Premium
Reflection from a deep interface in a strongly heterogeneous layered medium 1
Author(s) -
Lewicki Pawel,
Burridge Robert
Publication year - 1996
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/j.1365-2478.1996.tb00166.x
Subject(s) - wavelength , amplitude , scattering , optics , reflection (computer programming) , reflector (photography) , pulse (music) , waveform , physics , embedding , computational physics , geology , quantum mechanics , light source , voltage , detector , computer science , programming language , artificial intelligence
We consider the problem of acoustic pulse propagation through a layered medium with a reflector at one end. The fluctuations in the medium properties are assumed to be strong, i.e. of finite amplitude, rapid in comparison to the typical wavelength and to have statistical structure. The depth of the reflector is assumed to be large in comparison to the wavelength. In this regime, simple formulae for the reflected pulse and its arrival time at the surface are obtained. The amplitude of the pulse is broadened and attenuated as a result of multiple scattering: 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 understood. The theory is a natural extension of the long‐wavelength effective medium theory of Backus. The analysis is rigorous and based on the invariant embedding technique.