Data forHelioseismology Testing

Dali GeorgobianiMichigan State University

Presenting the results of

Bob Stein (MSU) & Åke Nordlund (NBI, Denmark)with

David Benson (Kettering University)

Stanford, July 29, 2008

Numerical Method

Staggered mesh

Non-linear, fully compressible, 3D, explicit

Spatial differencing:

6th order centered finite difference

Time advancement:

3rd order Runge-Kutta

Size and Resolution

• Size of the domain:

96 Mm x 96 Mm x 20 Mm

1000 x 1000 x 500 grid points

• Grid information:

dx = dy = 0.1 Mm

dz = 0.012–0.075 Mm

dt = 0.25 sec (saved every 60 sec)

Mean Atmosphere

Vertical Velocity at 2.5 & 8 Mm depth

Boxes show domain of earlier simulations at 6, 12, 24 & 48 Mm widths.

Vertical momentum at 0, 2, 4, 16 Mm

Vertical momentum vs depth

Velocity stream lines

Courtesy Chris Henze (NASA)

Finite time Lyapunov exponent(proxy for vorticity)

Courtesy Bryan Green (AMTI/NASA)

Available Datasets

• Website http://sha.stanford.edu/stein_sim

(some info)

• Contact Bob Stein stein@pa.msu.edu (more info)

Simulated data are being ingested into the new SDO JSOC database

Thanks to Rick Bogart for his extensive help with archiving!

Archived Data Description

• 9 variables: horizontal velocities Vx, Vz, vertical velocity Vy, temperature, density, pressure, internal energy, electron density, and

• Each snapshot of a variable is stored in a separate file; 9 variables at each time step are combined to be retrieved together

• Data are in FITS format

• Duration 511 minutes (360 minutes recorded, WIP)

• A snapshot of a variable occupies approximately 2 GB of disk space

• First and third directions are horizontal, second direction is vertical

• Vertical grid is provided separately

(The data will be available for retrieval soon – check with Rick)

Another Data Set

• 4 hour averages, with 2 hour overlap

• 6 variables: horizontal velocities Vx, Vz, vertical velocity Vy, temperature, density, and sound speed

• Simultaneous surface velocities

• Stored in the IDL SAVE format at MSU

• Work in progress… initial 6 variables calculated and stored, now adding internal energy E

Units of Variables

• Length is in 108 cm = 1 Mm

• Time is in 102 s

• Velocities Vx, Vz, and Vy are in 10 km/s

• Temperature is in K

• Density is in 10-7 g/cm3

• Pressure is in 105 dynes/cm2

• Internal energy is in 105 ergs/cm3

• Electron density is log cm-3

Data Analysis

• Power spectrum

• Tests of time-distance methods

Compare the results for the simulations and

the SOHO/MDI high-res observations

(211.5 Mm by 211.5 Mm patch, 512 min)

The following work was performed with

Junwei Zhao and Alexander Kosovichev

Power Spectra

Simulations MDI high-res data

Power Spectra

Simulations Hinode data

Velocity Spectra sqrt [k P(k)]

Time-Distance Diagram

TD Diagrams at Various Depths

Exploring Simulated Surface Structures

• Spatial filtering

• Spectral analysis

• f-mode time-distance analysis

• Local correlation tracking

Large Structures

Time-Distance Analysis

Horizontal Flow Fields

Simulations Inversions

Depth range is 2-3 Mm. The longest arrow corresponds to 300 m/s

Local Correlation Tracking

CorrelationcoefficientIs 0.99

But velocityamplitudes are under-estimated(~1.8 timeslower than in simulations)

These simulations provide an excellentopportunity to validate various techniques, widely used in solar physics and helio-seismology for directly obtaining otherwise inaccessible properties (subsurfaceflows, structures etc.)

On the other hand, these analysis techniques also help to examinehow realistic the simulations are

Conclusions