🌋Seismology Unit 12 – Seismic Tomography and Earth's Interior

Key Concepts and Terminology

• Seismic waves: Elastic waves generated by earthquakes or artificial sources that propagate through the Earth's interior
• P-waves (primary waves): Compressional waves that travel fastest and can pass through solids, liquids, and gases
• S-waves (secondary waves): Shear waves that travel slower than P-waves and can only pass through solids
• Seismic velocity: Speed at which seismic waves propagate through a medium, dependent on the material's elastic properties and density
• Seismic ray path: The path taken by a seismic wave as it travels through the Earth's interior, which can be bent or refracted due to changes in velocity
• Seismic attenuation: The loss of energy as seismic waves propagate through the Earth, caused by absorption and scattering
• Seismic anisotropy: The variation of seismic velocity with the direction of wave propagation, often due to the alignment of minerals or the presence of fractures
• Seismic heterogeneity: Variations in seismic velocity within the Earth's interior, which can be mapped using seismic tomography

Fundamentals of Seismic Waves

• Seismic waves are generated by the sudden release of energy during earthquakes or artificial sources (explosions, vibroseis)
• P-waves compress and expand the material they pass through, causing volume changes
  • P-wave velocity ($V_p$) is given by: $V_p = \sqrt{\frac{K + \frac{4}{3}\mu}{\rho}}$, where $K$ is the bulk modulus, $\mu$ is the shear modulus, and $\rho$ is the density
• S-waves cause shearing motion perpendicular to the direction of wave propagation
  • S-wave velocity ($V_s$) is given by: $V_s = \sqrt{\frac{\mu}{\rho}}$
• Surface waves (Rayleigh and Love waves) travel along the Earth's surface and are characterized by lower velocities and larger amplitudes compared to body waves
• Seismic waves are reflected, refracted, and converted at boundaries between materials with different elastic properties
• Seismic wave propagation is affected by the temperature, pressure, and composition of the Earth's interior
• Seismic attenuation is frequency-dependent, with higher frequencies attenuating more rapidly than lower frequencies

Seismic Tomography Techniques

• Seismic tomography is a technique that uses seismic wave travel times to create 3D images of the Earth's interior velocity structure
• Travel time tomography: Uses the arrival times of seismic waves to infer velocity variations along the ray paths
  • Involves solving an inverse problem to determine the velocity model that best fits the observed travel times
• Waveform tomography: Uses the full waveform of seismic signals to extract more detailed information about the Earth's interior
  • Considers the amplitude and phase of seismic waves, allowing for higher resolution images
• Fresnel volume tomography: Takes into account the finite-frequency nature of seismic waves and the volume of sensitivity around the ray path
• Adjoint tomography: Uses numerical simulations of seismic wave propagation and compares them with observed waveforms to iteratively improve the velocity model
• Seismic anisotropy can be incorporated into tomographic models to account for directional variations in velocity
• Joint inversion techniques combine seismic data with other geophysical data (gravity, electromagnetic) to further constrain the Earth's interior structure

Earth's Interior Structure

• The Earth's interior is divided into the crust, mantle, outer core, and inner core based on seismic velocity variations
• The crust is the outermost layer, with a thickness of ~5-70 km and P-wave velocities of ~5-7 km/s
  • Continental crust is thicker (~30-70 km) and more felsic compared to oceanic crust (~5-10 km)
• The mantle extends from the base of the crust to a depth of ~2900 km, with increasing P-wave velocities from ~8 km/s to ~13 km/s
  • The upper mantle includes the lithosphere and asthenosphere, with a low-velocity zone at ~100-200 km depth
  • The transition zone (~410-660 km depth) is characterized by sharp velocity increases due to mineral phase transitions
  • The lower mantle extends from ~660 km to the core-mantle boundary at ~2900 km depth
• The outer core is a liquid layer with a thickness of ~2200 km and P-wave velocities of ~8-10 km/s
  • S-waves cannot propagate through the outer core, indicating its liquid state
• The inner core is a solid layer with a radius of ~1220 km and P-wave velocities of ~11-12 km/s
  • The inner core exhibits seismic anisotropy, with faster velocities along the Earth's rotation axis

