David Caterina

Case studies of incorporation of prior information in electrical resistivity tomography: comparison of different approaches

Many geophysical inverse problems are ill-posed and their solution non-unique. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to incorporate prior information for electrical resistivity tomography (ERT): using a simple reference model, adding structural constraints to Occam’s inversion and using geostatistical constraints. We made the comparison on four real cases representing different field applications in terms of scales of investigation and level of heterogeneities. In those cases, when electromagnetic logging data are available in boreholes to control the solution, it appears that incorporating prior information clearly improves the correspondence with logging data compared to the standard smoothness constraint. However, the way to incorporate it may have a major impact on the solution. A reference model can often be used to constrain the inversion; however, it can lead to misinterpretation if its weight is too strong or the resistivity values inappropriate. When the computation of the vertical and/or horizontal correlation length is possible, the geostatistical inversion gives reliable results everywhere in the section. However, adding geostatistical constraints can be difficult when there is not enough data to compute correlation lengths. When a known limit between two layers exists, the use of structural constraint seems to be more indicated particularly when the limit is located in zones of low sensitivity for ERT. This work should help interpreters to include their prior information directly into the inversion process through an appropriate way.

A comparison study of different image appraisal tools for electrical resistivity tomography

To date, few studies offer a quantitative comparison of the performance of image appraisal tools. Moreover, there is no commonly accepted methodology to handle them even though it is a crucial aspect for reliable interpretation of geophysical images. In this study, we compare quantitatively different image appraisal indicators to detect artefacts, estimate depth of investigation, address parameters resolution and appraise ERT-derived geometry. Among existing image appraisal tools, we focus on the model resolution matrix (R), the cumulative sensitivity matrix (S) and the depth of investigation index (DOI) that are regularly used in the literature. They are first compared with numerical models representing different geological situations in terms of heterogeneity and scale and then used on field data sets. The numerical benchmark shows that indicators based on R and S are the most appropriate to appraise ERT images in terms of the exactitude of inverted parameters, DOI providing mainly qualitative information. In parallel, we test two different edge detection algorithms – Watershed’s and Canny’s algorithms – on the numerical models to identify the geometry of electrical structures in ERT images. From the results obtained, Canny’s algorithm seems to be the most reliable to help practitioners in the interpretation of buried structures. On this basis, we propose a methodology to appraise field ERT images. First, numerical benchmark models representing simplified cases of field ERT images are built using available a priori information. Then, ERT images are produced for these benchmark models (all simulated acquisition and inversion parameters being the same). The comparison between the numerical benchmark models and their corresponding ERT images gives the errors on inverted parameters. These discrepancies are then evaluated against the appraisal indicators (R and S) allowing the definition of threshold values. The final step consists in applying the threshold values on the field ERT images and to validate the results with a posteriori knowledge. The developed approach is tested successfully on two field data sets providing important information on the reliability of the location of a contamination source and on the geometry of a fractured zone. However, quantitative use of these indicators remains a difficult task depending mainly on the confidence level desired by the user. Further research is thus needed to develop new appraisal indicators more suited for a quantitative use and to improve the quality of inversion itself.

Electrical resistivity tomography to monitor enhanced biodegradation of hydrocarbons with Rhodococcus erythropolis T902.1 at a pilot scale

Petroleum hydrocarbons (HC) represent the most widespread contaminants and in-situ bioremediation remains a competitive treatment in terms of cost and environmental concerns. However, the efficiency of such a technique (by biostimulation or bioaugmentation) strongly depends on the environment affected and is still difficult to predict a priori. In order to overcome these uncertainties, Electrical Resistivity Tomography (ERT) appears as a valuable non-invasive tool to detect soil heterogeneities and to monitor biodegradation. The main objective of this study was to isolate an electrical signal linked to an enhanced bacterial activity with ERT, in an aged HC-contaminated clay loam soil. To achieve this, a pilot tank was built to mimic field conditions. Compared to a first insufficient biostimulation phase, bioaugmentation with Rhodococcus erythropolis T902.1 led to a HC depletion of almost 80% (6900 to 1600ppm) in 3months in the center of the contaminated zone, where pollutants were less bioavailable. In the meantime, lithological heterogeneities and microbial activities (growth and biosurfactant production) were successively discriminated by ERT images. In the future, this cost-effective technique should be more and more transferred to the field in order to monitor biodegradation processes and assist in selecting the most appropriate remediation technique.

