2.1 Seismic waves and their properties

Seismic waves are Earth's messengers, revealing its hidden layers and structures. They come in two main types: body waves that travel through Earth's interior, and surface waves that ripple along its surface.

These waves behave differently based on the materials they encounter. By studying their speeds, paths, and changes, scientists can map out Earth's inner workings, from its crust to its core.

Seismic Wave Types and Characteristics

Body Waves

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• P-waves (primary or compressional waves) are the fastest seismic waves and can travel through both solid and liquid materials
  • Cause particles to oscillate parallel to the direction of wave propagation, resulting in compression and rarefaction
  • Velocity typically ranges from 1.5 km/s in unconsolidated sediments to over 13 km/s in the Earth's inner core
• S-waves (secondary or shear waves) are slower than P-waves and can only travel through solid materials
  • Cause particles to oscillate perpendicular to the direction of wave propagation, resulting in shearing motion
  • Velocity is typically about 60% of the corresponding P-wave velocity in solid materials
  • Cannot propagate through liquids, such as the Earth's outer core

Surface Waves

• Rayleigh waves cause particles to move in an elliptical motion in the vertical plane, with both vertical and horizontal components
  • Slowest seismic waves and cause the most damage during earthquakes (ground rolling motion)
  • Velocity is slightly slower than S-waves in the same material
• Love waves cause particles to move side-to-side in a horizontal plane, perpendicular to the direction of wave propagation
  • Faster than Rayleigh waves but slower than body waves
  • Confined to the Earth's surface and shallow depths
  • Require a low-velocity layer overlying a high-velocity layer to propagate (waveguide effect)

Factors Influencing Seismic Wave Propagation

Elastic Properties and Density

• Seismic wave velocity is primarily controlled by the elastic moduli (bulk modulus and shear modulus) and density of the material
  • Higher elastic moduli and lower density result in faster wave velocities
  • P-wave velocity: $V_p = \sqrt{\frac{K + 4/3\mu}{\rho}}$, where $K$ is bulk modulus, $\mu$ is shear modulus, and $\rho$ is density
  • S-wave velocity: $V_s = \sqrt{\frac{\mu}{\rho}}$
• Temperature and pressure increase with depth in the Earth, affecting the elastic properties and density of materials
  • Increasing temperature generally reduces the elastic moduli (thermal expansion and weakening of atomic bonds)
  • Increasing pressure increases the elastic moduli and density (compression and closure of pores and cracks)

Anisotropy and Heterogeneity

• Anisotropy is the variation of elastic properties with direction, causing seismic waves to travel at different velocities depending on their direction of propagation
  • Common in layered or foliated rocks (sedimentary bedding, metamorphic foliation)
  • Can lead to shear wave splitting (birefringence) and azimuthal variations in velocity
• Heterogeneities, such as inclusions, fractures, and compositional variations, can cause scattering and attenuation of seismic waves
  • Scattering redistributes energy and can generate coda waves (late-arriving, scattered energy)
  • Attenuation is the loss of energy as waves propagate through a material, resulting in decreased amplitude and higher frequencies being attenuated more rapidly than lower frequencies

Seismic Wave Velocity and Attenuation

Velocity Variations in Earth Materials

• Seismic wave velocities vary depending on the type of material and its properties
  • Unconsolidated sediments: P-wave velocity ~1.5-2.5 km/s, S-wave velocity ~0.2-1.0 km/s
  • Consolidated sedimentary rocks: P-wave velocity ~2.5-6.0 km/s, S-wave velocity ~1.5-3.5 km/s
  • Crystalline rocks (igneous and metamorphic): P-wave velocity ~5.5-7.5 km/s, S-wave velocity ~3.0-4.5 km/s
  • Mantle: P-wave velocity ~7.5-13.0 km/s, S-wave velocity ~4.5-7.5 km/s
  • Outer core (liquid): P-wave velocity ~8.0-10.5 km/s, S-waves cannot propagate
  • Inner core (solid): P-wave velocity ~11.0-13.0 km/s, S-wave velocity ~3.5-4.5 km/s
• Velocity generally increases with depth due to increasing pressure and changes in material properties
  • Crustal velocity structure: gradual increase with depth, with discontinuities at major compositional boundaries (e.g., Moho)
  • Mantle velocity structure: gradual increase with depth, with discontinuities at phase transitions (e.g., 410 km and 660 km discontinuities)