Data Collection and Processing

• Seismic data is collected by a network of seismometers that record ground motion as a function of time
  • Seismometers can be deployed on land, on the ocean bottom, or in boreholes
• Seismic sources can be natural (earthquakes) or artificial (explosions, vibroseis)
  • Earthquake locations and magnitudes are determined using seismic data from multiple stations
• Raw seismic data is processed to remove noise, instrument response, and other artifacts
  • Filtering techniques (bandpass, lowpass, highpass) are used to isolate specific frequency ranges of interest
• Seismic phases (P, S, surface waves) are identified and picked on seismograms to determine their arrival times
  • Automated picking algorithms and manual picking by analysts are used to ensure accurate arrival time measurements
• Seismic data is quality-controlled and compiled into databases for use in tomographic studies
  • Data from multiple seismic networks and sources are often combined to improve coverage and resolution
• Seismic data processing also involves the calculation of source parameters (location, magnitude, focal mechanism) and the correction for path effects (attenuation, site response)

Interpretation of Tomographic Images

• Tomographic images represent the 3D velocity structure of the Earth's interior
  • High-velocity anomalies indicate colder, denser, or compositionally distinct regions
  • Low-velocity anomalies suggest hotter, less dense, or partially molten regions
• Velocity anomalies are often interpreted in terms of temperature variations, compositional differences, or the presence of fluids or melt
• Subducting slabs are imaged as high-velocity anomalies that penetrate into the mantle
  • Slab geometry and depth of penetration provide insights into subduction dynamics and mantle convection
• Mantle plumes are imaged as low-velocity anomalies that originate from the core-mantle boundary and rise through the mantle
  • Plumes are thought to be responsible for hotspot volcanism (Hawaii, Iceland) and large igneous provinces
• Seismic anisotropy in tomographic images can reveal patterns of mantle flow and deformation
  • Alignment of olivine crystals in the upper mantle can cause seismic anisotropy, with faster velocities parallel to the flow direction
• Tomographic images are often compared with results from geodynamic simulations and other geophysical data to develop integrated models of Earth's interior dynamics

Applications in Geophysics

• Seismic tomography is used to study the structure and evolution of the Earth's interior at various scales
  • Global tomography provides a broad overview of mantle heterogeneity and large-scale tectonic features
  • Regional tomography focuses on specific areas of interest (subduction zones, rift systems, cratons) to image smaller-scale structures
• Tomographic models are used to constrain the temperature, composition, and physical state of the Earth's interior
  • Velocity variations can be related to temperature and composition using mineral physics data and equations of state
• Seismic tomography is combined with other geophysical data (gravity, geoid, topography) to study the dynamics of the Earth's interior
  • Mantle convection patterns, plate driving forces, and the coupling between the lithosphere and asthenosphere can be investigated
• Tomographic images are used to guide the exploration and characterization of natural resources
  • Hydrocarbon reservoirs, geothermal systems, and mineral deposits can be identified based on their seismic velocity signatures
• Seismic hazard assessment and risk mitigation efforts rely on tomographic models to understand the distribution of seismic velocities and potential earthquake sources
  • Ground motion predictions and seismic microzonation studies use velocity models to estimate site-specific seismic hazards

Limitations and Future Directions

• Seismic tomography is limited by the uneven distribution of seismic sources and receivers, resulting in variable resolution and coverage
  • Improving the global seismic network and deploying dense temporary arrays can help mitigate this issue
• The resolution of tomographic images is limited by the wavelength of seismic waves and the density of ray paths
  • Developing advanced waveform imaging techniques and exploiting high-frequency data can improve resolution
• Tomographic models are non-unique, meaning that different velocity models can explain the same seismic data equally well
  • Incorporating additional constraints from mineral physics, geodynamics, and other geophysical data can reduce model ambiguity
• Seismic anisotropy and attenuation are often neglected or simplified in tomographic studies, leading to potential biases in velocity estimates
  • Developing more sophisticated anisotropic and attenuation models is an active area of research
• Computational limitations and the high cost of numerical simulations can hinder the development of high-resolution, full-waveform tomographic models
  • Advances in high-performance computing and the use of machine learning techniques can help overcome these challenges
• Future directions in seismic tomography include the integration of multi-scale, multi-parameter, and time-dependent imaging techniques to capture the complex dynamics of the Earth's interior
  • Joint inversion of seismic, gravity, electromagnetic, and geochemical data will provide a more comprehensive understanding of Earth's structure and evolution