## Details of ES4105 (Autumn 2019)

Level: 4 |
Type: Theory |
Credits: 4.0 |

Course Code | Course Name | Instructor(s) |
---|---|---|

ES4105 |
Inverse Theory |
Gaurav Shukla, Kajaljyoti Borah |

Syllabus |
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Digital Signal Processing: z-transform, Discrete Fourier Transform, aliasing, filtering, correlation, deconvolution.
Probability Theory (Random variables, Gaussian distribution, Testing the Assumption of Gaussian Statistics, Confidence Intervals), Solution of the Linear Gaussian and Non-Gaussian Inverse Problem (Least Square Problem, The Data and Model resolution matrix, The Unit Covariance matrix, The Trade-off of resolution and variance, Norm), Non-linear Inverse Problem, Tomography, Numerical Algorithms (solving Evendetermined, Underdetermined, Overdetermined and Eigen value Problem, Singular-Value Decomposition), Applications of Inverse Theory to Geophysics. |

References |
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1. Geophysical Data Analysis: Discrete Inverse Theory, William Menke, Volume 45, Internatonal Geophysics Series, Academic Press, INC.
2. Inverse Problem Theory and Methods for Model Parameters Estimation, Albert Tarantola, Society of Industrial and Applied Mathematics, Philadelphia. 3. Time Series Analysis and Inverse Theory for Geophysicists, David Gubins, Cambridge University Press, 2004. |

#### Course Credit Options

Sl. No. | Programme | Semester No | Course Choice |
---|---|---|---|

1 | IP | 1 | Not Allowed |

2 | IP | 3 | Elective |

3 | IP | 5 | Not Allowed |

4 | MR | 1 | Not Allowed |

5 | MR | 3 | Not Allowed |

6 | MS | 7 | Elective |

7 | RS | 1 | Elective |

8 | RS | 2 | Elective |