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Information about soil water content (SWC) in adequate spatial and temporal resolution is highly desired for a variety of scientific and practical applications. Cosmic-Ray Neutron Sensing (CRNS) has become an established method for passive SWC data collection, providing SWC information over several hectares, either by stationary CRNS sensors (local continuous measurements) or by mobile CRNS roving (expanding the footprint on certain field campaign days). Recent approaches of automatic rail-based CRNS roving (Rail-CRNS) allowed to expand the monitored areas further up to the kilometer scale in high temporal resolution. While a pilot study on Rail-CRNS provided promising results along the railway track, currently in daily resolution, it also raised the question of how transferable these SWC data are for areas not directly adjacent to the footprints along the railway. In this study, we have tested the performance of SWC regionalization by probabilistic predictions based on Rail-CRNS derived SWC data. A Monte Carlo approach was applied in regression random forest, using static (e.g. topographical indices, soil properties) and dynamic (precipitation) predictors and quantified their impact on the prediction accuracy. Using daily SWC values from a ~ 9 km long railway at the Harz mountain, Germany, recorded by the Rail-CRNS between September 2021 and July 2022, we predicted the daily spatial SWC variation for an area of ~ 85 km² and a period of 300 days on a 250 x 250 m grid. The resulting maps of gravimetric soil moisture showed realistic pattern for both, spatial and temporal SWC variation. The maps resolved spatial variation as related to land cover, seasonal SWC dynamics and individual responses of single areas to wetting and drying periods. As the demonstrated data represented the outcome of a relatively narrow area as given by the limited training Rail-CRNS data, the extension of the proposed approach by expanding the railway networks, by future technical improvements and by the automatization of the workflow has the clear potential to offer near real time SWC products for the large scale (> 100 km).

Upscaling of soil water content (SWC) information towards the large-scale (>10 km) is highly desired to address the increasing demand on SWC products at various sectors. Random forest (RF) regression has been suggested as suitable method to generate large SWC maps from a limited amount of observations. RF deals with multiple prediction variables (predictors) to derive the missing values of a desired variable (e.g. SWC) based on their internal relationship. Cosmic ray neutron sensing (CRNS) is an alternative method for passive SWC mapping and monitoring, either by stationary CRNS sensors or by mobile CRNS roving. CRNS has a certain advantage over most classical hydrogeophysical approaches because of its footprint at the hectares-scale and beyond, particularly true for roving data, which qualifies CRNS data as suitable input for RF regressions. However, commonly CRNS roving data contain a high amount of noise and outlier values, related to the statistical distribution of neutron counting, which hinders the signal interpretation and could lower the quality of the RF regression performance. There are so far two ways to overcome the noise problem and to achieve a higher data stability; i) increasing of the aggregation time, which decreases the signal uncertainty but also reduces the spatial resolution and ii) applying smoothing algorithms, e.g. interpolation or moving averages, which results in more stable values, but it does not solve the outlier problem. We used SWC data from CRNS roving along the Selketal catchment at the Harz mountain, Germany, to test the performance of a score criteria for an adaptive removal of potential outliers. The score criteria are internal test parameters, providing an indication about the probability of values that might be an outlier or not. Therefore, each observation was subject to a group of queries, asking its conformity to the surrounding values by selected statistical parameters. Based on the total score of the queries, the potentially unreliable observations were removed using various thresholds and used as input for the RF regression. RF regression was performed using static (e.g. topographical indices, soil properties) and dynamic (precipitation) predictors generating SWC maps from an area of ~2700 km². SWC input data were split into training (~2/3) and validation sets (~1/3). Preliminary results showed that the application of the score criteria resulted in more stable spatial pattern and improved the R² from 0.099 to 0.196, 0.266 and 0.308 for score 6, 4 and 3, respectably. Achieved root mean squared error also decreased with stronger filtering, ranging from 0.14 for the original datasets to 0.078 for score 3. However, by using the score 3 threshold, 22.4% of the data were omitted. Hence, an optimization between the amount of excluded data and the resulting improvement of prediction needs to be developed and tested. The implementation of the spatial relationship in-between the observations and a weighting of the score values according to their importance should further increase the performance. Due to its easy application and its adjustable criteria selection, the proposed filtering approach has the potential to become more popular in CRNS roving studies.

The current handling of data in earth observation, modelling and prediction measures gives cause for critical consideration, since we all too often carelessly ignore data uncertainty. We think that Earth scientists are generally aware of the importance of linking data to quantitative uncertainty measures. But we also think that uncertainty quantification of Earth observation data too often fails at very early stages. We claim that data acquisition without uncertainty quantification is not sustainable and machine learning and computational modelling cannot unfold their potential when analysing complex natural systems like the Earth. Current approaches such as stochastic perturbation of parameters or initial conditions cannot quantify uncertainty or bias arising from the choice of model, limiting scientific progress. We need incentives stimulating the honest treatment of uncertainty starting during data acquisition, continuing through analysis methodology and prediction results. Computational modellers and machine learning experts have a critical role, since they enjoy high esteem from stakeholders and their methodologies and their results critically depend on data uncertainty. If both want to advance their uncertainty assessment of models and predictions of complex systems like the Earth, they have a common problem to solve. Together, computational modellers and machine learners could develop new strategies for bias identification and uncertainty quantification offering a more all-embracing uncertainty quantification than any known methodology. But since it starts for computational modellers and machine learners with data and their uncertainty, the fundamental first step in such a development would be leveraging shareholder esteem to insistently advocate for reduction of ignorance when it comes to uncertainty quantification of data.

