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EARTH 260 (1)


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University of Waterloo
Earth Sciences
Tony Endres

Earth 260-Applied Geophysics 1 II.) SEISMIC METHODS Mechanical energy can travel through a medium as a wave, such as sound waves in air or water. Seismic waves are waves of mechanical energy that travel through the Earths interior. The traveltime and amplitude of these waves are measured to determine the structure of the subsurface. A.) Basic Concepts for Seismic Wave Propagation 1.)Stress and Strain a.)Stress a measure of the intensity of the mechanical force applied to a material. Consider the force applied uniformly across the face of a cube, the stress would be Force / Surface Area of the Face SI Units of stress: 2 2 Newtons / meter ( N / m ) = Pascal (Pa) There are different types of stress that can be applied to a material (e.g., pressure, traction or shear stress). b.)Strain a measure of the deformation (i.e., changes in shape and size) caused by an applied stress. 1 Earth 260-Applied Geophysics 1 Different types of strain correspond to differing types of stress (e.g., dilatational (or volumetric) strain, shear strain). Strain is a dimensionless quantity. 2.) Elastic Moduli a.)If the stress and strain are small in magnitude (which they generally are for seismic waves), there is a proportional relationship between them. Stress = Constant Strain (1) This proportionality constant is an elastic modulus that is a physical property of the material. Elastic moduli have the same SI units as stress (i.e., Pa). Note: This relationship is analogous to Hookes Law for springs. b.) The elastic modulus used is in this equation is determined by the stress and strain type. 1.) Bulk modulus K relates pressure P to volumetric strain . P = K (2) 2 Earth 260-Applied Geophysics 1 2.) Shear modulus (or Rigidity) relates shear stress to shear strain . = (3) There is no volume change associated with shear stress and strain; the deformation is a distortion in shape. Fluids (i.e., water and air) cannot support a shear stress; their shear modulus = 0. 3.)Types of Seismic Waves When the stress-strain relationships (i.e., constitutive relationships) are combined with the equations of motion nd (the generalized version of Newtons 2 Law: Fa= m ), we get the elastic wave equation that describes the propagation of mechanical waves through a material. From this equation, we find there are different types of seismic waves with distinctive characteristics. There are two groups of seismic waves: body and surface waves. 3 Earth 260-Applied Geophysics 1 a.) Body Waves 1.) These waves travel/propagate through the body (or interior) of a medium. 2.) There are two types (i.e., modes) of body waves that differ in terms of their particle motion relative to the propagation (i.e., travel) direction of the wave. Particle motion is determined by tagging a particle in the material; its movement as the wave passes is the particle motion. 3.) Compressional (longitudinal, primary or P-) waves a.)Particle motion is in the same direction as the wave propagates. b.)These waves have regions of dilatation/rarefraction and compression due to volume changes. c.) P-wave velocity: 4 K + 3 VP = = (4) 3 where is the density (in kg / m ) of the material. Note #1: SI units for velocity are m / s or km / s. Note #2: Density is introduced through the inertia terms in the equations of motion. 4
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