Source wavelet estimation for waveform inversion of crosshole georadar data

AbstractFor a wide range of environmental, hydrological, and engineering applications there is a fast growing need for high-resolution imaging. In this context, waveform tomographic imaging of crosshole georadar data is a powerful method able to provide images of pertinent electrical properties in near-surface environments with unprecedented spatial resolution. In contrast, conventional ray-based tomographic methods, which consider only a very limited part of the recorded signal (first-arrival traveltimes and maximum first-cycle amplitudes), suffer from inherent limitations in resolution and may prove to be inadequate in complex environments. For a typical crosshole georadar survey the potential improvement in resolution when using waveform-based approaches instead of ray-based approaches is in the range of one order-of- magnitude. Moreover, the spatial resolution of waveform-based inversions is comparable to that of common logging methods. While in exploration seismology waveform tomographic imaging has become well established over the past two decades, it is comparably still underdeveloped in the georadar domain despite corresponding needs. Recently, different groups have presented finite-difference time-domain waveform inversion schemes for crosshole georadar data, which are adaptations and extensions of Tarantola's seminal nonlinear generalized least-squares approach developed for the seismic case. First applications of these new crosshole georadar waveform inversion schemes on synthetic and field data have shown promising results. However, there is little known about the limits and performance of such schemes in complex environments. To this end, the general motivation of my thesis is the evaluation of the robustness and limitations of waveform inversion algorithms for crosshole georadar data in order to apply such schemes to a wide range of real world problems.One crucial issue to making applicable and effective any waveform scheme to real-world crosshole georadar problems is the accurate estimation of the source wavelet, which is unknown in reality. Waveform inversion schemes for crosshole georadar data require forward simulations of the wavefield in order to iteratively solve the inverse problem. Therefore, accurate knowledge of the source wavelet is critically important for successful application of such schemes. Relatively small differences in the estimated source wavelet shape can lead to large differences in the resulting tomograms. In the first part of my thesis, I explore the viability and robustness of a relatively simple iterative deconvolution technique that incorporates the estimation of the source wavelet into the waveform inversion procedure rather than adding additional model parameters into the inversion problem. Extensive tests indicate that this source wavelet estimation technique is simple yet effective, and is able to provide remarkably accurate and robust estimates of the source wavelet in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity as well as significant ambient noise in the recorded data. Furthermore, our tests also indicate that the approach is insensitive to the phase characteristics of the starting wavelet, which is not the case when directly incorporating the wavelet estimation into the inverse problem.Another critical issue with crosshole georadar waveform inversion schemes which clearly needs to be investigated is the consequence of the common assumption of frequency- independent electromagnetic constitutive parameters. This is crucial since in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behaviour. In particular, in the presence of water, there is a wide body of evidence showing that the dielectric permittivity can be significantly frequency dependent over the GPR frequency range, due to a variety of relaxation processes. The second part of my thesis is therefore dedicated to the evaluation of the reconstruction limits of a non-dispersive crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. I show that the inversion algorithm, combined with the iterative deconvolution-based source wavelet estimation procedure that is partially able to account for the frequency-dependent effects through an "effective" wavelet, performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Source-wavelet estimation during full-waveform inversion of ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole ground-penetrating radar (GPR) data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a recently published time-domain inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity of both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little to no trade-off between the wavelet estimation and the tomographic imaging procedures.

Waveform inversion of crosshole georadar data: influence of source wavelet variability and the suitability of a single wavelet assumption

Waveform-based tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of electrical properties in near-surface environments with unprecedented spatial resolution. A critical issue with waveform inversion is the a priori unknown source signal. Indeed, the estimation of the source pulse is notoriously difficult but essential for the effective application of this method. Here, we explore the viability and robustness of a recently proposed deconvolution-based procedure to estimate the source pulse during waveform inversion of crosshole georadar data, where changes in wavelet shape with location as a result of varying near-field conditions and differences in antenna coupling may be significant. Specifically, we examine whether a single, average estimated source current function can adequately represent the pulses radiated at all transmitter locations during a crosshole georadar survey, or whether a separate source wavelet estimation should be performed for each transmitter gather. Tests with synthetic and field data indicate that remarkably good tomographic reconstructions can be obtained using a single estimated source pulse when moderate to strong variability exists in the true source signal with antenna location. Only in the case of very strong variability in the true source pulse are tomographic reconstructions clearly improved by estimating a different source wavelet for each transmitter location.

