USE OF COUPLED LOCAL MINIMISATION TECHNIQUE FOR DEVELOPING AN ACCURATE GEOPHYSICAL DATA INVERSION ALGORITHM

Abstract

Optimization of a function is generally required in every field of physics. Optimization is performed generally to obtain the best result to a particular data set. Optimization is basically minimization of the cost function with respect to the parameters of the system on which optimization is being performed. Optimization is also carried out in Geophysics for performing Inversion that is the most important step of any Geophysical workflow. Inversion is performed to obtain the best fit subsurface geological model from the data set. To perform Inversion a proper technique/method must be used that provide efficient results with low computational space and time. Nowadays many efficient methods are available for performing Inversion very quickly. Geophysical inversion can be performed in two ways, first is minimizing the misfit between the observed/actual data set and theoretical/synthetic data set and the second is by using specialized techniques such as Simulated Annealing and Genetic Algorithm. The methods based on minimization of misfit function to obtain the global minimum i.e. the best fit model for example, Newton’s method, Conjugate Gradient and Quasi-newton method are generally based on find the gradient direction and moving to the next update. These methods are generally very fast to converge to a solution but the solution obtained by using them is usually not the Global minimum. As these methods use the negative direction of gradient the minimizer point gets stuck into the local minimum or the minimum of the valley in which the point is present. The specialized techniques like SA and GA are more efficient in providing the global minimum but are not much robust as they require large computational space and time. That are two most important things economically for any computational process. There is a trade off in both the ways to perform inversion, in first it is fast to converge to a solution but does not guarantee that the solution is the optimum one and the second provides optimum result but costlier to use. Due to such trade-offs a new method which is Gradient based but guarantees providing the Global minimum is the Coupled Local Minimizers(CLM) method. Coupled Local Minimizers(CLM) method is a new method that is Gradient based and applicable to perform global optimization of functions with multiple minima. That method is very efficient in providing the Global minimum and very fast to converge to it as it is using the gradient directions to proceed. It is based on cooperative search for the minimum, in which multiple (a population of) local optimizers (gradient based) are used which exchanges information amongst themselves (based on information sharing in Genetic Algorithm) as they are coupled using the synchronization constraints. The Combination of information iv sharing/coupled parallel strategy and fast convergence can provide the Global minimum efficiently i.e. an efficient Optimization Algorithm. This efficient method can be used to perform Geophysical Inversion of any data set. This method can provide the best fit model for the data set very quickly with low computational space and time as compared to the specialized methods. Due to the combination strategy used in CLM, it is able to provide Global minimum for the test function. Next it is applied for model updating and obtaining best fit model in Magnetotellurics for homogeneous half space, 2 layered and n-layered model. The results obtained are quite good very low error percentage. In my work I have also shown the comparison in working of Newton’s method and the CLM method as both are converging faster to a solution but CLM is providing the global minimum whereas the Newton’s method provides a minimum that can be global or local.