No abstract

We use Monte Carlo Markov chains to solve the Bayesian MT inverse problem in layered situations. The domain under study is divided into homogeneous layers, and the model parameters are the conductivity of each layer. We use an a priori distribution of the parameters which favours smooth models. For each layer, the a priori and a posteriori distributions are digitized over a limited set of conductivity values.  The Markov chain relies on updating the model parameters during successive scanning of the domain under study. For each step of the scanning, the conductivity is updated in one layer given the actual value of the conductivity in the other layers. Thus we designed an ergodic Markov chain, the invariant distribution of which is the a posteriori distribution of the parameters, provided the forward problem is completely solved at each step.  We have estimated the a posteriori marginal probability distributions from the simulated successive values of the Markov chain. In addition, we give examples of complex magnetotelluric impedance inversion in tabular situations, for both synthetic models and field situations, and discuss the influence of the smoothing parameter.

Electrical conductivity tomography is a well-established galvanometric method for imaging the subsurface electrical conductivity distribution. We characterize the conductivity distribution of a set of volcanic structures that are different in terms of activity and morphology. For that purpose, we developed a large-scale inversion code named ECT-3D aimed at handling complex topographical effects like those encountered in volcanic areas. In addition, ECT-3D offers the possibility of using as input data the two components of the electrical field recorded at independent stations. Without prior information, a Gauss-Newton method with roughness constraints is used to solve the inverse problem. The roughening operator used to impose constraints is computed on unstructured tetrahedral elements to map complex geometries. We first benchmark ECT-3D on two synthetic tests. A first test using the topography of Mt. St Helens volcano (Washington, USA) demonstrates that we can successfully reconstruct the electrical conductivity field of an edifice marked by a strong topography and strong variations in the resistivity distribution. A second case study is used to demonstrate the versatility of the code in using the two components of the electrical field recorded on independent stations along the ground surface. Then, we apply our code to real data sets recorded at (i) a thermally active area of Yellowstone caldera (Wyoming, USA), (ii) a monogenetic dome on Furnas volcano (the Azores, Portugal), and (iii) the upper portion of the caldera of Kīlauea (Hawai'i, USA). The tomographies reveal some of the major structures of these volcanoes as well as identifying alteration associated with high surface conductivities. We also review the petrophysics underlying the interpretation of the electrical conductivity of fresh and altered volcanic rocks and molten rocks to show that electrical conductivity tomography cannot be used as a stand-alone technique due to the non-uniqueness in interpreting electrical conductivity tomograms. That said, new experimental data provide evidence regarding the strong role of alteration in the vicinity of preferential fluid flow paths including magmatic conduits and hydrothermal vents.