Module 2: Ray theory, seismometry, seismic databases
Introduction to Observational Seismology
VNU Hanoi University of Science, Hanoi, 21–25 April 2025
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Slides, links to colab available on the workshop’s official website.
Topics cover:
Daily Schedule
What do we do today?
In the lecture, we learn about
In the exercises, we do
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“An earthquake is what happens when two blocks of the Earth suddenly slip past one another.”
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“Animation of the single-block "Earthquake Machine", a mechanical model of the earthquake process using a wood block, sandpaper, and rubber bands.”
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Keypoints:
Earthquakes happen on faults, which are either strike-slip, thrust (reverse), or normal.
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The Myanmar earthquake ruptured a long segment of the Sagaing fault. This strike slip fault is visible from space (similar to the San Andreas fault, CA).
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Bradley & Hubbard, 2025, Earthquake Insights
Moment magnitude (Mw) is the total energy released by an earthquake. It’s on log scale; one order of magnitude is equivalent to ~30 more energy released.
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The Richter scale (customized for California) used to be reported in the media, but not anymore.
The seismic wave equation
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Motion of a spring-mass system
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Constitute equation of elastic waves
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Stress
Strain
Elastic moduli
Stein & Wysession, 2003
The seismic wave equation is a hyperbolic partial differential equation that governs the propagation of seismic waves in elastic media.
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Further reading: Stein & Wysession, 2003 (a copy provided Resources)
Numerical simulation of seismic wave propagation in a spherical Earth model using the spectral element method (simulated on a super computer).
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Sóng khối (body waves) có tần số cao giúp nghiên cứu các cấu trúc sâu với độ phân giải cao nhất trong tất cả các phương pháp địa chấn.
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Sóng khối dọc (sóng dọc hay sóng P):
Sóng khối ngang (sóng ngang hay sóng S):
Source: IRIS
Sóng mặt (surface waves) lan tuyền gần với bề mặt Trái đất, ít được sử dung trong các nghiên cứu cấu trúc sâu.
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Sóng Rayleigh
Sóng Love
Body waves are generally nondispersive, while surface waves are.
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Stein & Wysession, 2003
Sóng dừng (standing waves) là dao động tự nhiên của các vật thể có kích thước hữu hạn. Tần số đặc trưng của các sóng dừng gọi là mốt (modes hay normal modes).
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Các sóng dừng trên một sợi dây hai đầu cố định.
Tần số của sóng dừng (các modes) quyết định các nốt nhạc.
Normal modes of the Earth, excited by large earthquakes, ring the Earth like a bell for several days.
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Stein & Wysession, 2003
Play with normal modes here: https://saviot.cnrs.fr/terre/index.en.html
Time domain
Frequency domain
Principles of seismometry
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World’s first earthquake detector was invented 2000 years ago in China
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A modern replica of Zhang Heng’s famous seismoscope.
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Stein & Wysession, 2003
Response of a pendulum seismometer is monochromatic
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One seismic station can have multiple sensors recording signals at different bandwidths.
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Electronic seismometers use an electric current to balance the relative motion of the mass to the frame.
It helps flatten the sensitivity bandwidth of broadband seismometers (BH? or HH?).
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Where to look for information about seismic stations (unfortunately, it does not work today for demonstration).
A seismometer records motions in 3D of ground vibrations, including one vertical and two horizontal components.
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The global seismograph network is non-homogeneous and often subjected to local socioeconomic conditions.
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~3,500 stations globally
Prof. Miller, RSES
Earthquake early warning systems give us “A few seconds matter.”
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Ray theory and Snell’s law
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The refraction is due to the difference of light speeds in different environtments (i.e., vair < vwater).
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https://smartclass4kids.com/refraction-of-light/
“Light travels between two points along the path that requires the least time, as compared to other nearby paths.”
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https://smartclass4kids.com/refraction-of-light/
Fermat’s principle
Snell’s law can be generalized to govern ray paths through the Earth’s interior, consisting of spherical shells.
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Standard phase names define their paths and their interaction with major layer of the Earth
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Britannica.com
Symbols | Descriptions |
P | compressional wave, upgoing or downgoing; in the crust or mantle, p is a strictly upgoing P-wave in the crust or mantle |
S | shear wave, upgoing or downgoing, in the crust or mantle, s - strictly upgoing S-wave in the crust or mantle |
K | compressional wave in the outer core |
I | compressional wave in the inner core |
J | shear wave in the inner core |
symbols | descriptions |
c | topside reflection off the core mantle boundary |
i | topside reflection off the inner core outer core boundary |
Travel time curves represent the travel time as a function of distance from a seismic source.
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Exercise overview
In-class exercise: Ray theoretical travel times and paths Open in Colab
Self-practice exercise: Triangulation of M5.2 Kon Tum 28/07/2024 earthquake Open in Colab
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Summaries
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