1306 
The energy which is transferred to a coast of length / 
is given by 
(2 
wo 
During storms this may reach the order of 10'*f ergs 
sect. The amplitude a of the corresponding microseisms 
with a period 7 and a wave velocity C at a distance D 
from the source is then given approximately [14] by 
2 TE 
~ BX ORC? sia iD @) 
If T = 7sec,C = 3 km sec, D = 10°, H = 10!f ergs 
(as found above), and a = 1 micron = 10-* mm, f must 
be of the order of 107%, that is, one-tenth of one per 
cent of the wave energy must be transferred to the 
coast in order to explain the microseisms by the surf 
action. This value is not unreasonable. No arguments 
against this theory have been published and the theory 
explains the microseisms of Type 7. 
Theory of Propagation of Waves from the Surface of 
the Ocean to the Bottom. In an attempt to calculate the 
energy transmitted from ocean waves at the surface to 
the ocean bottom, Scholte [35] supposed that waves of 
period T exist at the surface of the ocean. He started 
with the following equation given by Sezawa [37]: 
or 
Co) i 
which connects a displacement r (components wu, v, w) in 
the water with the velocity c of its propagation and in- 
cludes gravity waves as well as compressional waves. 
Scholte found under reasonable assumptions that near 
the surface of the ocean the ratio of the amplitudes of 
the gravitational and the elastic waves is of the order 
of 104 to 1. If the gravity waves at the surface have a 
height of 10 m, the elastic waves in the water would 
have an amplitude of the order of 1 mm. However, the 
gravity waves decrease exponentially with depth; the 
elastic waves change relatively little. Consequently, 
gravity waves should not be noticeable at great depths 
in the ocean (this result confirmed theoretical conclu- 
sions of earlier investigators), but elastic waves should 
remain perceptible with sensitive instruments down to 
the bottom of the ocean where they start the usual 
seismic waves in the surface layers. However, Scholte 
did not describe this latter process in detail. His paper 
is the only one giving quantitative results for the elastic 
microseismic waves at the ocean bottom. 
Theory of Propagation of Elastic Waves in a Medium 
Consisting of an Upper Layer of Water Overlying a Ho- 
mogeneous Layer of Solid Rock. Press and Ewing [31] 
have studied the propagation of elastic surface waves 
originating at the surface of an ocean with a homo- 
geneous bottom layer. They have used an equation de- 
veloped by Stoneley [38] which may be written in the 
following form: 
tan, a 
L 
_ pAl4. — By — ©} — (2 — B)’] 
rs EL = Oy 
a 
= cV(V-r) + gVu, (4) 
(5) 
MICROSEISMS 
where 
[J] 2-@ e-G 
H = depth of ocean; L = wave length (measured in a 
horizontal direction) of waves formed by constructive 
interference between elementary waves of length / 
which undergo multiple reflections at the boundary of 
the liquid layer at an angle of incidence 7; c = velocity 
of microseismic waves; w = velocity of sound in water 
(density 1.0); V and v are the velocities of longitudinal 
and transverse body-waves, respectively, in the mate- 
rial below the ocean which has the density p and is 
assumed to extend down to infinite depth. Scholte, too, 
has found and used this equation [35, equation bottom 
p. 674] apparently without recognizing the equation as 
Stoneley’s. If the velocity c is assumed, then H/L can 
be calculated from equation (5). If the depth H of the 
ocean is very small as compared with the wave length 
L, equation (5) becomes the well-known equation for 
Rayleigh waves in the surface of the solid bottom. For 
a more detailed theory, see Pekeris [30]. 
Press and Ewing assumed, for example, w = 114 km 
sec (velocity of elastic waves in water), V = 5.3 km 
sec and v = 2w = 3.0 km sec in the ocean bottom 
where the density p = 2.5, and Poisson’s ratio equals 
14. In order to get an exponential decrease of amplitudes 
with depth, that is, surface waves, A in equation (6) 
must be real (ce = w). Under their assumptions (which 
include 7 = 1.57) the curve giving the wave velocity 
as a function of H/1 consists of two branches (Fig. 3). 
PROPAGATION OF SOUND 
IN WATER (1), OVER ROCK (2) 
c= PHASE VELOCITY 
U= GROUP VELOCITY 
COMPRESSIONAL WAVE IN WATER 
COMPRESSIONAL WAVE IN ROCK 
SHEAR WAVE IN ROCK 
T = PERIOD OF SOUND WAVES 
H = DEPTH OF WATER 
Po =2.5p4 
V =¥3 v =2V3 w 
E==——° 
| ee 
+ RANCH 
7 8 
Yen eo 
0.6 O08 | 2 3.4 6 8 
ld 
wT 
0.2 03 0.4 
Fic. 3—Theoretical phase and group velocity in a system 
consisting of a liquid layer overlying an infinitely thick homo- 
geneous solid (under the specified assumptions). (After Press 
and Ewing [31].) 
For the first branch, c’ approaches the velocity of Ray- 
leigh waves in the ground if H/I is small. Under the 
assumptions made in the figure, this requires an ocean 
depth of not over a few hundred meters for waves with 
periods of 3 sec. If the ocean depth H increases beyond 
the wave length (J = 1.57) of the elastic waves in 
water, the velocity of the microseisms approaches the 
velocity of sound in water. 
