Acoustic Waves in Layered Media - From Theory to Seismic Applications

Abstract

Acoustic wave propagation in layered media is very important topic for many practical applications including medicine, optics and applied geophysics. The key parameter controlling all effects in layered media is the scaling factor given by the ratio between the wavelength and the layer thickness. Existing theory mostly covers the solutions derived for the low-frequency and high-frequency limits. In the first limit, when the wavelength is much larger than the layer thickness, the layered medium is substituted by an effective medium with the properties given by special technique called the Backus averaging. In the second limit, when the wavelength is much smaller than the layer thickness, we can use the ray theory to compute both reflection and transmission responses. In practice, the wavelength could be comparable with the layer thickness, and application of both frequency limits is no longer valid. In this chapter, we will mainly focus on the frequency-dependent effects for acoustic waves propagating through the layered media. We show that there are distinct periodically repeated patterns consisted of the passand stop-bands of very complicated configuration defined in frequency-slowness or frequencygroup angle domain that control the reflection and transmission responses. The edges between the passand stop-bands result in the caustics in the group domain. The quasishear waves in a homogeneous transversely isotropic medium could also results in the highfrequency caustics, but for the layered media, all wave modes can result in frequencydependent caustics. The caustics computed for a specific frequency differ from those observed at the lowand high-frequency limits. From physics point of view, the pass-bands correspond to the effective medium, while the stop-bands correspond to the resonant medium. We distinguish between the effects of scattering and intrinsic attenuation in layered media. The propagation of acoustic waves in a layered medium results in the energy loss due to scattering effect. The intrinsic attenuation is an additional effect which plays very important role in seismic data inversion. We provide the theoretical and numerical study to compare both effects for a periodically layered medium. We also investigate the complex frequency roots of the reflection/transmission responses. We also derive the phase velocity approximations in a layered medium. As the trial model for layered medium, we widely use the periodically layered medium with the limited number of parameters. The propagation of acoustic waves through a periodic layered medium is analyzed by an eigenvalue