REFLECTION FROM A DEEP INTERFACE IN A STRONGLY HETEROGENEOUS LAYERED MEDIUM

We consider the problem of acoustic pulse propagation through a layere d medium with a reflector at one end. The fluctuations in the medium p roperties are assumed to be strong, i.e. of finite amplitude, rapid in comparison to the typical wavelength and to have statistical structur e. The depth of the reflector is assumed to be large in comparison to the wavelength. In this regime, simple formulae for the reflected puls e and its arrival time at the surface are obtained. The amplitude of t he pulse is broadened and attenuated as a result of multiple scatterin g: the fine-layered structure of the medium can be characterized by a single constant which appears in the formula for the limiting waveform and which measures the size of the fluctuations in the medium. Within the theory, the commonly observed discrepancy between the integrated sonic traveltime and the seismic traveltime can be studied and underst ood. The theory is a natural extension of the long-wavelength effectiv e medium theory of Backus. The analysis is rigorous and based on the i nvariant embedding technique.