🌋Seismology Unit 9 – Magnitude Scales and Energy Release

Key Concepts

• Magnitude scales quantify the energy released by an earthquake at its source
• Different magnitude scales exist, each with its own advantages and limitations
• Energy release in earthquakes is related to the size of the fault rupture and the amount of slip
• Seismic moment ($M_0$) is a measure of the energy released by an earthquake, calculated as $M_0 = \mu AD$, where $\mu$ is the shear modulus, $A$ is the fault area, and $D$ is the average displacement
  • Seismic moment is expressed in Newton-meters (N·m) or Joules (J)
• Magnitude scales are logarithmic, meaning that each unit increase in magnitude represents a tenfold increase in the amplitude of the seismic waves and a 32-fold increase in energy release
• Magnitude scales are based on the amplitude of seismic waves recorded by seismometers
• Intensity scales, such as the Modified Mercalli Intensity (MMI) scale, describe the effects of an earthquake on people, structures, and the environment at a specific location

Types of Magnitude Scales

• Richter magnitude scale (ML) is the first widely used magnitude scale, developed by Charles Richter in 1935
  • Based on the maximum amplitude of seismic waves recorded by a Wood-Anderson seismometer at a distance of 100 km from the epicenter
  • Limited to earthquakes in Southern California and not accurate for large earthquakes (>6.5)
• Surface wave magnitude (Ms) is based on the amplitude of surface waves with a period of about 20 seconds
  • More accurate than ML for larger earthquakes, but still saturates around magnitude 8
• Body wave magnitude (mb) is based on the amplitude of P-waves with a period of about 1 second
  • Useful for deep earthquakes and can be calculated quickly, but also saturates around magnitude 6.5
• Moment magnitude (Mw) is based on the seismic moment and is the most widely used scale for larger earthquakes
  • Does not saturate and provides a consistent measure of earthquake size across all magnitudes
  • Calculated using the formula: $M_w = \frac{2}{3}\log_{10}(M_0) - 10.7$, where $M_0$ is the seismic moment in dyne-cm
• Duration magnitude (MD) is based on the duration of shaking recorded by a seismometer
  • Useful for smaller earthquakes and can be calculated quickly, but less accurate than other scales

Energy Release in Earthquakes

• The energy released by an earthquake is primarily in the form of seismic waves, which propagate through the Earth's interior and along its surface
• The amount of energy released depends on factors such as the size of the fault rupture, the amount of slip, and the elastic properties of the rock
• Seismic energy ($E_S$) is a small fraction (usually <10%) of the total energy released by an earthquake, with the rest being dissipated as heat due to friction on the fault plane
• Seismic energy can be estimated from the seismic moment using the formula: $E_S = \frac{M_0}{2\mu}$, where $\mu$ is the shear modulus (usually assumed to be 3 × 10^10 N/m^2 for the Earth's crust)
• The Gutenberg-Richter relationship describes the frequency of occurrence of earthquakes of different magnitudes in a given region and time period
  • Expressed as $\log_{10}N = a - bM$, where $N$ is the number of earthquakes with magnitude ≥ $M$, and $a$ and $b$ are constants specific to the region
• The $b$-value in the Gutenberg-Richter relationship is typically close to 1, meaning that for every unit increase in magnitude, the number of earthquakes decreases by a factor of 10
• Large earthquakes (>7) release significantly more energy than small earthquakes, but occur much less frequently
  • A magnitude 8 earthquake releases about 32 times more energy than a magnitude 7 earthquake, and about 1,000 times more energy than a magnitude 6 earthquake

Measurement Techniques

• Seismometers are instruments that measure ground motion and convert it into an electrical signal
  • Different types of seismometers are sensitive to different components of ground motion (vertical, horizontal, or rotational) and different frequency ranges
• Modern seismometers are based on the principle of inertia and consist of a mass suspended by springs or held in place by an electromagnetic force
  • As the ground moves, the mass remains stationary due to inertia, and the relative motion between the mass and the ground is measured
• Analog seismometers record ground motion on paper or photographic film, while digital seismometers convert the signal into a series of numerical values that can be stored and processed by computers
• Seismic networks consist of multiple seismometers installed at different locations to provide a more complete picture of earthquake activity in a region
  • Data from seismic networks are used to locate earthquakes, determine their magnitude and focal mechanism, and study the structure of the Earth's interior
• Seismic arrays are closely spaced groups of seismometers that can be used to improve the signal-to-noise ratio and detect smaller earthquakes
  • Arrays can also be used to study the directivity and propagation of seismic waves