For millennia, humans have gravitated towards coastlines for their resource potential and as geopolitical centres for global trade. A basic requirement ensuring water security for coastal communities relies on a delicate balance between the supply and demand of potable water. The interaction between freshwater and saltwater in coastal settings is, therefore, complicated by both natural and human-driven environmental changes at the land–sea interface. In particular, ongoing sea-level rise, warming and deoxygenation might exacerbate such perturbations. In this context, an improved understanding of the nature and variability of groundwater fluxes across the land–sea continuum is timely yet remains out of reach. The flow of terrestrial groundwater across the coastal transition zone and the extent of freshened groundwater below the present-day seafloor are receiving increased attention in marine and coastal sciences because they likely represent a significant yet highly uncertain component of (bio)geochemical budgets and because of the emerging interest in the potential use of offshore freshened groundwater as a resource. At the same time, “reverse” groundwater flux from offshore to onshore is of prevalent socio-economic interest, as terrestrial groundwater resources are continuously pressured by over-pumping and seawater intrusion in many coastal regions worldwide. An accurate assessment of the land–ocean connectivity through groundwater and its potential responses to future anthropogenic activities and climate change will require a multidisciplinary approach combining the expertise of geophysicists, hydrogeologists, (bio)geochemists and modellers. Such joint activities will lay the scientific basis for better understanding the role of groundwater in societally relevant issues such as climate change, pollution and the environmental status of the coastal oceans within the framework of the United Nations Sustainable Development Goals. Here, we present our perspectives on future research directions to better understand land–ocean connectivity through groundwater, including the spatial distributions of the essential hydrogeological parameters, highlighting technical and scientific developments and briefly discussing the societal relevance of that connectivity in rapidly changing coastal oceans.

Geoscientists invest significant effort to cope with uncertainty in Earth system observation and modeling. While general discussions exist about uncertainty and risk communication, judgment and decision-making, and science communication with regard to Earth sciences, in this article, we tackle uncertainty from the perspective of Earth science practitioners. We argue different scientific methodologies must be used to recognize all types of uncertainty inherent to a scientific finding. Following a discovery science methodology results in greater potential for the quantification of uncertainty associated to scientific findings than staying inside hypothesis-driven science methodology, as is common practice. Enabling improved uncertainty quantification could relax debates about risk communication and decision-making since it reduces the room for personality traits when communicating scientific findings.

Site characterization requires detailed and ideally spatially continuous information about the subsurface. Geophysical tomographic experiments allow for spatially continuous imaging of physical parameter variations, e.g., seismic wave propagation velocities. Such physical parameters are often related to typical geotechnical or hydrological target parameters, e.g. as achieved from 1D direct push or borehole logging. Here, the probabilistic inference of 2D tip resistance, sleeve friction, and relative dielectric permittivity distributions in near-surface sediments is constrained by ill-posed cross-borehole seismic P- and S-wave and radar wave traveltime tomography. In doing so, we follow a discovery science strategy employing a fully data-driven approach capable of accounting for tomographic ambiguity and differences in spatial resolution between the geophysical tomograms and the geotechnical logging data used for calibration. We compare the outcome to results achieved employing classical hypothesis-driven approaches, i.e., deterministic transfer functions derived empirically for the inference of 2D sleeve friction from S-wave velocity tomograms and theoretically for the inference of 2D dielectric permittivity from radar wave velocity tomograms. The data-driven approach offers maximal flexibility in combination with very relaxed considerations about the character of the expected links. This makes it a versatile tool applicable to almost any combination of data sets. However, error propagation may be critical and justify thinking about a hypothesis-driven pre-selection of an optimal database going along with the risk of excluding relevant information from the analyses. Results achieved by transfer function rely on information about the nature of the link and optimal calibration settings drawn as retrospective hypothesis by other authors. Applying such transfer functions at other sites turns them into a priori valid hypothesis, which can, particularly for empirically derived transfer functions, result in poor predictions. However, a mindful utilization and critical evaluation of the consequences of turning a retrospectively drawn hypothesis into an a priori valid hypothesis can also result in good results for inference and prediction problems when using classical transfer function concepts.

