Wave attenuation

Abstract

It is commonly observed that propagating waves lose amplitude sooner than might be expected for elastic media with smoothly varying properties. The explanation is in part that real materials are not elastic, and in part that real materials are not smoothly varying but have fine scale spatial fluctuations. We thus speak of anelastic attenuation, and attenuation due to scattering. Anelastic attenuation can be understood in a framework that allows for complex moduli relating stress and strain. A brief review will be given, of successful procedures for accommodating anelasticity in the computation of waveforms. The main part of this paper concerns attenuation of transmitted waves when forward scattering is dominant. This is the case for an elastic medium with a heterogeneous velocity structure when the typical fluctuation is spatially confined within less than a wavelength and the wave propagates over a sufficiently long path. The medium is found to have low-pass characteristics. The removal of high frequencies can often be summarized by a frequency-independent apparent Q. It is important in seismic prospecting to be able to determine whether observed amplitude decay is due to the presence of anelasticity and true dissipation, or to the presence of velocity fluctuations and resultant scattering. Numerical experiments indicate that when scattering dominates over anelasticity: (1) The coda of a transmitted wave contains relatively higher frequencies than the initial phase; (2) the attenuation deduced from the power spectrum of the transmitted wave is greater than that deduced from the phase spectrum; (3) compressional and shear wave apparent Q's are approximately equal; and (3) estimates of apparent Q made from reflected coda vary with frequency, while estimates made from the transmitted waves do not.