1. Measuring acoustic phase shifts between multiple atmospheric heights
Ruizhu Chen1,2 & Junwei Zhao2
1. Dept. Physics, Stanford Univ., Stanford, CA 94305
2 Hansen Experimental Physics Laboratory, Stanford Univ., Stanford, CA

2. Motivation
Compute acoustic phase shifts (travel-time differences) between multiple heights in quiet regions, along the same ray path but traveling in opposite directions. One purpose is to examine whether the difference is related to evanescent waves.
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
ΦAB’ - ΦB’A :
As shown in the figure, we have two formation height AB and A’B’, and we calculate …
One purpose..
In acoustic region the travel time in two directions, should be the same. If it’s in quiet region and averaged along directions.
But here since AB is in E Region. And transformation from

3. Motivation
Compute acoustic phase shifts (travel-time differences) between multiple heights in quiet regions, along the same ray path but traveling in opposite directions. One purpose is to examine whether the difference is related to evanescent waves.
Investigate the orbital-velocity dependence of measured phase shifts.
Because center-to-limb measurements are also related to different line-formation heights, the main purpose of this work is to investigate whether multi-height is one cause of center-to-limb effect.
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary

4. Data 4 sets of data: (Higher and Lower, AB and A’B’) ΦAB’ - ΦB’A :
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Data
ΦAB’ - ΦB’A :
4 sets of data: (Higher and Lower, AB and A’B’)
I3 and I0 (original data before calibration on Vorbit)
Line core (LC) and continuum intensity (Ic)
Doppler proxies at line core (LC) and line wing(LW)
AIA 1600Å and 1700Å broad lines.
By a method prescribed by these authors

5. Data 512 x 512 pixels; 0.06°/pix; 24 hrs long.
Each set of data is divided to five 8-hour intervals:
0-8h(++), 4-12h(+-), 8-16h(--), 12-20h(--), 16-24h(+-)
I3 and I0
Line core (LC) and continuum intensity (Ic)
Doppler proxies at Line core (LC) and line wing(LW)
AIA 1600Å and 1700Å broad lines
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
original
calibrated
proxy
independent
of Vorbit
Orbital velocity for data used
Line profile influenced by Vorbit
All data 512 squared
The first 3 sets are related to Vo, because
The Vo is shown in this figure.

6. Measurement ProcedureB’
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary A B’
Corss-correlation
function f (t, d)
distance
time
distance
frequency
phase change
ΔΦ (d , w)
By a method prescribed by these authors
ΦAB’ - ΦB’A
TAB’ - TB’A

7. I3 and I0 Formation height: 270 km (I3) and 20 km(I0)
0-8h(++), 4-12h(+-), 8-16h(--), 12-20h(--), 16-24h(+-)
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Distance (Mm)
Frequency (mHz)
ΦAB’ - ΦB’A = ΦI3 to I0 – ΦI0 to I3
Uppper five pannels are for the 5 T invertal.
Each panel , x , y. Colar
5 p shows dependence. And first panel ++.
K Rsun
Frequency (mHz)
Phase of cross spectrum

8. I3 and I0 Phase shift (rad) ΦAB’ - ΦB’A = ΦI3 to I0 – ΦI0 to I3
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Time difference (s)
TAB’ - TB’A = TI3 to I0 – TI0 to I3
Magenta。
Uppper 5 T. color is .
Lower is
It shows depence.
Distance (Mm)
ΔΦ (AB’-B’A) low freq (rad)
ΔΦ (AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
I3 & I0
~ 4
~ 2.5
~ 0.5
~3-4 ~3

9. Line core (LC) and continuum intensity(Ic)
Formation height: 270 km (LC) and 20 km(Ic)
Distance (Mm)
Frequency (mHz)
ΦAB’ - ΦB’A = ΦLC to Ic – ΦlC to Ic
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
K Rsun
Frequency (mHz)
Phase of cross spectrum

10. Line core (LC) and continuum intensity(Ic)
Phase shift (rad)
ΦAB’ - ΦB’A = ΦLC to Ic – Φic to LC
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Time difference (s)
TAB’ - TB’A = TLC to Ic – TIc to LC
Distance (Mm)
ΔΦ (AB’-B’A) low freq (rad)
ΔΦ (AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
LC & Ic
~2-3
~ 1
~ -0.5

