On Darbyshire's Method of Analysing Microseims

Abstract

In a recent paper with the same title as this letter, Hurst (1968) has made some comments on my work on microseisms (Iyer 1958, 1959). He points out an error in Darbyshire’s equations and the ‘ false conclusions ’ I reached from them. Mathematically speaking Hurst is right. For a point source model of microseisms composed of Rayleigh and Love waves, it is true that in the horizontal components, the Rayleigh and Love parts are correlated in an opposite sense. In other words, in the horizontal components when the Rayleigh waves are in phase, the Love waves are out of phase, and vice versa. This leads to the modifications in Darbyshire’s equations as Hurst has pointed out. 1 indicated this effect in my thesis (1959) though I did not use the idea and change Darbyshire’s equations. I developed the equations in which two out of the three correlation coefficients were shown to be adequate to solve for 8 and LIR, mainly because r,, was consistently a smaller quantity than r,, and r,,, and it was often difficult to determine the peak in the correlation functions as plotted by the photoelectric correlationmeter. This was to be expected as the correlation function was the composite of two independent functions, the Rayleigh part and the Love part. Hence it was considered desirable to avoid using r,,, to estimate 0, if possible. When this was found feasible, I decided to use the new equations. After all when a problem can be solved with two measurements, why use three, especially when the third quantity is not as stable as the other two? From another point of view also, it seems I was justified in modifying Darbyshire’s equations. In the light of developments that have taken place in the science of microseisms during the last ten years, a signal-plus-noise model for microseisms seems more realistic than a point Rayleigh-Love source. The fact that r,, M r,,:r,, in many cases seems to point out that the contribution to the correlation function made by what I called ‘ Love waves ’ was small. Work done by Haubrich et al. (1963) has shown that a good part of microseisms recorded at La Jolla consists of Rayleigh waves associated with an extended source, generated, probably by coastal ocean waves. Hence my work was a beginning of the concept of a point source of microseisms ‘ polluted ’ by isotropic noise. I called the noise ‘ Love waves ’, which is probably wrong. It can be seen that ‘ incoherent ’ noise in the horizontal components can lead to a positive value of I,.., which is very nearly equal to the product of r,, and rYz. One can generate models with Love and Rayleigh waves of varying degrees of isotropicity combined together. From our recent knowledge of the structure of microseismic sources gained by the use of extended seismic arrays, the sobering thought emerges that any model for microseismic sources is a beginning and not the end of the problem. Hence I would like to point out that my model of point source of Rayleigh waves mixed with Love waves from wide-angle sources is not ‘ a priori improbable ’, but one way of looking at the problem from data available at that time. I am grateful Of course, this game can be played in more ways also.