Gianluca Fiandaca

An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data

We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host. We present an overview of a mature and general algorithm for inversion of most electromagnetic and geoelectrical data, ground-based and airborne. The implementation uses a 1D formulation for electromagnetics and MRS responses, geoelectric responses are 1D and 2D, and the 3D sheet’s response implements an overburden of varying thickness and resistivity.

Mapping of landfills using time-domain spectral induced polarization data: the Eskelund case study

This study uses time-domain induced polarization data for the delineation and characterization of the former landfill site at Eskelund, Denmark. With optimized acquisition parameters combined with a new inversion algorithm, we use the full content of the decay curve and retrieve spectral information from time-domain IP data. Thirteen IP/DC profiles were collected in the area, supplemented by el-log drilling for accurate correlation between the geophysics and the lithology. The data were inverted using a laterally constrained 1D inversion considering the full decay curves to retrieve the four Cole-Cole parameters. For all profiles, the results reveal a highly chargeable unit that shows a very good agreement to the findings from 15 boreholes covering the area, where the extent of the waste deposits was measured. The thickness and depth of surface measurements were furthermore validated by el-log measurements giving in situ values, for which the Cole-Cole parameters were computed. The 3D shape of the waste body was pinpointed and well-defined. The inversion of the IP data also shows a strong correlation with the initial stage of the waste dump and its composition combining an aerial map with acquired results.

Sharp spatially constrained inversion with applications to transient electromagnetic data

Time-domain electromagnetic data are conveniently inverted by using smoothly varying 1D models with fixed vertical discretization. The vertical smoothness of the obtained models stems from the application of Occam-type regularization constraints, which are meant to address the ill-posedness of the problem. An important side effect of such regularization, however, is that horizontal layer boundaries can no longer be accurately reproduced as the model is required to be smooth. This issue can be overcome by inverting for fewer layers with variable thicknesses; nevertheless, to decide on a particular and constant number of layers for the parameterization of a large survey inversion can be equally problematic. Here, we present a focusing regularization technique to obtain the best of both methodologies. The new focusing approach allows for accurate reconstruction of resistivity distributions using a fixed vertical discretization while preserving the capability to reproduce horizontal boundaries. The formulation is flexible and can be coupled with traditional lateral/spatial smoothness constraints in order to resolve interfaces in stratified soils with no additional hypothesis about the number of layers. The method relies on minimizing the number of layers of non-vanishing resistivity gradient, instead of minimizing the norm of the model variation itself. This approach ensures that the results are consistent with the measured data while favouring, at the same time, the retrieval of horizontal abrupt changes. In addition, the focusing regularization can also be applied in the horizontal direction in order to promote the reconstruction of lateral boundaries such as faults. We present the theoretical framework of our regularization methodology and illustrate its capabilities by means of both synthetic and field data sets. We further demonstrate how the concept has been integrated in our existing spatially constrained inversion formalism and show its application to large-scale time-domain electromagnetic data inversions.

Data repeatability and acquisition techniques for time-domain spectral induced polarization

The Time Domain Induced Polarization (TDIP) technique is widely used in applied geophysics, particularly for environmental issues, for instance for delineating landfills or detecting leachate percolation. Because the reliability of IP data remains an issue at the field scale, this paper deals with the factors controlling data quality and compares different arrays and acquisition parameters for optimal collection of data in the field. The first part focuses on repeatability experiments carried out in the former Horlokke landfill (Denmark), in order to infer the degree of which a signal can be reproduced over time. Results show a good repeatability, with on average less than 10% of difference in raw data. Also, from the results it is inferred that the paramount parameter controlling repeatability is the IP signal level; a value of 2 mV is a sufficient threshold to ensure repeatability within 10% of data difference, although system dependant. The second part focuses on survey design and underlines the importance of keeping the geometrical factor low. This points to the choice of a relevant measurement protocol, which depends on the threshold of the geometrical factor, again depending on expected chargeability and resistivity, threshold voltage and injected current. Furthermore, acquisition parameters such as the duration of the pulse injection and data sampling have a significant effect on both the signal-to-noise ratio and resolution. A comprehensive comparison between three protocols, the gradient array, the linear grid and the dipole-dipole array, is shown and the choice of an acquisition sequence is discussed.

Geophysical investigations at the Himera archaeological site, northern Sicily

In this paper we present a geophysical survey that was carried out as a research activity during field trips to the Himera archaeological site, where relics of a large Greek settlement are still buried, effected by a joint group of archaeologists and geophysicists during an educational project. Two-dimensional (2D) resistivity and ground-penetrating radar (GPR) surveys were performed to locate buried archaeological structures at this archaeological site. The results of the GPR surveys show some anomalies characterized by semi-hyperbolic shapes. In some restricted areas of the town, two grids of parallel GPR profiles were acquired while time- and depth-slices were calculated to identify the extension of the buried structures. In fact, the shapes of many anomalies recognized in the slices seem to describe the distribution of the relics (i.e. walls, roads, etc.). A 2D electrical resistivity profile showed clear anomalies, which were connected with wall-like relics. This was also obtained by using on-site calibration on partially uncovered structures, while the low background resistivity values were interpreted as representing river deposits having different moisture characteristics. Recommendations were also given to the archaeological site-excavators, following which some of the results were confirmed by subsequent archaeological excavations.

