Optimized and robust experimental design: a non-linear application to EM sounding

Pragmatic experimental design requires objective consideration of several classes of information including the survey goals, the range of expected Earth responses, acquisition costs, instrumental capabilities, experimental conditions and logistics. In this study we consider the ramifications of maximizing model parameter resolution through non-linear experimental design. Global optimization theory is employed to examine and rank different EM sounding survey designs in terms of model resolution as defined by linearized inverse theory. By studying both theoretically optimal and heuristic experimental survey configurations for various quantities of data, it is shown that design optimization is critical for minimizing model variance estimates, and is particularly important when the inverse problem becomes nearly underdetermined. We introduce the concept of robustness so that survey designs are relatively immune to the presence of potential bias errors in important data. Bias may arise during practical measurement, or from designing a survey using an appropriate mode

Boundary element solutions for broad-band 3-D geo-electromagnetic problems accelerated by an adaptive multilevel fast multipole method

We have developed a generalized and stable surface integral formula for 3-D uniform inducing field and plane wave electromagnetic induction problems, which works reliably over a wide frequency range. Vector surface electric currents and magnetic currents, scalar surface electric charges and magnetic charges are treated as the variables. This surface integral formula is successfully applied to compute the electromagnetic responses of 3-D topography to low frequency magnetotelluric and high frequency radio-magnetotelluric fields. The standard boundary element method which is used to solve this surface integral formula quickly exceeds the memory capacity of modern computers for problems involving hundreds of thousands of unknowns. To make the surface integral formulation applicable and capable of dealing with large-scale 3-D geo-electromagnetic problems, we have developed a matrix-free adaptive multilevel fast multipole boundary element solver. By means of the fast multipole approach, the time-complexity of solving the final system of linear equations is reduced to O(m log m) and the memory cost is reduced to O(m), where m is the number of unknowns. The analytical solutions for a half-space model were used to verify our numerical solutions over the frequency range 0.001-300kHz. In addition, our numerical solution shows excellent agreement with a published numerical solution for an edge-based finite-element method on a trapezoidal hill model at a frequency of 2Hz. Then, a high frequency simulation for a similar trapezoidal hill model was used to study the effects of displacement currents in the radio-magnetotelluric frequency range. Finally, the newly developed algorithm was applied to study the effect of moderate topography and to evaluate the applicability of a 2-D RMT inversion code that assumes a flat air-Earth interface, on RMT field data collected at Smørgrav, southern Norway. This paper constitutes the first part of a hybrid boundary element-finite element approach to compute the electromagnetic field inside structures involving complex 3-D conductivity and permittivity distribution

A Synthetic Study to Assess the Applicability of Full-Waveform Inversion to Infer Snow Stratigraphy from Upward-Looking Ground-Penetrating Radar Data

Snow stratigraphy and liquid water content are key contributing factors to avalanche formation. Upward-looking ground penetrating radar (upGPR) systems allow nondestructive monitoring of the snowpack, but deriving density and liquid water content profiles is not yet possible based on the direct analysis of the reflection response. We have investigated the feasibility of deducing these quantities using full-waveform inversion (FWI) techniques applied to upGPR data. For that purpose, we have developed a frequency-domain FWI algorithm in which we additionally took advantage of time-domain features such as the arrival times of reflected waves. Our results indicated that FWI applied to upGPR data is generally feasible. More specifically, we could show that in the case of a dry snowpack, it is possible to derive snow densities and layer thicknesses if sufficient a priori information is available. In case of a wet snowpack, in which it also needs to be inverted for the liquid water content, the algorithm might fail, even if sufficient a priori information is available, particularly in the presence of realistic noise. Finally, we have investigated the capability of FWI to resolve thin layers that play a key role in snow stability evaluation. Our simulations indicate that layers with thicknesses well below the GPR wavelengths can be identified, but in the presence of significant liquid water, the thin-layer properties may be prone to inaccuracies. These results are encouraging and motivate applications to field data, but significant issues remain to be resolved, such as the determination of the generally unknown upGPR source function and identifying the optimal number of layers in the inversion models. Furthermore, a relatively high level of prior knowledge is required to let the algorithm converge. However, we feel these are not insurmountable and the new technology has significant potential to improve field data analysis