Attenuation Mechanisms and Quality Factor

• Attenuation is quantified by the quality factor (Q), which is inversely proportional to the energy loss per cycle
  • Higher Q values indicate lower attenuation and more efficient wave propagation
  • Q is frequency-dependent: $Q(\omega) = \frac{\omega}{2\alpha(\omega)V}$, where $\omega$ is angular frequency, $\alpha$ is attenuation coefficient, and $V$ is wave velocity
• Intrinsic absorption is the conversion of elastic energy to heat due to anelastic processes (e.g., grain boundary sliding, dislocation motion)
  • Increases with temperature and decreases with pressure
  • More significant in partially molten or fluid-rich regions (asthenosphere, magma chambers)
• Scattering is the redistribution of energy due to heterogeneities in the medium
  • Depends on the size, shape, and contrast of the heterogeneities relative to the seismic wavelength
  • More pronounced in highly fractured or heterogeneous regions (fault zones, volcanic areas)
• Geometrical spreading is the decrease in energy density with distance from the source due to the expansion of the wavefront
  • Causes amplitude to decrease with distance even in the absence of other attenuation mechanisms
  • Amplitude decays as $1/r$ for body waves and $1/\sqrt{r}$ for surface waves, where $r$ is distance from the source

Earth's Internal Structure from Seismic Waves

Seismic Wave Arrival Times and Amplitudes

• The difference in arrival times between P-waves and S-waves (S-P time) increases with distance from the source
  • Allows determination of the distance to the earthquake epicenter using travel-time curves or tables
  • S-P time increases sharply at distances corresponding to major discontinuities (e.g., core-mantle boundary)
• Seismic wave amplitudes provide information about the attenuation properties of the materials they pass through
  • Lower amplitudes indicate higher attenuation and can be used to identify regions of partial melting or fluid content
  • Amplitude variations with distance can also reveal the presence of discontinuities and velocity gradients

Seismic Discontinuities and Velocity Structure

• Seismic discontinuities are characterized by abrupt changes in seismic wave velocities and cause reflections and conversions between wave types
  • Mohorovičić discontinuity (Moho): boundary between the crust and mantle, marked by a sharp increase in P-wave velocity (6.0-7.5 km/s to 7.5-8.5 km/s)
  • Core-mantle boundary (CMB): boundary between the mantle and outer core, marked by a sharp decrease in P-wave velocity (13.0 km/s to 8.0 km/s) and disappearance of S-waves
  • Inner core boundary (ICB): boundary between the outer and inner core, marked by a sharp increase in P-wave velocity (10.5 km/s to 11.0 km/s) and reappearance of S-waves
• Seismic wave velocities increase with depth due to increasing pressure and changes in material properties
  • Causes seismic waves to refract (bend) according to Snell's law: $\frac{\sin\theta_1}{V_1} = \frac{\sin\theta_2}{V_2}$, where $\theta$ is the angle of incidence/refraction and $V$ is the wave velocity
  • Results in curved ray paths and the formation of shadow zones (regions where direct seismic waves are not observed)
  • The absence of direct S-waves beyond about 100° from the epicenter suggests the presence of a liquid outer core

Seismic Tomography and 3D Earth Structure

• Seismic tomography uses the arrival times and amplitudes of seismic waves from multiple sources and receivers to create 3D images of the Earth's interior
  • Travel-time tomography: uses the difference between observed and predicted travel times to invert for velocity variations
  • Attenuation tomography: uses the decay of seismic wave amplitudes to invert for attenuation variations
  • Waveform tomography: uses the complete waveform (shape and amplitude) to invert for velocity and attenuation variations
• Tomographic models reveal lateral variations in seismic wave velocity and attenuation, providing insights into the Earth's 3D structure
  • Mantle plumes: low-velocity, high-attenuation regions extending from the core-mantle boundary to the surface (e.g., Hawaii, Iceland)
  • Subducting slabs: high-velocity, low-attenuation regions extending from the surface to the lower mantle (e.g., Pacific Ring of Fire)
  • Large low-shear-velocity provinces (LLSVPs): broad, low-velocity regions in the lowermost mantle, possibly related to thermal or compositional variations