A b s o r p t i o n of Stationary Elastic Vibrations ili R o c k s 

E . V. K A E U S 

A q u a n t i t a t i v e interpretation of t h e ti-
namical charaeteristics of seismic waves in 
the E a r t h , revealed by t h e study of real 
inedia strueture, is possible in cases, when 
the parameters of elastic waves attenuation 
in rocks are known. I t is also i m p o r t a n t 
for a correet understanding of phvsical na-

bration. The elastic power supplied by the 
coil-moved vibration equal to 50 w a t t . This 
vibrator is used to set up continuous vibra-
tions a t frequencies ranging from 40 c/s t o 
5.000 c/s. I t is known t h a t stationary ela-
stic vibrations comprise t h e superposition 
of compressional, shear and surface (Ray-

F i g . l a 

ture of propagation of elastic waves and 
study of medianica! properties of rocks. 

To measure parameters, characterizing 
divergence and absorption of seismic waves, 
the seismoacoustic method based on ampli-
tude-and-phase measurement of elastic vi-
brations generated by a source of stationary 
harmonic vibration in rocks « in situ »: was 
used (1). 

For this purpose a special portable appa-
rature was coiistructed. The elastic waves 
are generated by t h e electrodynamical vi-

leigli) waves. [The dominant is the Ray-
leigh wave (2)]. These vibrations excited in 
the rock can be registered with maximum 
magniflcation about 20.000.000. To raise the 
effective sensitivity of t h e receiving device a 
special filtering system is used. The response 
charaeteristics make us enable to filtrate 
the signal within t h e frequencv band of 
a b o u t 2 c/s for any frequency of excitation. 

Fig. 1 gives an examplé of seismoacoustic 
observations in a mine a t a d e p t h of 250 
metres. The observations were carried out 



120 E. V. KARUS 

in D e c e m b e r of 1957, in silvinite p o t a s s i u m 
salt. T h e profile is 75 m e t r e s long. T h e 
observations were eonducted with t h e inter-
val of 0.5 m e t e r . This resulted in t h e crea-
t i o n of a system of reversed and overlapping 
a m p l i t u d e ( f i g . l a ) - a n d - p h a s e (fig.lb) curves, 
g r a p h s charaeterizing decrease of a m p l i t u d e 

w a v e l e n g t h A = 3 m . , t h e v a l u e of the 
phase velocity of t h e compressional wave 
d e t e r m i n e d b y t h e f o r m u l a : 

V<pR V<pP òxf ' 
where òx is t h e distance b e t w e e n t h e ondu-

and phase s h o f t with distance. These expe-
r ime n ta l d a t a can be used t o d e t e r m i n e b y 
t h e grapliical m e t h o d of difference t h e pha-
se velocity of t h e d o m i n a n t surface w a v e 
V<pR, t h e p h a s e velocity of compressional 
waves, V<pP index of t h e divergence f u n c -
tion « n » a n d a b s o r p t i o n coefficient. 

I n our e x a m p l e t h e m e a n value of t h e 
p h a s e velocity V<pR = 2.280 m/sec., t h e 

lation e x t r e m a on t h e p h a s e c u r v e and 
a m p l i t u d e c u r v e gives t h e v a l u e of t h e com-
pressional w a v e velocity V<pP = 4.200 m/sec. 
T h e index of t h e divergence f u n c t i o n « n » 
can b e d e t e r m i n e d b y a grapliical method 
of difference f r o m t h e s y s t e m of overlapping 
a m p l i t u d e curves (fig. l e ) . I n our case 

n = 0 . 5 ± 0 . 1 . 

Pig. l e 



ABSORPTION OP STATIONARY ELASTIC VIBRATIONS IN ROCKS 127 

The a b s o r p t i o n coeffieient can be deter- These seismoacoustic p a r a m e t e r s were de-
mined b y a graphical w a y f r o m system of termined in homogeneous rocks occurring 
reverse curves (fig. 1 d). T h e absorption near t h e E a r t h ' s surface, such as loess-like 

sandy loams, porphyrites, gneisses. Observa-
tions in mines helped t o d e t e r m i n e seismo-
acoustical p a r a m e t e r s of rocks occurring a t 
d e p t h s of 150-270 m., such as: a c m i t e cherts, 
sdvinite, jaspilite, different kinds of iron ore 
(magnetite, g e m a t i t e , m a r t i t e ) . 

