Signal Generated Seismic Noise

Abstract

Summary A typical seismic pulse generates a certain amount of incoherent wavemotion due to the scattering effect of small variations in the elastic properties of the Earth. This is recorded as ‘noise’ along with the main signal. When the problem is treated statistically, mean square amplitudes of the scattered waves, and fluctuations in amplitude and phase of the incident signal, can be calculated for wave-motion which is simpleharmonic in time. The results at low frequencies for an incident plane wave in an unbounded medium have already been reported. Extension to higher frequencies shows that the Rayleigh fourth-power law holds only for wavelengths greater than the linear extent of the scattering centres. If the inhomogeneities lie near a plane free surface, Rayleigh waves are generated. Amplitudes have been calculated for incident plane P and S waves. 1. Theory Even if the detailed structure of a heterogeneous Earth were known, the calculation of the precise properties of an elastic wave passing through such a region would be difficult if not impossible, depending upon the degree of heterogeneity. If we consider a completely heterogeneous region, one whose properties are only describable statistically, then the calculation of the properties of elastic wave propagation again becomes feasible. But now the properties of the scattered waves are themselves only describable statistically. If the scattering region is large compared with the size of individual scattering centres and the fluctuations in the elastic parameters are generally small, then the variation of the elastic parameters can be considered to be random and the properties of the scattered waves can be calculated in terms of the correlation functions. These functions are defined in the following manner :