Uranium is a naturally occurring element that can be found almost everywhere in rocks and soils throughout the earth's crust. One of its decay products, radon, is of gaining concern in recent years because this colourless, odourless, tasteless gas is proven to be responsible for many lung cancer cases each year. Analysing the spatial distribution of the uranium concentration in the ground surface can help predict radon hazard regions. In this study, two types of uranium measurements – airborne gamma-ray spectrometry (AGRS) and ground-based rock sample analysis via inductively coupled plasma mass spectrometry (ICP-MS) – are calibrated for the purpose. The two types of data with different sampling schemes are found to have a reasonable correlation to each other when using the mapped geology as categorical units. This finding confirms the feasibility of using geological maps as a first-order predictor to map uranium, and further radon, in a larger scale. We then apply the self-organizing maps (SOM) technique for a data-driven classification of rock types based on the measured uranium content. The presented study area is located at mid-Norway in the Trondelag county, the same study will be performed in other regions across Norway where both types of measurements are in abundance. This study contributes to an on-going project to map radon hazard zones throughout Norway. While the radon hazard is defined by the indoor radon level which is affected by two folds of factors – geogenic (uranium-rich subsurface) and anthropogenic (dwelling type, indoor air exchange, etc.), our work aims to single out the geogenic factor. Comparing to the current national Radon Awareness Map of Norway (URL: http://geo.ngu.no/kart/radon/ ), where bedrocks were categorized by their likelihood of hosting elevated indoor radon, our approach utilizes measured uranium concentration of the ground which has a more direct link to the bedrock types.

Probabilistic prediction of 2D or 3D distributions of sparsely measured borehole or direct-push logging data can contribute to solving hydrological, petroleum, or engineering exploration tasks. We use and improve a recently developed workflow constrained by ill-posed geophysical tomography to achieve 2D probabilistic predictions of geotechnical exploration target parameters that could only be measured by 1D borehole or direct-push logging. We use artificial neural networks (ANNs) to find the optimal prediction models between ensembles of equivalent geophysical tomograms and sparsely measured logging data. During the training phase of ANNs, we consider four different training strategies taking into account the logging data uncertainty and geophysical tomographic ambiguity to avoid data overfitting of the ANNs. Thus, we successfully transform the logging data uncertainty and geophysical tomographic reconstruction ambiguity as well as differences in spatial resolution of logging and tomographic models into the probabilistic 2D prediction of our target parameters in a data-driven manner, which allows application of our methodology to any combination of geophysical tomograms and hydrologic, petroleum, or engineering target parameters solely measured in boreholes. To illustrate our workflow, we use an available field data set collected at a field site south of Berlin, Germany, to characterize near-subsurface sedimentary deposits. In this example, we employ cross-borehole tomographic radar-wave velocity, P-wave velocity, and S-wave velocity models to constrain the prediction of tip resistance, sleeve friction, and dielectric permittivity as target parameters.

Near-surface geophysical techniques are extensively used in a variety of engineering, environmental, geologic, and hydrologic applications. While many of these applications ask for detailed, quantitative models of selected material properties, geophysical data are increasingly used to estimate such target properties. Typically, this estimation procedure relies on a two-step workflow including (1) the inversion of geophysical data and (2) the petrophysical translation of the inverted parameter models into the target properties. Standard deterministic implementations of such a quantitative interpretation result in a single best-estimate model, often without considering and propagating the uncertainties related to the two steps. We address this problem by using a rather novel, particle-swarm-based global joint strategy for data inversion and by implementing Monte Carlo procedures for petrophysical property estimation. We apply our proposed workflow to crosshole ground-penetrating radar, P-, and S-wave data sets collected at a well-constrained test site for a detailed geotechnical characterization of unconsolidated sands. For joint traveltime inversion, the chosen global approach results in ensembles of acceptable velocity models, which are analyzed to appraise inversion-related uncertainties. Subsequently, the entire ensembles of inverted velocity models are considered to estimate selected petrophysical properties including porosity, bulk density, and elastic moduli via well-established petrophysical relations implemented in a Monte Carlo framework. Our results illustrate the potential benefit of such an advanced interpretation strategy; i.e., the proposed workflow allows to study how uncertainties propagate into the finally estimated property models, while concurrently we are able to study the impact of uncertainties in the used petrophysical relations (e.g., the influence of uncertain, user-specified parameters). We conclude that such statistical approaches for the quantitative interpretation of geophysical data can be easily extended and adapted to other applications and geophysical methods and might be an important step toward increasing the popularity and acceptance of geophysical tools in engineering practice.

In near surface sedimentary exploration direct push technology has become popular for geophysical logging. The method is thought to have great potential to offer accurate information about the variability of physical parameters since the region of disturbed sedimentary formation due to probe injection is considered to be smaller compared to disturbances by classical borehole measurements. Technical and experimental design of direct push probes follow often those of established borehole probes. A systematic appraisal of the suitability of such tools for direct push logging procedure exposing the probes to a very high mechanical stress and rapid aging process has been missing in the past. Following a recently developed general framework for direct push system decomposition we analyze two different DC resistivity direct push probes with regard to their sensor interface. Simple laboratory experiments validate the setup of a numerical simulation of both probes revealing significant differences on the suitability of the chosen electrode arrangement. Differences in robustness with regard to surface abrasion result in changing probe responses which could, depending on the experimental design of the probe, cause resistivity value changes of almost 25% within approximately 15 operational hours, which leaves severe doubts about the suitability of established direct push logging probes for quantitative geophysical probing.

