1 of 35

Module 2: Ray theory, seismometry, seismic databases

Phạm Thành Sơn

ARC DECRA Fellow

ANU Research School of Earth Sciences

www.tsonpham.net

Introduction to Observational Seismology

VNU Hanoi University of Science, Hanoi, 21–25 April 2025

2 of 35

2

22/4/2025

Slides, links to colab available on the workshop’s official website.

Topics cover:

  • Module 1: Introduction, geographical mapping
  • Module 2: Ray theory, seismometry, seismic databases
  • Module 3: Geophysical inverse problem
  • Module 4: Seismic interferometry and study of the Earth’s structures
  • Module 5: Deep learning in seismology

Daily Schedule

  • 9:00–10:00 (AM) Morning lectures & briefings
  • 10:00–10:30 (AM) Morning break
  • 10:30–11:30 (AM) Walkthrough in-class exercises
  • 11:30–13:00 (AM) Lunch break
  • 13:00–16:00 (PM) Self-practice exercises, Q&A, and bonus projects (for interested students)

3 of 35

What do we do today?

In the lecture, we learn about

  • Elastic wave equation and seismic wave types
  • Ray theory and Snell’s law
  • Principle of seismometry and seismograms

In the exercises, we do

  • In-class exercise: Ray theoretical travel times and paths
  • Self-practice exercise: Triangulation of M5.2 Kon Tum 28/07/2024 earthquake

3

22/4/2025

4 of 35

An earthquake is what happens when two blocks of the Earth suddenly slip past one another.”

4

22/4/2025

5 of 35

Animation of the single-block "Earthquake Machine", a mechanical model of the earthquake process using a wood block, sandpaper, and rubber bands.”

5

22/4/2025

Keypoints:

  • Model for Forces, Faults, & Friction
  • Rubber band represents the elastic nature of the lithosphere
  • Sandpaper models friction between the plates
  • Energy is slowly stored, and is released unpredictably

6 of 35

Earthquakes happen on faults, which are either strike-slip, thrust (reverse), or normal.

6

22/4/2025

7 of 35

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).

7

22/4/2025

Bradley & Hubbard, 2025, Earthquake Insights

8 of 35

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.

8

22/4/2025

The Richter scale (customized for California) used to be reported in the media, but not anymore.

 

9 of 35

The seismic wave equation

9

22/4/2025

10 of 35

Motion of a spring-mass system

10

22/4/2025

 

 

11 of 35

Constitute equation of elastic waves

11

22/4/2025

 

 

Stress

Strain

Elastic moduli

Stein & Wysession, 2003

12 of 35

The seismic wave equation is a hyperbolic partial differential equation that governs the propagation of seismic waves in elastic media.

12

22/4/2025

 

Further reading: Stein & Wysession, 2003 (a copy provided Resources)

13 of 35

Numerical simulation of seismic wave propagation in a spherical Earth model using the spectral element method (simulated on a super computer).

13

22/4/2025

14 of 35

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.

14

22/4/2025

Sóng khối dọc (sóng dọc hay sóng P):

  • Phần tử dao động cùng phương truyền sóng
  • Tần số cao, vận tốc cao (5–13 km/s)
  • Lan truyền qua cả chất rắn và lỏng (tương tự như âm thanh)

Sóng khối ngang (sóng ngang hay sóng S):

  • Phần tử dao động vuông góc phương truyền sóng
  • Tần số thấp hơn, vận tốc thấp hơn
  • Chỉ lan truyền qua chất rắn

Source: IRIS

15 of 35

Sóng mặt (surface waves) lan tuyền gần với bề mặt Trái đất, ít được sử dung trong các nghiên cứu cấu trúc sâu.

15

22/4/2025

Sóng Rayleigh

  • Hình thành do sự tương tác của sóng P và sóng S gần bề mặt tự do.
  • Phần tử dao động trong mặt phẳng chứa phương truyền sóng.

Sóng Love

  • Hình thành do sự tương tác của sóng S với lớp đứt gãy gần bề mặt.
  • Phần tử dao động vuông góc mặt phẳng chứa phương truyền sóng.

16 of 35

Body waves are generally nondispersive, while surface waves are.

16

22/4/2025

Stein & Wysession, 2003

 

17 of 35

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).

17

22/4/2025

Các sóng dừng trên một sợi dây hai đầu cố định.

Tần số của sóng dừng (các modes) quyết định các nốt nhạc.

18 of 35

Normal modes of the Earth, excited by large earthquakes, ring the Earth like a bell for several days.

18

22/4/2025

Stein & Wysession, 2003

Play with normal modes here: https://saviot.cnrs.fr/terre/index.en.html

Time domain

Frequency domain

19 of 35

Principles of seismometry

19

22/4/2025

20 of 35

World’s first earthquake detector was invented 2000 years ago in China

20

22/4/2025

A modern replica of Zhang Heng’s famous seismoscope.

21 of 35

 

21

22/4/2025

Stein & Wysession, 2003

22 of 35

Response of a pendulum seismometer is monochromatic

22

22/4/2025

23 of 35

One seismic station can have multiple sensors recording signals at different bandwidths.

23

22/4/2025

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?).

24 of 35

24

22/4/2025

Where to look for information about seismic stations (unfortunately, it does not work today for demonstration).

25 of 35

A seismometer records motions in 3D of ground vibrations, including one vertical and two horizontal components.

25

22/4/2025

26 of 35

The global seismograph network is non-homogeneous and often subjected to local socioeconomic conditions.

26

22/4/2025

  • A small fraction are ‘permanent’, meaning they are installed for the long term and regularly serviced.
  • Most are temporary, meaning they are deployed during field campaigns, sometimes simply by burying them under thin soils.

~3,500 stations globally

Prof. Miller, RSES

27 of 35

Earthquake early warning systems give us “A few seconds matter.”

27

22/4/2025

28 of 35

Ray theory and Snell’s law

28

22/4/2025

29 of 35

The refraction is due to the difference of light speeds in different environtments (i.e., vair < vwater).

29

22/4/2025

https://smartclass4kids.com/refraction-of-light/

30 of 35

Light travels between two points along the path that requires the least time, as compared to other nearby paths.” 

30

22/4/2025

https://smartclass4kids.com/refraction-of-light/

Fermat’s principle

 

31 of 35

Snell’s law can be generalized to govern ray paths through the Earth’s interior, consisting of spherical shells.

31

22/4/2025

 

32 of 35

Standard phase names define their paths and their interaction with major layer of the Earth

32

22/4/2025

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

33 of 35

Travel time curves represent the travel time as a function of distance from a seismic source.

33

22/4/2025

34 of 35

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

34

22/4/2025

35 of 35

Summaries

  • Earthquakes are caused by the sudden release of seismic energy stored on a seismic fault.
  • A partial differential equation governs the propagation of seismic waves through the Earth's material.
  • Seismometers measure ground motions but are subjected to instrumental sensitivity.
  • Snell’s law governs ray paths subjected to high-frequency approximation.

35

22/4/2025