OBSERVATIONS AND THEORY OF MICROSEISMS 
The second branch in Fig. 3 begins if the ocean depth 
exceeds a value of approximately 1/3 (or about 14 7), 
which is normally more than 1 km. The corresponding 
wave velocity of the microseisms is about twice the 
sound velocity in water or about 3 km sec. If the 
ocean depth is smaller than the critical depth, the 
value of A in equation (6) becomes imaginary; the 
waves which correspond to this part of the branch are 
no longer surface waves. For H = 0, this corresponds 
to the second (physically nonexistent) branch of the 
solution for Rayleigh waves in a homogeneous layer. 
If the ocean depth exceeds a value of about four times 
the wave length, the velocity of the microseisms again 
becomes nearly equal to the velocity of longitudinal 
waves in water. 
Press and Ewing have pointed out that (as in other 
seismic surface waves) the group velocity and not the 
wave velocity should be investigated in a study of the 
amplitudes of continuous waves. The group velocity U 
is given by the equation, 
U=c—L— (7) 
Under the assumptions of Fig. 3, there is a minimum 
group velocity in the first branch and a maximum as 
well as a minimum group velocity in the second branch. 
All three values can be expected to be associated with 
an increase in amplitude in the course of time; under 
the assumptions used in Fig. 3, Press and Ewing find 
the values given in Table IJ. All three values for 7’ are 
Taste IJ. Pertops ror Grour VELocity Maxima AND 
Minima 
(After Press and Ewing [31]) 
T for 1 = 432 km 
Branch Group velocity U U/w H/L (sec) 
First Minimum 0.8 0.33 9.1 
Second Maximum 17 0.49 6.1 
Second Minimum 0.75 0.98 3.1 
within the range which is observed in microseisms. 
However, although the assumed ocean depth H = 414 
km is a fair average in many instances, it must be con- 
sidered that in many oceanic areas the depth is much . 
less and consequently the periods of the microseisms 
should vary greatly depending on H. Such a great vari- 
ation is not observed. However, the theory by Press 
and Hwing is a first approximation only; among other 
factors, the rather rapid increase in velocity with depth 
in the ocean bottom must be expected to affect the 
numerical results considerably. The effect of friction of 
the water on the sea bottom has no appreciable effect 
according to Menzel [26]. 
Scholte has not considered the effects of group veloc- 
ity. However, since he discusses the vibrations of the 
ocean bottom relatively close to the source, the effect 
of the group velocity is probably negligible; it takes 
many wave lengths before the accumulation of energy 
becomes appreciable in waves with periods near those 
of the maximum or minimum group velocity. However, 
effects of energy accumulation near extreme values of 
1307 
the group velocity have to be considered in the propa- 
gation of surface waves in the crustal layers. This has 
not been discussed by Scholte. 
Theoretical Periods of Pressure Waves in the Ocean. 
Comparison between the observed periods of micro- 
seisms and the simultaneous periods of ocean waves by 
Bernard [8] indicate that the periods of the microseis- 
mic waves frequently are about one-half of the periods 
of the corresponding ocean waves. Darbyshire [6, 7] 
confirmed the observations of Bernard by using exam- 
ples where a depression had a distance of the order of 
1000 miles from the west coast of the British Isles and 
comparing the ocean waves which arrived at the coast 
of Cornwall with the microseisms recorded at Kew. On 
the other hand, S. M. Mukherjee (unpublished manu- 
script) found that the periods of sea waves during the 
southwest monsoon in India are definitely not double 
the periods of microseisms. 
In detailed theoretical investigations Miche [27] has 
shown that in a stationary wave motion there are sec- 
ond-order pressure variations of twice the wave fre- 
quency. These variations are not attenuated to zero 
with depth. On the other hand Longuet-Higgins [23] 
(assuming meompressibility) found that beneath two 
wave trains with the same frequency travelling on the 
ocean in opposite directions, pressure fluctuations re- 
sult with a frequency double that of either wave and 
with amplitudes proportional to the produet of the 
wave amplitudes. Such mechanisms could produce the 
pressure changes near the surface which are assumed 
by Scholte in his theory [35]. 
All the mathematical theories mentioned thus far 
probably give a rough approximation, each from a dif- 
ferent angle, to a part of the causative mechanism 
which operates in microseisms. The theories of Miche, 
Longuet-Higgins, and Bernard could be combined with 
that of Scholte or that of Press and Ewing. In the lat- 
ter theory, the effect of the maximum and minimum 
group velocities on the amplitudes would be smaller if 
the source of the microseisms had strongly prominent 
periods. Such periods (possibly somewhat modified) 
should also appear in the microseisms. 
Theory of Propagation of Elastic Waves in the Ground 
Since microseisms are observed at stations on land, 
some theoretical results on the propagation of elastic 
waves in the earth’s crustal layers are needed for a dis- 
cussion of microseisms. 
Wave Types Observed in Microseisms. There are two 
major groups of seismic waves: (1) body waves (travel- 
ling through the interior of the material), and (2) sur- 
face waves. Group (1) contains longitudinal and trans- 
verse waves which have no noticeable dispersion, so 
that group velocity and wave velocity are practically 
the same. Group (2) includes Love waves (surface-shear 
Waves) in which the particles move in the surface of 
the earth perpendicular to the direction of propagation, 
and Rayleigh waves in which, theoretically at least, the 
particles describe ellipses with their longer axis in the 
vertical direction and their shorter axis in the direction 
of propagation. In seismograms produced by disturb- 