Magnitude vs. Intensity

• Magnitude and intensity are two different ways of measuring the size and impact of an earthquake
• Magnitude is a measure of the energy released by an earthquake at its source and is determined from seismic wave amplitudes
  • Magnitude is a single value that represents the size of an earthquake, regardless of location
• Intensity is a measure of the effects of an earthquake on people, structures, and the environment at a specific location
  • Intensity varies depending on factors such as distance from the epicenter, local geology, and building design
• The Modified Mercalli Intensity (MMI) scale is the most widely used intensity scale and ranges from I (not felt) to XII (total destruction)
  • Each level of the MMI scale is defined by a set of observable criteria, such as the level of shaking, damage to buildings, and changes in the environment
• Intensity maps show the distribution of earthquake effects over a region and can be used to identify areas of high damage or risk
  • Intensity data are collected through surveys of people's experiences and observations of damage
• While magnitude and intensity are related, they do not always correlate directly
  • A large magnitude earthquake may cause low intensities at distant locations, while a moderate magnitude earthquake may cause high intensities in a densely populated area with poor building construction

Applications in Seismology

• Magnitude scales are used to quickly assess the size and potential impact of an earthquake
  • Rapid magnitude determination is essential for earthquake early warning systems and emergency response
• Magnitude data are used to create seismic hazard maps, which show the probability of exceeding a certain level of ground shaking in a given region over a specified time period
  • Seismic hazard maps are used for building codes, insurance rates, and land-use planning
• Magnitude and energy release data are used to study the mechanics of earthquake rupture and the factors that control the size and frequency of earthquakes
  • Understanding these factors is important for improving earthquake forecasting and risk assessment
• Magnitude data are used to study the relationship between earthquakes and other geologic processes, such as volcanic eruptions and landslides
  • Changes in earthquake activity can sometimes precede or follow these events
• Magnitude and intensity data are used to study the attenuation of seismic waves as they travel through the Earth's interior
  • Attenuation data can provide information about the temperature, composition, and structure of the Earth's interior

Limitations and Challenges

• Magnitude scales are based on simplifying assumptions about the source and propagation of seismic waves
  • These assumptions may not always be valid, particularly for complex or unusual earthquakes
• Magnitude scales are subject to saturation, meaning that they may not accurately represent the size of very large earthquakes
  • Saturation occurs when the amplitude of seismic waves exceeds the dynamic range of the recording instrument or the linear elasticity of the Earth
• Magnitude scales are based on the amplitude of seismic waves, which can be affected by factors such as the radiation pattern of the earthquake source and the local geology at the recording site
  • These factors can introduce variability and uncertainty into magnitude estimates
• The relationship between magnitude and energy release is not always straightforward, particularly for small earthquakes or earthquakes with unusual source characteristics
  • The efficiency of seismic wave generation and the partitioning of energy between seismic waves and other forms of energy (such as heat) can vary depending on the earthquake
• Intensity data are subjective and can be affected by factors such as population density, building design, and cultural factors
  • Intensity data may not always provide a reliable or consistent measure of earthquake effects
• Rapid magnitude determination can be challenging for earthquakes that occur in remote or poorly instrumented areas
  • Magnitude estimates may be delayed or uncertain in these cases

Real-World Examples

• The 1960 Chile earthquake is the largest earthquake ever recorded, with a moment magnitude (Mw) of 9.5
  • The earthquake triggered a tsunami that caused damage as far away as Hawaii, Japan, and the Philippines
• The 2011 Tohoku earthquake in Japan had a moment magnitude (Mw) of 9.0 and caused widespread damage and loss of life
  • The earthquake triggered a massive tsunami that caused a nuclear accident at the Fukushima Daiichi power plant
• The 1906 San Francisco earthquake had a surface wave magnitude (Ms) of 7.8 and caused extensive damage and loss of life
  • The earthquake ruptured the San Andreas Fault for a length of about 300 km and was felt as far away as Nevada and Oregon
• The 1994 Northridge earthquake in Los Angeles had a moment magnitude (Mw) of 6.7 and caused widespread damage to buildings and infrastructure
  • The earthquake occurred on a previously unknown fault and highlighted the importance of seismic hazard mapping and building codes
• The 2010 Haiti earthquake had a moment magnitude (Mw) of 7.0 and caused widespread damage and loss of life
  • The earthquake occurred in a densely populated area with poor building construction and limited emergency response capabilities, leading to high casualties and a humanitarian crisis