🌋Seismology Unit 10 – Earthquake Location and Hypocenter Analysis

Key Concepts and Terminology

• Seismic waves propagate energy released during an earthquake through the Earth's interior and along its surface
• Body waves travel through the Earth's interior and include P-waves (primary or compressional) and S-waves (secondary or shear)
  • P-waves are longitudinal, compressing and expanding material in the direction of wave propagation
  • S-waves are transverse, causing particles to oscillate perpendicular to the direction of wave propagation
• Surface waves, like Rayleigh and Love waves, travel along the Earth's surface and are typically slower than body waves
• Seismographs record ground motion at a specific location, generating seismograms used to analyze earthquakes
• Earthquake location refers to determining the hypocenter (point of initial rupture) and epicenter (surface projection of the hypocenter)
• Travel time is the duration taken for seismic waves to propagate from the hypocenter to a seismograph station
• Velocity models describe the speed of seismic waves through different layers of the Earth, which is essential for accurate earthquake location
• Seismic phases are distinct arrivals of seismic waves on a seismogram (P, S, PP, SS, etc.) used to calculate travel times and locate earthquakes

Seismic Wave Propagation Basics

• Seismic waves are generated by the sudden release of energy during an earthquake, propagating through the Earth's interior and along its surface
• The two main types of seismic waves are body waves and surface waves
  • Body waves travel through the Earth's interior and include P-waves and S-waves
  • Surface waves travel along the Earth's surface and include Rayleigh and Love waves
• P-waves (primary or compressional waves) are the fastest seismic waves and can travel through solids, liquids, and gases
  • P-waves cause particles to oscillate parallel to the direction of wave propagation, creating compression and expansion
• S-waves (secondary or shear waves) are slower than P-waves and can only travel through solids
  • S-waves cause particles to oscillate perpendicular to the direction of wave propagation
• Surface waves are generated when body waves interact with the Earth's surface and are typically slower than body waves
  • Rayleigh waves cause particles to move in an elliptical motion in the vertical plane, similar to ocean waves
  • Love waves cause particles to move side-to-side horizontally, perpendicular to the direction of wave propagation
• Seismic wave velocities depend on the elastic properties and density of the materials they travel through, with waves traveling faster in denser, more rigid materials

Earthquake Location Methods

• Earthquake location involves determining the hypocenter (point of initial rupture) and epicenter (surface projection of the hypocenter)
• The most common method for locating earthquakes is the time-distance method, which uses the arrival times of seismic waves at multiple seismograph stations
  • P-wave and S-wave arrival times are picked from seismograms and used to calculate the distance between the earthquake and each station
  • The difference in arrival times between P-waves and S-waves (S-P time) increases with distance from the epicenter
• Triangulation is used to locate the epicenter by finding the intersection of circles centered at each seismograph station with radii equal to the calculated distances
• Depth is determined by comparing observed arrival times with theoretical travel times calculated using a velocity model of the Earth's interior
• The azimuth (direction) to the epicenter from each station can be determined using particle motion analysis or the polarization of P-waves
• More advanced methods, such as the double-difference and relative location techniques, can improve location accuracy by minimizing errors and using additional data (e.g., cross-correlation of waveforms)

Seismograph Networks and Data Collection

• Seismograph networks consist of multiple seismograph stations distributed over a region to monitor and locate earthquakes
  • Global networks (Global Seismographic Network) provide worldwide coverage for detecting and locating significant earthquakes
  • Regional networks (Southern California Seismic Network) offer denser station coverage for improved location accuracy and detection of smaller events within a specific area
• Seismographs record ground motion using a mass-spring system or force-feedback sensors (broadband seismometers) to generate seismograms
  • Modern seismographs typically record ground motion in three orthogonal components: vertical (Z), north-south (N), and east-west (E)
• Seismic data is collected continuously and transmitted in real-time to data centers for processing and analysis
  • Seismograms are digitized, and various filters (e.g., bandpass, lowpass) are applied to enhance specific frequency ranges and improve signal-to-noise ratios
• Earthquake catalogs are compiled from analyzed seismic data, containing information such as origin time, location, depth, magnitude, and focal mechanism
• Seismic data sharing and archiving facilitate research and collaboration among seismologists worldwide, with organizations like the Incorporated Research Institutions for Seismology (IRIS) managing and distributing data

