Zonation for 3D aquifer characterization based on joint inversions of multimethod crosshole geophysical data

Predictive groundwater modeling requires accurate information about aquifer characteristics. Geophysical imaging is a powerful tool for delineating aquifer properties at an appropriate scale and resolution, but it suffers from problems of ambiguity. One way to overcome such limitations is to adopt a simultaneous multitechnique inversion strategy. We have developed a methodology for aquifer characterization based on structural joint inversion of multiple geophysical data sets followed by clustering to form zones and subsequent inversion for zonal parameters. Joint inversions based on cross-gradient structural constraints require less restrictive assumptions than, say, applying predefined petro-physical relationships and generally yield superior results. This approach has, for the first time, been applied to three geophysical data types in three dimensions. A classification scheme using maximum likelihood estimation is used to determine the parameters of a Gaussian mixture model that defines zonal geometries from joint-inversion tomograms. The resulting zones are used to estimate representative geophysical parameters of each zone, which are then used for field-scale petrophysical analysis. A synthetic study demonstrated how joint inversion of seismic and radar traveltimes and electrical resistance tomography (ERT) data greatly reduces misclassification of zones (down from 21.3% to 3.7%) and improves the accuracy of retrieved zonal parameters (from 1.8% to 0.3%) compared to individual inversions. We applied our scheme to a data set collected in northeastern Switzerland to delineate lithologic subunits within a gravel aquifer. The inversion models resolve three principal subhorizontal units along with some important 3D heterogeneity. Petro-physical analysis of the zonal parameters indicated approximately 30% variation in porosity within the gravel aquifer and an increasing fraction of finer sediments with depth.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Implementing statistical learning methods through Bayesian networks. Part 1: a guide to Bayesian parameter estimation using forensic science data

As a thorough aggregation of probability and graph theory, Bayesian networks currently enjoy widespread interest as a means for studying factors that affect the coherent evaluation of scientific evidence in forensic science. Paper I of this series of papers intends to contribute to the discussion of Bayesian networks as a framework that is helpful for both illustrating and implementing statistical procedures that are commonly employed for the study of uncertainties (e.g. the estimation of unknown quantities). While the respective statistical procedures are widely described in literature, the primary aim of this paper is to offer an essentially non-technical introduction on how interested readers may use these analytical approaches - with the help of Bayesian networks - for processing their own forensic science data. Attention is mainly drawn to the structure and underlying rationale of a series of basic and context-independent network fragments that users may incorporate as building blocs while constructing larger inference models. As an example of how this may be done, the proposed concepts will be used in a second paper (Part II) for specifying graphical probability networks whose purpose is to assist forensic scientists in the evaluation of scientific evidence encountered in the context of forensic document examination (i.e. results of the analysis of black toners present on printed or copied documents).

Full-waveform inversion of cross-hole ground-penetrating radar data to characterize a gravel aquifer close to the Thur River, Switzerland

Cross-hole radar tomography is a useful tool for mapping shallow subsurface electrical properties viz. dielectric permittivity and electrical conductivity. Common practice is to invert cross-hole radar data with ray-based tomographic algorithms using first arrival traveltimes and first cycle amplitudes. However, the resolution of conventional standard ray-based inversion schemes for cross-hole ground-penetrating radar (GPR) is limited because only a fraction of the information contained in the radar data is used. The resolution can be improved significantly by using a full-waveform inversion that considers the entire waveform, or significant parts thereof. A recently developed 2D time-domain vectorial full-waveform crosshole radar inversion code has been modified in the present study by allowing optimized acquisition setups that reduce the acquisition time and computational costs significantly. This is achieved by minimizing the number of transmitter points and maximizing the number of receiver positions. The improved algorithm was employed to invert cross-hole GPR data acquired within a gravel aquifer (4-10 m depth) in the Thur valley, Switzerland. The simulated traces of the final model obtained by the full-waveform inversion fit the observed traces very well in the lower part of the section and reasonably well in the upper part of the section. Compared to the ray-based inversion, the results from the full-waveform inversion show significantly higher resolution images. At either side, 2.5 m distance away from the cross-hole plane, borehole logs were acquired. There is a good correspondence between the conductivity tomograms and the natural gamma logs at the boundary of the gravel layer and the underlying lacustrine clay deposits. Using existing petrophysical models, the inversion results and neutron-neutron logs are converted to porosity. Without any additional calibration, the values obtained for the converted neutron-neutron logs and permittivity results are very close and similar vertical variations can be observed. The full-waveform inversion provides in both cases additional information about the subsurface. Due to the presence of the water table and associated refracted/reflected waves, the upper traces are not well fitted and the upper 2 m in the permittivity and conductivity tomograms are not reliably reconstructed because the unsaturated zone is not incorporated into the inversion domain.

