4.1 Generation and propagation of Rayleigh waves
3 min read•august 9, 2024
are surface seismic waves that cause both vertical and horizontal . They're slower than body waves but often more destructive due to their large amplitudes and long durations.
These waves form when P and SV waves interact at the Earth's surface. They're generated more efficiently by shallow earthquakes and surface explosions. Understanding Rayleigh waves is crucial for assessing earthquake hazards and studying Earth's structure.
Rayleigh Wave Characteristics
Fundamental Properties of Rayleigh Waves
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- Rayleigh waves propagate along the Earth's surface as a type of seismic surface wave
- Surface waves travel slower than body waves and arrive later in seismograms
- Rayleigh waves cause both vertical and horizontal ground motion
- Particle motion follows a retrograde elliptical path near the surface
- of Rayleigh waves decreases exponentially with depth
Particle Motion and Amplitude Behavior
- Retrograde elliptical motion describes the path traced by particles as Rayleigh waves pass
- Particles move counterclockwise in a vertical plane parallel to the direction of wave propagation
- Elliptical motion becomes prograde at depths greater than approximately 0.2 wavelengths
- Amplitude decay with depth occurs more rapidly for higher waves
- Vertical component of motion typically larger than horizontal component at the surface
Comparison to Other Seismic Waves
- Rayleigh waves exhibit dispersive behavior, with different frequencies traveling at different velocities
- Lower frequencies penetrate deeper into the Earth and travel faster than higher frequencies
- Rayleigh waves cause rolling motion of the ground surface, distinct from the shaking caused by body waves
- Surface waves can circle the Earth multiple times after large earthquakes (R1, R2, R3 phases)
- Rayleigh waves often cause the most damage in earthquakes due to their large amplitudes and long durations
Rayleigh Wave Generation
Interaction of P and SV Waves at the Free Surface
- Free surface boundary condition requires stress-free surface, allowing wave conversion
- P-SV wave interaction at the surface generates Rayleigh waves
- Incident P waves partially convert to SV waves and vice versa at the free surface
- Constructive interference of these converted waves forms Rayleigh waves
- Energy from body waves becomes trapped near the surface, propagating as Rayleigh waves
Source Mechanisms and Efficiency
- Rayleigh waves generated more efficiently by shallow earthquake sources
- Vertical component of fault motion (dip-slip) produces stronger Rayleigh waves than horizontal motion (strike-slip)
- Surface explosions and impacts generate strong Rayleigh waves (nuclear tests, meteorite impacts)
- Rayleigh wave generation efficiency increases with increasing Poisson's ratio of the medium
- Theoretical models (Lamb's problem) predict Rayleigh wave generation from point sources
Factors Affecting Rayleigh Wave Propagation
- Velocity of Rayleigh waves slightly lower than shear wave velocity (typically 0.92VS)
- Rayleigh wave velocity depends on frequency and elastic properties of the medium
- Layered Earth structure causes and multiple Rayleigh wave modes
- Lateral heterogeneities in Earth structure can cause scattering and multipathing of Rayleigh waves
- Attenuation of Rayleigh waves affected by both geometrical spreading and intrinsic material properties
Key Terms to Review (16)
Amplitude: Amplitude refers to the maximum displacement of a wave from its rest position, essentially measuring how strong or intense the wave is. In seismology, it’s crucial because it helps indicate the energy released during an earthquake and can influence the interpretation of seismic data. Amplitude is not only important for understanding the strength of seismic waves but also plays a role in distinguishing between different types of waves and their behavior as they propagate through various geological structures.
Dispersion: Dispersion refers to the phenomenon where seismic waves travel at different speeds depending on their frequency, causing the waveforms to spread out over time. This is particularly significant in understanding how different seismic wave types and frequencies behave as they propagate through various geological materials, influencing the interpretation of seismograms and the analysis of waveforms.
Dispersion relation: A dispersion relation describes the relationship between wave frequency and wave number in a medium, showing how wave velocities depend on their frequency. This concept is crucial in understanding the propagation of different seismic waves through various materials, particularly in how the properties of the material influence wave behavior. It helps explain phenomena like group velocity and phase velocity, which are essential for analyzing seismic waveforms and interpreting subsurface structures.
