Syllabus
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Course Code: GP-404 Course Name: Geophysical Inversion |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Introduction Forward problems versus Inverse problems, continuous inverse problem, discrete inverse problem, formulation of inverse problems and their reduction to a matrix problem, linear inverse problems, classification of inverse problems, L1 norm inversion, least squares solution and minimum norm solution, concept of norms, concept of ‘a priori’ information, constrained linear least squares inversion, review of matrix theory, Geophysical inverse problems. |
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| 2 | Finite difference and Finite Element Method Introduction to finite difference method, forward, backward and central difference method, Application of finite difference method for solving Helmholtz equation. Introduction to finite element method, various steps, simple examples showing application of finite element method. |
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| 3 | Non-Linear Inversion Model and Data spaces, householder transformation, data resolution matrix, model resolution matrix, checkerboard resolution test, eigen values and eigen vectors, singular value decomposition (SVD), generalised inverses, Non-linear inverse problems, Gauss Newton method,, steepest descent (gradient) method, Marquardt-Levenberg method, Earthquake location problem, tomography problem, Inversion of gravity profiles due to simple geometrical shape, Applications of non-linear inversion techniques in seismology. |
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| 4 | Global Optimization Techniques: Probabilistic approach of inverse problems, maximum likelihood and stochastic inverse methods, Backus-Gilbert method, Global optimization techniques: genetic algorithm:Heat Bath algorithm, Metropolis algorithm, simulated annealing methods, neighbourhood algorithm, examples of applying global optimization techniques. |
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