Systematic decomposition and evaluation of existing sensor systems as well as the optimal design of future generations of direct push probes are of high importance for optimized geophysical experiments since the employed equipment is a constrain on the data space. Direct push technologies became established methods in the field of geophysical, geotechnical, hydrogeological, and environmental sciences for the investigation of the near subsurface. By using direct push sensor systems it is possible to measure in-situ parameters with high vertical resolution. Such information is frequently used for quantitative geophysical model calibration of interpretation of geotechnical and hydrological subsurface conditions. Most of the available direct push sensor systems are largely based on empirical testing and consecutively evaluated under field conditions. Approaches suitable to identify specific characteristics and problems of direct push sensor systems have not been established, yet. We develop a general systematic approach for the classification, analysis, and optimization of direct push sensor systems. First, a classification is presented for different existing sensor systems. The following systematic description, which is based on the conceptual decomposition of an existing sensor system into subsystems, is a suitable way to analyze and explore the transfer behavior of the system components and therefore of the complete system. Also, this approach may serve as guideline for the synthesis and the design of new and optimized direct push sensor systems.

This paper demonstrates a methodology for the automatic joint interpretation of high resolution airborne geophysical and space-borne remote sensing data to support geological mapping in a largely automated, fast and objective manner. At the request of the Geological Survey of Namibia (GSN), part of the Gordonia Subprovince of the Namaqua Metamorphic Belt situated in southern Namibia was selected for this study. All data – covering an area of 120 km by 100 km in size – were gridded, with a spacing of adjacent data points of only 200 m. The data points were coincident for all data sets. Published criteria were used to characterize the airborne magnetic data and to establish a set of attributes suitable for the recognition of linear features and their pattern within the study area. This multi-attribute analysis of the airborne magnetic data provided the magnetic lineament pattern of the study area. To obtain a (pseudo-) lithology map of the area, the high resolution airborne gamma-ray data were integrated with selected Landsat band data using unsupervised fuzzy partitioning clustering. The outcome of this unsupervised clustering is a classified (zonal) map which in terms of the power of spatial resolution is superior to any regional geological mapping. The classified zones are then assigned geological/geophysical parameters and attributes known from the study area, e.g. lithology, physical rock properties, age, chemical composition, geophysical field characteristics, etc. This information is obtained from the examination of archived geological reports, borehole logs, any kind of existing geological/geophysical data and maps as well as ground truth controls where deemed necessary. To obtain a confidence measure validating the unsupervised fuzzy clustering results and receive a quality criterion of the classified zones, stepwise linear discriminant analysis was chosen. Only a small percentage (8%) of the samples was misclassified by discriminant analysis when compared to the result obtained from unsupervised fuzzy clustering. Furthermore, a comparison of the aposterior probability of class assignment with the trustworthiness values provided by fuzzy clustering also indicates only slight differences. These observed differences can be explained by the exponential class probability term which tends to deliver either fairly high or low probability values. The methodology and results presented here demonstrate that automated objective pattern recognition can essentially contribute to geological mapping of large study areas and mineral exploration target generation. This methodology is considered well suited to a number of African countries whose large territories have recently been covered by high resolution airborne geophysical data, but where existing geological mapping is poor, incomplete or outdated.

Many hydrological, environmental, or engineering exploration tasks require predicting spatially continuous scenarios of sparsely measured borehole logging data. We present a methodology to probabilistically predict such scenarios constrained by ill-posed geophysical tomography. Our approach allows for transducing tomographic reconstruction ambiguity into the probabilistic prediction of spatially continuous target parameter scenarios. It is even applicable to data sets where petrophysical relations in the survey area are non-unique, i.e., different facies related petrophysical relations may be present. We employ static two-layer artificial neural networks (ANNs) for prediction and additionally evaluate, whether the training performance of the ANNs can be used to rank geophysical tomograms, which are mathematically equal reconstructions of physical parameter distributions in the ground. We illustrate our methodology using a realistic synthetic database for maximal control about the prediction performance and ranking potential of the approach. For doing so, we try to link geophysical radar and seismic tomography as input parameters to porosity of the ground as target parameter of ANN. However, the approach is flexible and can cope with any combination of geophysical tomograms and hydrologic, environmental or engineering target parameters. Ranking of equivalent geophysical tomograms based on additional borehole logging data is found to be generally possible, but risks remain that the ranking based on the ANN training performance does not fully coincide with the closeness of geophysical tomograms to ground truth. Since geophysical field data sets do usually not offer control options similar to those used in our synthetic database, we do not recommend the utilization of recurrent ANNs to learn weights for the individual geophysical tomograms used in the prediction procedure.

This article reflects discussions German and South African Earth scientists, statisticians and risk analysts had on occasion of two bilateral workshops on Data Integration Technologies for Earth System Modelling and Resource Management. The workshops were held in October 2012 at Leipzig, Germany, and April 2013 at Pretoria, South Africa, and were attended by about 70 researchers, practitioners and data managers of both countries. Both events were arranged as part of the South African-German Year of Science 2012/2013. The South African National Research Foundation (NRF, UID 81579) has supported the two workshops as part of the South African–German Year of Science activities 2012/2013 established by the German Federal Ministry of Education and Research and the South African Department of Science and Technology.