Comparison of seismic velocities derived from crystal orientation fabrics and ultrasonic measurements on an ice core

&amp;lt;p&amp;gt;Understanding the internal structure of glacier ice is of high interest for studying ice flow mechanics and glacier dynamics. The micro-scale deformation mechanisms cause a reorientation and alignment of the ice grains resulting in a polycrystalline structure with a strong anisotropy. By studying the crystal orientation fabric (COF), details about past and ongoing ice deformation processes can be derived. Usually, obtaining COF requires a work-intensive ice core analysis, which is typically carried out only at a few ice core samples. When similar information can be obtained from geophysical, for example, seismic experiments, a more detailed and more continuous image about the ice deformation would be available. &amp;lt;br&amp;gt;For checking the suitability of seismic data for such purposes, we have analysed the COF of several ice core samples extracted from Rhone Glacier, a temperate glacier located in the Central Swiss Alps. The COF analysis yield a polycrystalline elasticity tensor for a given volume of ice, from which we predicted seismic velocities for acoustic waves originating from any azimuth and inclination. The seismic data predicted were then verified with ultrasonic experiments conducted along the ice core in the vicinity of the analysed COF. Additional X-ray tomographic measurements yield further constraints about the microstructure, especially about the air bubble content in the ice affecting the data of the ultrasonic experiments. Predicted and measured velocities generally show a good match. This is a very encouraging result, because it suggests that in-situ measurements of seismic velocities can be employed for studying ice deformation. A possible option is to perform seismic cross-hole measurements within an array of boreholes drilled into the glacier ice.&amp;lt;/p&amp;gt; </jats:p

Ultrasonic velocity experiments on ice cores to complement fabric measurements

&amp;lt;p&amp;gt;The ice crystal structure and in particular the crystal orientation fabrics (COF) provide valuable information about the deformation history of ice sheets and glaciers. Therefore, COF analysis has been among the standard measurement techniques for most deep ice core drilling projects in the last three decades. The analysis depends on carefully prepared thin sections of ice that are measured with cross-polarised light microscopy or electron backscattering and diffraction (EBSD). The preparation of thin sections is labour-intensive and therefore only a discrete number of samples along the ice core is usually analysed. Geophysical methods such as ultrasonic sounding along the ice core could be employed to complement the discrete fabric data by providing data to fill the gaps. A suitable method needs to be reasonably fast, ideally non-invasive and provides unambiguous information in combination with the established methods.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;In our study, we demonstrate the feasibility of such ultrasonic experiments applied to an ice core to support the approved cross-polarised light microscopy method. Point-contact transducers transmitted ultrasonic waves into ice core samples from a temperate glacier. X-ray computer tomography measurements provide the required information to consider the effect of a two-phase medium (ice and air bubbles) in a porosity correction of the velocity. We determined the azimuthal variation of the seismic velocity. This variation is a result of seismic anisotropy due to the crystal orientation within the ice core volume. The measurements can be acquired within minutes and do not require an extensive preparation of ice samples.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;In addition, the COF of adjacent ice core samples was measured with cross-polarised light spectroscopy. From this, we derived the elasticity tensor and finally calculated the associated seismic velocities for the same azimuth and inclination angle as for the ultrasonic experiments. We compare these two velocity profiles and discover a significant discrepancy in presence of large ice grains. However, with an increasing number of ice grains both methods provide similar results. Although the ultrasonic measurements reveal some ambiguities, these can be resolved when considering the information derived from the standard analysis.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;We conclude that ultrasonic measurements along the ice core are suitable to support the established COF analysis for sufficiently small grains as found in polar cores. We recommend further exploration of the potential of the presented technique as it provides both the chance to obtain a continuous fabric profile and a direct link to large-scale seismic measurements in the vicinity of ice core drilling sites.&amp;lt;/p&amp;gt;</jats:p

