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Institute
Many geophysical inverse problems are known to be ill-posed and, thus, requiring some kind of regularization in order to provide a unique and stable solution. A possible approach to overcome the inversion ill-posedness consists in constraining the position of the model interfaces. For a grid-based parameterization, such a structurally constrained inversion can be implemented by adopting the usual smooth regularization scheme in which the local weight of the regularization is reduced where an interface is expected. By doing so, sharp contrasts are promoted at interface locations while standard smoothness constraints keep affecting the other regions of the model. In this work, we present a structurally constrained approach and test it on the inversion of frequency-domain electromagnetic induction (FD-EMI) data using a regularization approach based on the Minimum Gradient Support stabilizer, which is capable to promote sharp transitions everywhere in the model, i.e., also in areas where no structural a prioriinformation is available. Using 1D and 2D synthetic data examples, we compare the proposed approach to a structurally constrained smooth inversion as well as to more standard (i.e., not structurally constrained) smooth and sharp inversions. Our results demonstrate that the proposed approach helps in finding a better and more reliable reconstruction of the subsurface electrical conductivity distribution, including its structural characteristics. Furthermore, we demonstrate that it allows to promote sharp parameter variations in areas where no structural information are available. Lastly, we apply our structurally constrained scheme to FD-EMI field data collected at a field site in Eastern Germany to image the thickness of peat deposits along two selected profiles. In this field example, we use collocated constant offset ground-penetrating radar (GPR) data to derive structural a priori information to constrain the inversion of the FD-EMI data. The results of this case study demonstrate the effectiveness and flexibility of the proposed approach.
Information regarding the spatial distribution of soil water content is key in many disciplines and applications including soil and atmospheric sciences, hydrology, and agricultural engineering.
Thus, within the past decades various experimental methods and strategies have been developed to map spatial variations in soil moisture distribution and to monitor temporal changes.
Our study examines the combination of electrical resistivity mapping and point observations of soil moisture to infer the spatial and the temporal variability of soil moisture.
Over a period of around two years, we performed field measurements on six days to collect repeated electrical resistivity mapping data for a nine-hectare test site south-east of Berlin, Germany.
Permanently installed TDR probes, temporary TDR measurements within permanently installed tubes, and gravimetric measurements using soil samples provided soil moisture data at various selected points.
In addition, soil analysis and classification results are available for 132 regularly distributed positions up to depths of 1.2 m.
We compare and link three-dimensional resistivity models obtained via data inversion to soil composition and soil moisture as provided by our point data.
Both the soil samples and the resistivity models indicate a two-layer medium characterized by a sandy top layer with varying thickness and a loamy bottom soil.
For all six field campaigns, we observe similar resistivity patterns reflecting the temporally stable influence of soil texture.
While the overall patterns are stable, the range of resistivity values changes with soil moisture. Finally, to estimate spatial models of soil moisture, we link our soil moisture and resistivity data using empirical petrophysical models relying on a second order polynomial function.
We observe a mean prediction error for soil moisture of +/-0.034 m3 & BULL; m? 3 using all observation points while we notice that point-specific models further reduce the error.
Thus, we conclude that our experimental and data analysis strategies represent a reliable approach to establish site-specific models and to estimate three-dimensional moisture distribution including temporal variations.
A comprehensive workflow to analyze ensembles of globally inverted 2D electrical resistivity models
(2022)
Electrical resistivity tomography (ERT) aims at imaging the subsurface resistivity distribution and provides valuable information for different geological, engineering, and hydrological applications. To obtain a subsurface resistivity model from measured apparent resistivities, stochastic or deterministic inversion procedures may be employed. Typically, the inversion of ERT data results in non-unique solutions; i.e., an ensemble of different models explains the measured data equally well. In this study, we perform inference analysis of model ensembles generated using a well-established global inversion approach to assess uncertainties related to the nonuniqueness of the inverse problem. Our interpretation strategy starts by establishing model selection criteria based on different statistical descriptors calculated from the data residuals. Then, we perform cluster analysis considering the inverted resistivity models and the corresponding data residuals. Finally, we evaluate model uncertainties and residual distributions for each cluster. To illustrate the potential of our approach, we use a particle swarm optimization (PSO) algorithm to obtain an ensemble of 2D layer-based resistivity models from a synthetic data example and a field data set collected in Loon-Plage, France. Our strategy performs well for both synthetic and field data and allows us to extract different plausible model scenarios with their associated uncertainties and data residual distributions. Although we demonstrate our workflow using 2D ERT data and a PSObased inversion approach, the proposed strategy is general and can be adapted to analyze model ensembles generated from other kinds of geophysical data and using different global inversion approaches.
