3.3 Reflection and refraction of body waves
3 min read•august 9, 2024
When seismic waves hit boundaries between different rock layers, they bounce and bend. This and behavior follows specific laws, like , and depends on the differences between layers.
Understanding these principles is key to interpreting seismic data. By analyzing how waves reflect, refract, and convert between types, scientists can map out Earth's interior structure and composition.
Reflection and Refraction Principles
Fundamental Laws and Concepts
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- Snell's law governs the relationship between angles of incidence and refraction for waves passing through a boundary between two different media
- Formula for Snell's law expresses as , where θ represents angles and v represents velocities
- occurs when the angle of refraction equals 90 degrees, resulting in total internal reflection
- Calculation of critical angle uses the formula , where v₁ < v₂
- states every point on a acts as a source of secondary wavelets
- Secondary wavelets combine to form a new wavefront in the direction of wave propagation
Velocity Contrasts and Wave Behavior
- Velocity contrasts refer to differences in seismic wave velocities between different rock layers or media
- Higher velocity contrasts lead to stronger reflections and more pronounced refractions
- P-wave velocity contrasts typically range from 2 km/s in unconsolidated sediments to 8 km/s in the upper mantle
- S-wave velocities generally about 60% of P-wave velocities in the same medium
- Velocity contrasts affect wave propagation paths, creating complex patterns of reflections and refractions in the Earth's interior
- Understanding velocity contrasts crucial for interpreting seismic data and creating accurate Earth models
Seismic Wave Coefficients
Reflection and Transmission Coefficients
- Reflection coefficient (R) quantifies the amplitude ratio of reflected wave to incident wave
- Calculation of reflection coefficient uses the formula , where ρ represents and v represents velocity
- Reflection coefficient values range from -1 to 1, with higher absolute values indicating stronger reflections
- Transmission coefficient (T) measures the amplitude ratio of transmitted wave to incident wave
- Formula for transmission coefficient expressed as , ensuring energy conservation
- Coefficients depend on the contrast between media, calculated as the product of density and velocity
Mode Conversion and Energy Partitioning
- Mode conversion occurs when an incident P-wave or S-wave generates both P and S waves at an interface
- P-to-S conversion happens when a P-wave strikes an interface at non-normal incidence
- S-to-P conversion occurs when an S-wave encounters an interface, generating both P and S waves
- Energy partitioning describes how the energy of an incident wave distributes among reflected and transmitted waves
- Partitioning depends on the angle of incidence, velocity contrast, and densities of the media
- Understanding mode conversion and energy partitioning crucial for interpreting complex seismic records and identifying different wave arrivals
Seismic Wave Propagation
Travel Time Curves and Seismic Interpretation
- Travel time curves graphically represent the relationship between arrival times of seismic waves and their distance from the source
- Curves plot travel time on the vertical axis and distance on the horizontal axis
- Different seismic phases (direct waves, reflected waves, refracted waves) produce distinct curves on the travel time plot
- Slope of a travel time curve indicates the apparent velocity of the wave
- Crossover distance on travel time curves marks the point where refracted waves arrive before direct waves
- Interpreting travel time curves helps determine layer velocities, thicknesses, and depths in the Earth's structure
Advanced Seismic Analysis Techniques
- Ray tracing technique uses travel time curves to model seismic wave paths through the Earth
- Involves solving the eikonal equation to determine wave propagation paths in heterogeneous media
- Tomography utilizes travel time data to create 3D velocity models of the Earth's interior
- Involves inverting large datasets of seismic arrival times to reconstruct subsurface structures
- Waveform modeling compares synthetic seismograms with observed data to refine Earth models
- Requires solving the wave equation to simulate seismic wave propagation through complex media
Key Terms to Review (18)
Acoustic Impedance: Acoustic impedance is a measure of how much resistance a medium offers to the passage of sound waves through it. It is defined as the product of the medium's density and the speed of sound in that medium. This concept is crucial for understanding how seismic waves interact with different geological layers, affecting the reflection and refraction at interfaces.
