T h e W a v e g u i d e i n t h e Mantle o f the Earth 

a n d its p r o b a b l e p h y s i c a l n a t u r e 

b y M A G N I T S K Y V . A . , K H O R O S H E Y A V . V . (*) 

Ricevuto il 7 (liceiiibre 1960 

As far as we can see, B. Gutenberg was the first who points out 
the possibility of existence of a low-velocity layer in the upper parts 
of the Mantle (Gutenberg, 1926). I t is quite obvious that such a low-
velocity layer can act as channel conducting seismic energy. This was 
established by Caloi (1953, 1951) and Press and Ewing (1954, 1955). 

In present paper we report results of further investigations in that 
topic based on data from seismograms of 9 earthquakes recorded by 
seismic stations of USSR with epicentral distances in the range 22° 
to 150° (Table 1). 

There were used only seismograms with epicentral distances in 
which no overlap of Pa and Sa with any other phase could be suspected. 

Almost in every seismogram Pa and Sa phases can be clearly de-
tected (Fig. 1), however, the first arrival of the phase is often not very 
distinct. This is probably the main cause of considerable scattering 
in results. In Figure 2 are plotted travel times versus A. In spite of 
scattering of arrival times it is apparent that travel-time curves for 
Pa and Sa are straight lines, their equations are as follows 

This gives Telocity 8,3 km/sec and 4,47 km/sec for Pa and Sa re-
spectively. 

Periods of Pa are in range 5-12 sec, those of Sa in range 7 - 3 0 sec. 

V = 0,9558 + 0,2205 A 
r = 0,3780 + 0,4180 A O 

o Pa 
Sa 

(*) Paper read at the Helsinkv Assembly of the I.U.G.G., 1960. 



8 8 V . A . M A G N I T S K Y , V . V . K H O R O S H E V A 

There is familiar equation connecting amplitude A of seismic wave 
with distance r from the source 

A = Cr~~" e ~ar [1] 

G being constant, a - absorption coefficient, n - depends on the type 
of wave. For plane wave n = 0, for spherical wave n == 1, for cylindrical 

Table 1 

Nu D a t e A <P 
Depth 

km ni a k m
- 1 

1 11/X -56 1 5 1 , 3 E 4 5 , 4 N 100 TY^VZ 0,000143 
2 18/VIII - 5 4 1 7 5 , 0 W 2 1 , 5 S 170 iVi-iy* 0,000146 
3 23/V -56 1 7 8 , 5 W 1 5 , 5 S 400 0,000139 

4 7/VI -54 1 5 2 , 5 E 4,OS 460 Y 2 0,000156 

5 20/11 - 5 4 1 2 5 , 0 E 7 , 5 S 520 6M--7 0,000184 

6 16/VIII - 5 5 155,0 E 6,OS 200 6 *u-iy2 
7 31/111 - 5 5 1 2 4 , 0 E 8,ON 50 - 7 y4 
8 29/111 -54 3 , 5 W 37, ON 640 m-m 
9 21/111 -54 9 5 , 0 E 2 4 , 5 N 170 7 - 7 y2 

one n = 0,5. If we denote A0, r0 amplitude and distance at any arbitrary 
fixed point [1] becomes 

In A0/A r — r0 
In r\r0 " " In r/r0 

Plotting empirical values of [2] for earthquake of 11 October 1956 on 
Fig. 3 we obtain a straight line with n = 0,52 and a = 0,00014 k m - 1 . 
The inference is the Pa phase corresponds to a cylindrical wave. Hence 
it is evident from both the travel times and amplitudes that Pa phase 
is connected with the surface or channel wave. Velocity obtained exclu-
des the first supposition, consequently we must adopt the channel type 
to the wave in consideration. 