Spectral time-domain induced polarisation and magnetic surveying − an efficient tool for characterisation of solid waste deposits in developing countries

Time-domain induced polarisation and magnetic data were acquired to map and characterise the decommissioned and un-engineered municipal solid waste disposal site of the Kwame Nkrumah University of Science and Technology, located in the Kumasi Metropolis of Ghana. In this survey, 13 induced polarisation profiles 500–800 m long and 26 magnetic profiles 400–800 m long were acquired. In addition, two boreholes were drilled to help in the interpretation of the geophysical data. The study was carried out with the aim of determining the risk posed by the waste deposit to the quality of the soil and the ground water system, which is the main potable water supply for the Secondary School, the University Teaching Hospital and the Veterinary School, situated within the catchment area of the site. Full-decay 2-D time-domain induced polarisation inversions in terms of Cole–Cole parameters were used for interpreting the induced polarisation data. The chargeability, resistivity and normalised chargeability distributions, together with the magnetic results, aided in a full characterisation of the site geology, the waste and the associated pollution plume. In particular, clear contrasts in resistivity and the polarisation parameters were found between the saprolite layer and the granitic bedrock, which are the main lithological units of the area. Furthermore, it was found that the Kwame Nkrumah University of Science and Technology waste deposit is characterised by a low-chargeability and low-resistivity signature and that the low-resistivity area spreads out from the waste deposit into the permeable saprolite layer, indicating the presence of a leachate plume. A fracture zone in the granitic bedrock beneath the waste deposit, which is a potential conduit for leachate contamination of the ground water system, was also identified. The study thus provides the information needed for assessing the future impact of the waste on the water quality in the area and for designing risk-mitigation actions.

Depth of Investigation for Multi-parameters Inversions

We have developed a new robust concept for the calculation of the depth of investigation (DOI) for inversion problems described by several intrinsic parameters, like the spectral inversion of time-domain induced polarization data or the inversion of full-decay Nuclear Magnetic Resonance soundings. A calculation of the DOI is crucial for interpreting the geophysical models, as the validity of the model varies considerably with data noise and parameter distribution. Without the DOI estimate, it is difficult to judge when the information in the model is data-driven or is strongly dependent on the constraints and/or on the starting value. The proposed method is based on an approximated covariance analysis applied to the model output from the inversion while considering the data standard deviations. Furthermore, the cross-correlations between intrinsic parameters are taken into account in the computations, which is crucial when strong cross-correlations are expected. The new DOI estimate is described in detail and compared to the full covariance analysis on the model parameters using 2D spectral inversion of time-domain induced polarization data as an example. The DOI presented here behaves as anticipated on a synthetic model and is suggested as a general approach for model-spaces with more than one physical parameter.

Sharp Spatially Constrained Inversion

We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes this by allowing a reconstruction with a large number of layers, while preserving abrupt changes in the conductivity distribution. Instead of minimizing the norm of the vertical spatial variation of the model, in the focusing approach, it is the number of layers where the variations occur that is minimized. Thus, the results are compatible with the data and, at the same time, favor sharp transitions. The focusing strategy can also be used to constrain the 1D solutions laterally, guaranteeing that lateral sharp transitions are retrieved without losing resolution. By means of real and synthetic datasets, sharp inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user.

Mapping of Landfills Using Time-domain Spectral Induced Polarization Data - The Eskelund Case Study

This study uses time domain IP for the delineation and the characterization of the former Eskelund landfill, Denmark. With optimized acquisition parameters combined with a new inversion algorithm it is now possible to use the full content of the decay curve and retrieve spectral information from the time domain IP data. Thirteen IP/DC profiles were collected, supplemented by en el-log drilling for an accurate correlation between the geophysics and the lithology. The data were inverted using a laterally constrained 1D inversion considering the full decay curves to retrieve the four Cole-Cole parameters. For all profiles, the results reveal a highly chargeable unit with an impressive agreement to 15 boreholes. The thickness and the depths have been validated by el-log measurements giving in-situ values for the Cole-Cole parameters. The 3-D shape of the waste body has been delineated with a very high accuracy, and the south boundary of the landfill has been redefined based on these results. The inversion of the IP data also allows reconstruction of the waste history combining aerial maps with the results. Thus, this case study shows the relevance and the full benefits of using the TDIP data for the recognition and the characterization of landfill areas.

Integrated Geophysical Surveys in the Tarragona Cathedral

An integrated geophysical survey has been conducted at the Tarragona’s Cathedral (Catalonia, NE Spain) with the aim to detect the existence of archaeological remains of the Roman’s temple devoted to August. Many hypotheses have been proposed about its possible location, the last ones regarding the inner part of the Cathedral, which is one of the most famous temple of Spain (12th century) evolving from Romanesque to Gothic styles. A project including electrical resistivity tomography (ERT), ground probing radar (GPR) and frequency domain electromagnetics (FDEM) has been planned over one year and conducted during a week of intensive field survey. From all the methods applied, both ERT and GPR have provided some detailed information on subsoil structures. The ERT method has been applied with different techniques and arrays, ranging from standard Wenner-Schlumberger 2D sections to full 3D electrical imaging using the MYG array. Electrical resistivity data have been recorded extensively and therefore, 70.000 apparent resistivity data were available to obtain a full 3D image after an integrated inversion. In conclusion, some significant buried structures have been revealed providing conclusive information for archaeologists.