Constraining 3-D electrical resistance tomography with GPR reflection data forimproved aquifer characterization

Surface-based ground penetrating radar (GPR) and electrical resistance tomography (ERT) are common tools for aquifer characterization, because both methods provide data that are sensitive to hydrogeologically relevant quantities. To retrieve bulk subsurface properties at high resolution, we suggest incorporating structural information derived from GPR reflection data when inverting surface ERT data. This reduces resolution limitations, which might hinder quantitative interpretations. Surface-based GPR reflection and ERT data have been recorded on an exposed gravel bar within a restored section of a previously channelized river in northeastern Switzerland to characterize an underlying gravel aquifer. The GPR reflection data acquired over an area of 240×40 m map the aquifer's thickness and two internal sub-horizontal regions with different depositional patterns. The interface between these two regions and the boundary of the aquifer with then underlying clay are incorporated in an unstructured ERT mesh. Subsequent inversions are performed without applying smoothness constraints across these boundaries. Inversion models obtained by using these structural constraints contain subtle resistivity variations within the aquifer that are hardly visible in standard inversion models as a result of strong vertical smearing in the latter. In the upper aquifer region, with high GPR coherency and horizontal layering, the resistivity is moderately high (N300 Ωm). We suggest that this region consists of sediments that were rearranged during more than a century of channelized flow. In the lower low coherency region, the GPR image reveals fluvial features (e.g., foresets) and generally more heterogeneous deposits. In this region, the resistivity is lower (~200 Ωm), which we attribute to increased amounts of fines in some of the well-sorted fluvial deposits. We also find elongated conductive anomalies that correspond to the location of river embankments that were removed in 2002.

An approach to predicting bowing control parameter contours in violin performance

We present a machine learning approach to modeling bowing control parametercontours in violin performance. Using accurate sensing techniqueswe obtain relevant timbre-related bowing control parameters such as bowtransversal velocity, bow pressing force, and bow-bridge distance of eachperformed note. Each performed note is represented by a curve parametervector and a number of note classes are defined. The principal componentsof the data represented by the set of curve parameter vectors are obtainedfor each class. Once curve parameter vectors are expressed in the new spacedefined by the principal components, we train a model based on inductivelogic programming, able to predict curve parameter vectors used for renderingbowing controls. We evaluate the prediction results and show the potentialof the model by predicting bowing control parameter contours from anannotated input score.

Geological structure, recharge processes and underground drainage of a glacierised karst aquifer system, Tsanfleuron-Sanetsch, Swiss Alps

The relationships between stratigraphic and tectonic setting, recharge processes and underground drainage of the glacierised karst aquifer system `Tsanfleuron-Sanetsch' in the Swiss Alps have been studied by means of various methods, particularly tracer tests (19 injections). The area belongs to the Helvetic nappes and consists of Jurassic to Palaeogene sedimentary rocks. Strata are folded and form a regional anticlinorium. Cretaceous Urgonian limestone constitutes the main karst aquifer, overlain by a retreating glacier in its upper part. Polished limestone surfaces are exposed between the glacier front and the end moraine of 1855/1860 (Little Ice Age); typical alpine karrenfields can be observed further below. Results show that (1) large parts of the area are drained by the Glarey spring, which is used as a drinking water source, while marginal parts belong to the catchments of other springs; (2) groundwater flow towards the Glarey spring occurs in the main aquifer, parallel to stratification, while flow towards another spring crosses the entire stratigraphic sequence, consisting of about 800 m of marl and limestone, along deep faults that were probably enlarged by mass movements; (3) the variability of glacial meltwater production influences the shape of the tracer breakthrough curves and, consequently, flow and transport in the aquifer.