Unfortunately all other earthquakes have epicenters at great dis-
tances relatively to our stations. So we must use instead of [1] equation 

A = C (sin Zip'/a • e~aAR [3] 



T H E W A V E G U I D E I N T H E M A N T L E OF T H E E A R T H , E T C . 8 9 

I n [3] one takes in consideration the spherical shape of the channel. 
I n last column of table 1 are plotted a obtained by [3] for other earth-
quakes. These results are in apparent agreement with our previous 
conclusions. 

But what is the cause of the formation of the low-velocity layer! 
The common supposition is t h a t it is due to prevailing effect of increase 

Fig. 1. - Example of records of PA and SA phases ( E a r t h q u a k e 29/111-1954, 
6h17m06s, epicentral distance A = 31°,3). 

of temperature us compared with effect of increase in pressure. Velocity 
v would have minimum if dv/dh = 0. 
This gives 

( l l 
AT Up, J. m 
dh ( 3® ' 

Using the data from the work of Hughes and Cross (1951) we deduce 
the critical value of dT/dli in range 7 to 10 degrees per km. This seems 
to be too much. But if we take into consideration the temperature de-



9 0 V. A . M A G N I T S K Y , V . V . K H O R O S H E V A 

pendance of thermal conductivity (Peierls, 1955, Dugdall and McDonald, 
1955, Clark, 1956) in form 

* = ~ + BT3 [5] 

we infer that x has a minimum at the depths 50-100 km (Lubimova, 
1958). Let us take 1,2 • 10"" cal/cm2sec as average for the heat flow at 

Fig. 2. - Traval-times for Pa and Sa. 

the Earth's surface. Adopting usual content of heat generation in va-
rious types of rocks we bnd that gradient dT/dh can run up to 18 deg/km 
at 7t = 100 km beneath the continental crust and 15 deg/km at li = 50 
km beneath the oceanic crust. These values seem to be quitesu fficient 
to explain the formation of a low-velocity layer. 



T H E W A V E G U I D E I N T H E M A N T L E OF T H E E A R T H , E T C . 9 1 

Another explanation assumes the vitrification of the material of 
the mantle a t respective depths. For the volume increase by vitrification 
we can write (Frenkel, 1950) 

V V — 
= « W [6] ' o 

E denotes energy of activation. From [6] we obtain by differentiation 

AK AV , AV 3InE0 
= - f T " l n T ' " \ ; Tt t ' l Ka T 0 i o 3 In T 

K - incompressibility, E0 - energy of activation at zero pressure. 
Derivative 

DlnEo 
T I n V ~ 2 ' 5 

(Zharkov, 1958). 

1 / K 
Denoting 1/ — = v we hiul 

I Q 
dv 1 /dK dV 
v 2 \ K + ~V [ 8 ] 



9 2 V . A . M A G N I T S K Y , V . V . K H O R O S H E V A 

Now it follows 

/ , A V 3 lnE0\ 
I 1 + l n V0 • Yinv) [ 9 ] 

d v _ A Al i- • - A v a lnE° 
V ~ 2 V0 

A V 
For dunite —— 2%, consequently we have 

V0 
dv 

eg 6% 

which is in fair agreement with conditions in the low-velocity layer. 
Finally we shall take into account assumption that the compo-

sition of the mantle is of stone meteorites. So we suppose the 30% 
of the substance of the mantle consists of MgSi03. 

I t is established t h a t at the temperature approximatly 1000° C 
there is transition from rhombic modification of enstatite to protoenstatite 
with volume increase nearly 3% (Atlas, 1952, Smith, 1958). We may 
assume the energy of lattice of both modifications is expressed by 
equation 

U = [ 1 0 ] 
r r" L J 

A — Madelung constant being different for various modifications. 
B and n are determined by the nature of repulsive forces. As the cha-
racter of repulsive forces do not change during transition mentioned 
above, we can suppose in first approximation B and n being the same 
for both modifications. 

We have 
K dp dr 

[11] 

From [10] and [11] it follows 

<K\ K n Ap 

e 
. [12] 

\ p I o 3 o 

For most causes n is in the range 6 to 9, so decrease in velocity in low-
velocity layer can be suspected to be about 3%. 

