Inversion of multi-temporal geoelectrical field data sets: insights on noise characterization and regularization

Poster (2012, July 11)

Inversion of geoelectrical time-lapse data sets is increasingly growing as monitoring systems are being used in more applications such as seawater intrusion, landslides, remediation of contaminated sites ... [more ▼]

Inversion of geoelectrical time-lapse data sets is increasingly growing as monitoring systems are being used in more applications such as seawater intrusion, landslides, remediation of contaminated sites, landfill operation, shallow geothermal systems, or management of water resources. To date, several inversion strategies exist for taking into account the temporal dimension of the data. The most used nowadays are the independent inversion of multi-temporal data sets, the difference inversion, the temporally-constrained inversion, and the more recent process-based inversion. However, difference inversion schemes generally assume that part of the noise contained in the data cancels out when working with temporal data differences. Temporally-constrained inversion on the other hand assumes that the changes are localized and minor. Process-based inversion requires a more advanced knowledge of the system prior the inversion. In this study we demonstrate that the resolution of the time-lapse inversion scheme is mostly dependent on the quantification of the temporal behavior of the data error, on the resolution of the model-dependent pattern of the survey, and not on the regularization strategy. Our study is based on the imaging results of different data sets with different time and spatial scales, and with different degrees of geological complexity and resistivity contrast, The considered sites are a shallow sandy aquifer and a fractured hard rock aquifer where tracer experiments were performed and monitored using surface arrays. The two studied transport processes are advection, with velocities on the order of 10 m/hour and slower advection/diffusion processes. The strongest improvements were brought by using the data difference and a quantitative estimation of the data error. We found in particular a dependence of the time-lapse data error to the measured resistance (i.e., signal-to-noise-ratio), permitting to formulate an error model to describe the data error present in time-lapse data sets. We used minimum gradient support regularization to invert for model changes with enhanced contrast and found this technique more suited to time-lapse studies than for static images. Noise characterization and error models appear therefore as essential and the most impacting for a successful inversion both for static and time-lapse data whereas different spatio-temporal regularization techniques allowed to decrease artefacts but needs to be coherent with the process. [less ▲]

Incorporation of prior information in the regularized inversion of ERT data with CRTomo

Conference (2012, February 03)

The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically ... [more ▼]

The electrical resistivity tomography (ERT) inverse problem is ill-posed leading to non-uniqueness of its solution. A possible way to reduce the amount of mathematical solutions to more geologically plausible models is to incorporate priori information in the inversion process. In this presentation, we describe the implementation of three different techniques ways to go beyond standard Occam’s inversion for ERT with the code CRTomo : a simple reference model weighted by a user-defined parameter, a structural constraint defined by modifying the construction of the roughness matrix compared to standard Occam’s inversion and a geostatistical constraint based on a vertical correlation length deduced from borehole data to build the model covariance matrix and use it to regularize the inversion. With several examples, we show that the traditional smoothness constraint yield small contrasts of resistivity, far from the reality revealed by borehole measurements. Incorporating prior information from boreholes clearly or from another geophysical technique (like GPR or seismic refraction) improves the misfit with logging data. The choice of the prior information incorporation technique highly depends on which king of information is available and further developments are needed to extend the techniques to more complex cases. [less ▲]

Using geostatistical constraints in electrical imaging for improved reservoir characterization

Conference (2010, December 14)

Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two ... [more ▼]

Developing predictive models of reservoirs is often complicated by the spatial heterogeneities and the different scales which control flow and transport processes. In numerous studies over the past two decades, geophysical imaging techniques have proved very useful for reservoir characterization. However, the loss of resolution and the non-uniqueness of standard solutions to inverse problems strongly limit the use of such deterministic imaging approaches. On the other hand, the use of common geostatistical approaches for reservoir characterization, for instance from logging information, may be a difficult task, since accurate variogram information is difficult to obtain (dense sampling in the vertical and lateral directions), and also because a high number of conditioned simulations is needed to remove statistical bias. Combining the high spatial sampling of deterministic geophysical imaging methods with geostatistical constraints, valid in the whole image plane, appears as a very promising approach to enhance reservoir characterization. To do so, we use a parameterized model covariance matrix based on standard variogram functions and a prior model as regularization operator in the inversion of electrical resistance data. This way of including additional data is not restricted to electrical data but the variogram parameters may be also inferred from for example available textural or lithological information. The benefit of the presented approach is twofold: (i) It honors the spatial statistics of the reservoir and (ii) it alters the posterior model by further reducing model ambiguity inherent to the inversion compared to classical (smooth model) regularization. The proof of concept is given by synthetic studies carried out on random fields from Gauss simulations with varying (an)isotropic scale lengths using different model (co)variogram functions. We also demonstrate the approach on electrical field data combined with borehole electromagnetic data from two artificial sea inlets in the nature reserve "The Westhoek" near the French-Belgian border. The electromagnetic logs were used to calculate an experimental vertical variogram characteristic of the study site. The results enabled to determine the extension of the salt water plume laterally, and significantly enhance its extension in depth, but also in terms of total dissolved solid content. These observations are in agreement with the hydrogeological situation at the site. A comparison with borehole data shows that the results are much more plausible than results obtained with a traditional smoothness constraint used as regularization operator. In conclusion, the incorporation of geostatistical information, vertical variograms in our case, in the inverse process improves imaging capabilities for reservoir characterization significantly. [less ▲]

Detecting preferential flow and transport in soils using electrical resistivity tomography

Conference (2009)