R e s u l t s of d e t e r m i n i n g t h e seismoacou-
stical p a r a m e t e r s are as follows: 

1) On fig 2 we can see t h e chaning of 
t h e p h a s e velocity of t h e d o m i n a n t w a v e 
with t h e f r e q u e n e v f o r different rocks. F o r 
t h e rocks wicli occur a t t h e E a r t h ' s surface 
velocity increases w i t h t h e f r e q u e n c y rise, 
i. e. t h e p h e n o m e n o n of « Anomalous » de-
pression is observed f o r d o m i n a n t waves 
which in seismoacoustics seem to b e surface 
waves. B u t t h e silvinites h a v e n o r m a l di-
spersion, i. e. t h e m a i n pliase velocity de-
creases with f r e q u e n c y . 

2) T h e comparison of t h e given d a t a on 
fig. 3 leads t o t h e conclusion t h a t it is 
possible to d i f f e r e n t i a t e rocks b y a b s o r p t i o n 
of elastic waves. G r e a t a b s o r p t i o n is cha-
racteristic of loess-like s a n d y loams. Gneis-
ses h a v e g r e a t e r a b s o r p t i o n t h a n porpliyri-
tic rocks. 

M e t a m o r p h y c a l rocks and silvinite oc-
curring a t d e p t h s of 150-220 ni. a r e chara-
cterized b y lesser values of x a n d A t h a n 
those occurring n e a r t h e E a r t h ' s surface. 
Mine pressure a n d absence of decay pro-

coefficient here has t h e value x = 0.086 
1/m. T h e absorption decrement, t h e absor-
ption q u a l i t y f o r t h e wavelength A = - 0 . 1 3 . 

Vf[/sec] DtsperSion of phaSe 
veEocity gy stationary 

excitatLon 

Sitvinites 

porphyrites 

Gneisses 

rL 
2000 3000 4000 

Pig. 2 

The seismoacoustic m e t h o d was used to 
measure t h e p h a s e velocities, divergence in-
dices, coefficients a n d d e c r e m e n t s of t h e ab-
sorption of a r m o n i e elastic waves with fre-
quencies r a n g i n g f r o m 80 t o 4.500 c/s. 



128 E. V. KARUS 

cesses s t i p u l a t e m o r e elastieity and lesser 
values of a b s o r p t i o n p a r a m e t e r s a t a 
d e p t h . 

3) D e t e r i n i n a t i o n s of v, o b t a i n e d f o r 
different roeks show t h a t in t h e overwhel-
ming m a j o r i t y of roeks studied x increases 
with f r e q u e n c y b y a linear law within a 
wide f r e q u e n c y range, i. e. t h e value of t h e 
a b s o r p t i o n coefficient is p r o p o r t i o n a l to t h e 
f r e q u e n c y of excited oscillations: 

* = Pf 
T h e value /9, t h e f u n c t i o n a l coefficient in 

this equation is in practice d e t e r m i n e d 
b y t h e slope angle of t h e s t r a i g h t line 
a p p r o x i m a t i n g t h e g r a p h of d e p e n d a n c e 
of x to /. 

This t a b l e given t h e results of d e t e r m i n -
ing /? f o r different roeks. 

T a b l e 1 

N a m e of R o c k 
D e p t h of 

o c c u r r e n c e P ( s e c / m ) x IO
4 

G n e i s s e s . . 0 3 . 1 

l ' o r p l i y r i t e s . 0 1 . 2 

M a r t i t i c o r e . 262 2 . 0 

J a s p i l i t e s . . 212 1 . 0 

S i l v i n i t e s . . 247 0 . 6 

M a g n e t i t o - h e -
m a t i t i c o r e 267 0 . 2 

A c m i t e c h e r t s 267 0 . 4 

4) T h e values of t h e a b s o r p t i o n decre-
m e n t A of a rock di (ter, thougli t h e sensible 
law of c h a n g e of A w i t h f r e q u e n c y is ob-
served (fig. 4). This can b e seem f r o m t h e 
d e n i o n s t r a t e d d i a g r a m where changes w i t h 
f r e q u e n c y a r e p l o t t e d f o r : gneisses, p o r p h y -
rites, silvinite. T h e correlation of average 
values of p h a s e velocity V<pR a n d absorp-
tion d e c r e m e n t A f o r different roeks shows 
(fig. 5) t h a t roeks possessing a g r e a t e r ab-
sorption coefficient a r e characterized b y a 
lovv p h a s e velocity, i. e. inverse proportio-
n a l i t y is observed b e t w e e n A a n d VrpR. 

