3-D characterization of high-permeability zones in a gravel aquifer using 2-D crosshole GPR full-waveform inversion and waveguide detection

Reliable high-resolution 3-D characterization of aquifers helps to improve our understanding of flow and transport processes when small-scale structures have a strong influence. Crosshole ground penetrating radar (GPR) is a powerful tool for characterizing aquifers due to the method's high-resolution and sensitivity to porosity and soil water content. Recently, a novel GPR full-waveform inversion algorithm was introduced, which is here applied and used for 3-D characterization by inverting six crosshole GPR cross-sections collected between four wells arranged in a square configuration close to the Thur River in Switzerland. The inversion results in the saturated part of this gravel aquifer reveals a significant improvement in resolution for the dielectric permittivity and electrical conductivity images compared to ray-based methods. Consistent structures where acquisition planes intersect indicate the robustness of the inversion process. A decimetre-scale layer with high dielectric permittivity was revealed at a depth of 5-6 m in all six cross-sections analysed here, and a less prominent zone with high dielectric permittivity was found at a depth of 7.5-9 m. These high-permittivity layers act as low-velocity waveguides and they are interpreted as high-porosity layers and possible zones of preferential flow. Porosity estimates from the permittivity models agree well with estimates from Neutron-Neutron logging data at the intersecting diagonal planes. Moreover, estimates of hydraulic permeability based on flowmeter logs confirm the presence of zones of preferential flow in these depth intervals. A detailed analysis of the measured data for transmitters located within the waveguides, revealed increased trace energy due to late-arrival elongated wave trains, which were observed for receiver positions straddling this zone. For the same receiver positions within the waveguide, a distinct minimum in the trace energy was visible when the transmitter was located outside the waveguide. A novel amplitude analysis was proposed to explore these maxima and minima of the trace energy. Laterally continuous low-velocity waveguides and their boundaries were identified in the measured data alone. In contrast to the full-waveform inversion, this method follows a simple workflow and needs no detailed and time consuming processing or inversion of the data. Comparison with the full-waveform inversion results confirmed the presence of the waveguides illustrating that full-waveform inversion return reliable results at the highest resolution currently possible at these scales. We envision that full-waveform inversion of GPR data will play an important role in a wide range of geological, hydrological, glacial and periglacial studies in the critical zon

Full-waveform inversion of ground-penetrating radar data in frequency-dependent media involving permittivity attenuation

Full-waveform inversion (FWI) of ground-penetrating radar (GPR) data has received particular attention in the past decade because it can provide high-resolution subsurface models of dielectric permittivity and electrical conductivity. In most GPR FWIs, these two parameters are regarded as frequency independent, which may lead to false estimates if they strongly depend on frequency, such as in shallow weathered zones. In this study, we develop frequency-dependent GPR FWI to solve this problem. Using the τ-method introduced in the research of viscoelastic waves, we define the permittivity attenuation parameter to quantify the attenuation resulting from the complex permittivity and to modify time-domain Maxwell’s equations. The new equations are self-adjoint so that we can use the same forward engine to back-propagate the adjoint sources and easily derive model gradients in GPR FWI. Frequency dependence analysis shows that permittivity attenuation acts as a low-pass filter, distorting the waveform and decaying the amplitude of the electromagnetic waves. The 2-D synthetic examples illustrate that permittivity attenuation has low sensitivity to the surface multioffset GPR data but is necessary for a good reconstruction of permittivity and conductivity models in frequency-dependent GPR FWI. As a comparison, frequency-independent GPR FWI produces more model artefacts and hardly reconstructs conductivity models dominated by permittivity attenuation. The 2-D field example shows that both FWIs reveal a triangle permittivity anomaly which proves to be a refilled trench. However, frequency-dependent GPR FWI provides a better fit to the observed data and a more robust conductivity reconstruction in a high permittivity attenuation environment. Our GPR FWI results are consistent with previous GPR and shallow-seismic measurements. This research greatly expands the application of GPR FWI in more complicated media

Locating a weak change using diffuse waves (LOCADIFF) : theoretical approach and inversion procedure

We describe a time-resolved monitoring technique for heterogeneous media. Our approach is based on the spatial variations of the cross-coherence of coda waveforms acquired at fixed positions but at different dates. To locate and characterize a weak change that occurred between successive acquisitions, we use a maximum likelihood approach combined with a diffusive propagation model. We illustrate this technique, called LOCADIFF, with numerical simulations. In several illustrative examples, we show that the change can be located with a precision of a few wavelengths and its effective scattering cross-section can be retrieved. The precision of the method depending on the number of source receiver pairs, time window in the coda, and errors in the propagation model is investigated. Limits of applications of the technique to real-world experiments are discussed.Comment: 11 pages, 14 figures, 1 tabl

Full-waveform inversion of ground-penetrating radar data and its indirect joint petrophysical inversion with shallow-seismic data