We integrate the information of multiple tomographic models acquired from the earth’s surface by modifying a statistical approach recently developed for the integration of cross-borehole tomographic models. In doing so, we introduce spectral cluster analysis as the new core of the model integration procedure to capture the spatial heterogeneity present in all considered tomographic models and describe this heterogeneity in a fuzzy sense. Because spectral cluster algorithms analyze model structure locally, they are considered relatively robust with regard to systematically and spatially varying imaging capabilities typical for geophysical tomographic surveys conducted on the earth’s surface. Using a synthetic aquifer example, a fuzzy spectral cluster algorithm can be used to integrate the information provided by 2D tomographic refraction seismic and DC resistivity surveys. The integrated information in the fuzzy membership domain is then used to derive an integrated zonal geophysical model outlining the major structural units present in both input models. We also explain how the fuzzy membership information can be used to identify optimal locations for sparse logging of additional target parameters, i.e., porosity information in our synthetic example. We demonstrate how this sparse porosity information can be extrapolated based on all tomographic input models. The resultant 2D porosity model matches the original porosity distribution reasonably well within the spatial resolution limits of the underlying tomographic models. Consecutively, we apply this approach to a field data base acquired over a former river channel. Sparse information about natural gamma radiation is available and extrapolated on the basis of the fuzzy membership information obtained by spectral cluster analysis of 2D P-wave velocity and electrical resistivity models. This field data shows that the presented parameter extrapolation procedure is robust, even if the locations of target parameter acquisition have not been optimized with regard to the fuzzy membership information.

Summary We present a new approach for 2 D probabilistic prediction of sparsely measured target parameters, e.g., measured by direct push technology or borehole logging. Geophysical tomography is used to constrain the prediction. The presented approach fully accounts for tomographic ambiguity and transduces it into prediction uncertainty. Furthermore, errors of the logging data can be considered to avoid overfitting when learning the optimal link between tomograms and logging data by means of Artificial Neural Networks. Consideration of errors results in improved predictions, which we exemplary illustrate here by 2D sleeve friction prediction.

We employ a recently developed data-driven approach to exemplary infer a probabilistic 2D sleeve friction model constrained by ill-posed geophysical tomographic imaging and laterally sparse cone penetration logging data. The integration and inference approach is based on fuzzy concepts and can fully cope with unknown and even non-unique inter-relations between geotechnical parameters, such as sleeve friction, and multiple physical properties imaged by fully non-linear geophysical tomography, e.g. ensembles of equivalent seismic or radar velocity models. Such data-driven integration and inference approaches can be applied to complex databases and do not require the a priori selection of tomographic data sets believed to be particularly closely linked to the target parameter, e.g., sleeve friction and seismic shear wave velocity tomograms. However, in the sense of error propagation incorporation of all available tomographic data sets may inflate the range of the final probabilistic prediction, which is not desirable. In turn, discarding data sets not expected to be physically linked to the target parameter may hamper predictions and potentially result in overseeing weak and yet unrecognized, but eventually existing, physical links, which could have improved the inference of probabilistic geotechnical target parameter models.

The fuzzy partitioning Gustafson-Kessel cluster algorithm is employed for rapid and objective integration of multi-parameter Earth-science related databases. We begin by evaluating the Gustafson-Kessel algorithm using the example of a synthetic study and compare the results to those obtained from the more widely employed fuzzy c-means algorithm. Since the Gustafson-Kessel algorithm goes beyond the potential of the fuzzy c-means algorithm by adapting the shape of the clusters to be detected and enabling a manual control of the cluster volume, we believe the results obtained from Gustafson-Kessel algorithm to be superior. Accordingly, a field database comprising airborne and ground-based geophysical data sets is analysed, which has previously been classified by means of the fuzzy c-means algorithm. This database is integrated using the Gustafson-Kessel algorithm thus minimising the amount of empirical data processing required before and after fuzzy c-means clustering. The resultant zonal geophysical map is more evenly clustered matching regional geology information available from the survey area. Even additional information about linear structures, e. g. as typically caused by the presence of dolerite dykes or faults, is visible in the zonal map obtained from Gustafson-Kessel cluster analysis.

In this study, we use and extend a recently developed zonal cooperative inversion approach and apply it to the inversion of three independent geophysical field data sets. We invert crosshole P-wave, S-wave, and georadar data sets acquired in sand and gravel dominated unconsolidated sediments to detect and characterize different sedimentary units relevant for an engineering or hydrological site characterization. The zonal cooperative inversion of the three traveltime data sets results in a single subsurface model, which is a geophysical three-parameter model (P-wave, S-wave, and georadar velocity) outlining the major subsurface zonation while explaining all input data sets. Comparing our zonal model to direct push (DP) logging data (tip resistance, sleeve friction, and dielectric permittivity) shows good agreement; i.e., the zones in our geophysical model largely correspond to major DP parameter changes. Furthermore, we demonstrate how the sparse DP data can be inter- and extrapolated to the entire tomographic plane which allows for further geotechnical and hydrological interpretations. This study illustrates that the zonal cooperative inversion approach is highly flexible and an excellent tool to characterize a variety of environments in terms of multiple physical parameters.

