Introduction

The amplitude of seismic waves decreases with distance traveled as a result of four processes. First, waves spreading from any source of finite dimensions decrease in amplitude due to the increase in area of the wave front. This type of attenuation is called geometric spreading. Second, the waves may be dispersed; that is, their velocity of propagation is a function of their frequency of oscillation. Dispersion lengthens the pulse with distance of transmission with consequent attenuation of amplitude. Third, if the medium through which the waves are passing is not uniform in physical properties, the energy is split into reflected and refracted pulses at each boundary, as described by C. G. Knott (1899). For simple interfaces that are large compared with a wavelength, the resultant separate wave fronts may be recognizable and an appropriate fraction of the original energy associated with each. If many interfaces are closely spaced or are irregular in shape, as is commonly the case, the effect is to produce many subdivisions of the initial pulse traveling in a variety of directions. The energy is then said to be scattered. Scatter tends to spread the energy in time as well as in space, in as much as many small reflections feed energy backward, forward again, and to the side. The overall result can be very similar to dispersion: an increase in the time it takes the energy to pass a given location.