The nature of seismic noise

Abstract

When seismic signals from impulsive sources are reflected or refracted by discrete inhomogeneities in the seismic medium, ‘arrivals’ are recorded. If, however, the number of inhomogeneities becomes large and the distance between them becomes small, then interference among the arrivals takes place and source-caused ‘noise ’ is recorded. If the spacing between observatories is large compared with the spacing between and dimensions of the scatterers, the source-caused noise is incoherent. If the number of scatterers is large enough for the problem to be treated statistically, the noise has a random character. The properties of the noise can be computed by averaging statistically over all the signals due to the scattering from the ensemble of scatterers. Single scattering only is treated here. There are ‘local’ or ‘end’ effects corresponding to scattering near the source or the receiver which cannot be taken into account in the calculations. The main problem which has been treated is that of the scattering of body waves of P and S types in an unbounded inhomogeneous medium. The magnitudes of the scattered waves of all types— PP, PS, SP, SS —have been computed. In addition the phase shifts (time delays or advances) in incident P and S can be computed. It is found that body waves of either P or S type convert into scattered S waves with considerably greater ease than into scattered P waves. The comparative efficiency of these processes is about two orders of magnitude. Thus P waves show small phase shifts; S waves show large phase shifts. The waves between P and S are most likely of the character of S . The approximations in the calculations involve the assumptions of wavelength long compared with the dimensions of the scatterer and the dimensions of the scattering region long compared with wavelength. Under these conditions the approximations are those for Rayleigh scattering. Hence, in all the results, the scattering varies as the fourth power of the frequency and the mean square scattered energy is proportional to the linear dimension of the scattering region. At higher frequencies, the scattering changes from a fourth power dependence upon frequency to a second power dependence. This is a result which is obtained only for scattering by elastic media; it is not found in media without shear modulus. Experimental evidence for this high frequency effect has been found.