Travel Time Tables and Velocity Models

• Travel time tables provide the expected arrival times of seismic waves at various distances from an earthquake source based on a velocity model of the Earth's interior
  • Tables are calculated using seismic ray theory, which describes the path and travel times of seismic waves through the Earth
  • Different tables are used for different seismic phases (e.g., P, S, PP, SS) and account for the refraction and reflection of waves at layer boundaries
• Velocity models describe the speed of seismic waves through different layers of the Earth, which varies with depth and material properties
  • The most commonly used global velocity model is the Preliminary Reference Earth Model (PREM), which provides a one-dimensional representation of the Earth's velocity structure
  • Regional velocity models (e.g., Southern California Velocity Model) incorporate local geologic and tectonic information for improved accuracy in specific areas
• Seismic tomography techniques use travel time data from many earthquakes to create three-dimensional velocity models of the Earth's interior
  • Tomographic models help identify heterogeneities and anomalies in the Earth's structure, such as subducting slabs or mantle plumes
• Accurate velocity models are essential for precise earthquake location and for understanding the Earth's internal structure and dynamics

Hypocenter Determination Techniques

• Hypocenter determination involves estimating the location (latitude, longitude, depth) and origin time of an earthquake using seismic data from multiple stations
• The simplest method is the time-distance method, which uses the arrival times of P and S waves at each station to calculate distances and triangulate the epicenter
  • S-P times (the difference between S and P arrival times) are used to estimate distances, as the time difference increases with distance from the epicenter
  • Depth is determined by comparing observed arrival times with theoretical travel times calculated using a velocity model
• More advanced techniques, such as the least-squares method and the maximum likelihood method, minimize the residuals between observed and theoretical arrival times to find the best-fit hypocenter location
  • These methods account for uncertainties in arrival time picks and velocity models and provide error estimates for the calculated location
• The double-difference method improves location accuracy by minimizing the residuals between observed and theoretical travel time differences for pairs of earthquakes
  • This technique reduces the impact of velocity model errors and is particularly useful for relocating clusters of earthquakes (e.g., aftershock sequences)
• Relative location methods, such as master event relocation and waveform cross-correlation, use a well-located reference event to improve the locations of nearby earthquakes
  • These methods exploit the similarity of travel paths and waveforms for closely spaced events to minimize location errors

Error Analysis and Uncertainty

• Earthquake location uncertainties arise from various sources, including errors in arrival time picks, station distribution, and velocity models
  • Arrival time picking errors can result from noise, complex waveforms, or misidentification of seismic phases
  • Poor station coverage or an uneven distribution of stations can lead to poorly constrained locations, particularly for depth
  • Velocity model errors, such as incorrect layer velocities or unmodeled lateral heterogeneities, can cause systematic biases in location estimates
• Error ellipsoids or confidence regions are used to quantify the uncertainty in hypocenter locations
  • The size, shape, and orientation of the error ellipsoid depend on the station distribution and the quality of the data
  • Horizontal (epicentral) and vertical (depth) uncertainties are often reported separately, as depth is typically less well-constrained than the epicenter
• Statistical methods, such as bootstrap resampling or Bayesian inference, can be used to estimate location uncertainties and provide probability distributions for the hypocenter
• Comparing locations from different methods or velocity models can help assess the robustness of the solution and identify potential biases
• Improving location accuracy requires minimizing errors through better station coverage, more accurate arrival time picks, and refined velocity models
  • Techniques like double-difference and relative location methods can help reduce the impact of velocity model errors and improve the precision of relative locations within earthquake clusters

Real-World Applications and Case Studies

• Rapid and accurate earthquake location is crucial for earthquake early warning systems, which aim to provide alerts before strong shaking arrives
  • The U.S. Geological Survey's ShakeAlert system uses real-time seismic data to detect and locate earthquakes, estimating the intensity and arrival times of shaking for affected areas
• Earthquake location data is essential for seismic hazard assessment and risk mitigation
  • Identifying active faults, characterizing their behavior, and estimating the likelihood of future earthquakes helps inform building codes, land-use planning, and emergency preparedness
• Studying the distribution and patterns of earthquake locations can provide insights into tectonic processes and the structure of the Earth's interior
  • Subduction zones, such as the Cascadia Subduction Zone off the coast of North America, are characterized by distinct patterns of earthquake locations, including shallow thrust events and deep intraslab earthquakes
  • Mapping the locations of aftershocks following a large earthquake can help delineate the extent and geometry of the fault rupture, as demonstrated by the 2019 Ridgecrest, California earthquake sequence
• Precise earthquake locations are vital for nuclear test monitoring and discrimination
  • The Comprehensive Nuclear-Test-Ban Treaty (CTBT) relies on a global network of seismic stations to detect and locate potential nuclear explosions, with improved location accuracy helping to distinguish between natural earthquakes and human-induced events
• Induced seismicity, such as earthquakes caused by wastewater injection or hydraulic fracturing, requires accurate location methods to identify and mitigate the risks associated with these activities
  • The 2011-2012 earthquake sequence in Prague, Oklahoma, was linked to wastewater injection, with precise locations and depths of the events providing evidence for the causal relationship between injection and seismicity