10.2 Earthquake measurement and location

Seismographs and Earthquake Measurement

Seismographs are the primary instruments for detecting and recording ground motion during earthquakes. The data they produce, called seismograms, allows scientists to determine where an earthquake occurred, how strong it was, and what types of seismic waves it generated.

Functionality of seismographs

A seismograph has two main parts: a seismometer that detects ground motion, and a recording device that preserves that motion as data. The core operating principle relies on inertia. A heavy mass is suspended (by a spring or pendulum) so it stays relatively still while the frame of the instrument moves with the ground. That relative motion between the mass and the frame is what gets recorded.

There are two broad types:

• Mechanical seismographs use physical mechanisms (like a pen on a rotating drum) to record motion directly
• Electronic seismographs use digital sensors that convert ground motion into electrical signals, which are then amplified and recorded digitally

Seismographs record several types of seismic waves:

• P-waves (primary waves) arrive first because they travel fastest through rock
• S-waves (secondary waves) arrive next and are slower than P-waves
• Surface waves (Love and Rayleigh waves) travel along Earth's surface and typically cause the most damage; they arrive last and produce the largest amplitudes on a seismogram

Earthquake intensity scales

Two major scales are used to describe earthquake size, and they measure different things.

The Richter Scale measures the amplitude of the largest seismic wave recorded on a seismogram. It calculates what's called local magnitude ($M_L$) using:

$M_L = \log A - \log A_0$

where $A$ is the measured wave amplitude and $A_0$ is a reference amplitude that accounts for distance from the earthquake. Because it's a logarithmic scale, each whole number increase represents a tenfold increase in wave amplitude.

The Moment Magnitude Scale measures the total energy released by an earthquake. It first calculates the seismic moment ($M_0$):

$M_0 = \mu A D$

where $\mu$ is the rigidity of the rock, $A$ is the area of the fault that slipped, and $D$ is the average displacement along the fault. From there, moment magnitude ($M_w$) is calculated:

$M_w = \frac{2}{3}\log M_0 - 10.7$

Locating earthquake epicenters

Scientists pinpoint an earthquake's epicenter using a method called triangulation. Here's how it works:

1. Record arrival times at multiple stations. At least three seismic stations record the earthquake. Each station notes when the P-wave and S-wave arrived.
2. Calculate the S-P interval. Because P-waves travel faster than S-waves, the gap between their arrival times increases with distance. A larger S-P interval means the station is farther from the epicenter.
3. Determine epicentral distance. Using travel-time curves (graphs that plot wave arrival time versus distance), scientists convert each station's S-P interval into a distance from the epicenter. This can also be done with the formula: $\text{Distance} = (\text{S-P interval}) \times (\text{velocity factor})$
4. Draw circles. On a map, draw a circle around each station with a radius equal to its calculated distance. With one station, you know the earthquake was somewhere on that circle. With two, you narrow it to two possible points. With three or more stations, the circles intersect at a single point: the epicenter.

Interpretation of seismograms

A seismogram is a graph with time on the horizontal axis and amplitude (ground displacement) on the vertical axis. Reading one involves identifying several features:

• P-wave arrival appears first as a sudden, small-amplitude signal
• S-wave arrival follows with larger amplitude; the time gap between P and S arrivals is the S-P interval used for distance calculations
• Surface waves arrive after the S-wave and typically show the largest amplitudes on the record
• Coda waves are the gradually diminishing oscillations after the main wave arrivals, caused by scattering of seismic energy
• Background noise is the low-level signal present before the earthquake arrives

To determine the direction to the epicenter from a single station, scientists analyze the first motion of the P-wave (whether the ground initially moved toward or away from the source) and compare amplitudes on horizontal components oriented in different directions. However, pinpointing the actual epicenter location still requires data from multiple stations using the triangulation method described above.