29. Magnitude and Intensity Scales

Earthquakes are complex natural phenomena whose effects on the built environment must be understood quantitatively for proper design and mitigation. The assessment of an earthquake's strength is a fundamental step in seismic analysis and engineering design. To evaluate and communicate the impact and energy released during an earthquake, two distinct but complementary concepts are used: Magnitude and Intensity.

This introduction highlights the necessity of understanding earthquakes for safety and construction. It explains that two main concepts, magnitude and intensity, are essential for measuring earthquakes.

Think of earthquakes like a thunderstorm. Just like how we need to know if the storm is light or severe to prepare appropriately, engineers must gauge an earthquake's characteristics to ensure buildings can withstand its forces.

Magnitude scales are logarithmic measures of the total energy released by an earthquake. The magnitude is independent of the observer's location and is a fundamental parameter in seismology and earthquake-resistant design.

Magnitude measures how much energy is released during an earthquake. This measurement doesn’t change, no matter where you are located. It's crucial for designing structures that can resist earthquake forces.

Imagine a person yelling very loudly. No matter if you’re in a nearby room or a faraway block, the loudness is what we'll refer to as the volume of their shout—the magnitude of their sound.

• Developed by Charles F. Richter in 1935 for Southern California. • Based on the amplitude of seismic waves recorded by a Wood-Anderson seismograph. • Formula: M = log A − log A (δ) • where: – A is the maximum amplitude of ground motion. – A (δ) is a standard amplitude for a given distance. • Limitations: – Not suitable for large earthquakes (> M 6.5) due to saturation. – Applicable only to local events (up to ~600 km).

The Richter scale, created by Charles F. Richter, measures small earthquakes' energy using a specific instrument. Its formula assesses the largest wave amplitude, accounting for distance from the earthquake's epicenter. However, it's not perfect for larger quakes and has distance limits.

Think of measuring how hot water is using a thermometer that only works well for temperatures up to a certain point. Beyond that point, it doesn't give accurate readings.

• Calculated using amplitude of P-waves (primary waves). • Useful for detecting deep-focus and distant earthquakes. • Saturates for magnitudes above 6.5.

The Body-Wave Magnitude scale uses P-waves to measure energy from earthquakes. This method is effective for larger and deeper quakes that might be missed by other scales.

If you were listening to a band playing from far away, you might hear the base drum (primary wave) more distinctly than whispers (smaller seismic signals). This is similar to how P-waves are captured.

• Based on the amplitude of surface waves (Rayleigh or Love waves). • Calculated over a period of ~20 seconds. • Better suited for shallow and distant earthquakes.

The Surface-Wave Magnitude uses surface waves, which travel along the Earth's crust, measured over approximately 20 seconds. This method is effective for surface-level and remote quakes.

Imagine waves lapping lazily on a beach; they move along the surface of the ocean much like surface seismic waves move along the Earth's crust, relatable to our observations of ground shaking.

• Developed to overcome saturation issues of other scales. • Related to seismic moment: M = µAD • where: – µ: shear modulus of the rock (~30 GPa), – A: fault area, – D: average displacement. • Advantages: – Does not saturate. – Reliable for all sizes and types of earthquakes. – Adopted by most international agencies (e.g., USGS).

The Moment Magnitude scale improves on previous measurements by not saturating at high magnitudes. It calculates energy based on the geological characteristics of the earthquake itself, making it a favorite among global organizations.

Consider height measurements taken with different rulers. A ruler that can measure unlimited heights means it will always give an accurate reading, just like the Moment Magnitude scale for earthquakes.

Intensity refers to the perceived shaking and damage observed at a specific location due to an earthquake. It varies with distance from the epicenter, geology, and structural characteristics.

Seismic intensity measures how strong the shaking feels at specific places during an earthquake. The damage and sensation of tremors depend on how far a person is from the epicenter and the ground conditions.

When a neighbor plays loud music, how you feel the sound depends on how close you are to their house and whether you're indoors or outdoors. Similarly, intensity changes based on the earthquake's location.

• Qualitative scale ranging from I (not felt) to XII (total destruction). • Based on: – Human perception of shaking. – Damage to structures. – Ground deformation.

The MMI scale provides a subjective measure that ranges from feeling nothing to total destruction. It assesses not just physical damage but also how people experience the earthquake.

Think of tasting chili. One person might say it’s mild while another feels it’s extremely hot. The same occurs with earthquakes: one person may hardly notice while another might be very affected.

Aspect Magnitude Intensity Definition Energy released at source Effects at specific location Measurement tool Seismograph Field surveys, questionnaires Units Logarithmic scale (e.g., Mw, ML) Roman numerals (I–XII) Distance effect Constant for all locations Varies with location Usage Engineering calculations, Impact assessment, comparison insurance, public response

This section compares magnitude and intensity, emphasizing their key differences: magnitude quantifies energy from the earthquake's source, while intensity describes the earthquake's effects at certain locations, using different measurement tools and scales.

Imagine watching a movie. The magnitude is like the initial budget of the film (how grand it was), while intensity is like your reaction to its scenes (how it made you feel).

• Isoseismal lines connect points of equal intensity. • Help in visualizing spatial distribution of shaking. • Useful in identifying local amplification effects due to soil and terrain.

Isoseismal maps graphically show areas of equal earthquake intensity. They help to visualize where shaking was stronger or weaker, influenced by factors like local soil conditions.

Like a weather map showing rainfall amounts across different regions, an isoseismal map presents how shaking levels vary, helping us understand where the most significant impacts were felt.

Though distinct, empirical relationships exist: I = aM + b − clog R Where: • I: Intensity at a distance R, • M: Magnitude, • a, b, c: Empirical constants, • R: Distance from epicenter.

This equation illustrates how intensity can be predicted based on magnitude and distance. As scientists observe data from different earthquakes, they formulate patterns that help us relate the earthquake's energy to how intensely it is felt.

Think of a music concert. The louder the music (magnitude), the further you can hear it (distance), and eventually, it fades based on how far you are from the source (intensity).

• Magnitude is essential for: – Defining design basis earthquake (DBE) and maximum considered earthquake (MCE). – Estimating seismic loads using response spectra. • Intensity is important for: – Assessing local damage patterns. – Post-earthquake reconnaissance. – Insurance loss estimation.

Magnitude serves as a critical guide in engineering for determining safe design practices, while intensity informs assessments of potential damage and is key for disaster recovery, planning, and insurance.

Like using weather forecasts to prepare for dangerous storms, engineers rely on magnitude and intensity to ready buildings for earthquakes to minimize damage and losses.

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