Special Topics (Inverse modeling of exploration geophysics data)
- Fundamentals of geophysical data modelling, the philosophy of discreetization and parameterization in geophysical data modelling
- Preparation and pre-processing of geophysical data for inversion, designing structured and unstructured meshes, linear algebra, preliminary statistics and linear regression
- Definition of forward and inverse modelling of geophysical data
- Details of forward modeling (principles, mathematical relations and practical examples for different geophysical methods)
- Discretization of continuous inverse problems, formulation of inversion problems, categorization of inverse problems and their description
- Steps of unconstrained linear inversion of geophysical data and their solution algorithms, constrained linear inversion of geophysical data and their solution algorithms
- Solving nonlinear inversion problem through conversion to linear problem with the help of Taylor series expansion, unconstrained and constrained nonlinear inversion of geophysical data with Gauss-Newton/Levenberg-Marquardt/ridge regression/steepest descent optimization along with mentioning to practical examples and explaining their strengths and weaknesses
- Description of geophysical ill-posed problems, singular value decomposition, Tikhonov regularization algorithm, Lp-Lq algorithm, conjugate gradient method, lanczos bidiagonalization method, fast wavelet-based methods for inverse modelling
- Iterative methods in geophysical data modelling, Fourier-based and wavelet-based methods, Bayesian and stochastic methods, parametric and n-dimensional modelling of geophysical data with practical examples in mineral exploration
- Joint, cooperative, sequential,integrated and petrophysical clustering based inversion algorithms
- Computer assisted programming for geophysics data modeling in environments such as Python, Matlab, and so on.
- Implementation of inversion on real geophysical data (mineral case studies, geothermal resources, salt domes, oil fields, etc.) as a project
- Optimum selection of regularization parameters, application of structural constraint in inversion
- Analysis of error and uncertainty in linear and non-linear inversion, evaluation of the quality of the inversion solution with different statistical criteria, resolution matrix and estimation of the error range for parameters estimated from inversion by different methods with covariance matrix analysis