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Direct current systems employing a kinematic surveying strategy allow to analyze the electrical resistivity of the subsurface for large areas (i.e., several hectares). Typical applications are found in precision agriculture, archaeological prospecting and soil sciences. With the typical survey setting, the collected data sets are often characterized by a rather high level of noise and a rather coarse lateral sampling compared to data acquired with fixed electrodes. We therefore present an efficient one-dimensional inversion approach in which we put special attention on modeling the effects of noise. We apply this method to data recorded with a five-offset equatorial dipole-dipole system employing rolling electrodes. By performing several synthetic tests with realistic noise levels, we found that the considered five-configuration soundings allow for a reliable imaging of two-layer cases in the uppermost two meters of the subsurface, where the subsurface can be assumed to follow a horizontally layered geometry within 3 m around the system. By analyzing the corresponding sensitivity functions, we also show that the equatorial dipole-dipole array is relatively well suited for a 1D inversion approach compared to standard in-line electrode arrays. To illustrate this aspect, we show that our method can provide results similar to those obtained with a 2D Wenner imaging procedure for data recorded across a well-constrained 2D target. We finally apply our method to a large five-offset data set acquired in an agricultural study. The final pseudo-3D model of electrical resistivity is in accordance with borehole data available for the surveyed area. Our results demonstrate the applicability and the versatility of the presented inversion approach for large-scale data sets as they are typically collected with such rolling electrode systems. (C) 2017 Elsevier B.V. All rights reserved.
We present an algorithm that performs sequentially one-dimensional inversion of subsurface magnetic permeability and electrical conductivity by using multi-configuration electromagnetic induction sensor data. The presented method is based on the conversion of the in-phase and out-of-phase data into effective magnetic permeability and electrical conductivity of the equivalent homogeneous half-space. In the case of small-offset systems, such as portable electromagnetic induction sensors, for which in-phase and out-of-phase data are moderately coupled, the effective half-space magnetic permeability and electrical conductivity can be inverted sequentially within an iterative scheme. We test and evaluate the proposed inversion strategy using synthetic and field examples. First, we apply it to synthetic data for some highly magnetic environments. Then, the method is tested on real field data acquired in a basaltic environment to image a formation of archaeological interest. These examples demonstrate that a joint interpretation of in-phase and out-of-phase data leads to a better characterisation of the subsurface in magnetic environments such as volcanic areas.
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.
Ground-penetrating radar (GPR) is a standard geophysical technique used to image near-surface structures in sedimentary environments. In such environments, GPR data acquisition and processing are increasingly following 3D strategies. However, the processed GPR data volumes are typically still interpreted using selected 2D slices and manual concepts such as GPR facies analyses. In seismic volume interpretation, the application of (semi-)automated and reproducible approaches such as 3D attribute analyses as well as the production of attribute-based facies models are common practices today. In contrast, the field of 3D GPR attribute analyses and corresponding facies models is largely untapped. We have developed and applied a workflow to produce 3D attribute-based GPR facies models comprising the dominant sedimentary reflection patterns in a GPR volume, which images complex sandy structures on the dune island of Spiekeroog (Northern Germany). After presenting our field site and details regarding our data acquisition and processing, we calculate and filter 3D texture attributes to generate a database comprising the dominant texture features of our GPR data. Then, we perform a dimensionality reduction of this database to obtain meta texture attributes, which we analyze and integrate using composite imaging and (also considering additional geometric information) fuzzy c-means cluster analysis resulting in a classified GPR facies model. Considering our facies model and a corresponding GPR facies chart, we interpret our GPR data set in terms of near-surface sedimentary units, the corresponding depositional environments, and the recent formation history at our field site. Thus, we demonstrate the potential of our workflow, which represents a novel and clear strategy to perform a more objective and consistent interpretation of 3D GPR data collected across different sedimentary environments.
Ice complex deposits are characteristic, ice-rich formations in northern East Siberia and represent an important part in the arctic carbon pool. Recently, these late Quaternary deposits are the objective of numerous investigations typically relying on outcrop and borehole data. Many of these studies can benefit from a 3D structural model of the subsurface for upscaling their observations or for constraining estimations of inventories, such as the local carbon stock. We have addressed this problem of structural imaging by 3D ground-penetrating radar (GPR), which, in permafrost studies, has been primarily used for 2D profiling. We have used a 3D kinematic GPR surveying strategy at a field site located in the New Siberian Archipelago on top of an ice complex. After applying a 3D GPR processing sequence, we were able to trace two horizons at depths below 20 m. Taking available borehole and outcrop data into account, we have interpreted these two features as interfaces of major lithologic units and derived a 3D cryostratigraphic model of the subsurface. Our data example demonstrated that a 3D surveying and processing strategy was crucial at our field site and showed the potential of 3D GPR to image geologic structures in complex ice-rich permafrost landscapes.
