COURSE OBJECTIVES:
1. Introducing students to the problem of solving seismological and geophysical problems on the computer.
2. Selecting appropriate computer and numerical methods for solving basic seismological equations.
3. Connecting materials from seismological courses with practical work on a computer.
4. Successful application of computer methods in future professional and/or scientific work.
5. Developing the ability to select and use appropriate mathematical methods to solve inverse problems in seismology.
COURSE CONTENT:
1. Inverse methods in seismology. Determination of parameters in linear problems: least squares method, weighting the data, covariance matrices, ellipsoid errors, robust methods.
2. Undetermined problems.
3. Nonlinear problems: solving methods, quasi-linearization and iteration, damping, covariance and resolution matrices, error, application in earthquake location.
4. Continuous inverse theory: linear theory, Dirichlet condition, Spread, Error, and the Trade-off Curve, minimum norm, discretization, determination of parameters by Backus-Gilbert and Parke methods.
5. Numerical methods in seismology. Seismic waves and sources: elastic and scalar wave equation, rheology, boundary and initial conditions, fundamental solutions, seismic sources, scattering, solution of wave equation, linear regime.
6. Wave field in a discrete domain: strategies for computing wave propagation in a medium, physical domains and discrete value fields, application of parallel computing method.
7. Application of computer and inverse methods to seismological problems: tomography, wave propagation in a medium, simulation of seismic (ambient) noise.
LEARNING OUTCOMES:
After completion the course the student should be able to:
1. Recognize the problems mastered in previous seismological courses and solve them during the practical work on the computer.
2. Recognize and explain the basics of numerical and inverse methods, discuss and apply them to seismological problems.
3. Identify, compare and discuss favorable and unfavorable aspects of individual methods in solving complex inverse problems in seismology.
4. Prepare and analyze theoretical problems in seismology, evaluate and plan how to solve them with the help of a computer.
5. Independently carry out part of the practical work on the computer and recognize the importance of cooperation with colleagues.
LEARNING MODE:
Lectures and exercises attendance, study of notes and literature. Equation derivation and example analysis.
TEACHING METHODS:
Lectures and discussion, derivation of equations. Independent solving of exercises concerning the surface wave dispersion.
METHODS OF MONITORING AND VERIFICATION:
Regular class attendance, practical work, written and oral exam
TERMS FOR RECEIVING THE SIGNATURE:
Regular class attendance and solved homework assignments.
EXAMINATION METHODS:
Homework, written exam, oral exam. The final mark is weighted average of marks from homework (20 %), written exam (40%) and oral exam (40 %).
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