vorwärtsberechnungen die z.B. analytisch ausgeführt werden. D.h. wir nehmen eine mathematische Rechenvorschrift für die Berechnung der Wellenausbreitung stecken das Erdmodell rein und erzeugen so synthetische Seismogramme. Die systematische Veränderung des reingesteckten Modells kann dann Effekte der Wellenausbreitung aufzeigen.
Wenn die Modelle 3D und heterogen sind genügen analytische Ansätze nicht mehr und wir müssen kompliziertere numerische Ansätze heran ziehen.
Das Ergebnis sieht man im unteren Beispiel. Die durchgezogene Kurve sind die Daten eines Erdbebens und die gestrichelte Kurve ist das synthetische Ergebnis. Die Hauptmerkmale passen.
Motivation Why DG? Experiences Focus 3

4. Project aim
Adaptation of the new Discontinuous-Galerkin method to global/regional wave propagation
Code development
Benchmarking with elaborated numerical methods
High quality mesh generation
Application to models of complex geometries and strong material gradients
Main focus of the project is the technical improvement and verification of the code
To develop a modeling tool for the simulations of complex 3D earth models
Systematic code development is only possible with comparison to elaborated numerical methods.
Another crucial point beneath the code development is the question how we can generate high quality meshes .
The DG method uses unstructured tetrahedral grids which offer high flexibility in the mesh generation process.
But it is still not straightforward to mesh small scale structures easily.
requirements
Unstructured tetrahedral grid, PREM model
Motivation Why DG? Experiences Focus 4

5. Outline 1. Why do we develop global simulation tools?
2. Why do we use the Discontinuous-Galerkin method?
3. What are the experiences in applying the method?
4. How do we have to focus the developments?
At first a quick overview on my presentation outline.
After the motivation of the project i will answer the question why we are using DG.
So I will explain why and for which applications the dg method is useful.
And afterwards I will show some preliminary results on the application of the method to global scale simulations.
Finally i will conclude the important facts of my talk and give an outlook on the further development of the project.

6. FEM tools Spectral-Element method Why another algorithm?
High order method with spectral convergence
Structured hexahedral grid
Why another algorithm?
Ratio of element size: hmin/hmax <<1
SEM: global time step -> simulation “explodes”
Discontinuous-Galerkin method
Easy mesh refinement
Local system → easier to parallelize
SeisSol features: time integration as good as spatial approximation, local time stepping, local polynomial degree
Structured hexahedral grid (Komatitsch et al. (2002)
Determined defined given specified
DG ist auch viel flexibler was komplexe Gitter angeht. Heterogene Modelle und starke Geschwindigkeitsänderungen von einer Größenordnung können mit Hexaedern nicht ohne weiteres berücksichtigt werden. Übergang an Grenzschichten ist schwierig da neue Elemente eingefügt werden müssen. Statisch festlegen wo vergrößerung des gitters in bezug auf geschwindigkeit nötig ist. Momentan gibt es diese Modelle noch nicht, aber bald. Exaflop bald.
The discontinuous Galerkin method uses sophisticated triangulation methods for tetrahedra but this causes higher computational costs.
The crucial advantage is the effective and accurate grid generting process and its robustness when meshing any general shape.
In addition because of the arbitrarily high approximation order numerical dispersion effects are minimized.
Vorstellung dass es automatischen Gittererzeuger gibt, der Gridspacing an Modell anpasst.
Versagen von SpecFEM Diplomarbeit Matthias Meschede!!! Jacobian wird zu klein!
SEM – spektrale Konvergenz, Konvergenzordnung des Fehlers wenn Gitter kleiner wird. Inversion einer vollbesetzten globalen Massenmatrix ist furchtbar. Stärke von SpecFEM ist diagonale Massenmatrix mit CubedSphere.
Unstructured tetrahedral grid, PREM with refined Kernel
Motivation Why DG? Experiences Focus 6

7. Outline 1. Why do we develop global simulation tools?
2. Why do we use the Discontinuous-Galerkin method?
3. What are the experiences in applying the method?
4. How do we have to focus the developments?
At first a quick overview on my presentation outline.
After the motivation of the project i will answer the question why we are using DG.
So I will explain why and for which applications the dg method is useful.
And afterwards I will show some preliminary results on the application of the method to global scale simulations.
Finally i will conclude the important facts of my talk and give an outlook on the further development of the project.

8. Explosive source PREM no crust PREM with crust
High frequency simulation only on a regional scale
Problem: Boundary reflections
Motivation Why DG? Experiences Focus

9. Raw Mineos data look like this!
Realistic source
CMT: Norwegian Sea (M=6.0, )
Lat/Lon/Depth = 72.2°/0.84°/12km
dip ≈ 30°, oblique slip
Raw Mineos data look like this!
Any suggestions?
Motivation Why DG? Experiences Focus

10. Attenuation 1D iso PREM + explosive source + attenuation
Comparison of Mineos and SpecFEM
Difference in relaxation mechanisms or attn. model?
Motivation Why DG? Experiences Focus

11. 1. Why do we develop global simulation tools?
Outline
1. Why do we develop global simulation tools?
2. Why do we use the Discontinuous-Galerkin method?
3. What are the experiences in applying the method?
4. How do we have to focus the developments?
At first a quick overview on my presentation outline.
After the motivation of the project i will answer the question why we are using DG.
So I will explain why and for which applications the dg method is useful.
And afterwards I will show some preliminary results on the application of the method to global scale simulations.
Finally i will conclude the important facts of my talk and give an outlook on the further development of the project.

12. Conclusions
Benchmarking up to intermediate frequency and simple 1D isotropic Earth model works
Modeling Tasks:
1D-Model: Investigate differences for real source and visco-elastic modeling results
3D-Model: real source + attenuation (+ anisotropy)
Application: Cascadia, Europe…
Quest benchmark library
Code development:
Perfectly Matched Layers
Load balancing using space filling curves
Streamline routines
Motivation Why DG? Experiences Focus