Trans-dimensional Bayesian inversion of airborne transient EM data from Taylor Glacier, Antarctica

Abstract

Conventional regularized nonlinear inversion methods for estimating electrical conductivity from observed electromagnetic data seek to find a single model that fits the data while minimizing a user-imposed model regularization norm. By contrast, Bayesian sampling techniques produce a large suite of models, all of which fit the data adequately, providing a wealth of statistical information about the model parameters. Importantly, this includes quantitative uncertainty estimates as well as any statistical property of interest. In this work, we apply a Bayesian trans-dimensional Markov chain Monte Carlo scheme to recover subsurface conductivity from airborne transient electromagnetic (TEM) data collected over Taylor Glacier, Antarctica, to image subglacial hydrologic structure. We provide a synthetic model study, followed by inversions of real soundings. Our results identify a zone of conductive, wet sediments beneath the glacier, corroborating interpretations from previous studies that used regularized, smooth inversions. Our results provide, however, the opportunity to examine a rich suite of additional information, including uncertainty estimates on the conductivity within the conductive subglacial layer as well as quantitative estimates of its total conductance. We apply principles of Bayesian information theory for estimating the depth of investigation of the airborne TEM data and apply it to this data set. Additionally, we use the model ensemble to derive estimates of pore fluid resistivity within the conductive layer, with associated uncertainties. Finally, we use Bayesian model studies to explore the range of ice thicknesses and conductive layer thicknesses that could be resolved with ground or airborne TEM data if they had one to two orders of magnitude lower noise levels.

Characterisation of subglacial water using a constrained transdimensional Bayesian Time Domain Electromagnetic Inversion

“…6a) improvement on their unconstrained equivalents). Note, imaging beneath a conductive structure is difficult for the TEM method due to the attenuated signal (Blatter et al, 2018); however our constrained inversion results show the bottom of the conductive layers (in (b) -(e) to be much better resolved, i.e. to within < 10 meters.…”

“…Synthetic TEM responses were calculated from the 1D block models using the Leroi forward modelling algorithm 10 (Raiche, 2008), then 5% normally distributed random noise was applied to all time gates, a similar noise model to Blatter et al (2018), see The inversions were run using resistivity ranges shown in Table 2 using a maximum depth of 80 m, consistent with the estimated maximum DOI for this configuration. To highlight the benefit of additional depth constraints, MuLTI-TEM is separately run for an unconstrained case, and a case in which the depths of snow-ice and ice-bed horizons are fixed.…”

“…be inferred (Mosegaard andTarantola, 1995, Blatter et al, 2018). The computed posterior probability density function (pdf) provides a robust measure of DOI, highlighting model uncertainty at each depth (Blatter et al, 2018). To further reduce the parameter space and improve vertical resolution, the inversion can be constrained with complementary depth information (e.g., from borehole records or other geophysical sources), provided that the constrained depth is consistent across datasets.…”

Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to image freshwater aquifer offshore New Jersey

“…For more robust and accelerated convergence, we implement parallel tempering (PT), whereby multiple Markov chains are run in parallel, each with its own 'temperature' T. The chains at T = 1 are unmodified and will make up the model ensemble; the chains at temperatures T > 1 explore a 'tempered' model space and, by swapping models with colder chains after each MCMC step, allow for more robust and accelerated convergence to the high probability regions of model space. For a detailed description of our algorithm see Blatter et al (2018), Ray et al (2013a) and Ray & Key (2012); for a helpful discussion of MCMC, see Gilks et al (1995); and for a thorough discussion of PT with numerical examples, see Sambridge (2013).…”

“…The algorithm used in this work is the same as in Blatter et al (2018), except that here there is a water layer, which is sampled separately from the subsurface. At each step of the algorithm, a uniform random number is generated.…”