Both full-waveform inversion (FWI) of ground-penetrating radar (GPR) and shallow-seismic data have received special attention in the past decade because they allow the reconstruction of seismic and electromagnetic (EM) properties at high resolution. Research on the two FWIs includes: FWI of single geophysical data and joint FWI of multiple geophysical data. In this dissertation, I focus on GPR FWI in the former and joint petrophysical inversion (JPI) in the latter. In GPR FWI, the high computational costs and frequency-independent assumption are two problems that limit its development. To reduce computational costs, I apply a subset FWI (SFWI) to multi-offset GPR data. SFWI uses the data simulated on a model subset to approximate the data simulated on an entire model. Thus it obtains theoretical speedup and memory saving factor equal to the size ratio of the model and its subset. SFWI has higher or lower than expected speedups when combined with the source parallelization and model domain parallelization, respectively. The model subset depends on the illumination of the acquisition geometry used, for which I give rules of thumb by quantifying its effect on the simulation and inversion. Both 2-D synthetic and field data validate that SFWI provides results comparable to FWI but requires much lower computational costs than FWI. This study makes FWI an affordable technique for general users and promotes its application in addressing near-surface problems. The second problem means that dielectric permittivity and electrical conductivity are supposed to be frequency independent in most GPR FWI, which may lead to false estimates if they strongly depend on frequency. I develop frequency-dependent GPR FWI to solve this problem. Using the $\tau$-method introduced from the seismic community, I define the permittivity attenuation parameter to quantify the attenuation resulting from the complex permittivity. The new parameter acts as a low-pass filter, distorting the waveform and decaying the amplitude of the EM waves. The use of permittivity attenuation reduces the number of reconstructed parameters in frequency-dependent GPR FWI. The 2-D synthetic examples illustrate that permittivity attenuation is necessary for reconstructing permittivity and conductivity models in frequency-dependent media. The 2-D field example shows that frequency-dependent GPR FWI provides a better fit to the observed data and a more robust conductivity reconstruction in a high permittivity attenuation environment than frequency-independent GPR FWI. This research greatly expands the application of GPR FWI in more complicated media. Shallow-seismic and GPR FWI can provide complementary information for each other. Based on the sensitivity difference of the two data to petrophysical parameters, I propose indirect JPI, where seismic data are used for porosity reconstruction and GPR data are used for saturation reconstruction. Unlike conventional JPI, I first update the seismic and GPR parameters using non-petrophysical parametrizations and then transform the most reliable estimates to petrophysical parameters. The 2-D synthetic tests show that indirect JPI can provide more accurate and consistent results than conventional JPI. In addition, due to the rational use of the sensitivity of geophysical data to parameters, indirect JPI is more robust when uncertainties exist in petrophysical $a\;priori$ knowledge. More importantly, indirect JPI is flexible to integrate different types of seismic and EM waves and acquisition geometries depending on the target of interest, resulting in the best solution. Indirect JPI has been proven to be a promising approach for multiparameter reconstructions. To validate if indirect JPI can solve the real problem, I apply it for the first time to Love-wave and multi-offset surface GPR field data. It provides consistent imaging of near-surface targets with good accuracy by estimating seismic, EM, and petrophysical models. The inversion results are validated by direct-push technology and borehole measurements. This application suggests that indirect JPI can avoid conflicting geological interpretations that may arise in individual inversions and shows higher efficiency of information exchange than joint structural inversion. Furthermore, this method is robust with different petrophysical initial models and coefficients, for instance, Archie\u27s coefficients. The study verifies the feasibility of using indirect JPI to invert multiple geophysical field data and promotes the broader applicability of petrophysical methods. In summary, this dissertation (1) reduces the computational costs of GPR FWI and extends GPR FWI to frequency-dependent media, and (2) proposes a new joint strategy to combine GPR and shallow-seismic data and validates its performance through 2-D synthetic and field examples

The use of calibration techniques in gravitational wave astronomy

Approximations are commonly employed in realistic applications of scientific Bayesian inference, often due to convenience if not necessity. In the field of gravitational wave (GW) data analysis, fast-to-evaluate but approximate waveform models of astrophysical GW signals are sometimes used in lieu of more accurate models to infer properties of a true GW signal buried within detector noise. In addition, a Fisher-information-based normal approximation to the posterior distribution can also be used to conduct inference in bulk, without the need for extensive numerical calculations such as Markov chain Monte Carlo (MCMC) simulations. Such approximations can generally lead to an inaccurate posterior distribution with poor statistical coverage of the true posterior. In this article, we present a novel calibration procedure that calibrates the credible sets for a family of approximate posterior distributions, to ensure coverage of the true posterior at a level specified by the analyst. Tools such as autoencoders and artificial neural networks are used within our calibration model to compress the data (for efficiency) and to perform tasks such as logistic regression. As a proof of principle, we demonstrate our formalism on the GW signal from a high-mass binary black hole merger, a promising source for the near-future space-based GW observatory LISA.Comment: 24 pages, 12 figure

Advanced BEM-based methodologies to identify and simulate wave fields in complex geostructures

To enhance the applicability of BEM for geomechanical modeling numerically optimized BEM models, hybrid FEM-BEM models, and parallel computation of seismic Full Waveform Inversion (FWI) in GPU are implemented. Inverse modeling of seismic wave propagation in inhomogeneous and heterogeneous half-plane is implemented in Boundary Element Method (BEM) using Particle Swarm Optimization (PSO). The Boundary Integral Equations (BIE) based on the fundamental solutions for homogeneous elastic isotropic continuum are modified by introducing mesh-dependent variables. The variables are optimized to obtain the site-specific impedance functions. The PSO-optimized BEM models have significantly improved the efficiency of BEM for seismic wave propagation in arbitrarily inhomogeneous and heterogeneous media. Similarly, a hybrid BEM-FEM approach is developed to evaluate the seismic response of a complex poroelastic soil region containing underground structures. The far-field semi-infinite geological region is modeled via BEM, while the near-field finite geological region is modeled via FEM. The BEM region is integrated into the global FEM system using an equivalent macro-finite-element. The model describes the entire wave path from the seismic source to the local site in a single hybrid model. Additionally, the computational efficiency of time domain FWI algorithm is enhanced by parallel computation in CPU and GPU