Ground-penetrating radar (GPR) is an established geophysical tool to explore a wide range of near-surface environments. Today, the use of synthetic GPR data is largely limited to 2D because 3D modeling is computationally more expensive. In fact, only recent developments of modeling tools and powerful hardware allow for a time-efficient computation of extensive 3D data sets. Thus, 3D subsurface models and resulting GPR data sets, which are of great interest to develop and evaluate novel approaches in data analysis and interpretation, have not been made publicly available up to now. <br /> We use a published hydrofacies data set of an aquifer-analog study within fluvio-glacial deposits to infer a realistic 3D porosity model showing heterogeneities at multiple spatial scales. Assuming fresh-water saturated sediments, we generate synthetic 3D GPR data across this model using novel GPU-acceleration included in the open-source software gprMax. We present a numerical approach to examine 3D wave-propagation effects in modeled GPR data. Using the results of this examination study, we conduct a spatial model decomposition to enable a computationally efficient 3D simulation of a typical GPR reflection data set across the entire model surface. We process the resulting GPR data set using a standard 3D structural imaging sequence and compare the results to selected input data to demonstrate the feasibility and potential of the presented modeling studies. We conclude on conceivable applications of our 3D GPR reflection data set and the underlying porosity model, which are both publicly available and, thus, can support future methodological developments in GPR and other near-surface geophysical techniques.
Flow phenomena in the unsaturated zone are highly variable in time and space. Thus, it is challenging to measure and monitor such processes under field conditions. Here, we present a new setup and interpretation approach for combining a dye tracer experiment with a 4D ground-penetrating radar (GPR) survey. Therefore, we designed a rainfall experiment during which we measured three surface-based 3D GPR surveys using a pair of 500 MHz antennas. Such a survey setup requires accurate acquisition and processing techniquesto extract time-lapse information supporting the interpretation of selected cross-sections photographed after excavating the site. Our results reveal patterns of traveltime changes in the measured GPR data, which are associated with soil moisture changes. As distinct horizons are present at our site, such changes can be quantified and transferred into changes in total soil moisture content. Our soil moisture estimates are similar to the amount of infiltrated water, which confirms our experimental approach and makes us confident for further developing this strategy, especially, with respect to improving the temporal and spatial resolution. (C) 2015 Elsevier B.V. All rights reserved.
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.
Assessing uncertainty in refraction seismic traveltime inversion using a global inversion strategy
(2015)
To analyse and invert refraction seismic travel time data, different approaches and techniques have been proposed. One common approach is to invert first-break travel times employing local optimization approaches. However, these approaches result in a single velocity model, and it is difficult to assess the quality and to quantify uncertainties and non-uniqueness of the found solution. To address these problems, we propose an inversion strategy relying on a global optimization approach known as particle swarm optimization. With this approach we generate an ensemble of acceptable velocity models, i.e., models explaining our data equally well. We test and evaluate our approach using synthetic seismic travel times and field data collected across a creeping hillslope in the Austrian Alps. Our synthetic study mimics a layered near-surface environment, including a sharp velocity increase with depth and complex refractor topography. Analysing the generated ensemble of acceptable solutions using different statistical measures demonstrates that our inversion strategy is able to reconstruct the input velocity model, including reasonable, quantitative estimates of uncertainty. Our field data set is inverted, employing the same strategy, and we further compare our results with the velocity model obtained by a standard local optimization approach and the information from a nearby borehole. This comparison shows that both inversion strategies result in geologically reasonable models (in agreement with the borehole information). However, analysing the model variability of the ensemble generated using our global approach indicates that the result of the local optimization approach is part of this model ensemble. Our results show the benefit of employing a global inversion strategy to generate near-surface velocity models from refraction seismic data sets, especially in cases where no detailed a priori information regarding subsurface structures and velocity variations is available.