I n conclusion we w a n t to say, t h a t a 
t h o r o u g h investigati on of a b s o r b i n g proper-
ties of roeks w i t h t h e help of seismoacou-

stics m a y yield e x p e r i m e n t a l materials for 
s t u d y i n g t h e laws of t h e propagation of 
elastic waves in real m e d i a . I n particular, 

Aesoretl.or\ decrement 

F i g . 4 



ABSORPTION OF STATIONARY ELASTIC VIBRATIONS IN ROCKS 129 

the (lata obtained b y us confimi t h e con-
clusion iliade b y B. V. Deryagin who has 
explained t h e n a t u r e of seismic wave ab-

P i g . 5 

sorption based on t h e use of elastic a f t e r -
working f o r a speeially chosen f u n c t i o n of 
afterworking (4). 

ABSTRACT 

The seismoacoustic metliod based on am-
plitude and phase measurements of elastic 
oscillations caused by a source of stationary 
harmonic oscillations in rocks is used to 
study the character of divergence and ab-
sorption of seismic waves. The results of 
the experimental study of the absorbing 
properties of rocks by the seismoacoustic 
metlwd moke it possible to diffcrentiate rocks 
by absorption parameters. The greatest ab-
sorption is acquired by sedimentary rocks, 
the least — by erupted and metamorphized 
rocks. Inverse dependance between the veloci-
ty of elastic waves and absorption decre-
ment has been observed for different types of 
rocks. It ivas shown that for the prevailing 
majority of the rocks investigated the ab-
sorption coefficient increased with frequency 
under the linear late. 

It is pointed out that the experimental data 
obtained confimi the conclusions mode from 
the theory developed by B. V. Derjagin based 
on the phenomenon of the elastic after-cffect. 

RIASSUNTO 

Il carattere di divergenze e d'assorbimento 
delle onde sismiche è stato investigato me-
diante il metodo sismo-acustico basato sulle 
misurazioni di ampiezze e fasi delle oscilla-
zioni quali sono eccitate nelle roccia da una 
sorgente d'oscillazioni armoniche stazionarie. 

I risultati d'investigazione sperimentale 
mediante il m. s.-a. d'assorbimento della roc-
cia permettono di differenziare le roccie diver-
se secondo i parametri d'assorbimento. L'as-
sorbimento massimo è proprio di roccia se-
dimentaria il minimo di roccia d'eruzione e 
di roccia sottoposta a un metamorfismo. 

La proporzionalità inversa è stata osser-
vata tra la velocità delle onde elastiche e la 
diminuzione d'assorbimento per i tipi diversi 
di roccia. È dimostrato che il coefficiente d'as-
sorbimento è aumentato linearmente con la 
frequenza. È osservato il fenomeno della di-
spersione anomala della velocità di fase. 

I dati sperimentali ottenuti confermano le 
conclusioni della teoria basata sul fenomeno 
d'elasticità in seguito a quella svolta da 
B. V. Derjagin. 

B I B L I O G R A F I A 

F1) IVAIIUS, E . V . , P A S E C H N I K , I . P . , Methods 
of studying elastic and absorbing proper-
ties of rocks in their naturai occurrence by 
the methods of seismoaconstics, I z v e s t i a , 
A c . S e . U S S R . g e o p h y s . s e r . , 6 ( 1 9 5 4 ) . 

(2 ) — On the nature of the elastic waves excited 
in real media by a harmonic source, I z -
v e s t i a A c . S e . U S S R , g e o p h y s . s e r . , 2 
( 1 9 5 5 ) . 

(3) — Absorption of elastic waves in rocks by 
stationary excitation. I z v e s t i a A c . S e . U S 
S R , g e o p h y s . s e r . , 4 ( 1 9 5 8 ) . 

(4) L E R J A O I N , B . V . , Damping of seismic and 
acoustic waves and its independence on 
frequency. « J o u r n a l of G e o p h y s i c s », 3 - 4 
( 1 9 3 1 ) . 

Tne correfation of average 
voCues of ir, and a for different 

\ 
ì 
\ 
V PorphyrLtes 

\ 

Si£nnites ^ v^f"*0''" tes 
• GematiiTTr^e— . . flcr'ìite cAerts 

• Magnetite Ore