Transdimensional Electrical Resistivity Tomography

Abstract

This paper shows that imaging the interior of solid bodies with fully nonlinear physics can be highly beneficial compared to imaging with the equivalent linearized tomographic methods and that this is true for a variety of different types of physics. Including full nonlinearity provides interpretable uncertainties and far greater depth of image penetration into unknown targets such as the Earth's subsurface. We use an adaptively parameterized Monte Carlo method to invert electrical resistivity data for the conductivity structure of the Earth and demonstrate the method on two field data sets. Key results include the observation of directly interpretable uncertainty loops which define possible geometrical variations in the edges of isolated anomalies, hence quantifying the spatial resolution of these boundaries. These topologies of uncertainties are similar to those observed when performing fully nonlinear seismic traveltime tomography. This shows that loop‐like uncertainty topologies are expected in the solutions to a wide variety of tomographic problems, using a variety of data types and hence laws of physics (here the Laplace equation; in previous work the Eikonal or ray equations). We also show that the depth to which we can construct a tomographic image using electrical data is extended by up to a factor of 8 using nonlinear methods compared to linearized inversion using common standard linearized programs. These advantages come at the cost of significantly increased computation. All of these results are illustrated on both synthetic and real data examples.

Seismic Tomography Using Variational Inference Methods

“…They have been extended to transdimensional inversion using the reversible jump Markov chain Monte Carlo (rj‐McMC) algorithm (Green, ), in which the number of parameters (hence the dimensionality of parameter space) can vary in the inversion. Consequently, the parameterization itself can be simplified by adapting to the data, which can improve results on otherwise high‐dimensional problems (Bodin & Sambridge, ; Bodin et al, ; Burdick & Lekić, ; Galetti et al, , ; Galetti & Curtis, ; Hawkins & Sambridge, ; Malinverno & Leaney, ; Ray et al, ; Piana Agostinetti et al, ; Young et al, ; Zhang et al, , ). Although many tomographic applications have been conducted using McMC sampling methods (previous references, Crowder et al, ; Shen et al, , ; Zheng et al, ; Zulfakriza et al, ), they mainly address 1‐D or 2‐D tomography problems due to the high computational expense of MC methods.…”

Seismic Tomography Using Variational Inference Methods

“…They have been extended to trans-dimensional inversion using the reversible jump Markov chain Monte Carlo (rj-McMC) algorithm [25], in which the number and meaning of parameters (hence the dimensionality of parameter space) can vary in the inversion. Consequently the parameterization itself can be simplified by adapting to the data which improves results on otherwise high-dimensional problems [43,6,7,57,80,22,23,29,53,8,21,83,81]. Although many applications have been conducted using McMC sampling methods [previous references; 69,70,86,85,11], they mainly address 1D or 2D tomography problems due to the high computational expense of Monte Carlo methods.…”

Flexible Coupling in Joint Inversions: A Bayesian Structure Decoupling Algorithm

“…However, this algorithm is general and can be easily extended to the 2-D or 3-D cases. The RjMcMC algorithms have been used to recover 2-D and 3-D fields (e.g., Bodin, Sambridge, Tkalcic, et al, 2012;Galetti & Curtis, 2018;Piana Agostinetti et al, 2015). In this case, the field to be reconstructed is parameterized in terms of a variable number of Voronoi cells that are defined by a set of Voronoi nodes which can be moved within the investigated space.…”