Frequency-domain electromagnetic (FDEM) data are commonly inverted to characterize subsurface geoelectrical properties using smoothness constraints in 1D inversion schemes assuming a layered medium.
Smoothness constraints are suitable for imaging gradual transitions of subsurface geoelectrical properties caused, for example, by varying sand, clay, or fluid content. However, such inversion approaches are limited in characterizing sharp interfaces. Alternative regularizations based on the minimum gradient support (MGS) stabilizers can, instead, be used to promote results with different levels of smoothness/sharpness selected by simply acting on the so-called focusing parameter.
The MGS regularization has been implemented for different kinds of geophysical data inversion strategies. However, concerning FDEM data, the MGS regularization has only been implemented for vertically constrained inversion (VCI) approaches but not for laterally constrained inversion (LCI) approaches.
We present a novel LCI approach for FDEM data using the MGS regularization for the vertical and lateral direction. Using synthetic and field data examples, we demonstrate that our approach can efficiently and automatically provide a set of model solutions characterized by different levels of sharpness and variable lateral consistencies.
In terms of data misfit, the obtained set of solutions contains equivalent models allowing us also to investigate the non-uniqueness of FDEM data inversion.
We have developed a 1D laterally constrained inversion of surface-wave dispersion curves based on the minimum gradient support regularization, which allows solutions with tunable sharpness in the vertical and horizontal directions. The forward modeling consists of a finite-elements approach incorporated in a flexible nonparametric gradient-based inversion scheme, which has already demonstrated good stability and convergence capabilities when tested on other kinds of data. Our deterministic inversion procedure is performed in the shear-wave velocity log space as we noticed that the associated Jacobian indicates a reduced model dependency, and this, in turn, decreases the risks of local nonconvexity. We show several synthetics and one field example to demonstrate the effectiveness and the applicability of the proposed approach.
Uplift in the broken Andean foreland of the Argentine Santa Bárbara System (SBS) is associated with the contractional reactivation of basement anisotropies, similar to those reported from the thick-skinned Cretaceous-Eocene Laramide province of North America. Fault scarps, deformed Quaternary deposits and landforms, disrupted drainage patterns, and medium-sized earthquakes within the SBS suggest that movement along these structures may be a recurring phenomenon, with yet to be defined repeat intervals and rupture lengths. In contrast to the Subandes thrust belt farther north, where eastward-migrating deformation has generated a well-defined thrust front, the SBS records spatiotemporally disparate deformation along structures that are only known to the first order. We present herein the results of geomorphic desktop analyses, structural field observations, and 2D electrical resistivity tomography and seismic-refraction tomography surveys and an interpretation of seismic reflection profiles across suspected fault scarps in the sedimentary basins adjacent to the Candelaria Range (CR) basement uplift, in the south-central part of the SBS. Our analysis in the CR piedmont areas reveals consistency between the results of near-surface electrical resistivity and seismic-refraction tomography surveys, the locations of prominent fault scarps, and structural geometries at greater depth imaged by seismic reflection data. We suggest that this deformation is driven by deep-seated blind thrusting beneath the CR and associated regional warping, while shortening involving Mesozoic and Cenozoic sedimentary strata in the adjacent basins was accommodated by layer-parallel folding and flexural-slip faults that cut through Quaternary landforms and deposits at the surface.
