2 Seismic Wave Propagation and Earth models

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2. Seismic Wave Propagation and Earth models • appreciating how these source parameter estimates can be improved by using more realistic (2-D, 3-D) Earth models as well as later (secondary) phase onsets in the processing routines; and • being aware of the common assumptions and simplifications used in synthetic seismogram calculations that are increasingly used nowadays in seismological routine practice (see 2.5.4.4, 2.8, 3.5.3). 2.2 Elastic moduli and body waves 2.2.1 Elastic moduli Seismic waves are elastic waves. Earth material must behave elastically to transmit them. The degree of elasticity determines how well they are transmitted. By the pressure front expanding from an underground explosion, or by an earthquake shear rupture, the surrounding Earth material is subjected to stress (compression, tension and/or shearing). As a consequence, it undergoes strain, i.e., it changes volume and/or distorts shape. In an inelastic (plastic, ductile) material this deformation remains while elastic behavior means that the material returns to its original volume and shape when the stress load is over. The degree of elasticity/plasticity of real Earth material depends mainly on the strain rate, i.e., on the length of time it takes to achieve a certain amount of distortion. At very low strain rates, such as movements in the order of mm or cm/year, it may behave ductilely. Examples are the formation of geologic folds or the slow plastic convective currents of the hot material in the Earth’s mantle with velocity on the order of several cm per year. On the other hand, the Earth reacts elastically to the small but rapid deformations caused by a transient seismic source pulse. Only for very large amplitude seismic deformations in soft soil (e.g., from earthquake strong-motions in the order of 40% or more of the gravity acceleration of the Earth) or for extremely long-period free-oscillation modes (see 2.4) does the inelastic behavior of seismic waves have to be taken into account. Within its elastic range the behavior of the Earth material can be described by Hooke’s Law that states that the amount of strain is linearly proportional to the amount of stress. Beyond its elastic limit the material may either respond with brittle fracturing (e.g., earthquake faulting, see Chapter 3) or ductile behavior/plastic flow (Fig. 2.1). Fig. 2.1 Schematic presentation of the relationship between stress and strain. 2
3 2.2 Elastic moduli and body waves Elastic material resists differently to stress depending on the type of deformation. It can be quantified by various elastic moduli: • the bulk modulus κ is defined as the ratio of the hydrostatic (homogeneous all-sides) pressure change to the resulting relative volume change, i.e., κ = ΔP / (ΔV/V), which is a measure of the incompressibility of the material (see Fig. 2.2 top); • the shear modulus μ (or “rigidity”) is a measure of the resistance of the material to shearing, i.e., to changing the shape and not the volume of the material. Its value is given by half of the ratio between the applied shear stress τxy (or tangential force ΔF divided by the area A over which the force is applied) and the resulting shear strain exy (or the shear displacement ΔL divided by the length L of the area acted upon by ΔF) , that is μ = τxy/2 exy or μ = (ΔF/A) / (ΔL/L) (Fig. 2.2 middle). For fluids μ = 0, and for material of very strong resistance (i.e. ΔL → 0) μ → ∞; • the Young’s modulus E (or “stretch modulus”) describes the behavior of a cylinder of length L that is pulled on both ends. Its value is given by the ratio between the extensional stress to the resulting extensional strain of the cylinder, i.e., E = (F/A) / (ΔL/L) (Fig. 2.2 bottom); • the Poisson’s ratio σ is the ratio between the lateral contraction (relative change of width W) of a cylinder being pulled on its ends to its relative longitudinal extension, i.e., σ = (ΔW/W) / (ΔL/L) (Fig. 2.2 bottom). Fig. 2.2 Deformation of material samples for determining elastic moduli. Top: bulk modulus κ; middle: shear modulus μ; bottom: Young’s modulus E and Poisson’s ratio σ. a – original shape of the volume to be deformed; b – volume and/or shape after adding pressure ΔP to the volume V (top), shear force ΔF over the area A (middle) or stretching force F in the direction of the long axis of the bar (bottom).
Page 1: CHAPTER 2 Seismic Wave Propagation
Page 5 and 6: 5 2.2 Elastic moduli and body waves
Page 11 and 12: 11 2.3 Surface waves S waves are al
Page 13 and 14: 2.3.2 Dispersion and polarization 1
Page 15 and 16: 15 2.3 Surface waves Strictly speak
Page 17 and 18: 17 2.3 Surface waves (Z-E) plane, w
Page 19 and 20: 2.3.4 Mantle surface waves 19 2.3 S
Page 21 and 22: 2.4 Normal modes 21 2.4 Normal mode
Page 23 and 24: 23 2.4 Normal modes First observati
Page 25 and 26: 2.5 Seismic rays, travel times, amp
Page 43 and 44: 2.6 Seismic phases and travel times
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Overlay to Fig. 2.47 2.6 Seismic ph
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2.6 Seismic phases and travel times
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57 2.7 Global Earth models on verti
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59 2.7 Global Earth models As shown
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61 2.7 Global Earth models The mode
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2.8 Synthetic seismograms and wavef
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2 Seismic Wave Propagation and Earth models

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