Finite Differences - LMUigel/Lectures/NMG/... · 2010. 7. 14. · ¾Compact codes ¾Easy to...
Transcript of Finite Differences - LMUigel/Lectures/NMG/... · 2010. 7. 14. · ¾Compact codes ¾Easy to...
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1Computational seismology - applications
Computational seismology: applications
Finite DifferencesCartesian grids
Fault zone wavesLos Angeles Basin Earthquake scenarios (Olsen)
Spherical gridsGlobal SH and P-SV wave propagationSpherical sections – waves in subduction zones
Spectral Element MethodRegular grids
Time reversal (Finite source inversion)Full waveform inversion on a continental scale
Irregular/unstructured gridsSoil-structure interactionEarthquake scenarios
Global wave propagation (Komatitsch and Tromp)
Discontinuous Galerkin Methods: WHY?
With studies by Jahnke, Fohrmann, Cochard, Käser, Fichtner, Stuppazzini, Ripperger, Nissen- Meyer, Kremers, Brietzke, a.o., (all LMU) as well as Olsen, Komatitsch, Tromp a.o.
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2Computational seismology - applications
The Forward Problem … a glossary …
What method should I use for a specific problem?
Numerical Methodslow-order vs. high order methods; FD, FE, SE, FV, DG, BE; global vs. local
time stepping
Geometrical complexity, computational gridsregular, unstructured, adaptive meshes; conforming vs. non-conforming
meshes; tetrahedral vs. hexahedral grids (combinations)
Parallelizationmesh partitioning, load balancing, optimization, multi-platform implementations,
parallel scaling
Large data volume handlingpost-processing, visualization, transfer and storage
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3Computational seismology - applications
Finite Differences
FD approximations in space and timeSimple to understandCompact codesEasy to parallelizeHard to get boundary conditions (free surface, absorbing) accurate„brute force“ approach
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4Computational seismology - applications
FD Cartesian Grids
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5Computational seismology - applications
FD – Fault zone wave propagation
Aftershock recordingsafter the 1999 M7.4 Izmit earthquake
From:Ben-Zion, Peng, Okaya, Seeber, Armbruster, Michael, Ozer, SSA2002
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6Computational seismology - applications
FZ trapped waves
Near fault
At distance (about 300m) from fault
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Observations across FZ
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8Computational seismology - applications
Benchmarking
Comparison of analytical solution (Ben-Zion, 1990)with staggered FD method
Comparison of analytical solution (Ben-Zion, 1990)with staggered FD method
unfiltered filtered
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9Computational seismology - applications
FZ discontinuities
Is FZ continuous at depth?Is FZ continuous at depth?
FZ continuousFZ continuous
FZ discontinuousFZ discontinuous
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10Computational seismology - applications
Shallow fault zones
Considerable FZ trapped wave energy generated.
Considerable FZ trapped wave energy generated.
Receivers
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Volume that generates FZ waves
Receiver
Fohrmann et al. 2002.
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12Computational seismology - applications
Earthquake scenarios based on FD
A number of stunningvisualizations of earthquakescenarios can be found here(code by Kim Olsen, SDSU):
http://visservices.sdsc.edu/projects/scec/t erashake/2.1/
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Earthquake scenarios Los Angeles
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14Computational seismology - applications
FD Cartesian Grids3-D with topography
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15Computational seismology - applications
Volcanoes
What is the contribution of topography to scattering?Can we simulate the seismic signatures of pyroclastic flows?
What is the contribution of topography to scattering?Can we simulate the seismic signatures of pyroclastic flows?
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Blocky topography
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Particle Motions
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FD Spherical Gridsaxisymmetric
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19Computational seismology - applications
Waves in spherical coordinates
Equations of motion (velocity – stress)
(.) = 0 Axisymmetric
Models
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Grids in spherical geometry
P-SV
SH
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21Computational seismology - applications
SH wave propagation
Red and yellow denote positive and negative displacement
Wavefield for source at 600km depth.
Symmetry axis
z.B. Igel und Weber, 1995Chaljub und Tarantola, 1997
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22Computational seismology - applications
Benchmarking
DSM: Direct solution method by Geller, Cummins, ...
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23Computational seismology - applications
Towards 3-D global wave propagation
multi-domainmulti-domain unstructuredunstructured
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24Computational seismology - applications
Global P-wave propagation
PKiKP
PK(P)
PcPP
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25Computational seismology - applications
Waves through random mantle models
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26Computational seismology - applications
SH - Wave effects
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27Computational seismology - applications
Is the mantle faster than we think?
