Waves and Rays in Earth-Type Materials with Damping

What is it about?

The 1st Edition of this book is a rigorous, self-contained exposition of the mathematical theory for wave propagation in layered media with arbitrary amounts of intrinsic absorption. The 2nd Edition extends the exposition to include the theory of general viscoelastic rays and head waves. These theories, previously not published in another book, provide solutions for many of the fundamental wave-propagation and ray-theory problems of seismology and other fields in the general context of any viscoelastic media with a linear response (elastic or anelastic). The 1st Edition provides the viscoelastic solutions for P and S body waves, reflection-refraction problems, Rayleigh- and Love-Type surface waves, and response of multiple layers to incident waves. The 2nd Edition (in press) extends these results to include solutions for the forward and inverse ray theory problems in horizontal and spherical anelastic media with and without gradients. It provides the solutions for head waves and the simple computation steps for general ray tracing algorithms in any horizontal or spherical anelastic layered model. The 2nd edition provides laboratory and empirical evidence that confirms recently revealed characteristics of anelastic waves, such as velocity, particle motion and attenuation that vary with angle of incidence and contrasts in intrinsic material absorption at boundaries. The book is written in a simple format that provides the opportunity to teach the classic subject of elastic wave propagation and ray theory in the broader context of any media with a linear response without undue complications in the mathematics.

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Why is it important?

The results in the 2nd Edition entitled “Viscoelastic Waves and Rays in Layered Media” explain observed characteristics of two- and three-dimensional anelastic body and surface waves, head waves, and general rays in the Earth not accounted for by elastic or one-dimensional anelastic models. The general ray theory results predict measurable variations in travel-time and amplitude-attenuation for P and S waves induced by contrasts in intrinsic material absorption at anelastic near-surface and teleseismic boundaries in the Earth. They specify the computation steps for forward ray-tracing algorithms based on exact anelastic solutions valid for any linear anelastic media, whether it be soft soil or material deep within the Earth’s mantle. The 2nd Edition also provides the solutions for the inverse ray-theory problem derived from solutions of the generalized Herglotz-Wiechert integral for viscoelastic media. The solutions permit the inference of material-damping characteristics from observations of travel time and amplitude attenuation as observed for seismic arrivals at the surface. The solution of the inverse problem together with the forward ray tracing algorithms based on exact solutions provide the mathematical framework to improve models of anelastic material response for a wide variety of applications, especially those involving tomography as applied in exploration and marine geophysics, crustal and tele seismic seismology, and non-destructive testing of materials.

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