By Peter M. Shearer
This textbook is excellent. the writer emphasizes at the mathematical flavor within the description of seismic and geologic gains. in the event you examine issues on a mathematical viewpoint, this can be the on you need to have on your "library".
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Additional info for Introduction to Seismology
The displacement field, u, is an important concept and we will refer to it often in this book. It is an absolute measure of position changes. In contrast, strain is a local measure of relative changes in the displacement field, that is, the spatial gradients in the displacement field. Strain is related to the deformation, or change in shape, of a material rather than any absolute change in position. For example, extensional strain is defined as the change in length with respect to length. 01 (1%) everywhere in the string.
This is generally assumed valid in seismology, but the spatial derivatives (advection terms) are very important in fluid mechanics. 11) where λ and µ are the Lame´ parameters and the strain tensor is defined as eij = 12 (∂i uj + ∂j ui ). 11), we obtain τij = λδij ∂k uk + µ(∂i uj + ∂j ui ). 13) provide a coupled set of equations for the displacement and stress. These equations are sometimes used directly at this point to model wave propagation in computer calculations by applying finite-difference techniques.
2 Stress and strain Any quantitative description of seismic wave propagation or of earthquake physics requires the ability to characterize the internal forces and deformations in solid materials. We now begin a brief review of those parts of stress and strain theory that will be needed in subsequent chapters. Although this section is intended to be self-contained, we will not derive many equations, and the reader is referred to any continuum mechanics text (Malvern, 1969, is a classic but there are many others) for further details.