Introduction to Seismology by Peter M. Shearer

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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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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.

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