Comparison of Ray and Full-Wave SH-Wave Seismograms in Attenuating Layered Media

Abstract

An approximate but accurate calculation of seismic wavefields in smooth (without interfaces) isotropic or anisotropic, inhomogeneous, attenuating media using ray theory is possible with the aid of the so-called weak-attenuation concept (WAC). In WAC, the attenuating medium is regarded as a perturbation of an elastic reference medium. The extension of this concept to layered media was prevented for a long time by problems with evaluation of the reflection and transmission (R/T) coefficients of plane waves in attenuating media, and by the role of inhomogeneous waves in this process. The R/T coefficients represent a fundamental part of ray calculations in layered media. It turned out that the problems are related to a limited applicability of the correspondence principle to reflection and transmission. Recently, this problem was solved by the use of WAC. It opened the way to the calculation of seismic wave fields in layered, attenuating media. Before such a calculation, it is necessary to solve several important problems. It is well known that the incidence of a wave at an interface separating attenuative media generates inhomogeneous body waves. These waves are not implicitly included in WAC. Therefore, it is important to find out how their absence affects the results of ray calculations with WAC. In this paper, we check the accuracy of such calculations by comparing synthetic ray seismograms with full-wave seismograms, which are considered to be an accurate reference. For simplicity and transparency, we focus on the problem of reflection and transmission of SH-waves in 2D horizontally layered isotropic attenuating media, since SH-waves are decoupled from P–SV waves and thus allow a simpler treatment. Another reason for the use of SH-waves is the availability of the full-wave code designed for SH-waves. Use of more complicated structures and other types of waves would lead to artefacts, which would mask the effects of attenuation. The results of the comparison show that outside singular regions, such as the critical region or the vicinity of the Brewster angle, ray theory with WAC provides results that closely approximate those obtained using full-wave modeling. Applicability of WAC to other types of waves and more realistic structures is thus open.