SECT. 5] MICROSEISMS 711 



concluded, however, that the micro-ratio technique was not a very rehable 

 method of estimating storm position. 



5. Estimation of Direction from the Nature of Microseisms 



Work on direction finding was carried out in Great Britain by the writer 

 (1954). If the microseisms are pure Rayleigh waves, the tangent of the bearing 

 angle should be given by : 



where x is the r.m.s. amplitude of the E-W component and y that of the N-S 

 component. The quadrant of approach is determined from the phase relation- 

 ships. If the microseisms consist of a mixture of Rayleigh and Love waves, the 

 problem becomes more complicated. If 6 is the bearing angle, R{t) the displace- 

 ment due to the Rayleigh wave and L{t) that due to the Love wave at any 

 instant, 



X = R{t) sin e + L{t) Bin d 



y = JR{t) cos e + L{t) cos d 



z = kR{t), where k is the Rayleigh constant. 



If it is assumed that the two kinds of waves come from the same source, and it 

 is assumed that E{t) and L{t) are uncorrelated, 



X = [^)2 sin2 e + L(J)^ cos2 6]''- 



y = [R{t)^ cos2 d+T{i)^ sin2 ^]'/^ 



z = k[R{t)^V'- 

 The maximum correlation between the horizontal and vertical components, 

 allowing for the phase difference, is, 



r^, = kR{t)^ sin dl{R{t)'^-[R{t)'^ sin2 d + L{t)^ cos2 e]}'^ 



= 'R{i) sin ei[R{i)^ sin2 d + L{f)^ cos2 6]''^ 

 and similarly 



ry, = 'R{t) cos dl[R{i)^ cos2 d + L{iy- sin2 dyK 



Thus x-rxz = R{t) sin 6 and y-ryz= R{t) cos 6 and therefore 



tan 6 = X- Txzly ■ Vyx. 



It was also shown by Iyer (1959) that 



tan2 ^ (l/r^e2_i)>/./(i/^^^2_i)>i (1) 



and 



'L{t)^lR{t)^ = {\iry^'^-\)H^^rxz^-\Y^. (2) 



(1) and (2) are very useful as the actual amplitudes of the waves are not re- 

 quired and the sensitivities of seismographs tend to vary over a period of years. 