Analysis of an iterative deconvolution approach for estimating the source wavelet during waveform inversion of crosshole ground-penetrating radar data

A major issue in the application of waveform inversion methods to crosshole georadar data is the accurate estimation of the source wavelet. Here, we explore the viability and robustness of incorporating this step into a time-domain waveform inversion procedure through an iterative deconvolution approach. Our results indicate that, at least in non-dispersive electrical environments, such an approach provides remarkably accurate and robust estimates of the source wavelet even in the presence of strong heterogeneity in both the dielectric permittivity and electrical conductivity. Our results also indicate that the proposed source wavelet estimation approach is relatively insensitive to ambient noise and to the phase characteristics of the starting wavelet. Finally, there appears to be little-to-no trade-off between the wavelet estimation and the tomographic imaging procedures.

Evaluation of the reconstruction limits of a frequency-independent crosshole georadar waveform inversion scheme in the presence of dispersion

Waveform tomographic imaging of crosshole georadar data is a powerful method to investigate the shallow subsurface because of its ability to provide images of pertinent petrophysical parameters with extremely high spatial resolution. All current crosshole georadar waveform inversion strategies are based on the assumption of frequency-independent electromagnetic constitutive parameters. However, in reality, these parameters are known to be frequency-dependent and complex and thus recorded georadar data may show significant dispersive behavior. In this paper, we evaluate synthetically the reconstruction limits of a recently published crosshole georadar waveform inversion scheme in the presence of varying degrees of dielectric dispersion. Our results indicate that, when combined with a source wavelet estimation procedure that provides a means of partially accounting for the frequency-dependent effects through an "effective" wavelet, the inversion algorithm performs remarkably well in weakly to moderately dispersive environments and has the ability to provide adequate tomographic reconstructions.

Enhancing the vertical resolution of surface georadar data

There are far-reaching conceptual similarities between bi-static surface georadar and post-stack, "zero-offset" seismic reflection data, which is expressed in largely identical processing flows. One important difference is, however, that standard deconvolution algorithms routinely used to enhance the vertical resolution of seismic data are notoriously problematic or even detrimental to the overall signal quality when applied to surface georadar data. We have explored various options for alleviating this problem and have tested them on a geologically well-constrained surface georadar dataset. Standard stochastic and direct deterministic deconvolution approaches proved to be largely unsatisfactory. While least-squares-type deterministic deconvolution showed some promise, the inherent uncertainties involved in estimating the source wavelet introduced some artificial "ringiness". In contrast, we found spectral balancing approaches to be effective, practical and robust means for enhancing the vertical resolution of surface georadar data, particularly, but not exclusively, in the uppermost part of the georadar section, which is notoriously plagued by the interference of the direct air- and groundwaves. For the data considered in this study, it can be argued that band-limited spectral blueing may provide somewhat better results than standard band-limited spectral whitening, particularly in the uppermost part of the section affected by the interference of the air- and groundwaves. Interestingly, this finding is consistent with the fact that the amplitude spectrum resulting from least-squares-type deterministic deconvolution is characterized by a systematic enhancement of higher frequencies at the expense of lower frequencies and hence is blue rather than white. It is also consistent with increasing evidence that spectral "blueness" is a seemingly universal, albeit enigmatic, property of the distribution of reflection coefficients in the Earth. Our results therefore indicate that spectral balancing techniques in general and spectral blueing in particular represent simple, yet effective means of enhancing the vertical resolution of surface georadar data and, in many cases, could turn out to be a preferable alternative to standard deconvolution approaches.

The connectome mapper: an open-source processing pipeline to map connectomes with MRI.

Researchers working in the field of global connectivity analysis using diffusion magnetic resonance imaging (MRI) can count on a wide selection of software packages for processing their data, with methods ranging from the reconstruction of the local intra-voxel axonal structure to the estimation of the trajectories of the underlying fibre tracts. However, each package is generally task-specific and uses its own conventions and file formats. In this article we present the Connectome Mapper, a software pipeline aimed at helping researchers through the tedious process of organising, processing and analysing diffusion MRI data to perform global brain connectivity analyses. Our pipeline is written in Python and is freely available as open-source at www.cmtk.org.

Technical note: Preliminary estimation of rockfall runout zones

Rockfall propagation areas can be determined using a simple geometric rule known as shadow angle or energy line method based on a simple Coulomb frictional model implemented in the CONEFALL computer program. Runout zones are estimated from a digital terrain model (DTM) and a grid file containing the cells representing rockfall potential source areas. The cells of the DTM that are lowest in altitude and located within a cone centered on a rockfall source cell belong to the potential propagation area associated with that grid cell. In addition, the CONEFALL method allows estimation of mean and maximum velocities and energies of blocks in the rockfall propagation areas. Previous studies indicate that the slope angle cone ranges from 27° to 37° depending on the assumptions made, i.e. slope morphology, probability of reaching a point, maximum run-out, field observations. Different solutions based on previous work and an example of an actual rockfall event are presented here.