Asthenosphere: The asthenosphere is a semi-fluid layer of the Earth's mantle, located beneath the lithosphere, which plays a crucial role in tectonic plate movement. It is characterized by its ability to flow and deform under pressure, enabling the lithospheric plates to glide over it. This property connects it to the generation of seismic waves, the reflection and refraction of body waves, and the overall dynamics of the Earth's internal structure.
Critical Angle: The critical angle is the specific angle of incidence above which a seismic wave cannot pass through a boundary and is instead reflected back into the medium. This concept is vital in understanding how seismic waves interact with different layers of the Earth, influencing the paths they take and how they can be detected at the surface.
Density: Density is defined as the mass per unit volume of a material, typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). This property is crucial for understanding how seismic waves travel through different materials within the Earth, as density affects wave speed and behavior.
Elasticity: Elasticity refers to the ability of materials, including rocks and minerals in the Earth, to deform and return to their original shape when stress is applied. This property is crucial for understanding how seismic waves travel through different layers of the Earth and interact with its internal structure, as well as how waves reflect and refract at boundaries between different materials.
Huygens' Principle: Huygens' Principle states that every point on a wavefront can be considered as a source of secondary wavelets, which spread out in all directions at the same speed as the original wave. This principle helps to explain how waves propagate through different media and relates directly to concepts like velocity models, ray paths, and the behavior of waves during reflection and refraction.
Lithosphere: The lithosphere is the rigid outer layer of the Earth, consisting of the crust and the uppermost part of the mantle. It plays a critical role in various geological processes, including the behavior of seismic waves and the movement of tectonic plates, influencing everything from earthquakes to mountain formation.
P-waves: P-waves, or primary waves, are the fastest type of seismic waves that travel through the Earth, moving in a compressional manner. They can propagate through both solid and liquid materials, making them essential for understanding the Earth's internal structure and behavior during seismic events.
Raypath: A raypath is the trajectory that seismic waves take as they travel through different layers of the Earth's interior. Understanding raypaths is crucial in seismology, as they help explain how waves reflect and refract at boundaries between different materials, which can provide insights into the structure and properties of the Earth's subsurface.
Reflection: In seismology, reflection refers to the bouncing back of seismic waves when they encounter a boundary between different types of geological materials. This process is crucial for understanding the internal structure of the Earth, as it helps identify different layers and their properties by analyzing how seismic waves behave at these boundaries.
Refraction: Refraction is the bending of seismic waves as they pass through different layers of the Earth's interior, caused by variations in wave speed due to changes in material properties. This phenomenon is crucial for understanding how seismic waves travel and interact with different geological structures, which aids in identifying seismic phases, analyzing travel time curves, and interpreting seismograms.
S-waves: S-waves, or secondary waves, are a type of seismic wave that move through the Earth during an earthquake. They are characterized by their transverse motion, which means they move the ground perpendicular to the direction of wave propagation, and are only able to travel through solid materials, making them crucial for understanding Earth's internal structure.
Seismograph: A seismograph is an instrument that measures and records the vibrations of the ground caused by seismic waves, such as those generated by earthquakes. It captures the intensity, duration, and frequency of these vibrations, which are crucial for understanding seismic events and the Earth's internal structure.
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.
Shadow zone: A shadow zone is an area on the Earth's surface where seismic waves, specifically P-waves and S-waves, are not detected following an earthquake. This phenomenon occurs due to the refraction and reflection of body waves as they travel through different layers of the Earth's interior, which have varying densities and material properties.
Snell's Law: Snell's Law describes how seismic waves change direction when they pass through different layers of material with varying properties, specifically concerning their velocities. This fundamental principle is crucial for understanding how waves refract and reflect as they encounter boundaries within the Earth's subsurface, influencing methods of data interpretation in seismology.
Velocity: In seismology, velocity refers to the speed at which seismic waves travel through different materials in the Earth. This concept is crucial for understanding how waves propagate and interact with geological structures, influencing methods used to interpret subsurface conditions and locate seismic events.
Wavefront: A wavefront is an imaginary surface representing points of a wave that oscillate in unison, moving through a medium. This concept is crucial in understanding how seismic waves propagate, interact with different geological structures, and change direction as they encounter boundaries between materials with varying properties.