Jahnke, Thorne, Cochard, Igel, GJI, 2008
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28Computational seismology - applications
FD Spherical Grids3-D sections
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29Computational seismology - applications
Spherical section – regular grid
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30Computational seismology - applications
Waves in spherical sections
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31Computational seismology - applications
Subduction zones
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32Computational seismology - applications
Subduction zones
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33Computational seismology - applications
Can we observe such effects?
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34Computational seismology - applications
Spectral element methodCartesian grids
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35Computational seismology - applications
Synthethic experiment: source inversion
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36Computational seismology - applications
True source
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37Computational seismology - applications
Seismograms
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38Computational seismology - applications
Time reversal – point source
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39Computational seismology - applications
Time reversal: real network
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40Computational seismology - applications
Time reversal: ideal network
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41Computational seismology - applications
Real data: Tottori earthquake
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42Computational seismology - applications
Reverse movie
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43Computational seismology - applications
Focus time
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44Computational seismology - applications
Projection on fault
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45Computational seismology - applications
Spectral element methodspherical regular grids
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46Computational seismology - applications
Simple example
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47Computational seismology - applications
Ray coverage – initial model
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48Computational seismology - applications
Sensitivity kernels
S velocity P velocity Density
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49Computational seismology - applications
Final model
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50Computational seismology - applications
Before - After
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Improvement
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52Computational seismology - applications
Spectral element methodUnstructured grids
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53Computational seismology - applications
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54Computational seismology - applications
Grenoble basin
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55Computational seismology - applications
The bridge
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Soil – structure interaction
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57Computational seismology - applications
Spectral element methodGlobal wave propagation(Komatitsch and Tromp)
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58Computational seismology - applications
Cubed Sphere
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59Computational seismology - applications
Alaska, Denali, M 7.9, 2002
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60Computational seismology - applications
Observations - Synthetics
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61Computational seismology - applications
Observations - Synthetics
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62Computational seismology - applications
Discontinuous GalerkinWhy (the hell) do we need another method?
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63Computational seismology - applications
Waves on unstructured grids? tetrahedral
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64Computational seismology - applications
Arbirtrarily high-orDER - Discontinuous Galerkin
Combination of a discontinuous Galerkin methodwith ADER time integration
Piecewise polynomial approximation combined withfluxes across elements (finite volumes)
Time integration as accurate as spatialapproximation, applicable also to strongly irregularmeshes (not so usually for FD, FE, SE)
Method developed in aero-acoustics and computational fluid dynamics
The scheme is entirely local, no large matrix inversion-> efficient parallelization
Drawback: Algorithms on tetrahedral grids slowerthan spectral element schemes on hexahedra
Combination of a discontinuous Galerkin methodwith ADER time integration
Piecewise polynomial approximation combined withfluxes across elements (finite volumes)
Time integration as accurate as spatialapproximation, applicable also to strongly irregularmeshes (not so usually for FD, FE, SE)
Method developed in aero-acoustics and computational fluid dynamics
The scheme is entirely local, no large matrix inversion-> efficient parallelization
Drawback: Algorithms on tetrahedral grids slowerthan spectral element schemes on hexahedra
Several articles in Geophys. J. Int., Geophysics, a.o. by Käser, Dumbser, de la Puente, and co-workers
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65Computational seismology - applications
Use high precision (i.e., high-order polynomials) only where necessary
High precision where cells are large (high velocities)
Low precision where cells are small (because of structural heterogeneities)
Use high precision (i.e., high-order polynomials) only where necessary
High precision where cells are large (high velocities)
Low precision where cells are small (because of structural heterogeneities)
O4
O5
O6
O7
Käser et al. (2006)
Dumbser, Käser and Toro, GJI, 2007
P - adaptivity
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66Computational seismology - applications
Same color means same processor
Same color means same processor
Mesh Partitioning and Parallel Computing the problem of load blancing
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67Computational seismology - applications
Topographic effects
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68Computational seismology - applications
Topographic Effects
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69Computational seismology - applications
Regional and Global Wave Propagation crust, crust, crust!
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70Computational seismology - applications
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71Computational seismology - applications
Minimum occurring wave speed
Global wave propagation … keeping the number of points per wavelength constant …
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72Computational seismology - applications
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73Computational seismology - applications
Benchmarking DG vs. SE
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74Computational seismology - applications
The sound of volcanoesEruption, 15. Juni, 2006
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75Computational seismology - applications
Reservoir applications(Schlumberger Doll Rese
task: model also steel casing!
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76Computational seismology - applications
Summary
Computational 3-D wave propagation finds isnow applications in almost all fields of Earth sciencesThere is not ONE method that works best for all problemsMaking codes work on large computers will bemore and more a challengeThe most promising methods for the comingyears seems FD (still), SE, and DG