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.
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.
phase velocity, dispersion curve, spatial auto-correlation (SPAC) method, surface wave, Rayleigh wave, Love wave
|✔ Specialist skills||Intercultural skills||Communication skills||✔ Critical thinking skills||✔ Practical and/or problem-solving skills|
Important points will be written on the blackboard. Students will understand the details through the project.
|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|
Leon Cohen, "Time Frequency Analysis: Theory and Applications," Prentice Hall, 1994.
Students' knowledge of the topics on this course will be assessed through presentation and resume of the project.
Basics of Stochastic Process for Earthquake Engineering (UDE.S431) is strongly required. Programming skills and environment for numerical calculation are required.