Image Appraisal Tools for Electrical Resistivity Tomography

Image appraisal is a problem frequently encountered in electrical resistivity Tomography (ERT), and more generally in non-linear geophysical Inversion. It may include several aspects such as the identification of the geometry of buried structures, the detection of numerical artefacts, the estimation of the depth of Investigation or the exactitude of inverted parameters. Geophysicists can rely on several Tools published in the literature to address these issues. However, few studies offer a quantitative comparison on the performance of these Tools concerning the different mentioned aspects. Moreover, to our knowledge, there is no commonly accepted methodology to handle image appraisal. in this contribution, we compared quantitatively the ability of different image appraisal indicators to reach different objectives (geometry, artefacts, depth of Investigation, parameter resolution). Among possible image appraisal Tools, the model resolution matrix (MRM), the cumulative sensitivity matrix (CSM) and the depth of Investigation index (DOI) are the most cited ones and were studied here. We compared them first on numerical models representing different geological situations. This numerical benchmark showed that indicators based on the MRM and CSM were the more appropriate to appraise ERT images in terms of the geometry of structures and the exactitude of inverted parameters, DOI providing mainly qualitative Information. On this basis, we propose a methodology to appraise field ERT images focusing on the resolution and geometric aspects (others being implicitly studied). First, True Synthetic Models (TSM), representing simplified cases of field ERT images, are built using available Information. then, through forward modelling, synthetic ERT data are computed and inverted to provide the inverted Synthetic Models (ISM). Afterwards, a comparison between TSM and ISM (or their gradients for geometry) is made in order to define the errors on inverted parameters. This discrepancy is then plotted with respect to resolution indicator values and points out in every tested cases a resolution range over which the errors abruptly increase allowing the definition of threshold values. the final step consists in applying the threshold values on the field ERT images and to validate the results with a posteriori knowledge.

Long-term ERT monitoring of biogeochemical changes of an aged hydrocarbon contamination

Adequate management of contaminated sites requires information with improved spatio-temporal resolution, in particular to assess bio-geochemical processes, such as the transformation and degradation of contaminants, precipitation of minerals or changes in groundwater geochemistry occurring during and after remediation procedures. Electrical Resistivity Tomography (ERT), a geophysical method sensitive to pore-fluid and pore-geometry properties, permits to gain quasi-continuous information about subsurface properties in real-time and has been consequently widely used for the characterization of hydrocarbon-impacted sediments. However, its application for the long-term monitoring of processes accompanying natural or engineered bioremediation is still difficult due to the poor understanding of the role that biogeochemical processes play in the electrical signatures. For in-situ studies, the task is further complicated by the variable signal-to-noise ratio and the variations of environmental parameters leading to resolution changes in the electrical images. In this work, we present ERT imaging results for data collected over a period of two years on a site affected by a diesel fuel contamination and undergoing bioremediation. We report low electrical resistivity anomalies in areas associated to the highest contaminant concentrations likely due transformations of the contaminant due to microbial activity and accompanying release of metabolic products. We also report large seasonal variations of the bulk electrical resistivity in the contaminated areas in correlation with temperature and groundwater level fluctuations. However, the amplitude of bulk electrical resistivity variations largely exceeds the amplitude expected given existing petrophysical models. Our results suggest that the variations in electrical properties are mainly controlled by microbial activity which in turn depends on soil temperature and hydrogeological conditions. Therefore, ERT can be suggested as a promising tool to track microbial activity during bioremediation even though further research is still needed to completely understand the bio-geochemical processes involved and their impact on electrical signatures.

How to incorporate prior information in geophysical inverse problems: deterministic and geostatistical approaches.

Many geophysical inverse problems are ill-posed leading to non-uniqueness of the solution. It is thus important to reduce the amount of mathematical solutions to more geologically plausible models by regularizing the inverse problem and incorporating all available prior information in the inversion process. We compare three different ways to go beyond standard Occam’s inversion for electrical resistivity tomography (ERT) using electromagnetic logging data in the context of salt water infiltration: a simple reference model, a structural constraint and a geostatistical constraint based on a vertical correlation length. Results with the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly improves the misfit with logging data. If a good reference model can always be used, it can lead to misinterpretation if its weight is too strong. When the computation of the correlation length is possible, the geostatistical inversion gives satisfactory results everywhere in the section. In this specific case, the geostatistical approach seems to be a more robust way to incorporate prior information. The structural constraint seems to be more indicated when integrating information from other geophysical methods such as GPR or seismic.

A Saline Tracer Test Monitored with ERT to Detect Preferential Flow/Transport Paths in Limestones

The success of a tracer test highly depends on the number and the localisation of the sampling wells. When preferential solute transport paths are expected, one needs to set up carefully the tracer test to recover information such as the local groundwater flow direction and an estimate of the transport velocities. In this work, we used electrical resistivity tomography (ERT) to monitor a saline tracer test. This experiment was performed in fractured limestones where high transport velocities and strong dilution effects were expected. This required a continuous injection and fast ERT acquisition. Two different salt concentrations (40 and 160 g/l) were injected to deal with dilution effects. We also tested the resolution and the depth of investigation of our dipole-dipole sequence by changing the electrode spacing. Two transversal (and a longitudinal) profiles were placed every 20 m from the injection well. During the first test, a maximum of -8 % (-16 % in the second) change of electrical resistivity was observed in the nearest ERT profile while no change occurred in the other ones. We were then able to estimate the transport velocities in addition to the local groundwater flow direction even if the dilution effects were important.