Uplift in the broken Andean foreland of the Argentine Santa Bárbara System (SBS) is associated with the contractional reactivation of basement anisotropies, similar to those reported from the thick-skinned Cretaceous-Eocene Laramide province of North America. Fault scarps, deformed Quaternary deposits and landforms, disrupted drainage patterns, and medium-sized earthquakes within the SBS suggest that movement along these structures may be a recurring phenomenon, with yet to be defined repeat intervals and rupture lengths. In contrast to the Subandes thrust belt farther north, where eastward-migrating deformation has generated a well-defined thrust front, the SBS records spatiotemporally disparate deformation along structures that are only known to the first order. We present herein the results of geomorphic desktop analyses, structural field observations, and 2D electrical resistivity tomography and seismic-refraction tomography surveys and an interpretation of seismic reflection profiles across suspected fault scarps in the sedimentary basins adjacent to the Candelaria Range (CR) basement uplift, in the south-central part of the SBS. Our analysis in the CR piedmont areas reveals consistency between the results of near-surface electrical resistivity and seismic-refraction tomography surveys, the locations of prominent fault scarps, and structural geometries at greater depth imaged by seismic reflection data. We suggest that this deformation is driven by deep-seated blind thrusting beneath the CR and associated regional warping, while shortening involving Mesozoic and Cenozoic sedimentary strata in the adjacent basins was accommodated by layer-parallel folding and flexural-slip faults that cut through Quaternary landforms and deposits at the surface.
In near- surface geophysics, ground-based mapping surveys are routinely used in a variety of applications including those from archaeology, civil engineering, hydrology, and soil science. The resulting geophysical anomaly maps of, for example, magnetic or electrical parameters are usually interpreted to laterally delineate subsurface structures such as those related to the remains of past human activities, subsurface utilities and other installations, hydrological properties, or different soil types. To ease the interpretation of such data sets, we have developed a multiscale processing, analysis, and visualization strategy. Our approach relies on a discrete redundant wavelet transform (RWT) implemented using cubic-spline filters and the a trous algorithm, which allows to efficiently compute a multiscale decomposition of 2D data using a series of 1D convolutions. The basic idea of the approach is presented using a synthetic test image, whereas our archaeogeophysical case study from northeast Germany demonstrates its potential to analyze and process rather typical geophysical anomaly maps including magnetic and topographic data. Our vertical-gradient magnetic data show amplitude variations over several orders of magnitude, complex anomaly patterns at various spatial scales, and typical noise patterns, whereas our topographic data show a distinct hill structure superimposed by a microtopographic stripe pattern and random noise. Our results demonstrate that the RWT approach is capable to successfully separate these components and that selected wavelet planes can be scaled and combined so that the reconstructed images allow for a detailed, multiscale structural interpretation also using integrated visualizations of magnetic and topographic data. Because our analysis approach is straightforward to implement without laborious parameter testing and tuning, computationally efficient, and easily adaptable to other geophysical data sets, we believe that it can help to rapidly analyze and interpret different geophysical mapping data collected to address a variety of near-surface applications from engineering practice and research.
The in-phase response collected by portable loop-loop electromagnetic induction (EMI) sensors operating at low and moderate induction numbers (<= 1) is typically used for sensing the magnetic permeability (or susceptibility) of the subsurface. This is due to the fact that the in-phase response contains a small induction fraction and a preponderant induced magnetization fraction. The magnetization fraction follows the magneto-static equations similarly to the magnetic method but with an active magnetic source. The use of an active source offers the possibility to collect data with several loop-loop configurations, which illuminate the subsurface with different sensitivity patterns. Such multiconfiguration soundings thereby allows the imaging of subsurface magnetic permeability/susceptibility variations through an inversion procedure. This method is not affected by the remnant magnetization and theoretically overcomes the classical depth ambiguity generally encountered with passive geomagnetic data. To invert multiconfiguration in-phase data sets, we propose a novel methodology based on a full-grid 3-D multichannel deconvolution (MCD) procedure. This method allows us to invert large data sets (e.g. consisting of more than a hundred thousand of data points) for a dense voxel-based 3-D model of magnetic susceptibility subject to smoothness constraints. In this study, we first present and discuss synthetic examples of our imaging procedure, which aim at simulating realistic conditions. Finally, we demonstrate the applicability of our method to field data collected across an archaeological site in Auvergne (France) to image the foundations of a Gallo-Roman villa built with basalt rock material. Our synthetic and field data examples demonstrate the potential of the proposed inversion procedure offering new and complementary ways to interpret data sets collected with modern EMI instruments.