We present a practical algorithm for determining the Bayesian solution of non-linear inverse problems with a limited number of parameters. This approach allows the use of very general conditional probability density functions (pdfs of the data given the model parameters) and a priori pdfs (prior beliefs upon the parameters). The results consist in the a posteriori marginal pdfs of the model parameters. The marginal pdfs describe the additional information (if any) brought by the data to the prior knowledge about the model parameters.We have paid a special attention to the numerical calculation of the a posteriori pdfs and we propose a solution which enables the simultaneous determination of the numerical estimates of the a posteriori pdfs and their uncertainties.With the help of a practical example (the 1-D magnetotelluric inverse problem) with synthetic and real data, we show that in most cases, the a posteriori marginal pdfs are complicated functions and cannot be predicted from the data pdf or the a priori pdfs. Consequently, the standard analyses applied to the same data sets such as the maximum likelihood techniques or the asymptotic estimation technique would lead to severely biased estimates of the parameters. This remark is likely to be true for any non-linear inverse problem.

A tensor magnetotelluric test survey was carried out in the region of Santa Catarina, located in the Chalco sub-basin of the Mexico Basin. The objective was to define the stratification at depth with an emphasis on the geometry of the main aquifer of that region which is partially known from DC resistivity soundings and drilling. High-quality magnetotelluric soundings could be recorded in the immediate vicinity of large urban zones because the sub-surface is very conductive. Interpretation shows that the solid bedrock is located at a depth of at least 800 m to the south and 1300 m to the north; it could, however, be much deeper. Using complementary DC resistivity sounding and well-logging data, three main layers have been defined overlying the bedrock. These layers are, from surface to bottom, an unsaturated zone of sand, volcanic ash and clay about 10 m thick, followed by a very conductive (1.5 ohm·m) 200 m thick layer of sand and ash with intercalated clay, saturated with highly mineralized water, and finally a zone with resistivity increasing gradually to 60 ohm·m. The investigated deep aquifer constitutes most of this third layer. It consists of a sequence of sand, gravel, pyroclastites and mainly fractured basalts. MT resistivity soundings and magnetic transfer functions also indicate that a shallow resistive structure is dipping, from the northwest, into the lacustrine deposits of the basin. This geologic feature is likely to be highly permeable fractured basaltic flows, which provide a channel by which water contaminated by the Santa Catarina landfill may leak into the basin.

This work presents a method to find rock conductivities in a zone from electromagnetic measurements on the surface of the earth. It uses a stochastic algorithm to find a Bayesian estimator of the conductivities. The algorithm is tested on a synthetic model made up of an heteregeneous thin sheet inbedded in a stratified substratum.

A simple impedance tensor analysis of four magnetotelluric soundings recorded over the ECORS section of the Rhine Graben shows that for periods shorter than about 30 s, induction dominates over channelling. For longer periods, 2-D induction galvanically distorted by surface heterogeneities and/or current chanelled in the Graben can explain the observations; the role of chanelling becomes dominant at periods of the order of a few hundred seconds. In the area considered, induction appears to be controlled by inclusions of saline water in a porous limestone layer (Grande Oolithe) and not by the limits of the Graben with its crystalline shoulder (Vosges). The simple analysis is supported by tipper analyses and by the results of schematic 2-D modelling.

Other| November 01, 1990 Resultats de sondages magnetotelluriques sous-marins et structure thermique de la lithosphere oceanique P. Tarits; P. Tarits Author Inst. Phys. Globe, Paris, France Search for other works by this author on: GSW Google Scholar V. Jouanne V. Jouanne Author Search for other works by this author on: GSW Google Scholar Bulletin de la Société Géologique de France (1990) VI (6): 921–931. https://doi.org/10.2113/gssgfbull.VI.6.921 Article history first online: 03 Mar 2017 Cite View This Citation Add to Citation Manager Share Icon Share Twitter LinkedIn Tools Icon Tools Get Permissions Search Site Citation P. Tarits, V. Jouanne; Resultats de sondages magnetotelluriques sous-marins et structure thermique de la lithosphere oceanique. Bulletin de la Société Géologique de France 1990;; VI (6): 921–931. doi: https://doi.org/10.2113/gssgfbull.VI.6.921 Download citation file: Ris (Zotero) Refmanager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu nav search search input Search input auto suggest search filter All ContentBy SocietyBulletin de la Société Géologique de France Search Advanced Search This content is PDF only. Please click on the PDF icon to access. First Page Preview Close Modal You do not currently have access to this article.