Earth's crust: The earth's crust is the outermost layer of the Earth, consisting of solid rocks and minerals that vary in composition and thickness. It is where all terrestrial life exists and serves as the foundation for geological processes, including the generation and propagation of seismic waves, such as Rayleigh waves. The crust is primarily divided into two types: continental crust, which is thicker and less dense, and oceanic crust, which is thinner and denser.
Earthquake engineering: Earthquake engineering is a branch of engineering that focuses on designing and constructing structures to withstand seismic forces caused by earthquakes. This field involves understanding how seismic waves, including Rayleigh waves, interact with buildings and infrastructure, ensuring their safety and resilience during seismic events. By applying principles of physics and materials science, earthquake engineering aims to mitigate the effects of earthquakes on the built environment.
Frequency: Frequency refers to the number of oscillations or cycles that occur in a given time period, typically measured in Hertz (Hz). In seismology, frequency is critical for understanding the characteristics of seismic waves and how they interact with different geological structures, influencing everything from wave behavior to the interpretation of seismic data.
Ground motion: Ground motion refers to the movement of the Earth's surface caused by seismic waves during an earthquake. It is a key factor in understanding how earthquakes affect structures and landscapes, and it can be measured and recorded using specialized instruments. Analyzing ground motion helps in interpreting seismograms, designing effective seismographs, and understanding the propagation of different seismic waves, including Rayleigh waves.
Love Waves: Love waves are a type of surface seismic wave that causes horizontal shaking of the ground. They move in a side-to-side motion, perpendicular to the direction of wave propagation, which makes them particularly damaging during an earthquake. Understanding Love waves helps in identifying seismic phases and studying the Earth’s structure, revealing important insights into seismic wave behavior and propagation.
Mantle: The mantle is a thick layer of rock located between the Earth's crust and the outer core, making up about 84% of Earth's total volume. It plays a critical role in seismic wave propagation and the dynamics of plate tectonics, influencing everything from travel time calculations to the generation of seismic waves.
Rayleigh waves: Rayleigh waves are a type of surface seismic wave that travels along the Earth's surface, characterized by an elliptical motion of particles. These waves play a critical role in seismology, as they help identify seismic phases and provide insights into Earth’s structure and composition.
Seismometer: A seismometer is an instrument that detects and records the motion of the ground caused by seismic waves from earthquakes or other vibrations. It plays a crucial role in understanding seismic activity by capturing the details of seismic waves, enabling scientists to analyze their characteristics and origins.
Site characterization: Site characterization is the process of assessing and describing the physical, geological, and geotechnical properties of a specific location, particularly in relation to seismic activity. This includes evaluating soil types, bedrock conditions, and other factors that influence how seismic waves propagate through the ground. Understanding site characteristics is essential for predicting how structures will respond to earthquakes and can significantly affect the generation and behavior of seismic waves like Rayleigh waves.
Spectral Analysis: Spectral analysis is a method used to analyze the frequency components of seismic signals by transforming time-domain data into the frequency domain. This technique helps identify the characteristics of seismic noise and enhances the understanding of underlying seismic events. By breaking down complex seismic signals, spectral analysis aids in improving data collection, interpreting surface waves, and understanding wave propagation, leading to better insights into Earth’s structure.
Surface wave phenomena: Surface wave phenomena refer to the unique behaviors and characteristics of seismic surface waves, which travel along the Earth's surface and are responsible for a significant portion of the shaking felt during an earthquake. These waves, primarily Rayleigh and Love waves, exhibit distinct motion and energy propagation, impacting structures and the geological environment. Understanding surface wave phenomena is crucial for assessing earthquake damage and developing effective engineering solutions to mitigate risks.
Wave equation: The wave equation is a fundamental mathematical representation that describes how waves propagate through different media. It captures the relationship between wave speed, wavelength, frequency, and the characteristics of the medium, making it crucial for understanding various types of seismic waves as they travel through the Earth's layers.
Wave speed: Wave speed refers to the speed at which a wave travels through a medium, which is influenced by the medium's properties and the type of wave. Understanding wave speed is crucial for analyzing how seismic waves, such as surface waves and S-waves, propagate through the Earth and for interpreting the data used in studies of Earth's structure.