1. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations Joe Werne (1) Keith Julien (2) (1) NorthWest Research Associates, Inc. (NWRA) Colorado Research Associates Division (CoRA) 3380 Mitchell Lane, Boulder, CO 80301 werne@cora.nwra.com (2) Department of Applied Mathematics University of Colorado, Boulder, CO julien@colorado.edu

2. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations Code Development:  Cartesian Geometry  Linear Acoustic Modes  3D MHD  Spectral Accuracy in all 3 Directions  3 rd -order Runge-Kutta time stepping w/internal Newton-Raphson iteration scheme for implicit operations  Currently generalizing and adapting wave-radiation formalism for acoustic-wave radiation

3. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations Test Cases:  Acoustic wave-packet propagation, inviscid evolution 1)1-D with constant sound speed (test diffusion/dispersion) 2)3-D density anomaly (coin in two orientations)

4. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 1) 1-D with constant sound speed (test numerical diffusion/dispersion): gridpoint 0  t140  t280  tAfter 2400  t, amplitude drops by  0.7%. Negligible dispersion and diffusion errors.

5. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 2) 3-D density anomaly (coin in two orientations): 12.5 Mm 50 Mm C 0 =36 km/s C 1 =50 km/s

6. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 2) 3-D density anomaly (coin in two orientations):

7. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 2) 3-D density anomaly (coin in two orientations): 22 Mm  4Mm  5 mHz

8. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 2) 3-D density anomaly (coin in two orientations):

9. Julien, Werne CU, CoRA/NWRAFebruary 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations 2) 3-D density anomaly (coin in two orientations): February 2004Julien, Werne CU, CoRA/NWRA

10. February 2004 Progress on Forward Modeling for Acoustic-Propagation Simulations Continued Test Work:  Sound-speed perturbations  Subsurface flows  Subsurface magnetic fields