Analysis of time-lapse ground-penetrating radar (GPR) data can provide information regarding subsurface hydrological processes, such as preferential flow. However, the analysis of time-lapse data is often limited by data quality; for example, for noisy input data, the interpretation of difference images is often difficult. Motivated by modern image-processing tools, we have developed two robust GPR attributes, which allow us to distinguish amplitude (contrast similarity) and time-shift (structural similarity) variations related to differences between individual time-lapse GPR data sets. We tested and evaluated our attributes using synthetic data of different complexity. Afterward, we applied them to a field data example, in which subsurface flow was induced by an artificial rainfall event. For all examples, we identified our structural similarity attribute to be a robust measure for highlighting time-lapse changes also in data with low signal-to-noise ratios. We determined that our new attribute-based workflow is a promising tool to analyze time-lapse GPR data, especially for imaging subsurface hydrological processes.
Enhancing the resolution and accuracy of surface ground-penetrating radar (GPR) reflection data by inverse filtering to recover a zero-phased band-limited reflectivity image requires a deconvolution technique that takes the mixed-phase character of the embedded wavelet into account. In contrast, standard stochastic deconvolution techniques assume that the wavelet is minimum phase and, hence, often meet with limited success when applied to GPR data. We present a new general-purpose blind deconvolution algorithm for mixed-phase wavelet estimation and deconvolution that (1) uses the parametrization of a mixed-phase wavelet as the convolution of the wavelet's minimum-phase equivalent with a dispersive all-pass filter, (2) includes prior information about the wavelet to be estimated in a Bayesian framework, and (3) relies on the assumption of a sparse reflectivity. Solving the normal equations using the data autocorrelation function provides an inverse filter that optimally removes the minimum-phase equivalent of the wavelet from the data, which leaves traces with a balanced amplitude spectrum but distorted phase. To compensate for the remaining phase errors, we invert in the frequency domain for an all-pass filter thereby taking advantage of the fact that the action of the all-pass filter is exclusively contained in its phase spectrum. A key element of our algorithm and a novelty in blind deconvolution is the inclusion of prior information that allows resolving ambiguities in polarity and timing that cannot be resolved using the sparseness measure alone. We employ a global inversion approach for non-linear optimization to find the all-pass filter phase values for each signal frequency. We tested the robustness and reliability of our algorithm on synthetic data with different wavelets, 1-D reflectivity models of different complexity, varying levels of added noise, and different types of prior information. When applied to realistic synthetic 2-D data and 2-D field data, we obtain images with increased temporal resolution compared to the results of standard processing.
Modern mobile devices (i.e. smartphones and tablet computers) are widespread, everyday tools, which are equipped with a variety of sensors including three-axis magnetometers. Here, we investigate the feasibility and the potential of using such mobile devices to mimic geophysical experiments in the classroom in a table-top setup. We focus on magnetic surveying and present a basic setup of a table-top experiment for collecting three-component magnetic data across well-defined source bodies and structures. Our results demonstrate that the quality of the recorded data is sufficient to address a number of important basic concepts in the magnetic method. The shown examples cover the analysis of magnetic data recorded across different kinds of dipole sources, thus illustrating the complexity of magnetic anomalies. In addition, we analyze the horizontal resolution capabilities using a pair of dipole sources placed at different horizontal distances to each other. Furthermore, we demonstrate that magnetic data recorded with a mobile device can even be used to introduce filtering, transformation, and inversion approaches as they are typically used when processing magnetic data sets recorded for real-world field applications. Thus, we conclude that such table-top experiments represent an easy-to-implement experimental procedure (as student exercise or classroom demonstration) and can provide first hands-on experience in the basic principles of magnetic surveying including the fundamentals of data acquisition, analysis and processing, as well as data evaluation and interpretation.
Crosshole traveltime tomography using particle swarm optimization a near-surface field example
(2012)
Particle swarm optimization (PSO) is a relatively new global optimization approach inspired by the social behavior of bird flocking and fish schooling. Although this approach has proven to provide excellent convergence rates in different optimization problems, it has seldom been applied to inverse geophysical problems. Until today, published geophysical applications mainly focus on finding an optimum solution for simple, 1D inverse problems. We have applied PSO-based optimization strategies to reconstruct 2D P-wave velocity fields from crosshole traveltime data sets. Our inversion strategy also includes generating and analyzing a representative ensemble of acceptable models, which allows us to appraise uncertainty and nonuniqueness issues. The potential of our strategy was tested on field data collected at a well-constrained test site in Horstwalde, Germany. At this field site, the shallow subsurface mainly consists of sand- and gravel-dominated glaciofluvial sediments, which, as known from several boreholes and other geophysical experiments, exhibit some well-defined layering at the scale of our crosshole seismic data. Thus, we have implemented a flexible, layer-based model parameterization, which, compared with standard cell-based parameterizations, allows for significantly reducing the number of unknown model parameters and for efficiently implementing a priori model constraints. Comparing the 2D velocity fields resulting from our PSO strategy to independent borehole and direct-push data illustrated the benefits of choosing an efficient global optimization approach. These include a straightforward and understandable appraisal of nonuniqueness issues as well as the possibility of an improved and also more objective interpretation.