Statistical modeling of violin bowing parameter contours

We present a framework for modeling right-hand gestures in bowed-string instrument playing, applied to violin. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing gesture parameter cues. We model the temporal contour of bow transversal velocity, bow pressing force, and bow-bridge distance as sequences of short segments, in particular B´ezier cubic curve segments. Considering different articulations, dynamics, andcontexts, a number of note classes is defined. Gesture parameter contours of a performance database are analyzed at note-level by following a predefined grammar that dictatescharacteristics of curve segment sequences for each of the classes into consideration. Based on dynamic programming, gesture parameter contour analysis provides an optimal curve parameter vector for each note. The informationpresent in such parameter vector is enough for reconstructing original gesture parameter contours with significant fidelity. From the resulting representation vectors, weconstruct a statistical model based on Gaussian mixtures, suitable for both analysis and synthesis of bowing gesture parameter contours. We show the potential of the modelby synthesizing bowing gesture parameter contours from an annotated input score. Finally, we point out promising applicationsand developments.

Analysis of sensitivity with respect to a compositional parameter : A comment on 'Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling' by L. Loosvelt and co-authors

A comment about the article “Local sensitivity analysis for compositional data with application to soil texture in hydrologic modelling” writen by L. Loosvelt and co-authors. The present comment is centered in three specific points. The first one is related to the fact that the authors avoid the use of ilr-coordinates. The second one refers to some generalization of sensitivity analysis when input parameters are compositional. The third tries to show that the role of the Dirichlet distribution in the sensitivity analysis is irrelevant

Detection and characterization of hydraulically active fractures in a carbonate aquifer: Results from self-potential, temperature and fluid conductivity logging along a 260-m-deep borehole in the Combioula hydrothermal system in the southwestern Swiss Alps

A geophysical and geochemical study has been conducted in a fractured carbonate aquifer located at Combioula in the southwestern Swiss Alps with the objective to detect and characterize hydraulically active fractures along a 260-m-deep borehole. Hydrochemical analyses, borehole diameter, temperature and fluid electrical conductivity logging data were integrated in order to relate electrokinetic self-potential signals to groundwater flow inside the fracture network. The results show a generally good, albeit locally variable correlation of variations of the self-potential signals with variations in temperature, fluid electrical conductivity and borehole diameter. Together with the hydrochemical evidence, which was found to be critical for the interpretation of the self-potential data, these measurements not only made it possible to detect the hydraulically active fractures but also to characterize them as zones of fluid gain or fluid loss. The results complement the available information from the corresponding litholog and illustrate the potential of electrokinetic self-potential signals in conjunction with temperature, fluid electrical conductivity and hydrochemical analyses for the characterization of fractured aquifers, and thus may offer a perspective for an effective quantitative characterization of this increasingly important class of aquifers and geothermal reservoirs.

3D crosshole ERT for aquifer characterization and monitoring of infiltrating river water

