2019 Microtremor Survey Techniques using Theory of Stochastic Process

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Academic unit or major
Graduate major in Urban Design and Built Environment
Instructor(s)
Morikawa Hitoshi 
Course component(s)
Lecture
Day/Period(Room No.)
Tue3-4(G323)  
Group
-
Course number
UDE.S531
Credits
1
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

This course discusses a technique named spatial auto-correlation (SPAC) method, which estimates phase velocity from microtremor data, on a basis of theory of stochastic process. Array observation of microtremors is useful technique to estimate ground structure through the phase velocity of surface waves. SPAC method is one of most popular techniques for the objective. After introducing the physics and theory of surface waves, the methods are discussed to estimate the phase velocity using vertical component and three components of microtremors. Furthermore, generalization of the SPAC method is shown as advanced techniques.
The grading policy is based on a project and its presentation and resume. For the project, the following topic is requested: (1) numerical simulation for propagation of microtremors, under given power spectrum and dispersion curve, (2) estimation of phase velocity using SPAC method, (3) comparing estimated phase velocities with given dispersion curve, (4) discussion of the reason of the errors.

Student learning outcomes

Students will have the following skills and knowledge after finishing this course:
(1) Students can understand physical meaning of phase velocity.
(2) Students can understand the theoretical background of SPAC method for Rayleigh wave, and can estimate phase velocities using their own program code.
(3) Students can understand the theoretical background of SPAC method for Love wave.
(4) Students can understand generalization of the SPAC method.

Keywords

phase velocity, dispersion curve, spatial auto-correlation (SPAC) method, surface wave, Rayleigh wave, Love wave

Competencies that will be developed

Intercultural skills Communication skills Specialist skills Critical thinking skills Practical and/or problem-solving skills
- -

Class flow

Important points will be written on the blackboard. Students will understand the details through the project.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Surface wave and phase velocity, on the project what's surface wave, definition of phase velocity, about the project
Class 2 Formulation of spatial auto-correlation (SPAC) method --- for vertical component formulation of SPAC method for vertical component, spectral representation of microtremors
Class 3 Solution of spatial auto-correlation (SPAC) method --- for vertical component solution of SPAC method for vertical component, SPAC coefficients, First kind of Bessel function with 0th order, estimation of phase velocity
Class 4 Formulation of spatial auto-correlation (SPAC) method --- for vertical and horizontal components formulation of SPAC method for three components, Rayleigh and Love waves
Class 5 Solution of spatial auto-correlation (SPAC) method --- for vertical and horizontal components solution of SPAC method for three components, SPAC coefficients, First kind of Bessel function with 1st order, estimation of phase velocity
Class 6 Generalization of SPAC method by Cho et al. generalization of SPAC method by Cho et al.
Class 7 Generalization of SPAC method by the representation using complex coherence function (CCF) generalization of SPAC method using CCF
Class 8 Presentation and discussion of the project Presentation and discussion of the project

Textbook(s)

Leon Cohen, "Time Frequency Analysis: Theory and Applications," Prentice Hall, 1994.

Reference books, course materials, etc.

H. Morikawa:morikawa.h.aa@m.titech.ac.jp

Assessment criteria and methods

Students' knowledge of the topics on this course will be assessed through presentation and resume of the project.

Related courses

  • UDE.S431 : Basics of Stochastic Process for Earthquake Engineering

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basics of Stochastic Process for Earthquake Engineering (UDE.S431) is strongly required. Programming skills and environment for numerical calculation are required.

Other

The contents and schedule will be changed to adjust students' understanding.

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