11. Line core (LC) and continuum intensity(Ic)
Phase shift (rad)
ΦAB’ - ΦB’A - mean ( ΦAB’ - ΦB’A )
3mHz
3.5mHz
4mHz
5mHz
6mHz
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Time difference (s)
TAB’ - TB’A – mean ( TAB’ - TB’A )
3mHz
3.5mHz
4mHz
5mHz
6mHz
Distance (Mm)
ΔΦ (AB’-B’A) low freq (rad)
ΔΦ (AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
LC & Ic
~2-3
~ 1
~ -0.5
0.3
~ 0.1

12. Doppler proxy at line core and line wing
Formation height assumed same as line core and continuum: 270 km (LC) and 20 km(LW)
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Doppler proxy: LW=(I0-I5)/(I0+I5)
(Nagashima et al. (2014) LC=(I2-I3)/(I2+I3)

13. Doppler proxy at line core and line wing
Doppler proxy: LW=(I0-I5)/(I0+I5)
(Nagashima et al. (2014) LC=(I2-I3)/(I2+I3)
Formation height: 270 km (LC) and 20 km(Ic)
Distance (Mm)
Frequency (mHz)
ΦAB’ - ΦB’A = Φlc to lw – Φlw to lc
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
K Rsun
Frequency (mHz)
Phase of cross spectrum

14. Doppler proxy at Line core and line wing
Phase shift (rad)
ΦAB’ - ΦB’A = Φlc to lw – Φlc to lw
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Time difference (rad)
TAB’ - TB’A = Tlc to lw – Tlc to lw
Distance (Mm)
ΔΦ (AB’-B’A) low freq (rad)
ΔΦ (AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
LC & LW
~ -0.2 <0
~ -0.5
~ -0.8
0.2 ~ 0.5
1 ~ 2.5

15. AIA 1600Å and 1700Å broad lines
Formation height: 480 km (LC) and 360 km(Ic)
Distance (Mm)
Frequency (mHz)
ΦAB’ - ΦB’A = Φ – Φ1600 to 1700
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
K Rsun
Frequency (mHz)
Phase of cross spectrum

16. AIA 1600Å and 1700Å broad lines I3 & I0 1.3 π π Phase shift (rad)
ΦAB’ - ΦB’A = Φ1600 to – Φ1700 to 1600
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Time difference (rad)
TAB’ - TB’A = T1600 to – T1700 to 1600
Distance (Mm)
ΔΦ (AB’-B’A) low freq (rad)
ΔΦ (AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
AIA
~ -0.5
~ -0.8
~ -1.2
ΔΦ (AB’-B’A)
ΔΦ ( Vorbit)
I3 & I0
1.3 π π

17. Summary 270 20 ~ 4 >0 ~ 2.5 ~ 0.5 ~3-4 ~3 ~2-3 >0 ~ 1 ~ -0.5 0.3
Higher formation height (km)
Lower formation height
(km)
ΔΦ (AB’-B’A) low freq (rad) ΔΦ
(AB’-B’A)
5 mHz (rad)
6 mHz (rad)
ΔΦ ( Vorbit)
small freq (rad)
large freq (rad)
I3 & I0
270 20
~ >0
~ 2.5 ~
~3-4 ~3
LC & Ic
~2-3 >0
~ 1
~ -0.5
0.3
~ 0.1
LC&LW
~ <0
~ -0.8
0.2 ~ 0.5
1 ~ 2.5
AIA
480
360
~ <0 ~
Motivation
Data
Method
Results
I3 & I0
LC &Ic
LC & LW
AIA
Summary
Phase shifts from I3 and I0 are dominant by orbital velocity. Phase shifts from calibrated LC & Ic, and Doppler proxies at LC & LW, both have non-ignorable dependence on the orbital velocity.
Acoustic travel time (phase) between multiple heights is asymmetric with respect to directions.
ΦAB’ - ΦB’A for low frequencies are positive from line core & continuum intensity data, and negative from line core & line wing of Doppler proxy, AIA 1600Å & 1700Å data. It is unclear why is the sign different.
Waves of 6mHz don’t cut off, but always has a negative phase shifts.
Multiple formation heights will cause a phase shifts , which may be one cause center-to-limb effect.