Partitioning cluster analyses are powerful tools for rapidly and objectively exploring and characterizing disparate geophysical databases with unknown interrelations between individual data sets or models. Despite its high potential to objectively extract the dominant structural information from suites of disparate geophysical data sets or models, cluster-analysis techniques are underused when analyzing geophysical data or models. This is due to the following limitations regarding the applicability of standard partitioning cluster algorithms to geophysical databases: The considered survey or model area must be fully covered by all data sets; cluster algorithms classify data in a multidimensional parameter space while ignoring spatial information present in the databases and are therefore sensitive to high-frequency spatial noise (outliers); and standard cluster algorithms such asfuzzy [Formula: see text]-means (FCM) or crisp [Formula: see text]-means classify data in an unsupervised manner, potentially ignoring expert knowledge additionally available to the experienced human interpreter. We address all of these issues by considering recent modifications to the standard FCM cluster algorithm to tolerate incomplete databases, i.e., survey or model areas not covered by all available data sets, and to consider spatial information present in the database. We have evaluated the regularized missing-value FCM cluster algorithm in a synthetic study and applied it to a database comprising partially colocated crosshole tomographic P- and S-wave-velocity models. Additionally, we were able to demonstrate how further expert knowledge can be incorporated in the cluster analysis to obtain a multiparameter geophysical model to objectively outline the dominant subsurface units, explaining all available geoscientific information.

Unsupervised classification techniques, such as cluster algorithms, are routinely used for structural exploration and integration of multiple frequency bands of remotely sensed spectral datasets. However, up to now, very few attempts have been made towards using unsupervised classification techniques for rapid, automated, and objective information extraction from large airborne geophysical data suites. We employ fuzzy c-means (FCM) cluster analysis for the rapid and largely automated integration of complementary geophysical datasets comprising airborne radiometric and magnetic as well as ground-based gravity data, covering a survey area of approximately 5000 km(2) located 100 km east- south-east of Johannesburg, South Africa, along the south-eastern limb of the Bushveld layered mafic intrusion complex. After preparatory data processing and normalisation, the three datasets are subjected to FCM cluster analysis, resulting in the generation of a zoned integrated geophysical map delineating distinct subsurface units based on the information the three input datasets carry. The fuzzy concept of the cluster algorithm employed also provides information about the significance of the identified zonation. According to the nature of the input datasets, the integrated zoned map carries information from near-surface depositions as well as rocks underneath the sediment cover. To establish a sound geological association of these zones we refer the zoned geophysical map to all available geological information, demonstrating that the zoned geophysical map as obtained from FCM cluster analysis outlines geological units that are related to Bushveld-type, other Proterozoic- and Karoo-aged rocks.

Collecting different geophysical data sets at the same object and site offers the opportunity to reduce uncertainties and ambiguities in data analysis and interpretation. To be effective, the different available data sets should be linked during the model-generation process, e.g. by cooperative inversion. In this study, we apply a recently developed zonal cooperative inversion approach based on fuzzy c-means cluster analysis to a non-destructive testing experiment. After briefly reviewing the fundamentals of the inversion strategy, we present a synthetic study investigating the potential of the method to detect air-filled voids in masonry by using ultrasonic and georadar traveltime data. Then, we present and discuss laboratory experiments including the results of cooperatively inverted ultrasonic and georadar traveltimes collected at a masonry test specimen. The geometry of the specimen is known and is thus an ideal test object for a first-time real application of the novel zonal cooperative inversion procedure. Compared to the results of separate inversions of ultrasonic and georadar traveltimes, the zonal cooperative inversion allows for an improved delineation of the size and position of the cavities. The P-wave and georadar velocities determined for the model regions corresponding to the cavities are also improved.

In many near-surface geophysical applications, it is now common practice to use multiple geophysical methods to explore subsurface structures and parameters. Such multimethod-based exploration strategies can significantly reduce uncertainties and ambiguities in geophysical data analysis and interpretation. We propose a novel 2D approach based on fuzzy [Formula: see text]-means cluster analysis for the cooperative inversion of disparate data sets. We show that this approach results in a single zonal model of subsurface structures in which each zone is characterized by a set of different parameters. This finding implies that no further structural interpretation of geophysical parameter fields is needed, which is a major advantage compared with conventional inversions that rely on a single input data set and cooperative inversion approaches.

Traditional approaches to surveying well catchments usually involve investigations at two quite different spatial scales: very high resolution borehole-based studies and low resolution tracer and pump tests. In recent years, various researchers have attempted to fill the wide gap between the two scales of acquired data by using a variety of geophysical tools that have high-to-medium resolution capabilities. Although geophysical surveying may be relatively straightforward at many locations, there are numerous regions where topography, the presence of ubiquitous metal objects and/or a lack of suitably placed boreholes cause the acquisition, processing, inversion and interpretation of certain types of geophysical data to be extremely challenging. It was neces- sary for us to address such problems in an investigation of an active well catchment near Zurich, Switzerland. The principal goals of our project were to determine the geometries and physical properties of the shallow sedimentary layers, with emphasis on a key water-bearing gravel unit. To achieve these goals, four different geophysical methods were employed. In a first step, frequency-domain electromagnetic measurements allowed the locations of buried metal pipes to be established. A 2D tomographic seismic refraction survey then provided information on the interface between the low-velocity surface loamy topsoil and underlying high-velocity morainal material. The high electrical resistivity of the important gravel unit allowed its upper boundary to be outlined in 2D models derived from geoelectric data and its lower boundary to be deline- ated in models based on 1D linked inversions of geoelectric and transient electromagnetic data.