Ground-based magnetic surveying is a common geophysical method to explore near-surface environments in a non-destructive manner. In many typical applications (such as archaeological prospection), the resulting anomaly maps are often characterized by low signal-to-noise ratios and, thus, the suppression of noise is a key step in data processing. Here, we propose the steering kernel regression (SKR) method to denoise magnetic data sets. SKR has been recently developed to suppress random noise in images and video sequences. The core of the method is the steering kernel function which represents a robust estimate of local image structure. Using such a kernel within an iterative regression based denoising framework, helps to minimize image blurring and to preserve the underlying structures such as edges and corners. Because such filter characteristics are desirable for random noise attenuation in potential field data sets, we apply the SKR method for processing high-resolution ground-based magnetic data as they are typically collected in archaeological applications. We test and evaluate the SKR method using synthetic and field data examples and also compare it to more commonly employed denoising strategies relying, for example, on fixed filter masks (e.g., Gaussian filters). Our results show that the SKR method is successful in removing random and acquisition related noise present in our data. Concurrently, it preserves the local image structure including the amplitudes of anomalies. As demonstrated by derivative based transformations, the mentioned filter characteristics significantly impact subsequent processing steps and, therefore, result in an improved analysis and interpretation of magnetic data. Thus, the method can be considered as a promising and novel approach for denoising ground-based magnetic data.
In an attempt to map the shallow geometry of the Maleme Fault Zone (North Island, New Zealand) and estimate vertical displacements of selected fault strands, we have collected 2D and 3D georadar data using 100 MHz antennae. The 2D data consisted of three parallel georadar lines recorded perpendicular to the axis of the well-defined graben of the Maleme Fault Zone. These similar to 160 in long lines, which were 7.5 m apart, crossed several fault strands on either side of the graben axis. The processed georadar sections revealed two prominent parallel reflections that originated from the boundaries of Late Pleistocene lacustrine and tephra deposits. Distinct vertical offsets of these reflections allowed us to estimate displacernents at individual fault strands across the entire inner graben. The total displacements represented by these offsets was similar to 10-20% greater than that inferred from geomorphological studies, thus demonstrating the limitations of surface observations for determining cumulative fault movements. The 3D georadar data set, recorded across an area of similar to 70x similar to 20 in to one side of the graben axis, provided key details on individual fault strands. For the 3D visualization of fault-related structures, various spatial attribute analyses based on the cosine of the instantaneous phase proved to be useful
There are far-reaching conceptual similarities between bi-static surface georadar and post-stack, "zero-offset" seismic reflection data, which is expressed in largely identical processing flows. One important difference is, however, that standard deconvolution algorithms routinely used to enhance the vertical resolution of seismic data are notoriously problematic or even detrimental to the overall signal quality when applied to surface georadar data. We have explored various options for alleviating this problem and have tested them on a geologically well-constrained surface georadar dataset. Standard stochastic and direct deterministic deconvolution approaches proved to be largely unsatisfactory. While least-squares-type deterministic deconvolution showed some promise, the inherent uncertainties involved in estimating the source wavelet introduced some artificial "ringiness". In contrast, we found spectral balancing approaches to be effective, practical and robust means for enhancing the vertical resolution of surface georadar data, particularly, but not exclusively, in the uppermost part of the georadar section, which is notoriously plagued by the interference of the direct air- and groundwaves. For the data considered in this study, it can be argued that band- limited spectral blueing may provide somewhat better results than standard band-limited spectral whitening, particularly in the uppermost part of the section affected by the interference of the air- and groundwaves. Interestingly, this finding is consistent with the fact that the amplitude spectrum resulting from least-squares-type deterministic deconvolution is characterized by a systematic enhancement of higher frequencies at the expense of lower frequencies and hence is blue rather than white. It is also consistent with increasing evidence that spectral "blueness" is a seemingly universal, albeit enigmatic, property of the distribution of reflection coefficients in the Earth. Our results therefore indicate that spectral balancing techniques in general and spectral blueing in particular represent simple, yet effective means of enhancing the vertical resolution of surface georadar data and, in many cases, could turn out to be a preferable alternative to standard deconvolution approaches.
