A Framework for Online Inversion-Based 3D Site Characterization

Transcription

1 A Framework for Online Inversion-Based 3D Site Characterization Volkan Akcelik, Jacobo Bielak, Ioannis Epanomeritakis,, Omar Ghattas Carnegie Mellon University George Biros University of Pennsylvania Loukas F. Kallikovas University of Texas at Austin Eui Joong Kim Duke University

2 Overall goal: Site characterization Reconstruct soil profile in terms of material parameters, such as shear and compressional wave velocities, density, attenuation. Reconstruction results in time-dependent inverse wave propagation problem. Inverse problems use in situ measurements. To effectively reconstruct the desired information from the field test data, we need robust, efficient, and scalable forward and inverse three-dimensional wave propagation solvers.

3 Complexity of inverse elastic wave propagation multiple spatial scales o wavelengths vary from O(10m) to O(1000m) multiple temporal scales o O(0.01s) to resolve highest frequencies of source highly irregular basin geometry highly heterogeneous soils material properties source parameters are only observable indirectly

4 Elastic wave propagation model Variable-slip kinematic source model USGS

5 1994 Northridge earthquake Computational domain Surface shear wave velocity Shear wave velocity at depth Octree-based hex mesh, partitioned by ParMetis Detail of hexahedral mesh

6 Comparison with observations the good Obregon Park, LA

7 Comparison with observations the bad Hollywood Storage, LA

8 Verification against other codes -R. Graves -Archimedes -Quake

9 SCEC Community Velocity Model for SoCal,, v.3 (H. Magistrale,, S. Day, R. Clayton, R. Graves) Harold Magistrale,, SDSU

10 Inverse problem: Use in situ measurements to improve soil model SCEC Phase III strong motion database: Observations from 28 earthquakes and 281 stations

11 Least squares parameter estimation formulation of inverse wave propagation inversion fields sources receivers data misfit displacements forward seismic wave propagation model target local minimum

12 Behavior of misfit function F in direction of material perturbation Source frequency 3 x x Frequency of perturbation of material field x x x 104 Ill-conditioning & rank rank deficiency deficiency x Multiple minima low med high low medium high

13 Least squares parameter estimation formulation of inverse wave propagation inversion fields sources receivers data misfit displacements forward seismic wave propagation model target local min. Tikhonov reg. local min. Tikhonov reg. + multiscale Total var reg + multiscale Total var, section

14 Inverse scalar wave propagation (antiplane( shear) FS AB AB AB

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16 A Gauss-Newton Newton-Schur-CG method Instead, How to use solve? Gauss-Newton Straighforward approximation dense and approach solve by conjugate intractable, gradients: e.g. for largest problem we solve: Instead, use Gauss o form Hessian-vector products on the fly o 17 million wave propagations to set up linear system o Hessian guaranteed to be positive definite o 2 petabytes to store it o quadratic convergence for good fit problems, linear ootherwise 3 hours on an exaflops/s machine for one Newton o each iteration CG iteration requires 1 forward, 1 adjoint wave propagation -> > parallelizes as well as forward problem o need good preconditioner (but difficult, since Hessian not available)

17 Solution algorithm: Multiscale-Gauss Gauss-Newton-CG-LMBFGS Multiscale continuation over grid and source frequency o Inexact Gauss-Newton nonlinear iteration Conjugate gradient solution of reduced Hessian system (each matvec requires N s forward & adjoint wave propagation solutions) Preconditioner:» limited memory BFGS (Morales-Nocedal Nocedal)» initialized with several iterations of Frankel s s method (two-step stationary method) to invert

18 Algorithmic scalability for 3D acoustic inversion example Mesh independence of nonlinear iterations Mesh independence of linear iterations

19 Inversion examples 2D shear, 3D acoustic, and 3D elastic models Synthetic inversion (some with 5% added noise) Piecewise bi/trilinear finite element approximation of state, adjoint,, and material property Explicit time integration PETSc ( implementation Up to 257x257x257 grid (17 million inversion parameters) on 2048 processors (~12h) Up to 225 surface receivers

20 Material inversion: multiscale continuation (64 receivers)

21 Material inversion: target vs. inverted displacement history at a receiver

22 Material inversion: target vs. inverted velocity history at non-receiver location

23 Multiscale inversion: Target vs. inverted isosurfaces,, level 1

24 Multiscale inversion: Target vs. inverted isosurfaces,, level 2

25 Multiscale inversion: Target vs. inverted isosurfaces,, level 3

26 Multiscale inversion: Target vs. inverted isosurfaces,, level 4

27 Multiscale inversion: Target vs. inverted isosurfaces,, level 5

28 Multiscale inversion: Target vs. inverted isosurfaces,, level 6

29 Multiscale inversion: Target vs. inverted isosurfaces,, level 7

30 Multiscale inversion: Target vs. inverted isosurfaces,, level 8

31 Multiscale inversion: Target vs. inverted isosurfaces,, level 9

32 Comparison of target and inverted material models: 3D acoustic and elastic Acoustic medium, p-wave p velocity Elastic medium, s-wave s velocity

33 A Framework for Online Inversion-based 3D Site Characterization Excite the soil and collect surface and downhole ground motion data at a particular field location Transmit the data back to high-end supercomputing facilities Perform inversion to predict the distribution of material properties Identify regions of greatest remaining uncertainty in the material properties Provide guidance on where next set of field tests should be conducted

34 Conclusions: Inverse earthquake modeling Multilevel continuation forces successive iterates to remain within basin of attraction of global minimum Total variation regularization very effective at localizing sharp material interfaces Outer and inner iterations are mesh-independent Algorithmic, parallel, and overall scalability follow Despite algorithmic and parallel scalability, number of forward/adjoint adjoint solutions is large (equivalent to ~800 wave propagations for 129^3 grid) But algorithmic infrastructure is in place

35 Ongoing and Future work Hessian preconditioner improvements necessary Regularization parameter selection for real data Incorporation of multiresolution octree grids Inversion for anelastic attenuation parameters Incorporation of dynamic fault rupture model, and inversion for fault parameters Incorporation of prior (SCEC community velocity model) High-resolution 3D earthquake inversion for multiple earthquake sources is a major computational challenge