The hydrogeological properties and responses of a productive aquifer in northeastern Switzerland are investigated. For this purpose, 3D crosshole electrical resistivity tomography (ERT) is used to define the main lithological structures within the aquifer (through static inversion) and to monitor the water infiltration from an adjacent river. During precipitation events and subsequent river flooding, the river water resistivity increases. As a consequence, the electrical characteristics of the infiltrating water can be used as a natural tracer to delineate preferential flow paths and flow velocities. The focus is primarily on the experiment installation, data collection strategy, and the structural characterization of the site and a brief overview of the ERT monitoring results. The monitoring system comprises 18 boreholes each equipped with 10 electrodes straddling the entire thickness of the gravel aquifer. A multi-channel resistivity system programmed to cycle through various four-point electrode configurations of the 180 electrodes in a rolling sequence allows for the measurement of approximately 15,500 apparent resistivity values every 7 h on a continuous basis. The 3D static ERT inversion of data acquired under stable hydrological conditions provides a base model for future time-lapse inversion studies and the means to investigate the resolving capability of our acquisition scheme. In particular, it enables definition of the main lithological structures within the aquifer. The final ERT static model delineates a relatively high-resistivity, low-porosity, intermediate-depth layer throughout the investigated aquifer volume that is consistent with results from well logging and seismic and radar tomography models. The next step will be to define and implement an appropriate time-lapse ERT inversion scheme using the river water as a natural tracer. The main challenge will be to separate the superposed time-varying effects of water table height, temperature, and salinity variations associated with the infiltrating water.

Quantitative multi-parameter mapping of R1, PD(*), MT, and R2(*) at 3T: a multi-center validation.

Multi-center studies using magnetic resonance imaging facilitate studying small effect sizes, global population variance and rare diseases. The reliability and sensitivity of these multi-center studies crucially depend on the comparability of the data generated at different sites and time points. The level of inter-site comparability is still controversial for conventional anatomical T1-weighted MRI data. Quantitative multi-parameter mapping (MPM) was designed to provide MR parameter measures that are comparable across sites and time points, i.e., 1 mm high-resolution maps of the longitudinal relaxation rate (R1 = 1/T1), effective proton density (PD(*)), magnetization transfer saturation (MT) and effective transverse relaxation rate (R2(*) = 1/T2(*)). MPM was validated at 3T for use in multi-center studies by scanning five volunteers at three different sites. We determined the inter-site bias, inter-site and intra-site coefficient of variation (CoV) for typical morphometric measures [i.e., gray matter (GM) probability maps used in voxel-based morphometry] and the four quantitative parameters. The inter-site bias and CoV were smaller than 3.1 and 8%, respectively, except for the inter-site CoV of R2(*) (<20%). The GM probability maps based on the MT parameter maps had a 14% higher inter-site reproducibility than maps based on conventional T1-weighted images. The low inter-site bias and variance in the parameters and derived GM probability maps confirm the high comparability of the quantitative maps across sites and time points. The reliability, short acquisition time, high resolution and the detailed insights into the brain microstructure provided by MPM makes it an efficient tool for multi-center imaging studies.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

Monte Carlo Methods in Parameter Estimation of Nonlinear Models

Yksi keskeisimmistä tehtävistä matemaattisten mallien tilastollisessa analyysissä on mallien tuntemattomien parametrien estimointi. Tässä diplomityössä ollaan kiinnostuneita tuntemattomien parametrien jakaumista ja niiden muodostamiseen sopivista numeerisista menetelmistä, etenkin tapauksissa, joissa malli on epälineaarinen parametrien suhteen. Erilaisten numeeristen menetelmien osalta pääpaino on Markovin ketju Monte Carlo -menetelmissä (MCMC). Nämä laskentaintensiiviset menetelmät ovat viime aikoina kasvattaneet suosiotaan lähinnä kasvaneen laskentatehon vuoksi. Sekä Markovin ketjujen että Monte Carlo -simuloinnin teoriaa on esitelty työssä siinä määrin, että menetelmien toimivuus saadaan perusteltua. Viime aikoina kehitetyistä menetelmistä tarkastellaan etenkin adaptiivisia MCMC menetelmiä. Työn lähestymistapa on käytännönläheinen ja erilaisia MCMC -menetelmien toteutukseen liittyviä asioita korostetaan. Työn empiirisessä osuudessa tarkastellaan viiden esimerkkimallin tuntemattomien parametrien jakaumaa käyttäen hyväksi teoriaosassa esitettyjä menetelmiä. Mallit kuvaavat kemiallisia reaktioita ja kuvataan tavallisina differentiaaliyhtälöryhminä. Mallit on kerätty kemisteiltä Lappeenrannan teknillisestä yliopistosta ja Åbo Akademista, Turusta.