I n conclusion it is necessary to emphasise that all three causes 
of formation of low-velocity layer seem to be quite adequate to ex-
plain it and it is impossible to choose one of them without any addi-
tional data. 



T H E W A V E G U I D E I N T H E M A N T L E OF T H E E A R T H , ETC. 9 3 

SUMMARY 

Records on seismic stations in USSR confirm the existance of Pa 
and Sa phases in no correspondance to any well known phase. The travelti-
me curves of Pa and Sa phases are obtained as being straight lines. Velocities 
of Pa and Sa are 8,30 ± 0,0-3 kmlsec and 4,57 ± 0,03 km/sec respectively. 
Decrease in amplitudes as well as the form of travel-time curves indicates 
that Pa and Sa are cylindrical waves. It is supposed Pa and Su travelling 
along a low-velocity channel in astenosphere. Formation of such a layer 
is due to vitrification of material at the depth of some 100-200 km. 

RIASSUNTO 

Le registrazioni effettuate nelle stazioni sismiche in U.R.S.S. conferma-
no Vesistenza di fasi Pa ed Sa senza corrispondenza con alcuna fase gia 
nota. Le curve del tempo di cammino delle Pa ed Sa risultano linee rette. 
Le velocita delle Pa ed Sa sono rispettivamente di 8,30 ± 0,03 km/sec e 
4,57 ztz 0,03 km/sec. Le diminuzioni di ampiezza e la forma della curva 
del tempo di tragitto indicano che le Pa ed Sa sono onde cilindriche. Si sup-
pone che le Pa ed Sa si muovano su un canale a bassa velocita nella asteno-
sf era. La formazione di un simile strato e dovuta alia vetrificazione del ma-
teriale alia profondita di circa 100-200 km. 

R E F E R E N C E S 

A T L A S L . , The polymorphysm of MgSiO3. « J o u r n . Geol. », 6 0 , 2 , ( 1 9 5 2 ) . 
C L A R K S . P., Effect of radiative transfer of temperature in the Earth. « Bull. 

Geol. Soc. Amer. », 67, 5, (1956). 
C A L O I P., Onde longitudinali e trasversali guidate dell'astenosfera. « Rend. 

Acad. Naz. Line. », ser. 8, 15, 6, (1953). 
— L' astenosf era come canale-guida dell' energia sismiea. « Ann. Geof. », 7, 4, 

(1954). 
D U G D A L L , M C D O N A L D Q . , Lattice thermal conductivity. « Phys. Rev. », 9 8 , 6, 

(1955). 
F R E N K E L J . I . , Introduction in the theory of metals. Moscow (in Russian) 1 9 5 0 . 
G U T E N B E R G B . , Untersuehungen zur Frage, bis zu welcher Tiefe die Erde 

kristallin ist. « Zeitschr. Geopliys. », 2, 1, ( 1 9 2 6 ) . 



9 4 V . A. M A G N I T S K Y , V . V . K H O R O S H E V A 

H U G H E S D. S . , C R O S S J . H., Elastic wave velocities in rocks at high pressures 
and temperatures. « Geophys. », 16, 4, (1951). 

L U B I M O V A H. A., Thermal history of the Earth with consideration of the va-
riable thermal conductivity of its mantle. « Geoph. J o u r n . Roy. A s t r . 
Soc. », 1, 2, (1958). 

P E I E R L S R. E., Quantum theory of solids. Oxford, 1955. 
P R E S S P., E W I N G M., P and S velocities at great distances. « Bull. Geol. Soc. 

Amer.», 65, 1, (1954). 
— — Waves with P and S velocity at great distances. « Proc. N a t . Acad. 

Sc. », 41, 1, (1955). 
S M I T H J . V., Crystal structure of protoenstatite. « Bull. Geol. Soc. Am. », 6 9 , 

12, 2, (1958). 
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mantle. «Proc. Ac. Sc. USSR », ser. Geophys. 4 (in Russian) 1958.