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Transcript of buv [IUWV VdEwVdxyP]z|{r}~}p l p 8 $ } @ ! ' {2 @...
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Surface
a)
FDG
RT G
RT
Kirchhoff
CMB
Finite Difference Regionb)
vτzy τxy
Reflected
Total
Scattered
n=1
n=3
n=N
m=1
m=3
m=M
Surface
CMB
SH
SH
SH
SH
PREM500 km
315 320 325315 320 325315 320 325315 320 325315 320 325315 320 325
GRT
HY
ScSS
Velocity
t - 5 * ∆ (seconds)
315 320 325315 320 325315 320 325315 320 325315 320 325315 320 325
GRT
HY
Velocity
t - 5 * ∆ (seconds)
500 km
Surfacea)
GRT
CMBFD
GRT GRT
WKB
Kir
chh
off
25 km
Vs = 5 km/s
PREM
b)
c) t=387.75 sec d) t=389.75 sec
e) t=391.75 sec f) t=393.75 sec
500 km
Surfacea)
GRT
CMBFD
GRT GRT
WKB
Kir
chh
off
25 km
Vs = 5 km/s
PREM
b)
c) t=387.75 sec d) t=389.75 sec
e) t=391.75 sec f) t=393.75 sec
core
man
tle
S
ScS
Sd
iff
80
110
core
man
tle
S
ScS
Sd
iff
80
110
98
100
102
104
106
108
580 600
GRT98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
GRT
98
100
102
104
106
108
580 600
Sdiff
a)
dis
tan
ce (
deg
ree)
t-9*∆ (sec)
HY
HY
HY
HY
HY
HY
HY
HY
HY
HY
HY
Sdiff
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
GRT
76
78
80
82
84
86
88580 600
Sdiff
76
78
80
82
84
86
88580 600
b)
t-9*∆ (sec)
HY
HY
HY
HY
HY
HY
HY
HY
HY
HY
HY
Sdiff
970503970904970904
951006
950823
971128971128
970902
IIIIIIIIIIIIIII
970902
IIIIIIIII
ESK
MM18
MM17
MM16
MM15
MM14
MM13
MM12
MM11
MM09
MM08
MM07
MM06
MM05 MM04
MM03
MM02
100
102
104
106
108
110
0 20
Sdiff
a)
dis
tan
ce (
deg
ree)
CCM
MM17
MM16
MM15
MM14
MM13
MM12
MM09
MM08
MM07
96
98
100
102
104
106
108
1100 20
Sdiff
12
b)
ANMO
ANMO
BAR
BKR
COR
COR
CPP
FPC
FUR
GSC HEC MLAC
MTP
MWC
NEE
PAS
PFO
SBC
SNCC
SOT
SVD
TUC
TUC
VTV
82
84
86
88
90
92
94
96
0 20
Sdiff
c)
100
102
104
106
108
110
0 20
Sdiff
d)
dis
tan
ce (
deg
ree)
t (sec)
96
98
100
102
104
106
108
1100 20
Sdiff
1 2
1
2
e)
t (sec)
82
84
86
88
90
92
94
96
0 20
Sdiff
f)
t (sec)
sa61
sa59
sa60
sa63 sa45 sa64 sa70 sa66
sa46 sa71 sa65 sa67
sa47 sa51 sa68 sa55
sa72
sa56
sa76
sa75
sa80
sa63
100
102
104
106
108
0 20
Sdiff
12
3
a)
dis
tan
ce (
deg
ree)
sa24 sa18
sa31 sa25 bosa
sa39 sa32
sa11
sa81
sa22 sa16
sa13
sa23
sa12
sa13
sa31
sa37
sa38
sa40
sa39
96
98
100
102
104
0 20
Sdiff
1 2
b)
sa61 sa59
sa60
sa63 sa45
sa64
sa70 sa66
sa65 sa67 sa47
sa68
sa76
sa75
sa80
sa24 sa18
sa31 sa25 bosa
sa39 sa32
sa11 sa81
sa16
sa23
sa12
sa31
sa37
sa38
sa40
sa39
82
84
86
88
90
92
94
96
0 20
Sdiff
1 2
c)
100
102
104
106
108
0 20
Sdiff
12
3
123
d)
dis
tan
ce (
deg
ree)
t (sec)
96
98
100
102
104
0 20
Sdiff
1 2
1
2
e)
t (sec)
82
84
86
88
90
92
94
96
0 20
Sdiff
1 2
1
2
f)
t (sec)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600
0
098 100
102
104
106
108
580
590
600300 km
0%10
%
0% -
10%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%20
%
0% -
20%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%10
%
0% -
10%
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%20
%
0% -
20%
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600
0
098 100
102
104
106
108
580
590
600300 km
0%
3%
0% -
3%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
3%
0% -
3%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
3%
0% -
3%
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
3%
0% -
3%
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600
0
098 100
102
104
106
108
580
590
600300 km
0%
6%
0% -
6%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
6%
0% -
6%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
6%
0% -
6%
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
6%
0% -
6%
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600
0
0
98 100
102
104
106
108
580
590
600300 km
0%
9%
0% -
9%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
9%
0% -
9%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
580
590
600
0
0
11
22
33
580
590
600300 km
0%
9%
0% -
9%
1 2 3
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
9%
0% -
9%
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600300 km
0%
12%
0% -
12%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
00
580
590
600300 km
0%
12%
0% -
12%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
11
22
33
580
590
600300 km
0%
12%
0% -
12%
1 2 3
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%
12%
0% -
12%
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600300 km
0%
3%
0% -
3%
+ U
LV
Z (
45km
,-10
%)
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600300 km
0%
3%
0% -
3%
+ U
LV
Z (
45km
,-15
%)
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600300 km
0%
3%
0% -
3%
+ U
LV
Z (
30km
,-15
%)
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600300 km
0%
3%
0% -
3%
+ U
LV
Z (
30km
,-20
%)
d)
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
98 100
102
104
106
108
580
590
600
Sd
iff
IAS
P91
Dat
a
98 100
102
104
106
108
580
590
600
0
0
98 100
102
104
106
108
580
590
600300 km
2%12
%
2% -
12%
a)distance (degree)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
00
11
22
33
580
590
600300 km
2%12
%
2% -
12%
b)
t-9*
∆ (s
ec)58
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
058
059
060
0
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
11
22
33
580
590
600300 km
0%10
%
0% -
10%
c)
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
580
590
600
Sd
iff
IAS
P91
Dat
a
580
590
600
0
0
580
590
600300 km
0%10
%
0% -
10%
d)
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
82 84 86 88 90 92 94 96
020
0
0
82 84 86 88 90 92 94 96
020
300 km
2%
8%
2% -
8%
a)distance (degree)
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
0
0
020
300 km
0%
7%
0% -
7%
b)
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
0
0
020
300 km
0%
6%
0% -
6%
c)
(sec
)
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
020
0
0
020
300 km
0%
5%
0% -
5%
d)
(e.g., F e,Al,C a-P v) (e.g., Mg-P v)
C MB
300 km
De
pth
(te
mp
era
ture
) in
cre
ase
s
y1 x1
y2 x2
E
liqudusliqudus
solid
αβ (km/s)
S hear V elocityP hase Diagram
0
F
M
0
100
200
300
400
500
600
700
800
Case 1
CMBTemperature, K
Dep
th (
km)
geotherm
Solidus (South Atlantic)
So
lidu
s (C
entr
al P
acif
ic)
geotherm (Central Pacific)
geotherm (South Atlantic)
Case 2
CMBTemperature, K
So
lidu
s