Lecture 9

• seismology

  the study of low-frequency elastic vibrations and waves in the solid Earth

  consists of three fundamental elements

  • source
  • earth response
  • reciever
• artificial sources - explosions

  • airguns used in a marine explorations survey
  • vibroseis trucks
  • nuclear tests
• applications

  • earthquakes and tectonics
  • earthquake hazards
  • earth structure
  • imaging of subsurface reservoirs
  • hydrocarbons
  • hydrogen
  • CO2 storage
  • geothermal
  • aquifers
  • site investigation
  • wind farms
  • archaeology
  • civil engineering
  • environmental protection (groundwater & pollution monitoring)
  • identifying nuclear explosions
  • comprehensive test ban treaty
• vibrations

  • displacement at a given point in space and what is recorded by a seismometer
  • vibrations are characterised by their frequency f
• waves

  • transmission of energy at a constant speed (e.g. the movement of ripples in a water tank)
  • waves are characterised by their wavelength λ, speed V and spatial frequency k
• the amplitude is the maximum size of the oscillation, and is the same for both vibrations and waves
• V=fλ i.e. the wave speed is the product of the frequency and the wavelength
• the material property that we 'see' in a seismic image is then the wave speed. it may or (occasionally) may not indicate differences in rock type, and the same rock type can have quite variable wave speed
• if V=fλ f=V/λ - low frequency -> long wavelength

  lower frequency -> larger structures, further away, lower resolution

  higher frequency -> smaller, nearer, structures at high resolution
• seismic waves are elastic waves, radiating from a natural or artificial source in a solid. In an elastic material Hooke's Law applies for small strains

  
• strain relaxes back to zero after a half-cycle. there is no permanent deformation or energy loss in an ideal elastic material
• the constant proportionality (the stiffness, or the slope of the line drawn, often called the elastic modulus) depends on the type of elastic deformation
• Young' modulus

  small cuboid deformed by extensional force F

  • stress = force/area = F/A
  • strain = extension/original length = δl/l

  $E=$$\frac{stress}{strain}=$$\frac{\left(\frac{F}{A}\right)}{\left(\frac{δl}{l}\right)}$
• stress has the units of Nm^-2, the same as pressure

  strain is dimensionless (m/m)
• Axial modulus

  if the sides are fixed then the elastic constant is known as the axial modulus Ψ

  $Ψ=$$\frac{\left(\frac{F}{A}\right)}{\left(\frac{δl}{l}\right)}$
• shear modulus

  if the material is deformed in shear δl is perpendicular to l

  the rigidity (shear) modulus μ is $μ=$$\frac{\left(\frac{F}{A}\right)}{\left(\frac{δl}{l}\right)}$
• bulk modulus

  if the force is uniform in all directions, the deformation is isotropic. Such a force is known as hydrostatic, since this is the way water, and all fluids, can deform

  $K=$$\frac{\left(\frac{F}{A}\right)}{\left(\frac{δV}{V}\right)}$
• elastic constants are related to one another

  $Ψ=$$K+$$\frac{4}{3}μ$
• an isotropic stress is known as a pressure. the main difference between wave propagation in a solid and in liquids or gases is that liquids and gases have no shear strength. waves in these media are called acoustic waves, and their properties depend only on the bulk modulus