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The deterministic geophysical inversion methods are dominant when inverting magnetotelluric data whereby its results largely depends on the assumed initial model and only a single representative solution is obtained. A common problem to this approach is that all inversion techniques suffer from non-uniqueness since all model solutions are subjected to errors, under-determination and uncertainty. A statistical approach in nature is a possible solution to this problem as it can provide extensive information about unknown parameters. In this paper, we developed a 1D Bayesian inversion code based Metropolis-Hastings algorithm whereby the uncertainty of the earth model parameters were quantified by examining the posterior model distribution. As a test, we applied the inversion algorithm to synthetic model data obtained from available literature based on a three layer model (K, H, A and Q). The frequency for the magnetotelluric impedance data was generated from 0.01 to 100 Hz. A 5% Gaussian noise was added at each frequency in order to simulate errors to the synthetic results. The developed algorithm has been successfully applied to all types of models and results obtained have demonstrated a good compatibility with the initial synthetic model data.

A Bayesian Inference Approach to Reduce Uncertainty in Magnetotelluric Inversion: A Synthetic Case Study