A simple anisotropy correction procedure for acoustic wood tomography

Anisotropy of acoustic propagation velocities is a ubiquitous feature of wood. This needs to be considered for successful application of travel time tomography, an increasingly popular technique for non-destructive testing of living trees. We have developed a simple correction scheme that removes first-order anisotropy effects. The corrected travel-time data can be inverted with isotropic inversion codes that are commercially available. Using a numerical experiment, we demonstrate the consequences of ignoring anisotropy effects and outline the performance of our correction scheme. The new technique has been applied to two spruce samples. Subsequent inspection of the samples revealed a good match with the tomogram

Crystallographic analysis of temperate ice on Rhonegletscher, Swiss Alps

Crystal orientation fabric (COF) analysis provides information about the c-axis orientation of ice grains and the associated anisotropy and microstructural information about deformation and recrystallisation processes within the glacier. This information can be used to introduce modules that fully describe the microstructural anisotropy or at least direction-dependent enhancement factors for glacier modelling. The COF was studied at an ice core that was obtained from the temperate Rhonegletscher, located in the central Swiss Alps. Seven samples, extracted at depths between 2 and 79 m, were analysed with an automatic fabric analyser. The COF analysis revealed conspicuous four-maxima patterns of the c-axis orientations at all depths. Additional data, such as microstructural images, produced during the ice sample preparation process, were considered to interpret these patterns. Furthermore, repeated high-precision global navigation satellite system (GNSS) surveying allowed the local glacier flow direction to be determined. The relative movements of the individual surveying points indicated longitudinal compressive stresses parallel to the glacier flow. Finally, numerical modelling of the ice flow permitted estimation of the local stress distribution. An integrated analysis of all the data sets provided indications and suggestions for the development of the four-maxima patterns. The centroid of the four-maxima patterns of the individual core samples and the coinciding maximum eigenvector approximately align with the compressive stress directions obtained from numerical modelling with an exception for the deepest sample. The clustering of the c axes in four maxima surrounding the predominant compressive stress direction is most likely the result of a fast migration recrystallisation. This interpretation is supported by air bubble analysis of large-area scanning macroscope (LASM) images. Our results indicate that COF studies, which have so far predominantly been performed on cold ice samples from the polar regions, can also provide valuable insights into the stress and strain rate distribution within temperate glaciers

Interpolation of landslide movements to improve the accuracy of 4D geoelectrical monitoring

Measurement sensors permanently installed on landslides will inevitably change their position over time due to mass movements. To interpret and correct the recorded data, these movements have to be determined. This is especially important in the case of geoelectrical monitoring, where incorrect sensor positions produce strong artefacts in the resulting resistivity models. They may obscure real changes, which could indicate triggering mechanisms for landslide failure or reactivation. In this paper we introduce a methodology to interpolate movements from a small set of sparsely distributed reference points to a larger set of electrode locations. Within this methodology we compare three interpolation techniques, i.e., a piecewise planar, bi-linear spline, and a kriging based interpolation scheme. The performance of these techniques is tested on a synthetic and a real-data example, showing a recovery rate of true movements to about 1% and 10% of the electrode spacing, respectively. The significance for applying the proposed methodology is demonstrated by inverse modelling of 4D electrical resistivity tomography data, where it is shown that by correcting for sensor movements corresponding artefacts can virtually be removed and true resistivity changes be imaged

Continuous monitoring of the temporal evolution of the snowpack using upward-looking ground penetrating radar technology

Snow stratigraphy and water percolation are key parameters in avalanche forecasting. It is, however, difficult to model or measure stratigraphy and water flow in a sloping snowpack. Numerical modeling results depend highly on the type and availability of input data and the parameterization of the physical processes. Furthermore, the sensors themselves may influence the snowpack or be destroyed due to snow gliding and avalanches. Radar technology allows non-destructive scanning of the snowpack and deducing internal snow properties. If the radar system is buried in the ground, it cannot be destroyed by avalanche impacts or snow creep. During the winter seasons 2010-2011 and 2011-2012 we recorded continuous data with upward-looking pulsed radar systems (upGPR) at two test sites. We demonstrate that it is possible to determine the snow height with an accuracy comparable to conventional snow depth measuring devices. We determined the bulk volumetric liquid water content and tracked the position of the first stable wetting front. Wet-snow avalanche activity increased, when melt water penetrated deeper into the snowpack