We present a novel methodology to probabilistically predict spatial distributions of sparsely measured borehole logging data constrained by multiple geophysical crosshole tomograms. In doing so, we fully account for the ambiguity of the tomographic model reconstruction procedure by taking advantage of a recently developed fully non-linear inversion approach. We use Artificial Neural Networks to link the results of the non-linear inversion with sparse information of tip resistance logging data. Additionally, we achieve information during the training phase of the ANN about the compliancy of tomographic models found by the inversion with the available logging data, which may help to identify those tomographic models that may reconstruct the subsurface more realistically.

Technological advancements result in the continuous development of geophysical acquisition systems allowing for an ever-increasing amount of data recorded within a distinct time period. Current airborne geophysical databases covering intermediate sized survey areas comprise usually billions of digital readings. The sheer size of the available amount of information and rapid data acquisition capacities are increasing the pressure on Earth scientists to accelerate the data processing and information extraction procedures. We review the strength and weaknesses of current classical data analysis and integration approaches relying heavily on the skills and experience of a human interpreter and statistical approaches analyzing data sets strictly numerically. We highlight the need to develop new and intelligent data mining approaches suitable to combine and learn the strengths of the statistical and classical data analysis and integration approaches which may bear the potential to advance our understanding of geological processes and interrelations.

Inversions of an individual geophysical data set can be highly nonunique, and it is generally difficult to determine petrophysical parameters from geophysical data. We show that both issues can be addressed by adopting a statistical multiparameter approach that requires the acquisition, processing, and separate inversion of two or more types of geophysical data. To combine information contained in the physical-property models that result from inverting the individual data sets and to estimate the spatial distribution of petrophysical parameters in regions where they are known at only a few locations, we demonstrate the potential of the fuzzy [Formula: see text]-means (FCM) clustering technique. After testing this new approach on synthetic data, we apply it to limited crosshole georadar, crosshole seismic, gamma-log, and slug-test data acquired within a shallow alluvial aquifer. The derived multiparameter model effectively outlines the major sedimentary units observed in numerous boreholes and provides plausible estimates for the spatial distributions of gamma-ray emitters and hydraulic conductivity.

Geophysical techniques offer the potential to tomographically image physical parameter variations in the ground in two or three dimensions. Due to the limited number and accuracy of the recorded data, geophysical model generation by inversion suffers ambiguity. Linking the model generation process of disparate data by jointly inverting two or more data sets allows for improved model reconstruction. Fully nonlinear inversion using optimization techniques searching the solution space of the inverse problem globally enables quantitative assessment of the ambiguity inherent to the model reconstruction. We used two different multiobjective particle swarm optimization approaches to jointly invert synthetic crosshole tomographic data sets comprising radar and P-wave traveltimes, respectively. Beginning with a nonlinear joint inversion founded on the principle of Pareto optimality and game theoretic concepts, we obtained a set of Pareto-optimal solutions comprising commonly structured radar and P-wave velocity models for low computational costs. However, the efficiency of the approach goes along with some risk of achieving a final model ensemble not adequately illustrating the ambiguity inherent to the model reconstruction process. Taking advantage of the results of the first approach, we inverted the database using a different nonlinear joint-inversion approach reducing the multiobjective optimization problem to a single-objective one. Computational costs were significantly higher, but the final models were obtained mutually independently allowing for objective appraisal of model parameter determination. Despite the high computational effort, the approach was found to be an efficient nonlinear joint-inversion formulation compared to what could be extracted from individual nonlinear inversions of both data sets.

Near surface seismic imaging bears a high potential to enhance geotechnical site characterization. We highlight recent advances made in S-wave tomography for characterizing near surface unconsolidated sediments. This comprises progress in experimental setup and acquisition technology for local scale S-wave tomography. We discuss the development of mobile seismic crosshole tomography solely building on temporary installations realized by direct push technology as well as a modular borehole geophone chain suitable for operation in shallow and slim near surface boreholes. These technical developments are accompanied by progress in geophysical model generation, i.e., fully non-linear inversion strategies suitable for routine application and model uncertainty appraisal. We link S-wave and P-wave tomographic models to geotechnical target parameters and evaluate recent developments made for high resolution ground-truthing using direct push technology for geotechnical and stratigraphic analyses. To be able to provide improved regional scale seismic properties we advanced the Rayleigh wave based imaging of S-wave velocity variations using diffusive wavefield theory for modeling the full microtremor H/V spectral ratio for receivers at the surface and in depth.

Geophysical model reconstruction by data inversion is usually ill-posed and suffers ambiguity due to limited number and accuracy of the available observations. Joint inversion of different data sets allows for mutually improved reconstruction of physical parameter models underlying each of the available data sets, but considering the limited number and accuracy of available observations, some ambiguity remains. Here, we use particle swarm optimization to jointly invert synthetic GPR and P-wave crosshole tomographic data sets. Model parameterization is guided by the results of a zonal cooperative inversion based on local search optimization of an initial guess. Global optimization is first done to explore the Pareto front of the joint inverse problem in a very efficient way. Consecutively, the area behind a selected location of the Pareto front is explored to be able to assess the model reconstruction ambiguity inherent to the available data and chosen parameterization.

