Pseudo-2-D Transdimensional Bayesian Inversion of the Full Waveform TEM Response From PRBS Source
Qingyun Di, Hai Li, Guoqiang Xue, Linbo Zhang
Abstract
Transient electromagnetic method (TEM) is an important tool for mapping the subsurface resistivity. As the electromagnetic fields with different frequencies reach different depth of the Earth, the resolution of TEM method is closely related to the spectrum properties of its source signal. The pseudorandom binary sequence (PRBS) is a recently applied source signal and is thought to be superior to the conventional square wave for its adjustable frequency range and density. However, to invert the response from this optimized source, the pure secondary field needs to be extracted from the full waveform response in which parts of useful information is lost inevitably. We thus propose to directly invert the full waveform TEM response from the excitation of PRBS using a transdimensional framework. We use the reverse-jump Markov chain Monte Carlo (RJ-MCMC) sampler to get the model ensemble so that the posterior of the model can be obtained. The PRBS source is convolved with the impulse response of the Earth to fit the recorded full waveform response. The 2-D model space is discretized using a two-stage binary tree and updates in parallel, which dramatically improve the sampling efficiency. The synthetic examples compare the results from the conventional time-domain step response and the full waveform response and demonstrate that the proposed method obtains higher resolution and can better resolve the interface in the shallow and moderate depth. Furthermore, the real data example recovers the model structure that is consistent with the geologic inference, providing alternate evidence for the conjecture of the Sanshandao fault.