Genetic differentiation in Silene dioica metapopulations: estimation of spatiotemporal effects in a successional plant species

Silene dioica is a diploid, dioecious, perennial, insect-pollinated herb and part of the deciduous phase of primary succession in Skeppsvik Archipelago, Gulf of Bothnia, Sweden. These islands are composed of material deposited and left underwater by melting ice at the end of the last ice age. A rapid and relatively constant rate of land uplift of 0.9 cm per year continually creates new islands available for colonization by plants. Because the higher deposits appear first, islands differ in age. Because it is possible to estimate the ages of islands and populations of plant species belonging to early stages of succession, the genetic dynamics occurring within an age-structured metapopulation can be investigated in this archipelago. Fifty-two island populations of S. dioica of known ages, sizes, and distances from each other were studied through electrophoretic data. A number of factors increase the degree of genetic differentiation among these island populations relative to an island model at equilibrium. Newly founded populations were more differentiated than those of intermediate age, which suggests that colonization dynamics increase genetic variance among populations. The very old populations, which decrease in size as they approach extinction, were more differentiated than intermediate-aged populations. Isolation by distance occurs in this system. Colonizers are likely to come from more than one source, and the migrant pool model best explains colonization events in the archipelago. Degree of environmental exposure also affects population differentiation.

Estimation of the correlation structure of crustal velocity heterogeneity from seismic reflection data

Numerous sources of evidence point to the fact that heterogeneity within the Earth's deep crystalline crust is complex and hence may be best described through stochastic rather than deterministic approaches. As seismic reflection imaging arguably offers the best means of sampling deep crustal rocks in situ, much interest has been expressed in using such data to characterize the stochastic nature of crustal heterogeneity. Previous work on this problem has shown that the spatial statistics of seismic reflection data are indeed related to those of the underlying heterogeneous seismic velocity distribution. As of yet, however, the nature of this relationship has remained elusive due to the fact that most of the work was either strictly empirical or based on incorrect methodological approaches. Here, we introduce a conceptual model, based on the assumption of weak scattering, that allows us to quantitatively link the second-order statistics of a 2-D seismic velocity distribution with those of the corresponding processed and depth-migrated seismic reflection image. We then perform a sensitivity study in order to investigate what information regarding the stochastic model parameters describing crustal velocity heterogeneity might potentially be recovered from the statistics of a seismic reflection image using this model. Finally, we present a Monte Carlo inversion strategy to estimate these parameters and we show examples of its application at two different source frequencies and using two different sets of prior information. Our results indicate that the inverse problem is inherently non-unique and that many different combinations of the vertical and lateral correlation lengths describing the velocity heterogeneity can yield seismic images with the same 2-D autocorrelation structure. The ratio of all of these possible combinations of vertical and lateral correlation lengths, however, remains roughly constant which indicates that, without additional prior information, the aspect ratio is the only parameter describing the stochastic seismic velocity structure that can be reliably recovered.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Is the formula of Traub still up to date in antemortem blood glucose level estimation?

According to the hypothesis of Traub, also known as the 'formula of Traub', postmortem values of glucose and lactate found in the cerebrospinal fluid or vitreous humor are considered indicators of antemortem blood glucose levels. However, because the lactate concentration increases in the vitreous and cerebrospinal fluid after death, some authors postulated that using the sum value to estimate antemortem blood glucose levels could lead to an overestimation of the cases of glucose metabolic disorders with fatal outcomes, such as diabetic ketoacidosis. The aim of our study, performed on 470 consecutive forensic cases, was to ascertain the advantages of the sum value to estimate antemortem blood glucose concentrations and, consequently, to rule out fatal diabetic ketoacidosis as the cause of death. Other biochemical parameters, such as blood 3-beta-hydroxybutyrate, acetoacetate, acetone, glycated haemoglobin and urine glucose levels, were also determined. In addition, postmortem native CT scan, autopsy, histology, neuropathology and toxicology were performed to confirm diabetic ketoacidosis as the cause of death. According to our results, the sum value does not add any further information for the estimation of antemortem blood glucose concentration. The vitreous glucose concentration appears to be the most reliable marker to estimate antemortem hyperglycaemia and, along with the determination of other biochemical markers (such as blood acetone and 3-beta-hydroxybutyrate, urine glucose and glycated haemoglobin), to confirm diabetic ketoacidosis as the cause of death.

Molecular estimation of dispersal for ecology and population genetics

The dispersal process, by which individuals or other dispersing agents such as gametes or seeds move from birthplace to a new settlement locality, has important consequences for the dynamics of genes, individuals, and species. Many of the questions addressed by ecology and evolutionary biology require a good understanding of species' dispersal patterns. Much effort has thus been devoted to overcoming the difficulties associated with dispersal measurement. In this context, genetic tools have long been the focus of intensive research, providing a great variety of potential solutions to measuring dispersal. This methodological diversity is reviewed here to help (molecular) ecologists find their way toward dispersal inference and interpretation and to stimulate further developments.