Sea level rise and coastal erosion have inundated large areas of Arctic permafrost. Submergence by warm and saline waters increases the rate of inundated permafrost thaw compared to sub-aerial thawing on land. Studying the contact between the unfrozen and frozen sediments below the seabed, also known as the ice-bearing permafrost table (IBPT), provides valuable information to understand the evolution of sub-aquatic permafrost, which is key to improving and understanding coastal erosion prediction models and potential greenhouse gas emissions. In this study, we use data from 2D electrical resistivity tomography (ERT) collected in the nearshore coastal zone of two Arctic regions that differ in their environmental conditions (e.g., seawater depth and resistivity) to image and study the subsea permafrost. The inversion of 2D ERT data sets is commonly performed using deterministic approaches that favor smoothed solutions, which are typically interpreted using a user-specified resistivity threshold to identify the IBPT position. In contrast, to target the IBPT position directly during inversion, we use a layer-based model parameterization and a global optimization approach to invert our ERT data. This approach results in ensembles of layered 2D model solutions, which we use to identify the IBPT and estimate the resistivity of the unfrozen and frozen sediments, including estimates of uncertainties. Additionally, we globally invert 1D synthetic resistivity data and perform sensitivity analyses to study, in a simpler way, the correlations and influences of our model parameters. The set of methods provided in this study may help to further exploit ERT data collected in such permafrost environments as well as for the design of future field experiments.
Sea level rise and coastal erosion have inundated large areas of Arctic permafrost. Submergence by warm and saline waters increases the rate of inundated permafrost thaw compared to sub-aerial thawing on land. Studying the contact between the unfrozen and frozen sediments below the seabed, also known as the ice-bearing permafrost table (IBPT), provides valuable information to understand the evolution of sub-aquatic permafrost, which is key to improving and understanding coastal erosion prediction models and potential greenhouse gas emissions. In this study, we use data from 2D electrical resistivity tomography (ERT) collected in the nearshore coastal zone of two Arctic regions that differ in their environmental conditions (e.g., seawater depth and resistivity) to image and study the subsea permafrost. The inversion of 2D ERT data sets is commonly performed using deterministic approaches that favor smoothed solutions, which are typically interpreted using a user-specified resistivity threshold to identify the IBPT position. In contrast, to target the IBPT position directly during inversion, we use a layer-based model parameterization and a global optimization approach to invert our ERT data. This approach results in ensembles of layered 2D model solutions, which we use to identify the IBPT and estimate the resistivity of the unfrozen and frozen sediments, including estimates of uncertainties. Additionally, we globally invert 1D synthetic resistivity data and perform sensitivity analyses to study, in a simpler way, the correlations and influences of our model parameters. The set of methods provided in this study may help to further exploit ERT data collected in such permafrost environments as well as for the design of future field experiments.
Electromagnetic induction (EMI) sensors using sufficiently low-frequency harmonic sources and sufficiently small loop separations operate in the low-induction-number (LIN) domain for a relatively wide range of background conductivity. These systems are used in diverse near-surface investigations including applications from soil sciences, hydrology, and archaeology. The special case of portable multiconfiguration EMI sensors operating at frequencies <= 20 kHz offers the possibility of using a fast linear deconvolution method to interpret multichannel data sets in three dimensions. Here, we have developed a fast 3D inversion/deconvolution method regularized with 3D smoothness constraints and formulated in the hybrid spectral-spatial domain. Compared with other linear approaches, the spectral-spatial domain formulation significantly reduces the computational cost of the processing and opens the door for real-time 3D interpretation of large data sets consisting of more than 100,000 data points. First, we test our proposed algorithm on synthetic data sets computed with the full Maxwell theory. Then, we apply our method to a real four-configuration EMI data set acquired to map the thickness of peat layers embedded in a sandy environment. For the synthetic and the field example, we compared our result with the result obtained using a standard point-by-point 1D nonlinear inversion approach. This comparison demonstrates that the proposed methodology provides superior lateral resolution compared with the 1D nonlinear inversion, at the same time significantly reducing the computational cost of the processing.
Foreword
(2019)