Electromagnetic Full Waveform Inversion based on Bayesian Markov-chain Monte-Carlo Method

Abstract

Straight-ray-based inversion technique to estimate attenuation rate from electromagnetic tomography in coal mine has been available to geophysicists for over twenty years. This method gives a good computational efficiency but not a satisfy resolution. On account of the increasing computational power, accurate forward modeling can be included in advanced inversion approaches such that the full-waveform content can be exploited. Conventional full-waveform inversion methods are referred to as deterministic and are based on the minimization of an error term between the forward responses and the observed waveforms at each trace location. It is commonly used to give a ‘best estimate’ or ‘most likely’ case, regardless of the attendant uncertainties--which is the nature of most geophysical problems. Deterministic method is also easy to be trapped in a local minimum if there is not a good start model .To address this limitation, we present a probabilistic full-waveform inversion method in Bayesian formulation. In this formulation, solution to inverse problem is a probability density function refers to as posteriori distribution which describes all information available. Make use of Bayesian theorem combined with Markov-chain Monte-Carlo (MCMC) sampling, we can generate stochastic realizations from the posteriori distribution of model parameters. Bayesian-MCMC methods can incorporate any information that can be expressed in terms of probabilities and provide more precise model parameter even with an arbitrary initial model. In case study, we explore the performance of electromagnetic fullwaveform inversion with MCMC through a simple synthetic tomographic example in coal mine, dielectric permittivity values of a moisture anomaly in coal seam can be obtained with a good resolution. Results demonstrate the feasibility of our statistical inversion method. Keywords—radio image method; full waveform inversion; Baysian; Monto-Carlo simulation; Markov-chain ;prior;posterior