Joint inversion of different data sets is an increasingly popular strategy because it helps to reduce uncertainties and ambiguities in data analysis and interpretation. In this study, we use a particle swarm optimization (PSO) based inversion strategy to jointly invert crosshole P-wave and GPR traveltime data sets for the detailed characterization of near-surface sediments at a well-constrained test site in Horstwalde, Germany. At this site, the subsurface is characterized by sand- and gravel-dominated glaciofluvial sediments and exhibits a well-defined layering at the scale of our crosshole data, which allows for using a flexible layer-based model parametrization. Our inversion strategy includes the generation and analysis of a representative ensemble of acceptable models, which allows us to appraise uncertainties and non-uniqueness of the inverted velocity models. Analysing the final ensemble and comparing the resulting velocity models with borehole and direct-push (DP) data, demonstrates that the layered structure, which was found by PSO-based inverson, is in reasonable agreement with major variations in the borehole and DP-parameters. I am a PhD student and I would like to be considered for the AGAP-Quality Award.

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.

In many near-surface geophysical studies it is now common practice to collect co-located disparate geophysical data sets to explore subsurface structures. Reconstruction of physical parameter distributions underlying the available geophysical data sets usually requires the use of tomographic reconstruction techniques. To improve the quality of the obtained models, the information content of all data sets should be considered during the model generation process, e.g., by employing joint or cooperative inversion approaches. Here, we extend the zonal cooperative inversion methodology based on fuzzy c-means cluster analysis and conventional single-input data set inversion algorithms for the cooperative inversion of data sets with partially co-located model areas. This is done by considering recent developments in fuzzy c-means cluster analysis. Additionally, we show how supplementary a priori information can be incorporated in an automated fashion into the zonal cooperative inversion approach to further constrain the inversion. The only requirement is that this a priori information can be expressed numerically; e.g., by physical parameters or indicator variables. We demonstrate the applicability of the modified zonal cooperative inversion approach using synthetic and field data examples. In these examples, we cooperatively invert S- and P-wave traveltime data sets with partially co-located model areas using water saturation information expressed by indicator variables as additional a priori information. The approach results in a zoned multi-parameter model, which is consistent with all available information given to the zonal cooperative inversion and outlines the major subsurface units. In our field example, we further compare the obtained zonal model to sparsely available borehole and direct-push logs. This comparison provides further confidence in our zonal cooperative inversion model because the borehole and direct-push logs indicate a similar zonation.

Particle swarm optimization (PSO) is a relatively new global optimization approach inspired by the social behavior of birds and fishes. Although this approach has proven to provide excellent convergence rates in different optimization problems, it has seldom been used in geophysical inversion. Here, we propose a PSO-based inversion strategy to jointly invert GPR and P-wave seismic traveltimes from co-located crosshole experiments. Using a synthetic data example, we demonstrate the potential of our approach. Comparing our results to the input models as well as to velocity models found by separately inverting the data using a standard linearized inversion approach, illustrates the benefits of using an efficient global optimization approach for such a joint inversion problem. These include a straightforward appraisal of uncertainty, non-uniqueness, and resolution issues as well as the possibility of an improved and more objective interpretation.

We extend the zonal cooperative inversion (ZCI) approach based on fuzzy c-means cluster analysis and conventional single-input data set inversion algorithms for the cooperative inversion of data sets with partially co-located model areas. This is done by considering recent modifications made to the fuzzy c-means cluster algorithm. We apply the extended ZCI to cooperatively invert two crosshole tomographic traveltime data sets with partly co-located model areas. Additionally, we demonstrate how additional a priori information can be incorporated in the ZCI methodology. The ZCI results in a single geophysical model outlining the major subsurface zonation. Available ground-truth data support our zonal geophysical model and, thus, prove the applicability of the proposed inversion approach.

Cluster analyses are powerful tools for rapidly exploring disparate geophysical models with unknown interrelations. Despite its high potential to objectively extract the dominant structural information from suites of disparate geophysical models, cluster analysis techniques are not commonly used, yet, when analyzing suites of geophysical models. This is due to the following limitations: (i) The considered model area must be fully covered by all models subjected to cluster analysis, (ii) cluster algorithms usually ignore spatial information present in the data bases and are therefore sensitive to high-frequent spatial noise (outliers), and (iii) cluster algorithms, such as fuzzy c-means (FCM), classify data in an unsupervised fashion, potentially ignoring expert knowledge additionally available to the experienced human interpreter and not present in the geophysical data base. In this study, we address all of these issues by modifying and regularizing the standard FCM cluster algorithm to tolerate incomplete data bases incorporating model areas not covered by all available data sets and to consider spatial information present in the data base. We evaluate this new regularized missing value fuzzy c-means (RMVFCM) algorithm in a synthetic study and apply it to a field data base comprising partially co-located crosshole tomographic velocity models.